Physical movement helps students engage in, investigate, and understand mathematics concepts
Young adolescents undergo more rapid and
profound changes than at any other time in their
development (NMSA, 2010). Adolescence is a pivotal
stage for cognitive, social-emotional, and physical
development. Middle school educators understand
the developmental uniqueness of this age group and
seek to provide activities that fully engage the young
adolescent. One way to accomplish this is through
kinesthetic learning. We define kinesthetic learning
as an instructional strategy that connects physical
movement and social interaction with academic
content. Kinesthetic activities incorporate physical
exercise, stretching, and cross-body movements and
are specifically connected to subject matter. The goal
is to get students actively engaged and “learning by doing” as they investigate mathematics concepts
through physical movement.
The Importance of Physical Activity
According to the U.S. Department of Health and
Human Services (2018), adolescence “is a critical
period for developing movement skills, learning
healthy habits, and establishing a firm foundation
for lifelong health and well-being” (p. 47). Regular
physical activity in children and adolescents
promotes health and fitness, and the beneficial
effects of exercise on learning are well documented.
Movement increases the heart rate and stimulates
brain function, which facilitates a child’s ability to
learn. The U.S. Department of Health and Human
Services specifically advocates physical activity for
brain health. They state that regular physical activity
“results in improved cognition including performance
on academic achievement tests, executive function,
processing speed, and memory” (p. 40) as well as a
reduced risk of depression. The cognitive benefits of
physical activity apply to all students, including those
with conditions such as attention deficit hyperactivity
Numerous studies support the conclusion that
physical activity has a positive influence on memory,
concentration, and classroom behavior. These studies
indicate a significant positive correlation between
fitness and standardized test scores in math.
Furthermore, students who are more physically fit
have fewer absences and fewer disciplinary referrals.
These findings remain statistically significant when
controlling for race, socioeconomic status, and gender.
There are many ways to actively engage students in
learning mathematics content. Students “learn by
doing” when they use their hands, arms, legs, and
bodies as tools for learning. We advocate the use of
purposeful movement that is directly connected to
the content being taught. This is very different than
asking students to recite multiplication tables while
doing jumping jacks. We argue that many students
have procedural knowledge but lack conceptual
Instead of asking students to memorize isolated facts
and algorithms, consider asking students to dramatize
mathematics concepts through motion. For example,
students can act out points on a Cartesian coordinate
system and walk through shifting and stretching
functions. A Twister mat can be used to introduce the
concept to younger students. Other kinesthetic activities might include acting out operations on a number
line; teaching translations, rotations, and reflections
by dancing the Electric Slide; and finding the mean,
median, and mode of a data set after constructing a
human graph. What follows are descriptions of three
kinesthetic activities that can be used to support and
extend specific mathematics concepts.
The Metric Handshake/Metric Salute
Many students in the U.S. struggle to associate
benchmarks to metric units of length. In order to
strengthen their knowledge, hands-on measuring is
beneficial. Estimating using familiar body measures
can assist with foundational understanding. For
example, for a young adolescent, the distance
between one shoulder bone and the length of the
other arm with fingers extended is about one meter.
The distance between the space from the thumb and
pinky is approximately one decimeter. The distance
across the tip of the pinky is approximately one
centimeter. The thickness of a fingernail is about
one millimeter. This leads to a fun, cool handshake
students can use to greet one another.
Listed here are step-by-step motions for practicing
four basic benchmark measures of length.
- While holding your right hand with fingers
extended to your left shoulder in a saluting
formation, call out “Salute.”
- Extend your right hand, palm down with fingers
straight, from the left shoulder position to fully
extended to the right. Say, “meter.”
- Move palm up and extend thumb and pinky finger
(pointer, tall man, and ring man fingers curled
down into palm). Say, “decimeter.”
- Hold the pinky in a vertical position while folding
in all other fingers. Call out, “centimeter.”
- Rotate the pinky a quarter turn to display the
thickness of the fingernail. Call out, “millimeter.”
- For additional cool factor and pizzazz, students
can join pinkies to finalize the metric signals in a
Angle exercises utilize the arms as the rays of an
angle. While everyone is standing, the leader calls
a type of angle while the others attempt to model
it. To model a right angle, for example, hold one arm
parallel to the floor in a horizontal direction and the
other in a vertical direction. To model an acute angle,
position the arms closer together with a narrow space
between them. Modeling an obtuse angle moves the
arms wider. Arms extended in opposite directions
represents a straight angle of 180°. To challenge
students and accelerate the pace, gradually increase
the call rate of the angle types. If space is limited, it
may be necessary to use fingers instead of arms to
demonstrate the angles.
Once the basic angle concepts are introduced,
prompt students to consider other measurements. If
a right angle is 90°, what is the measure of half that
angle? What type of angle is it? What if an angle is
exactly halfway between a right angle and a straight
angle? What type of angle is it? What is its measure?
Discuss that an acute angle is between 0° and 90°.
Discuss characteristics of obtuse angles and the
measures between 90° and 180°. Progress to calling
more complex angles using specific measurements. The students’ performance with the arm motions can
provide valuable formative assessment opportunities.
Angle exercises establish benchmark
measurements and set the foundation for students’
progression to measuring angles with a protractor.
We can then connect their arm motions with the
procedure for precision measuring with the protractor.
Help your students learn the characteristics of
quadrilaterals. Students often find it difficult to
classify quadrilaterals and distinguish between the
categories. Is a square a rectangle? Is a rectangle a
square? Are all rectangles squares? Are rectangles
parallelograms? Some rectangles are rhombi. All
squares are rhombi, rectangles, and parallelograms.
Quadrilateral stretches will give students the
opportunity to model quadrilaterals and explore
how small changes impact their similarities and
- With a little stretch of the imagination and the
arms, students can make air figures modeling
quadrilaterals. Start by demonstrating a common
quadrilateral. To model a square, hold both arms
up in front of your body and bent at the elbows.
With forearms straight up and equidistant, the
width represents congruent sides. Imagine the top
and bottom sides. With all sides equal and right
angles, the quadrilateral is a square.
- From this position, stretch the square by
sliding the forearms to the right (and/or left).
The quadrilateral changes to a rectangle (and
technically a parallelogram). Lean both forearms to
the right to transform the rectangle into a unique parallelogram. This demonstrates a lazy, leaning
parallelogram by holding both arms up bent at
the elbows, shoulder length apart, and tilted in
the same direction. The arms represent the width.
Imagine the top and bottom sides as the length.
In a parallelogram, opposite sides are congruent
and parallel. Keeping the forearms tilted, slide the
arms toward each other until the width aligns with
the height. The parallelogram has now achieved
another title, transforming into a rhombus.
Straighten the shape with vertical forearms again
and re-make the square.
- Vary the order of the quadrilateral stretches and
discuss how stretching and tilting, widening,
narrowing, transforms the shape and changes its
properties. Slide the forearms back together and
upright to re-create the square. Discuss the various
names of the figure. Tilt the square to create a
rhombus. Stretch the square to create a rectangle.
- Start with a leaning parallelogram. Slide the
forearms in to make a rhombus. Stand it upright
to make a square. Stretch the square to make
a rectangle. All squares are parallelograms,
rectangles, and rhombi. Some rhombi are squares,
but only when they have right angles.
- Be sure to emphasize that there are several ways
to model parallelograms. All square, rectangles,
and rhombi are classified as parallelograms.
- Create a trapezoid by collapsing one vertical side
of a square or rectangle. Identify the stretch as
modeling a “right trapezoid.” What figure can be
demonstrated by collapsing both vertical sides—an
- To challenge students and accelerate the pace,
gradually increase the call rate of the types of
Middle level educators value young adolescents
and understand the complex developmental needs
of this age group. Kinesthetic learning facilitates
students’ physical development by providing more
opportunities for movement; social development
with more interaction; emotional development with
more engagement; and cognitive development
with active learning. Kinesthetic strategies offer purposeful learning experiences and provide
alternatives to whole-class lecture. Students learn
by doing as they move their bodies to investigate
mathematics concepts. We all want our students to
be active learners rather than passively receiving
information. We argue that physical movement and
social interaction are essential in the middle school
classroom. In this way, teachers can meet the unique
developmental needs of young adolescents while
effectively teaching mathematics content.
National Middle School Association. (2010). This we
believe: Keys to educating young adolescents.
Westerville, OH: Author.
U.S. Department of Health and Human Services (2018).
Physical activity guidelines for Americans (2nd
ed.). Washington, DC. Retrieved from: https://health.gov/paguidelines/second-edition/pdf/Physical_Activity_Guidelines_2nd_edition.pdf
Deborah McMurtrie, PH.D. is an assistant professor
and middle level education coordinator /program director
for South Carolina’s Center of Excellence in Middle-level
Interdisciplinary Strategies for Teaching (CEMIST) at the
University of South Carolina, Aiken.
Bridget Coleman, PH.D. is an assistant professor and
leads the Secondary Mathematics Education program
at the University of South Carolina, Aiken. She’s also the
past president of the South Carolina Professors of Middle
Level Education (SC-PoMLE).
Published in AMLE Magazine
, April 2020.
Engaging middle schoolers in local issues helps them apply knowledge and become informed citizens
Environmental science knowledge intertwined with
cultural practices have ripple effects that impact many
aspects of society. For example, the increase in the use
of fertilizer and practices of overfishing have resulted
in red tides and dead zones within waterways, where
nothing is able to grow. It is important for students to
have formal instruction to engage with these topics,
preparing them to be scientifically literate members
of society. A powerful way to engage middle school
learners is to use socio-scientific issues to teach
environmental science. Socio-scientific issues (SSI) are
those that deal with topics that can be debated and
relate scientific understanding to making real world
decisions (Zeidler & Kahn, 2014).
We cannot assume that middle school students
have had experience with meaningful high-quality,
hands-on science units. Therefore, it is important
to provide them with appropriately challenging
coursework that meets individual needs. Teaching
with SSIs reaches students that come to the classroom
with a wide range of background knowledge. This
article provides an example of an SSI unit in which
students review their knowledge of scientific thinking,
ask self-designed experimental questions, and conduct
an experiment to test their question. Their final
writing project allows students to use their knowledge
of science and their community to propose a solution
to a local need. First, a brief overview will be provided
about the value of these types of strategies.
Benefits of Exploring Local Socio-Scientific Issues
The National Science Teaching Association (NSTA)
asserts that students need to know, understand, and
be able to apply their knowledge of science (NSTA,
2016). This is part of being a scientifically literate
member of society. To do this, students must be
exposed to lessons that explore socio-scientific issues
and be taught how to use their knowledge in a local
context. Learning in this manner is highly engaging
and personalizes science as a practice for students
(Birmingham & Barton, 2013). Additionally, using local
events provides an opportunity for students to connect
personal experiences to the content they are learning
and allows them to contribute to the community.
The utilization of SSIs also supports the middle
school concept advocated for by AMLE. For example,
students learn science concepts and applications
in the science classroom, discuss issues of policy in
social studies, refine their writing and communication
skills in English language arts, and plan for budgets in
the mathematics classroom. Integrated learning such
as this is a powerful method for students to make realworld
connections and understand content at a deeper
level. In the next section, a brief unit of instruction is
provided that demonstrates an example of teaching an
SSI in the context of an ecology lesson.
SSI Environmental Science Lesson
This unit of instruction allows students to apply
scientific practices in context and makes learning
relevant for students. It fits in an instructional
sequence where students have previously learned
about asking scientific questions, experimental
design, and a basic knowledge of ecology and needs of
plants. Students are placed into research groups.
This lesson begins with the teacher showing the class
an image of a vacant city lot (see figure 1).
Students are asked to quietly write out reflections on
the following questions:
- Describe the abiotic and biotic factors that you see
in this environment.
- What is growing here? Why?
- What types of plants might we want to grow here?
- How could we engineer this environment to grow
your chosen plant?
After five minutes of individual reflection, students
discuss their answers in a group. The teacher places
four posters around the room with the previous
questions written on top of each as a prompt. This
small group discussion allows students to build
on prior knowledge and brainstorm ideas. A group
representative writes the responses on the posters.
During group writing, the teacher reads the responses
to formatively assess student thinking. Then, she
leads class discussions on each of the topics. Students
are then presented with the project topic: They will
determine needs of plants that they choose to grow in
Community Garden – Lab Practice
To acclimate students to this type of research, they
complete a practice lab analysis. Analysis should be
completed in research teams, with student discussion
about each of the prompts. During this time, the
teacher formatively assesses student knowledge of
experimental design and responds appropriately to
clear up misconceptions. This activity allows students
to practice their research skills that will be needed for
future activities and provides an opportunity to practice
collaboration (see practice worksheet in figure 2).
Explore: Research Proposal
Groups identify a plant that they wish to grow in
this space. They justify the choice of a plant using
a combination of research and knowledge of their
local community. Each group develops a research
proposal to identify needs of the chosen plant in their
local environment. Students complete the planning
template (see figure 3) and turn it in to the teacher
for approval. After approval, they execute their
experiments by collecting data over the next month.
Students develop their scientific practice skills while
taking ownership of their work as they watch their
Research Proposal – Community Garden Initiative
(In order for your project to be funded your plan
must be complete!)
- My question: (Remember the format)
- Experimental Design:
a. Independent Variable (you can only have one)
b. Dependent variable (what you are measuring)
c. Constants (you should have many)
d. Procedure: (step-by-step, be specific)
***Describe the types of data you will collect***
e. Qualitative data:
f. Quantitative data:
Explain: Poster Presentation
Finally, students present their findings through a
poster presentation. The presentation highlights their
experimental question, methods, and findings from
their research. The conclusion section contains a
discussion about whether their proposed plant would
be a good fit for their neighborhood environment
and in what ways it will serve a community need.
The teacher assists students in putting their posters
together and facilitates student presentations to
the class. This activity helps students develop their
scientific writing and speaking skills.
Evaluate: Individual Persuasive Essay
After the groups have presented their findings,
students use their knowledge of all groups’ research
to write a two paragraph persuasive essay arguing
which plant should be planted in the vacant lot. The
argument should be made based on ways this plant
meets community needs, the requirements for growth,
and the amount of work/cost required to engineer the
plot of land. They make their claim using evidence
from the research findings. This essay provides a rich
opportunity for students to use their knowledge and
skills in a real-life situation, forming a good foundation
for developing scientific literacy.
This activity could be modified to include all content
area teachers. For example:
Social Studies – In depth research about identifying
needs of communities, study of their local economy
and community, or a study of food deserts, https://www.tolerance.org/lesson/food-deserts-causesconsequences-and-solutions
English Language Arts – Writing letters to the local
city council proposing their plan
Mathematics – Determining a budget and space
requirements for the implementation of scaling up
Cross-curricular learning benefits students by allowing
them to apply skills in a more complex manner.
This project helps students learn to think scientifically,
solidify their understanding about the needs of plants,
and apply their knowledge to serve a local need. All
aspects develop students toward the goal of becoming
a scientifically literate member of society. Although
this example demonstrates the use of socio-scientific
learning within an urban environment, the process could
be replicated and modified to fit any school community.
For example, students in a rural environment could
explore the impact of local farming practices on water
quality. Regular practice engaging in these types of
activities engages students to promote civic action. Civic
action by scientifically literate members of society is
critical to maintain good stewardship of our local, state,
and national communities.
Birmingham, D. & Barton, A. (2013). Putting on a
green carnival: Youth taking educated action
on socio-scientific issues. Journal of Research in
Science Teaching, 51(3), 286-314.
National Science Teaching Association (NSTA). (2016).
NSTA Position Statement: Teaching science in the
context of societal and personal issues. Retrieved
Zeidler, D. & Kahn, S. (2014). It’s debatable: Using
socio-scientific issues to develop scientific literacy
K-12. Arlington, VA: NSTA Press.
Lise Falconer, M.A., NBCT is a middle school
science specialist with the Alabama Math, Science,
and Technology Initiative (AMSTI) at the University of
Alabama at Birmingham.
Published in AMLE Magazine
, April 2020.
STEM starts with the end in mind
By the time students transition to high school, the disparity between girls' and boys' interest in STEM is already evident. Three decades of research show that an average of 15.7% of freshman girls express interest in STEM careers in comparison to 39.5% of their male peers. With 75% of the fastest-growing occupations over the next decade requiring preparation in STEM, girls will be left behind from the workforce of the future. Girls need more opportunities to see how STEM comes to life in careers that interest them.
The Light A Spark initiative is encouraging young girls to consider a career in STEM by introducing them to exciting and unexpected STEM careers. The three tips I encourage middle school teachers to use to close the gender gap in STEM-based careers are detailed below.
Exposure to Interest-Based Careers
Growing up, math always came easily to me. One day, my middle school teacher saw my doodles and asked if I wanted to be a fashion designer. Although I had a love for fashion, architecture seemed like the more obvious career choice because math was my strong suit. She helped me understand that mathematics plays an essential role in fashion design.
My STEM background has allowed me to develop cutting-edge, highly technical creations. Arguably, the coolest project I've worked on was incorporating electromagnetic engineering into a gown, where any movement would cause the gown to change colors.
A huge challenge is that STEM is often disregarded due to perceived difficulty, which discourages students from pursuing STEM long-term. However, if educators shared the unexpected careers involving STEM, a student's interest can override feelings of inadequacy.
Show Diverse Representation
While part of the equation is connecting students to interest-based STEM careers, another part of the battle is shifting beliefs that a career is not for them because they don't see role models they relate to.
One of my fellow STEM Innovators in the Light A Spark initiative, Anisha Vyas, learned of her dream job from an engineering professor who mentioned working with a theme park. Now, she's a Ride & Show Engineer for Universal Studios and travels the world opening parks across America, Europe, and Asia.
However, at first, it wasn't easy being an "Indian girl with a Chicagoan accent" in a field dominated by men. When she started, she remembered thinking: I am all the diversity in the room, and she questioned whether that was why she had a seat at the table, but she decided in that moment to believe she brings as much to the table as her male counterparts.
Elevating Anisha's story can inspire those who are interested in her career path, but also for those who'll face the same barriers, discrimination, or share the same fears, and ultimately inspire them to follow in her footsteps.
Share Relatable Stories
Another fellow innovator, Diana Ma, combined her passion for basketball and statistics by helping the Lakers maintain a competitive advantage as a data scientist. As a woman in statistics and professional sports, Diana found herself a trailblazer on two fronts, which, inevitably, led her to battling imposter syndrome to get to where she is today.
When she was in college, she had to complete an assignment using any data set she wanted. Naturally, as an avid basketball fan, she chose to use NBA stats. She attended an event featuring a director of basketball analytics. After the event, she introduced herself to discuss her project and ask for advice. As a result, he shared that the Indiana Pacers were hiring basketball analytics interns. She debated whether she should apply. After taking the plunge, she received an internship offer, launching her dream career.
Sharing relatable stories like Diana's can be the tipping point for girls when they face self-doubt. But as Diana says, "It's always going to be a boy's club if women don't create a space for themselves."
Leveling the playing field requires coming together for young girls in STEM and stoking the fire to burn throughout the career of their choosing by celebrating diversity and risk taking and embracing the insatiably curious who are willing to take on some of our more complex problems. For middle school educators, to #LightASpark starts with a sharing a story.
Learn more at lightaspark.org and join the conversation by using #LightASpark.
Angela Fuentes is the co-founder and CEO of FortyTwentyAM, Pattern Maker, and Faculty at Fashion Institute of Design & Merchandising (FIDM) in Los Angeles, CA.
Published February 2020.
Facilitating rich discourse to engage students and develop confidence
Through education, teachers influence change in their students' mindsets, which in turn can help students become successful individuals (Yeager & Dweck, 2012). We believe that the best teachers guide, motivate, and inspire their students. Teaching mathematics effectively is crucial to developing students who can solve problems and persevere. In AMLE's position paper (2010), This We Believe: Keys to Educating Young Adolescents, there is an emphasis on both Active Learning, in which students are engaged and are situated at the center of purposeful learning, and Challenging Curriculum, which promotes curriculum that incorporates students' ideas and questions. Here we consider how these characteristics can be employed in the mathematics classroom.
A Glimpse into a Mathematics Classroom
Students in the sixth grade mathematics classroom participated in a geometry unit in which the pedagogical focus was how we presented the lessons and promoted motivation through the use of growth mindset to help students feel confident and achieve success. Before starting with the lesson, we allowed time for students to express how they felt about the unit they were about to begin. Some students expressed feelings of being overwhelmed. Others, shared feelings of discomfort about geometry in general with statements such as "I feel ugh about it. Geometry isn't really my thing. It's a little confusing for me." This activity allowed us the opportunity to acknowledge students' feelings and assure them the goal was to create a positive mathematics learning experience.
Each lesson began with bell work in which students were to work independently for approximately two minutes before sharing their strategies with their shoulder partner. The task was to find the area of a shaded figure by applying knowledge about triangles and rectangles. Students needed to identify the information given to help them attempt the task and determine what was needed to be successful. They needed to develop a strategy to find the area of the rectangle and a triangle and then understand that the task was asking them to subtract both areas to find the shaded part. After working on the task and sharing with their partners, a whole-class discussion was conducted starting with the recording of all strategies used by the students. When the strategies were shared, students were asked to look around the classroom to observe how many of their classmates thought and attempted the problem in the same manner. This practice was used to ease student anxiety or doubts about the way they attempt mathematics problems. Then, students were asked to explain and try at least one of the strategies written on the board. Once a student demonstrated it, another student was encouraged to critique their peers' work. A different student was called to elaborate on what was shared and explain their rationale. Up to three students were called to critique their reasoning of others every time they worked on a problem.
This practice helped students make sense of their reasoning as well as that of others while deepening understanding of the skills presented. The following is an excerpt from the class using the mathematical practices of critiquing another students' reasoning:
Teacher: Let's see, Elijah can you explain what she did?
Elijah: Uhm…she did something wrong…she needed to divide the area of the triangle by two.
Elijah: She needed to divide the triangle in half.
Teacher: Do we all agree on that?
Teacher: So, you are telling me that you should divide the triangle by two? Is that it?
Teacher: Why is it that we need to divide by two?
Alanis: Because the triangle is half of a square.
Teacher: Because the triangle is half of a square. Kyra, what do you think of that? Agree or disagree?
Teacher: Why do you agree?
Kyra: Because if you take that triangle and you put it in one of the sides, it means you can have another one of it.
As the lesson progressed, students asked questions and shared their understanding of different strategies with their peers. By using effective questioning practices, students deepened their knowledge and articulated their own conclusions. Students who showed anxiety when trying to answer questions had the opportunity to gather their thoughts, listen to others before answering, and respond when they felt ready. This problem fostered a stress-free environment in which students felt at liberty not only to express their thoughts but also to accept their failures.
Before moving on with the lesson, the teacher assured the class how confident and proud she felt about their performance. She also used humor to express the need to challenge them more. This practice seemed to help students feel more confident and ready to do the mathematics at hand.
Teacher: All of you already know? WOW, then I should not even be teaching this lesson!
Before the challenge was given, students had the opportunity to reflect on their learning and the way they felt about the lesson. At all times, students demonstrated being engaged and responded enthusiastically to what the teacher proposed to them. An excerpt from the lesson is below.
Halie: I was kind of overwhelmed but now not that much, because I didn't know where really we were going to go to, but now that I know what I need to do it's kind of easy.
Emily B.: What reduced my overwhelmedness was how it was just like finding the area, but then just like adding another number to multiply to find the volume of the entire shape. It made things more simple to understand and see how to process it…it was just simpler.
Teacher: So, this is helping you? This strategy of seeing the floor first and then stacking it up is helping you?
Emily B.: Mhmm
Teacher: Ok, Kyra.
Kyra: I am not overwhelmed anymore because if you really just think about it…because with me and my brain it goes; ok, I see this problem…this problem looks hard, but then when you actually explain it, we see…and then you ask questions, show models…it's not that hard.
Teacher: Does that mean I can give you a challenge?
While students were describing how they felt about the lesson, they started sharing which strategies helped them the most. One strategy they liked the most when conceptually understanding how to find the volume of a rectangular prism was "the stacking strategy," because that is how they named it. This strategy was based on knowing that the volume of a shape can be given by finding the area of the base of the shape (a rectangle) and then "stacking" the same number of blocks or the same area given one on top of the other until the height had been reached. One of the students was able to connect this strategy of finding volume to a real world situation in which the first floor of a two-story house would represent the area of the base and the top floor would give the height. Another student, using this same idea, connected the same example to how the surface area of the house could be identified by how much paint or wallpaper the house would need.
During the challenge, students were encouraged to attempt to solve all problems given. Those who were able to get to the solution quickly were encouraged to use other strategies to support their findings. One significant thing noticed was how students persevered and showed strong effort when trying to solve the problem given. The prompt most students use is the use of positive language and the word "yet." The idea behind it is the belief that a student can change how they feel and the way they work on a problem by affirming that, even if they do not grasp the concept or strategy at that particular moment, they still believe they can understand it with a little bit more effort and perseverance. This strategy is called "The Power of Yet."
Through our experience, it is clear that incorporating more mathematical discourse and fostering a growth mindset belief in the middle school mathematics classroom can help students develop more confidence and achieve higher levels of mathematical understanding, which aligns with the Active Learning and Challenging Curriculum characteristics of This We Believe. Classroom discourse motivates students and promotes engagement in the classroom, and it encourages students to believe in their abilities, persevere into solving the problems given, and change the perceptions they might have of how they do mathematics.
National Middle School Association. (2010). This we believe: Keys to educating young adolescents. Westerville, OH: Author.
Yeager, D. S., & Dweck, C. S. (2012). Mindsets that promote resilience: when students believe that personal characteristics can be developed. Educational Psychologist, 47(4), 302-314.
Lynnette Sanchez-Gonzalez is a 5-9 mathematics High Impact Teacher and curriculum leader at South Seminole Academy, Seminole County, Florida.
Megan Nickels, Ph.D. is an assistant professor of STEM education in the College of Community Innovation and Education and College of Medicine at the University of Central Florida.
Published in AMLE Magazine
, August 2019.
Students build and print objects while developing proportional reasoning and technology skills
Each year we explore new and innovative ways to teach middle grades students the foundational concepts and skills they need for algebra such as proportional reasoning. This year, we engaged students in a scale modeling project using 3D technology. Throughout the project, students had complete autonomy, engaged meaningfully in proportional reasoning, and took home something tangible to represent their work.
In our scale modeling project, students were tasked with creating a scaled version (i.e., stretch or shrink) of a real-world object. Students had complete freedom to choose their object and were only given the requirement that the object must come from the real world. They could choose real-world objects such as famous building structures, animals, sporting equipment, automobiles, and much more.
Before diving into the task, students became familiar with the 3D design platform Tinkercad by creating a free online Tinkercad account (www.tinkercad.com) and completing tutorials to learn the basics of the program. Some students were already familiar and had accounts of their own. Other students were not as familiar, but quickly became comfortable with this technology. After learning the basics of Tinkercad, students were ready to dive into the project!
Choosing an Object and Finding the Actual Dimensions
After learning how to use Tinkercad, students chose a real-world object to scale. They selected a variety of different objects such as a book, a car, a wooden raft, electronics, sporting equipment, and a pair of shoes. However, a few students struggled with the idea that their object had to be “real-world.”
For example, one student originally chose a picture on the Internet that incorporated music, one of her passions. After having a discussion about scaling and what is considered a real-world object, she readjusted her thoughts and chose a book in the classroom as her object, using a ruler to determine its dimensions (see Figure 1).
Some students were able to physically measure the dimensions of their object while others had to research the dimensions online. For example, one student chose his favorite car, a Nissan Skyline GT-R, as his real-world object and used the Internet to research the dimensions of the car. Another student chose a log raft. When searching online for the dimensions of the log raft, he could only find dimensions for inflatable log rafts. After several minutes he tried a new strategy by searching with the phrase “how to build a log raft,” which took him to a wiki page that showed him step-by-step how to build a log raft and included the dimensions of each component.
Scaling the Object – Fitting the Printing Plate
All students were given the same criteria and constraints for scaling their object. Essentially, the scaled version of their object had to fit on the printing plate of the 3D printer. This meant that the object would need to print with a maximum length less than seven inches, a maximum width less than 5 inches, and a maximum height less than 6 inches. Because every student identified a unique object to scale, each student had to determine their own scale factor (as long as it fit within those dimensions). Because of the uniqueness of each student’s project, there were multiple possible solution paths and strategies for determining the scale factor.
The student who chose the Nissan Skyline GT-R knew he had to greatly scale down his object, but was unsure about how to go about it. We engaged him in meaningful discourse about scale factor. During this conversation he mentioned that half the size of the car would still be too big to print. He determined this by using his calculator and multipling each dimiension by 1/2 in order to show the dimensions of half the size of the car. This allowed us to assess his understanding of scale factor, where we noticed that although he was able to procedurally calculate scale factor, he struggled to understand what it represented.
We encouraged him to think of another scale factor of the Nissan Skyline GT-R dimensions that might be small enough to fit the printing plate. He then tested a scale factor of 1/12 but discovered the scaled model would still be too big to fit the printing plate. To work more efficiently, the student decided to only multiply the length by different potential scale factors as a first step because it was the largest of the dimensions.
For his next attempt, he chose a much smaller scale factor of 1/45, which he found fit well within the constraints of the printing plate, and he opted to find a larger scale that still worked (he wanted to create the largest model car he could). This student eventually settled on 1/26 as his scale factor and used it to find the dimensions of each part of his scaled car as shown in Figure 2.
Building and Printing the Object
After appropriately scaling their objects to fit the printing plate on the 3D printer, students were excited and ready to build their scaled objects in Tinkercad. Students approached the design process in different ways. The student scaling the book started by creating a rectangular prism. She placed the rectangular prism on the grid and changed the size of it to match the dimensions of her scaled book. She then created the spine of the book using the “hole” feature and personalized the cover of her book using the same feature. Finally she added a piece to the top to create a chain and it was ready to be printed! See Figure 3 for her finished product.
The student who created the model Nissan Skyline GT-R started by building the wheel base of his car. He continued adding pieces to the grid, all while using the correct dimensions, to make his object look more like a car (see Figure 4). In the end, although his car did not look exactly like his favorite car, he was extremely proud of the time and effort he put into creating his scaled model. The true excitement of the project came from the building and printing of the objects. Students greatly enjoyed seeing their scaled object printed as well as those of their classmates.
For this scale modeling project, students chose an object, found its actual dimensions, and used scale factors to determine appropriate dimensions for scaling the object that met the space constraints of the printing plate. Students were able to use their scaled dimensions to recreate their object using the Tinkercad 3D design software.
This project provided students with the opportunity to build, personalize, and print their object, allowing for an engaging student-centered experience while also developing students’ 21st century technology skills. The project also gave students the opportunity to recognize the multiplicative relationship with scaling (stretching and shrinking), further preparing them for the algebra learning they would soon experience in high school.
Students finished the project with their own scaled 3D printed object and a more concrete understanding of scaling and proportional reasoning because they physically experienced the scaling process!
Our scale modeling project addressed key mathematics content and practice standards (as in CCSSM; CCSSI 2010) for the middle grades. This project aligns to the ratios and proportions domain (6.RP.3 and 7.RP.2), the expressions and equations domain (6.EE.9), and the geometry domain (7.G.1 and 8.G.4). The project also addresses Standard for Mathematical Practice 6, Attend to Precision and Practice 8, Look for and Express Regularity in Repeated Reasoning.
Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org.
Michele Ough is a math teacher at Millennium Middle School, Sanford, Florida.
Sarah B. Bush, Ph.D., is an associate professor of K-12 STEM education at the University of Central Florida, Orlando.
Published March 2019.
Science, Technology, Engineering, and Mathematics (STEM) education continues to emphasize the teaching of skills that are relevant to today's information driven economy (Jamali, Nurulazam Md Zain, Samsudin & Ale Ebrahim, 2017). Teaching in STEM areas frequently involves real-world problems, problem solving, critical thinking, and creativity that enrich student learning outcomes (Akerson, Burgess, Gerber, Guo, Khan & Newman, 2018; Chalmers, Carter, Cooper & Nason, 2017; Turner 2013). English (2017) argued that STEM has the potential to positively impact student achievement and motivation as long as the integrity of the disciplines is maintained and teachers have the necessary knowledge and resources to effectively implement STEM activities in the classroom. Also, the research agenda of the Middle Level Education Research Special Interest Group (Mertens, Caskey, Bishop, Flowers, Strahan, Andrews, & Daniel, 2016) included several key components that relate to STEM teaching and learning. These components include a call for development of integrated curriculum research and research in problem-based and project-based learning that is relevant to learners. Related research supports the design, construction, and implementation of simple or complex investigations that are critical to effective STEM learning.
Tenets of This We Believe addressed:
- Students and teachers engaged in active learning
- Curriculum is challenging, exploratory, integrative, and relevant
- Educators use multiple learning and teaching approaches
STEM education is a complex idea encompassing multiple content areas and processes including scientific reasoning, computational thinking, engineering design, and mathematical practices (Bybee, 2011). To advance STEM learning and teaching, a better understanding of current research is crucial given the high visibility of STEM education and the paucity of research in this area. A comprehensive review of current research in STEM middle grades education focused on three themes: (a) students: knowledge, attitudes, motivation, and career interests; (b) teachers: preparation, pedagogical practices, and professional development; and (c) schools: curriculum components, after school programs, and assessment.
Students: Knowledge, Attitudes, Motivation, and Career Interests
These research studies, focused on students and STEM education, most often discussed how students develop identities (Tan, Calabrese Barton, Kang, & O'Neill, 2013) and their attitudes and self-efficacy towards STEM subject areas and future STEM-related careers (Guzey, Harwell, & Moore, 2014; Hiller & Kitsantas, 2014). Several researchers argued that the reasoning behind the recent move towards STEM education in K-12 schools is to improve students' motivation for learning (Degenhart et al., 2007). Additionally, disparities in STEM performance based on gender (Levine, Serio, Radaram, Chaudhuri, & Talbert, 2015) and learning disabilities (Lam, Doverspike, Zhao, Zhe, & Menzemer, 2008) are highlighted through quantitative and qualitative studies.
Student identities are critical to successful understanding and learning in STEM environments. Jurow (2005) alluded to this notion in her case study research on how students' figured worlds influence their approach to mathematical tasks. Jurrow's ethnography and discourse analysis found that designers and facilitators of STEM curricula must realize "students participate and are asked to participate in [multiple figured worlds] when we ask them to engage in projects" (Jurow, 2005, p.62). These identities shape students' interpretation of the content and practices of the discipline. Jurow (2005) also highlighted the relevance of understanding student's participation in figured worlds from cultural and historical perspectives.
Kim (2016), using a pairwise t-test of 123 female students' pre- and post-attitude surveys for her study, Inquiry-Based Science and Technology Enrichment Program (InSTEP), found middle school aged girls' attitudes changed positively toward science when participating in inquiry-based programs. Tan and associates (2013) in their case study explored a related concept—identities-in-practice--among non-white middle school girls and their desire for a career in STEM-related fields. By differentiating the narrated and embodied identities-in-practice, the authors highlighted a fundamental issue in our current understanding of the role of identities and learning: "These girls who, on paper, make outstanding science grades and articulate future career goals in STEM-related fields, could be considered exemplary female science students who are 'on track' and who need no special attention, when in fact, they very much do" (p. 1175).
Woolley, Rose, Orthner, Akos, and Jones-Sanpei (2013) reported the importance of using career relevance as an instructional strategy by showing positive effects on mathematics achievement. Their case study looked at how middle grades students used exploratory statistical procedures and multilevel modeling in real-world applications to increase their mathematical understanding. Based on their findings, they recommended school districts focus on improving career development efforts at the middle level as much as they do at the high school level. Other studies have also supported increasing student awareness of STEM careers for both in- and out-of-school settings in order to improve student motivation and attitudes (Chen & Howard, 2010; Wyss, Heulskamp & Siebert, 2012).
It is interesting to note that Levine et al. (2015), using a paired t-test comparison of pre- and post-camp survey analysis, reported that female students tend to change their ideas about STEM to be more positive and are more willing to perceive themselves in STEM careers after participating in authentic STEM-PBL (Problem-Based Learning) activities. Lam et al. (2008) argued for the inclusive nature of a STEM learning environment by highlighting the positive changes in attitudes and beliefs among middle grades students with learning disabilities based on a paired t-test comparison of pre- and post-program surveys. The research studies discussed above highlighted the positive social aspects of project-based learning. At the same time, there are challenges and limitations to using STEM-based pedagogical approaches.
For instance, Mooney and Laubach (2002) researched middle grades students' attitudes and perceptions toward engineering and relevant careers when participating in Adventure Curricula, open-ended and inquiry-based engineering scenarios. Using a t-test comparison of pre- and post-program participant surveys, they summarized that students must have prolonged exposure to affect their perception and knowledge of engineering. While many of these research studies focused on the social aspects of learning in a STEM environment, cognitive aspects, such as exploring integrated content and practices that are developmentally appropriate for middle grades students, were not discussed.
Teachers: Preparation, Pedagogical Practices, and Professional Development
Commonly discussed research ideas in STEM teaching included the attitudes and perceptions of teachers towards their pedagogical practices (Asghar, Ellington, Rice, Johnson, & Prime, 2012), their beliefs on the role of STEM education within and outside their classrooms (Wang, Moore, Roehrig, & Park, 2011), and the struggle with the open-ended nature of student-centered pedagogy when using STEM PBLs (Lesseig, Nelson, Slavit, & Seidel, 2016). Lesseig et al. (2016) in their case study stated that STEM content delivery is successful through open-ended, inquiry, PBL-based learning environments that are student-centered instead of the current traditional structures that offer limited opportunities for promoting such instructional strategies. They also argued for the necessity of a paradigm shift by teachers from a transmitter of knowledge to a facilitator of learning.
STEM classroom practices are directly correlated to teachers' prior educational experiences and perceptions of the role of their discipline area in STEM. In their case study, Wang et al. (2011) reported that mathematics teachers view STEM integration as a way to provide real-world contexts for mathematical concepts, the science teacher views problem solving as the key in STEM integration, and the engineering teacher views STEM integration as an opportunity to combine problem solving with content knowledge of both science and mathematics. Teachers in all three of these areas had difficulties integrating technology into their classrooms beyond the use of computers as a tool for background research. Lesseig et al. (2016) further stated,
Teachers had difficulty creating design challenges that were truly interdisciplinary and admitted that the majority of their projects focused on science at the expense of in-depth mathematics, focused on mathematics with only superficial connections to science, or more commonly, focused on the engineering design process with few explicit ties to mathematical and scientific concepts. (p. 183)
The issue was that these teachers did not learn existing connections between and among science, technology, engineering, and mathematics. For example, one obvious connection is the use of science and mathematics content knowledge and skills inherent in the engineering and design of everyday technological products such as cell phones. Given the lack of teachers' knowledge of these connections, it is important to make these connections explicit for teachers so they can identify and demonstrate them to their students. Typically, teachers are not academically trained in engineering and technology though they are expected to design and teach STEM lessons that include the T and the E in STEM. One obvious solution recommended to address this problem is providing university-based professional development (Lesseig et al., 2016). Other solutions based on a constant comparative analysis of teacher interviews are providing teachers with time and support for more collaboration with subject area teachers and providing access to experts in developing lessons and activities with clear STEM connections (Stohlmann, Moore, & Roehrig, 2012).
Knezek, Christensen, Tyler-Wood, and Periathiruvadi (2013) in their quasi-experimental design-based research focused on improving STEM classrooms recommends "... schools/policymakers/districts/universities should provide additional training opportunities to increase the teaching skills necessary to implement an inquiry-based approach to STEM learning in the classroom" (p. 114). On the other hand, Jordan, DiCicco, and Sabella (2017) in their multiple case study of teachers, found teachers who are content area experts may not be child development experts. Hence, these teachers need additional support in pedagogical aspects such as student-centered instruction, classroom management, and cognitive developments of adolescents. These studies underscore limitations with fast-track alternative certification programs that often reduce exposure to in-depth pedagogical development.
Schools: Curriculum Components, After-School Programs, and Assessment
Research on students and teachers included social aspects of STEM teaching and learning such as attitudes, beliefs, and perceptions towards STEM education, and the factors that influenced them. The central research ideas focused on schools include STEM integration in the disciplines (Guzey, Moore, Harwell, & Moreno, 2016), the different avenues in which STEM-based curricula is utilized with students includes after-school programs (Chittum, Jones, Akalin, & Schram, 2017), summer camps (Mohr‐Schroeder et al., 2014), and the nature of assessment when engineering and technology is integrated into science and mathematics classrooms (Harwell et al., 2015).
The curricular aspects of STEM teaching and learning are frequently explored as part of the design of components, programs, and activity involving STEM integration (Wang et al., 2011). Wang et al. (2011) highlighted, "One of the biggest educational challenges for K-12 STEM education is that few general guidelines or models exist for teachers to follow regarding how to teach using STEM integration approaches in their classroom" (p. 2). Currently, STEM integration is explored through approaches that are multidisciplinary (Russo, Hecht, Burghardt, Hacker, & Saxman, 2011), open-ended and inquiry-based (Mooney & Laubach 2002), hands-on (Lam et al., 2008; Knezek et al., 2013; & Levine et al., 2016), project-based learning (Slavit, Nelson, & Lesseig, 2016), and use of real-world applications (Bozdin, 2011). Slavit and colleagues (2016) noted in their narrative case study that the role of teachers during innovative school start-ups such as STEM-focused schools "... is a complex mixture of learner, risk-taker, inquirer, curriculum designer, negotiator, collaborator, and teacher" (p.14).
Researchers found that teachers faced with integrating STEM in their classrooms lack content knowledge and skills, specifically in engineering and technology subject areas (Jordan et al., 2017; Lesseig et al., 2016; & Wang et al., 2011). In their qualitative analysis of artifacts and videos of classroom implementation, LópezLeiva, Roberts-Harris, and von Toll (2016) recommended collaboration between classroom teachers and university faculty both in the field of education and specific content subjects as a way to bridge the content knowledge and skills gap. Based on their findings, classroom teachers and university faculty collaborated to create MESSY, an integrated teaching and learning experience on motion. MESSY students worked through a process of collective inquiry to co-construct their conceptions of motion. This sub-theme of universities providing support for teachers on content knowledge and research-based STEM pedagogical strategies has been a recurring implication of these studies.
Researchers recommend the use of real-world connections in designing a STEM based curricula. In his mixed-methods study, Bozdin (2011) found that urban classroom learners' STEM-specific skills such as spatial thinking can be formally taught by incorporating geospatial information technology tools such as GIS and Google Earth. Also, Hiller and Kitsantas (2014) engaged students in a citizen science program in which students collaborated with naturalists and professional field biologists to study horseshoe crab speciation. Through a series of statistically significant self-efficacy, interest, outcome expectations, and content knowledge measures, they concluded that "providing this type of experience as part of a formal classroom program is a viable means for promoting student achievement and STEM career motivation" (p. 309).
STEM curricula are predominantly used in after-school programs and summer enrichment experiences as a supplementary intervention. In their embedded mixed methods research study, Mohr‐Schroeder et al. (2014) listed typical supplementary STEM-based experiences such as field trips, hands-on learning from subject experts, and working collaboratively as a team. Chittum et al. (2017) investigated curricular elements that motivated student engagement at Studio STEM, an after-school STEM program. One of the key findings from their mixed-methods study was the importance of presenting information to students in a way that relates to their lives and the real world. Harwell et al. (2015) in their embedded mixed methods research study focused on another area of promise, the development and evaluation of psychometrically sound assessment tools to measure the impact of STEM-oriented instruction. They recommended developing assessments with multiple choice items that are easily scored and include 10 or 15 items per content area including engineering and technology in addition to typical science and mathematics questions.
To date, research has focused on small populations of students, teachers, and schools, generally a la carte STEM programs used as explorations and enrichment. The central research idea involving STEM students is that they must envision themselves as STEM learners, take ownership of their learning, and engage in learning environments that are meaningful to them and directly relate to possible STEM careers. The literature focusing on teachers highlighted the lack of a proper research-based framework to guide and support STEM integration in an authentic manner instead of adapting it based on teachers' anecdotal evidences. Also emphasized in the literature is the need for teacher preparation and sustainable professional development focused on both STEM content and pedagogy. There is a real and urgent need for research-based STEM frameworks to inform curricular and instructional changes for preservice and in-service teacher education. The major takeaway from the literature on schools is that both administrators and teachers need to be more purposeful in integrating engineering and technology into mathematics and science classrooms instead of adding supplementary STEM lessons, activities, and programs. The current state of the literature provides middle level educators with a foundation on which to build effective STEM teaching and learning programs that can successfully address the current limitations to meaningful STEM education.
Akerson, V. L., Burgess, A., Gerber, A., Guo, M., Khan, T. A., & Newman, S. (2018). Disentangling the meaning of STEM: implications for science education and science teacher education. Journal of Science Teacher Education, 29(1), 1–8.
Asghar, A., Ellington, R., Rice, E., Johnson, F., & Prime, G. M. (2012). Supporting STEM education in secondary science contexts. Interdisciplinary Journal of Problem-based Learning, 6(2), 4.
Bodzin, A. M. (2011). The implementation of a geospatial information technology (GIT)‐supported land use change curriculum with urban middle school learners to promote spatial thinking. Journal of Research in Science Teaching, 48(3), 281–300.
Bybee, R. W. (2011). Scientific and engineering practices in K–12 classrooms: Understanding a framework for K–12 science education. Science Teacher, 78(9), 34–40.
Chalmers, C., Carter, M. L., Cooper, T., & Nason, R. (2017). Implementing "big ideas" to advance the teaching and learning of science, technology, engineering, and mathematics (STEM). International Journal of Science and Mathematics Education, 15(1), 25–43.
Chen, C. H., & Howard, B. C. (2010). Effect of live simulation on middle school students' attitudes and learning toward science. Educational Technology & Society, 13(1), 133–139.
Chittum, J. R., Jones, B. D., Akalin, S., & Schram, Á. B. (2017). The effects of an afterschool STEM program on students' motivation and engagement. International Journal of STEM Education, 4(1), 11.
Degenhart, S. H., Wingenbach, G. J., Dooley, K. E., Lindner, J. R., Mowen, D. L., & Johnson, L. (2007). Middle school students' attitudes toward pursuing careers in science, technology, engineering, and math. NACTA Journal, 52–59.
English, L. D. (2017). Advancing elementary and middle school STEM education. International Journal of Science and Mathematics Education, 15(1), 5–24.
Guzey, S. S., Harwell, M., & Moore, T. (2014). Development of an instrument to assess attitudes toward science, technology, engineering, and mathematics (STEM). School Science and Mathematics, 114(6), 271–279.
Guzey, S. S., Moore, T. J., Harwell, M., & Moreno, M. (2016). STEM integration in middle school life science: student learning and attitudes. Journal of Science Education and Technology, 25(4), 550–560.
Harwell, M., Moreno, M., Phillips, A., Guzey, S. S., Moore, T. J., & Roehrig, G. H. (2015). A study of STEM assessments in engineering, science, and mathematics for elementary and middle school students. School Science and Mathematics, 115(2), 66–74.
Hiller, S. E., & Kitsantas, A. (2014). The effect of a horseshoe crab citizen science program on middle school student science performance and STEM career motivation. School Science and Mathematics, 114(6), 302–311.
Jamali, S.M., Nurulazam Md Zain, A., Samsudin, M.A., & Ale Ebrahim, N. (2017). Self- efficacy, scientific reasoning, and learning achievement in the stem PjBL literature. The Journal of Nusantara Studies (JONUS), 2(2), 29–43.
Jordan, R., DiCicco, M., & Sabella, L. (2017). "They sit selfishly." beginning STEM educators' expectations of young adolescent students. Research in Middle Level Education Online, 40(6), 1–14.
Jurow, A. S. (2005). Shifting engagements in figured worlds: middle school mathematics students' participation in an architectural design project. The Journal of the Learning Sciences, 14(1), 35–67.
Kim, H. (2016). Inquiry-based science and technology enrichment program for middle school-aged female students. Journal of Science Education and Technology, 25(2), 174-186.
Knezek, G., Christensen, R., Tyler-Wood, T., & Periathiruvadi, S. (2013). Impact of environmental power monitoring activities on middle school student perceptions of STEM. Science Education International, 24(1), 98–123.
Lam, P., Doverspike, D., Zhao, J., Zhe, J., & Menzemer, C. (2008). An evaluation of a STEM program for middle school students on learning disability related IEPs. Journal of STEM Education: Innovations and Research, 9(1/2), 21.
Lesseig, K., Nelson, T. H., Slavit, D., & Seidel, R. A. (2016). Supporting middle school teachers' implementation of STEM design challenges. School Science and Mathematics, 116(4), 177–188.
Levine, M., Serio, N., Radaram, B., Chaudhuri, S., & Talbert, W. (2015). Addressing the STEM gender gap by designing and implementing an educational outreach chemistry camp for middle school girls. Journal of Chemical Education, 92(10), 1639–1644.
LópezLeiva, C., Roberts-Harris, D., & von Toll, E. (2016). Meaning making with motion is messy: Developing a STEM learning community. Canadian Journal of Science, Mathematics and Technology Education, 16(2), 169–182.
Mertens, S. B., Caskey, M. M., Bishop, P., Flowers, N., Strahan, D., Andrews, G., & Daniel, L. (Eds.) (2016). The MLER SIG research agenda. Retrieved from http://mlersig.net/mler-sig-research-agendaproject/
Mohr‐Schroeder, M. J., Jackson, C., Miller, M., Walcott, B., Little, D. L., Speler, L., ... & Schroeder, D. C. (2014). Developing middle school students' interests in STEM via summer learning experiences: see Blue STEM camp. School Science and Mathematics, 114(6), 291–301.
Mooney, M. A., & Laubach, T. A. (2002). Adventure engineering: a design centered, inquiry based approach to middle grade science and mathematics education. Journal of Engineering Education, 91(3), 309–318.
Russo, M., Hecht, D., Burghardt, M. D., Hacker, M., & Saxman, L. (2011). Development of a multidisciplinary middle school mathematics infusion model. Middle Grades Research Journal, 6(2).
Slavit, D., Nelson, T. H., & Lesseig, K. (2016). The teachers' role in developing, opening, and nurturing an inclusive STEM-focused school. International Journal of STEM Education, 3(1), 7.
Stohlmann, M., Moore, T. J., & Roehrig, G. H. (2012). Considerations for teaching integrated STEM education. Journal of Pre-College Engineering Education Research (J-PEER), 2(1), 4.
Tan, E., Calabrese Barton, A., Kang, H., & O'Neill, T. (2013). Desiring a career in STEM‐related fields: how middle school girls articulate and negotiate identities‐in‐practice in science. Journal of Research in Science Teaching, 50(10), 1143–1179.
Turner, K. (2013). Northeast Tennessee educators' perception of STEM education implementation. (Published doctoral dissertation). East Tennessee State University.
Wang, H. H., Moore, T. J., Roehrig, G. H., & Park, M. S. (2011). STEM integration: teacher perceptions and practice. Journal of Pre-College Engineering Education Research (J-PEER), 1(2), 2.
Woolley, M. E., Rose, R. A., Orthner, D. K., Akos, P. T., & Jones-Sanpei, H. (2013). Advancing academic achievement through career relevance in the middle grades: a longitudinal evaluation of CareerStart. American Educational Research Journal, 50(6), 1309–1335.
Wyss, V. L., Heulskamp, D., & Siebert, C. J. (2012). Increasing middle school student interest in STEM careers with videos of scientists. International Journal of Environmental and Science Education, 7(4), 501–522.
Chittum, J. R., Jones, B. D., Akalin, S., & Schram, Á. B. (2017). The effects of an afterschool STEM program on students' motivation and engagement. International Journal of STEM Education, 4(1), 11.
This research on Studio STEM, an after-school STEM program, explores two different aspects, (1) the student beliefs of science, and (2) the components of the curriculum that motivated students to engage. Both qualitative and quantitative data including science beliefs surveys, a Studio STEM questionnaire. and interviews were analyzed. One of the major findings is that motivational beliefs about pursuing a college degree of the participants of the Studio STEM program were more resilient than the control group. The statistical analysis reveals a significant difference in achievement values, perceptions of achievement, and intentions to attend college. Authors also highlight that participation in the STEM program was voluntary and, hence, the students could already have better beliefs about STEM. One possible solution to rectify this limitation is to compare the pre- and post-beliefs of the same set of students to see if there is a change in beliefs before and after participation.
Mohr‐Schroeder, M. J., Jackson, C., Miller, M., Walcott, B., Little, D. L., Speler, L., ... & Schroeder, D. C. (2014). Developing middle school students' interests in STEM via summer learning experiences: See Blue STEM camp. School Science and Mathematics, 114(6), 291–301.
The authors of this article use a mixed-methods approach to investigate and report their findings on the changes in middle level students' attitudes, perceptions, and interest in and toward STEM fields and careers before and after participating in a summer STEM camp, an informal learning environment that utilizes STEM pedagogical strategies. The students at the See Blue STEM Camp were exposed to engineering design, visual-spatial reasoning mathematics, neurobiology, environmental sustainability, astronomy, LEGO Robotics, aerospace engineering, mathematical modeling, and neuroscience. The findings include an overall 3.1% increase in middle level students' interest in a career in STEM while comparing their responses in a pre- and post-career survey. Two themes emerged from the qualitative data, Camp is "fun" and therefore they want to learn more and camp is engaging which further explains the increase in STEM career interests.
Wang, H. H., Moore, T. J., Roehrig, G. H., & Park, M. S. (2011). STEM integration: teacher perceptions and practice. Journal of Pre-College Engineering Education Research (J-PEER), 1(2), 2.
This article compellingly presents the impact of teacher belief systems on their use and integration of engineering in their classroom through directly collected data from the case study. It is evident that teachers will integrate engineering in the manner that is most comfortable to them and that this decision is highly correlated to their beliefs about the value and purpose of STEM integration. Each of the specific cases clearly correlate to the above claim, and all case study teachers believe that problem solving is the key to the integration process and technology was the most difficult aspect during STEM integration. The professional development for the teachers that the authors used focused majorly on the students' and teachers' understanding of engineering design principle and lacks a holistic approach of informing the teachers about the influence of theirs as well as parents' and students' belief systems on teaching and learning.
Focus on the STEM subjects (2011). [Special Issue]. Middle School Journal, 43(1).
This special themed issue provides practical exemplars of STEM in middle school classrooms. The articles respond to a vision of a challenging, exploratory, and integrative curriculum and meaningful learning for students as identified in This We Believe: Keys to Educating Young Adolescents (NMSA, 2010). Articles include examples of STEM integration and discussions about issues in building STEM related skills across the curriculum. Articles include examples of using inquiry-oriented instruction (Hagevik; Longo), promoting the use of real-world STEM connections (Kalchman; Zuercher), developing literacies for STEM contexts (Wood, et al.), and an overview of a STEM program implementation in an entire school (Stohlmann, et al.). The issue takes a special look at engineering with an emphasis on technology tools and content connections to mathematics and science that are used to solve real-world problems that are of interest to bettering humanity.
Engineering Everywhere. https://www.eie.org/engineering-everywhere
K-12 Resources for Science, Technology, Engineering, and Mathematics Education. http://www.nsfresources.org/
Resources and Downloads for STEM: https://www.edutopia.org/article/STEM-resources-downloads
Teach Engineering: STEM curriculum for K-12. https://www.teachengineering.org/
Ten Great STEM Sites for the Classroom. http://www.educationworld.com/a_lesson/great-stem-web-sites-students-classroom.shtml
Premkumar Pugalenthi is a doctoral candidate at the University of North Carolina at Charlotte. He is interested in the cognitive aspects of learning and teaching when engineering and technology is integrated in science and mathematics classrooms.
Alisa B. Wickliff is the associate director of the Center for Science, Technology, Engineering and Mathematics Education. She is interested in STEM education leadership and STEM learning and teaching.
David K. Pugalee is professor of education at the University of North Carolina at Charlotte where he is the director of the Center for Science, Technology, Engineering and Mathematics Education. He is interested in language and communication and how they influence STEM teaching and learning.
Pugalenthi, P., Wickliffe, A.B., & Pugalee, D.K. (2019). Research summary: STEM in the middle grades. Retrieved [date] from http://www.amle.org/Publications/ResearchSummary/
Published March 2019.
Using the power of words to explore math content, careers, and self-reflection
Reading and writing are powerful learning tools that can be used effectively in the math classroom to draw connections between mathematics and its application to the other school disciplines and the real world. Projects like those described in my previous article, "Integrating Global Education in the Middle School Math Classroom," can foster quantitative literacy, hone analytical and critical thinking abilities, and encourage reading facts, news, and information in a more reasoned and methodical way—skills that are necessary to raise competent, positive, productive citizens.
The power of words can be harnessed to benefit mathematics education in other ways, as well, such as to fight the stereotype threat. The stereotype threat is defined as a situation in which individuals are at risk of confirming negative stereotypes about their racial, ethnic, gender, or cultural group. Research has shown that the stereotype threat also contributes to lower performance among women in math and science.
So we chose International Women's Day (March 8) to celebrate the accomplishments of women mathematicians using a page of Plus magazine with some of the best articles, podcasts, videos, and interviews that have been written by, about, or with major input from female mathematicians and physicists.
I set up a blog with Edublogs that explained the simple guidelines of the project and looked on as my students chose one item from the list, described its content and their own responses, and blogged about it. Here are some of their posts. (Edublogs, like other blogging tools for education, allows you to choose settings and privacy degrees as well as different levels of monitoring students' posts.)
Role models and inspirational stories can provide strong support and motivation in the study of mathematics—and here again, writing can be put to good use. Every year I ask my students to interview a contemporary woman engaged in a mathematics career then write an essay based on their interview. If both the interviewee and the student agree, the essay is submitted to the essay contest organized annually by the Association for Women in Mathematics (AWM). In class we discuss the guidelines for the project and we brainstorm questions. More importantly, however, it is in our classroom conversation that we find out how mathematics is entwined in innumerable professions, not just the standard ones that immediately come to mind.
Over the years my students have interviewed women from all walks of life, from nurses and pediatricians to fashion designers, bankers, actuaries, business owners, app creators, techies, economists, stock exchange traders, genetic counselors, software developers, infectious disease researchers, political statisticians, lawyers, EPA environmentalists, engineers, accountants, photographers, epidemiologists, neuro/computer scientists, econometricians, realtors, and yes, also math and computer science professors and teachers. Some of these women have achieved their dreams at great personal cost; others had to overcome difficulties, biases, unexpected challenges; all speak of perseverance, grit, dedication, "sticking to it." The heartfelt and often wise advice they share is authentic and therefore meaningful for the students. Find some students' essays in this student-created website called Inspirations, and others on the AWM website.
Finally, writing is a great way to get students' feedback on a variety of topics, for instance on a particular project I have asked them to do, especially if it is a new project. I usually give the students a series of questions or prompts that relate to the various aspects of the project as a self-reflection exercise. Their thoughts allow me to gauge the impact of the activity and develop improvements; at the same time the students feel they have a voice, and their feedback is useful and important.
Self-reflection in which the students express their thoughts in paragraphs is much more helpful for me than when they circle numbers to respond to questions. This way students can express their opinions more clearly and reveal their attitudes, anxieties and joys, difficulties and successes, concerns and expectations, and become more engaged in their own learning and more involved with the running and managing of math class. I find these self-reflections particularly useful at student-parent-teacher conference time. An exercise in metacognition, this type of writing also opens communications, strengthens the student-teacher relationship, and builds trust.
As school schedules and curricula are ever more crowded, class time becomes a crucial commodity. Projects like those described here are particularly useful for math educators because they are low investment in terms of class time. The emphasis on creativity, initiative, inquiry, exploration, independent work, extensive reading and research—all features of enriching tasks—produces high return in terms of interest and excitement for mathematics. Furthermore, they appeal to a wider pool of learners and may attract students who consider themselves more readers and writers than mathematicians.
Giving students choice and agency encourages them to take ownership of their own learning. My students responded enthusiastically to these undertakings, and enjoyed sharing them with their families—who were appreciative of the final products—and with the rest of the school community.
Alessandra King is a mathematics teacher and middle school mathematics coordinator for Holton-Arms School, an independent school for girls in grades 3-12 in Bethesda, Maryland.
Published January 2019.
Using children's literature to explore "rich" representations and purposeful tools in mathematics
"Everything seems cheap—when was this book made?" asked one student as we embarked on an activity to engage students in a meaningful exploration focused on mathematical modeling and connections using the children's literature book, Alexander, Who Used to Be Rich Last Sunday (Viorst 1978). In this account, Alexander is given $1.00 by his grandparents and, despite his best efforts to save his money, quickly spends his dollar. Students were quick to notice the price of goods today are much more expensive than in 1978, and they were interested in this meaningful context and humorous story.
In this article, we describe our work with students to make connections across decimals, fractions, and percentages as well as how Alexander's money-spending journey can be modeled using two representations (strip graphs and circle graphs) and two tools (a speech bubble and a fraction wheel). The cornerstone of this work is the explicit link of the same components of Alexander's expenditure of $1.00 to different visual models via the use of representations and tools that support students in making sense of the context. Our activity engaged students in several of the Common Core State Standards for Mathematical Practices including Model with Mathematics (MP4) and Use Appropriate Tools Strategically (MP5).
Our Alexander Exploration
Our exploration can best be organized into five parts: (1) introducing the story, (2) constructing and interpreting the strip graph representation, (3) constructing and interpreting the circle graph representation, (4) estimating with a fraction wheel tool, and (5) culminating reflection questions.
Introducing the Story
To introduce Alexander, student groups of three or four were given one strip of cash register tape that was approximately 110 centimeters long and a meter stick. Next, each group prepared their strip marking units of one centimeter with tick marks across the top of their strip for the full length of the meter. This prompted a brief review of the units on a meter stick by discussing the length of a meter, centimeter (the unit used), and half-centimeter (not used).
Then we began to read the story. Students were immediately interested in Alexander and his family as we built the context. Once we got to the point in the story where Alexander was about to start spending his dollar, we paused and asked student groups to prepare to mark their strip graph with his expenditures using markers.
Constructing and Interpreting the Strip Graph Representation
We started the strip graph together when we read Alexander's first expenditure, which was "when I used to be rich, I went to Pearson's Drug Store and got bubble gum. And after the gum stopped tasting good, I got more gum. And even though I told my friend David I'd sell him all the gum in my mouth for a nickel, he still wouldn't buy it. Good-bye fifteen cents" (Viorst 1978, p. 12). On the strip graph, student groups marked off 15¢ by counting 15 units (not counting tick marks but instead using unit sized jumps) to represent the amount and labeled the section "Gum 15¢." Then they passed the marker to the next student in their group, taking turns to record each expense.
Then students read about the rest of Alexander's journey and worked independently to document the remaining expenditures on their strip graph (see Figure 1). We also found that one group had incorrectly prepared their strip graph. When they got to the last expenditure they realized they only had 18 jumps left, when they needed 20:
Student 1: We only have 18 left.
Teacher: Oh, and you needed 20, so what could have happened?
Student 2: Let's check them (students and teacher work together to check strip graph)
Teacher: What is happening here? (teacher points to a space on the strip graph larger than a centimeter)
Student 1: Oh, we must have forgotten to make tick marks for two of the centimeters.
Student 2: Can we just add two centimeters to the end (of the strip)?
Teacher: If you could, what would that represent on your strip graph?
Student 2: What do you mean?
Teacher: Then how much would you have in total?
Student 1: OH – we would be showing $1.02
Teacher: What is problematic about that?
Student 1: Alexander only had $1.00
Discussions such as the one highlighted here identify the importance of constantly refocusing students on the meaning of the representation, in this case reminding students that the strip graph represented how Alexander spent his $1.00. Until we prompted this group to reason why they couldn't just add two tick marks to the end of their strip, they had temporarily lost the connection between their strip graph and the context.
After students finished creating their strip graphs, each group received a speech bubble, which is a tool used to communicate ideas and discoveries. Then students were given the following prompt: What do you notice? What is your strip graph saying (focusing on the mathematics)? Write a statement that helps you reason about Alexander's expenditures. We wanted students to not just read the graph (e.g., Alexander spent four cents on the magic trick) but instead to read "between the graph" or "beyond the graph" (Curcio, 1987). Groups negotiated what to put on their speech bubbles and their responses varied in sophistication. Some groups combined expenditures of "like things" such as fines or things Alexander could eat and reported on the total they represented (e.g., gum and chocolate bar totaled 26¢). Other groups made comparisons such as how much was spent on fines compared to other expenditures. Several groups created multi-step problems by combining and comparing amounts. Most interesting, some groups used fractions in their speech bubbles. One group stated that 4/20 of Alexander's money was spent at the garage sale. When we asked this group how they got 4/20, they stated that "We had 20/100 to represent the garage sale, which simplifies to 4/20." This allowed us the opportunity to thank this group for being precise by using the word simplify rather than reduce, as fractions do not actually get smaller. Figure 2 showcases one group's speech bubble as they considered how much Alexander spent on average for each expenditure. We were impressed that this group reasoned about the strip graph in this way, considering we had not mentioned or suggested they explore the average.
Constructing and Interpreting the Circle Graph Representation
The next representation converted the groups' strip graphs into circle graphs. To do so, they taped their strip graph end-to-end, creating a loop that was then centered on a piece of chart paper. All students in a group worked to construct the best circle possible with their strip graph loop by having one student trace the outline of the loop onto the chart paper while the others held it stable. Then, keeping the loop in the same position, students created tick marks on the circumference to model where the line on the loop matched each expenditure. Students labeled each section with the expenditure and amount and when complete moved the loop to the side. Next, a point was placed in the middle of the circle and students used a straightedge to draw segments out to their tick marks, creating sectors representing Alexander's different expenditures.
Once all groups completed their circle graphs (see Figure 3), each group received a second speech bubble and the following prompt: Now that you have a circle graph that gives you a "bird's eye view" of the data, what do you notice? You can use the word "about" as you write your statement. Given the flexibility to use the word "about" empowered students to think about estimating amounts that were "about" a particular fraction. One group noticed that "betting, gum, and the garage sale make up about 1/2 of the circle."
Estimating with a Fraction Wheel Tool
We found this to be the perfect opportunity to introduce students to a fraction wheel (Figure 4), made from two paper plates. We asked the question, Can you find some combination of expenditures that are about 1/4 of your circle? 1/3? We circulated with the plate and had students test their hypotheses by placing the plate in the middle of the circle as they matched amounts that they estimated were about 1/4 or 1/3 of their circle graph to the wheel. We were especially interested in one student's abstract thinking when he mentioned that if he could move around (reorder) the expenditures on the circle graph, there would be different amounts that could combine to be about 1/4 or 1/3 on the fraction wheel. Figure 5 highlights an example of students' fractional thinking for this second speech bubble, as they considered using "about" in their statement.
Culminating Reflection Questions
Figure 6 - Culminating Reflection Questions
After students considered Alexander's expenditures through the use of two representations and two tools they were given a set of culminating reflection questions (Figure 6) focused on getting students to think about their models, the tools they used, and connections to the context. While we used all of these questions with our classes, you could easily pick and choose a subset of these questions that best meet the needs of your students.
- What different representations or strategies did you use to think
about Alexander's expenditures? Which representation worked best in
helping you think deeply about the problem?
When did you problem solve in this lesson? Can you give an example?
What tools did you use to help you think about Alexander's expenditures? Why those toools and not others?
What did you struggle with during this lesson? How did you work past that struggle?
When did you have a bright idea during today's lesson? How did that idea come to you?
Did you ever have to be precise today? Can you give an example?
What patterns did you notice today? Why are patterns important to notice?
Did anyone in your group have a brilliant idea today? What was that idea?
Did you make sense of mathematics today? When did that happen?
This activity offered an engaging and meaningful way to explore multiple representations of the data from Alexander's money-spending adventure using graphs and interpreting the information in words and through the use of tools. We hope our discussion of this exploration inspires other teachers to try this activity as well as others that incorporate children's literature in their own classrooms, finding ways in which to best meet the needs of their own students.
Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382-393.
Viorst, J. (1978). Alexander, who used to be rich last Sunday. New York: Atheneum.
Sarah B. Bush is an associate professor of K-12 STEM education at the University of Central Florida, Orlando, Florida.
Karen S. Karp is a professor in the School of Education at Johns Hopkins University, Baltimore, Maryland.
Kathryn R. Cohan is a fifth grade mathematics and science teacher at Holy Trinity Parish School in Louisville, Kentucky.
Published in AMLE Magazine
, October 2018.
How STEM pedagogy is adaptable and accessible in any classroom
Project-Based Learning (PBL) is the current teaching practice being implemented in classrooms to develop 21st century skills and engage students in a deeper level of learning by presenting authentic, complex problems for students to solve over an extended period of time. There is plenty of educational research to support the methodology, however time and curriculum in varying districts make effective PBL a challenge.
PBL requires time and curriculum alignment that districts across the country simply do not have. What can you do when instructional time is precious because of mandated days for testing? What can you do when your content is not aligned with other content areas?
There is an alternative to PBL that is easy to access and garners the same measurable results: STEM pedagogy. For a decade, STEM has been on the education platform, do we really understand what STEM is? The assumption is that the acronym means exactly what it stands for: science, technology, engineering, and math. STEM is being offered as a class or offered in isolation in science and math classes. STEM is the misunderstood cousin of PBL. STEM is a pedagogy that develops 21st century skills and engages students in deeper levels of learning through authentic and complex problem solving experiences.
How to STEM
STEM pedagogy can be accessed in any classroom by any content teacher. There is no need to cross team plan with other content areas or carve out large chunks of instructional time to problem solve.
STEM pedagogy uses a 5E lesson plan approach. The 5Es are: engage, explore, explain, evaluate, and elaborate. The 5E lesson establishes the framework of the problem to be solved. The lesson can be tailored to meet instructional time constraints—in other words, it can be a week long or a month long. The 5Es offer teachers the opportunity to meet the needs of their students. Teachers often have awesome ideas for content but aren't sure how to design the lessons. STEM is misinterpreted because the creation of models and prototypes are considered "crafts" rather than actual problem solving.
Next Generation Science Standards, Common Core State Standards, and local standards are easily connected in STEM pedagogical practice with a 5E lesson plan. Stepping outside the box and looking at standards as they relate to instruction allows opportunities for students to grow and flourish. However, there is some risk-taking that can make most educators, even the seasoned veteran, a little uncomfortable. Giving students a question and then turning them loose to solve it is a little akin to taking the training wheels off a bicycle for the first time.
The main ingredient to successful STEM practice is to allow students room to figure it out. It's tempting to give them answers but resisting that urge and guiding them instead is key.
What STEM Pedagogy Looks Like in Practice
I implemented STEM pedagogy in a seventh grade language arts class before reading the novel Drums, Girls, and Dangerous Pie by Jordan Sonnenblick. The story is centered around the lead character's brother who has leukemia. Many students in the classroom had no personal connection to childhood leukemia. Over a one-week period before introducing the novel, the students researched leukemia, created a model of healthy blood cells and cancer cells, presented their models with a narrative to explain the disease to a group of students, and launched the Pennies for Patients fundraiser for children with leukemia.
When the novel was introduced with a book talk, every student was invested when they learned that leukemia played a role in the plot. Every student read the book both in class and at home. We read the climax together as a read aloud in the class and (spoiler alert) there was a need for tissues. The students also raised more money than ever for the Pennies for Patients fundraiser that year.
Through the 5E lesson students completed authentic research on a topic. At the same time, the seventh grade students were learning about human body systems, and so they generated questions for further investigation. They also used math skills to look at and analyze data surrounding leukemia. Cross cutting concepts and standards were covered in all facets with this 5E lesson.
Need More Evidence for STEM Pedagogy?
How about introducing some science fiction into science class? While the seventh graders were learning about body systems, they were reading Dr. Jekyll and Mr. Hyde by Robert Louis Stevenson in science class. Students were able to make connections between the changes that happened to Dr. Jekyll when he introduced chemicals into his body.
The novel was a segue into the chemistry unit and students developed public service messages that were broadcast over the morning announcements about tobacco, caffeine, and drugs. They conducted the research and they produced the media products.
If you are about to teach a novel in language arts, why not look for real world connections? For example, many novels cover issues about the environment, catastrophic events, and social justice. All of these can be connected to complex problems where students can engage, explore, and explain.
Before reading Life as We Knew It by Susan Beth Pfeffer in eighth grade language arts, have students build models to explain why the moon is so important to the dynamics of Earth's systems, make predictions about what would happen if the system was disrupted, and develop solutions to those problems.
Ask kids in social studies how calendars are created and have students make something to explain it. The Civil War is in your curriculum? Have students create a game about the Underground Railroad or Reconstruction. Then let them play the games in class. Build a simple telescope when talking about the Renaissance. The list is endless.
The Humanities and Sciences Together
And the Oscar goes to … STEAM! The arts and sciences are meant to be together. Building a well-rounded student means including creativity and fostering deeper understanding through questioning. When students engage with content by questioning and designing solutions, there is no limit to what they can discover. Engage with students with arts integration by including music in the classroom. Display art and ask them what they see or wonder. Art integration routines can be included in any classroom on any day to help students engage in the world in a new way. A student doesn't have to be a musician, dancer, actor, singer, or Picasso to engage in the arts. They simply need the exposure so they can frame the question "I wonder… ?"
A Case for STEM
The 5E Lesson for STEM—and use of Next Generation Science Standards—unlocks so much potential for problem solving, authentic research, and creating and presenting solutions. Students make real connections to content, develop deeper understanding, and experience higher levels of rigor and grit.
The Project-Based Learning model and STEM pedagogy are closely related and have similar outcomes, while STEM is more accessible and adaptable than PBL. Teachers who have limited resources, including time and budget, can use STEM practices in the classroom to develop 21st century skills and foster deeper meaning by infusing multiple disciplines into a new whole.
Technology helps us communicate; math is the language; science and engineering are the processes for thinking; and all this leads to innovation. Project-Based Learning may fade away, as many practices do over time as the education pendulum swings. However, the need for STEM will continue to be in demand as we ensure that we are producing students who can improvise, adapt, and overcome challenges.
Students integrating their knowledge and using all available tools at their disposal to solve complex problems that haven't even been created yet … that's the value of STEM.
Michele Schuler is an eighth grade science teacher at Meade Middle School, Fort Meade, Maryland.
Published September 2018.
Creating meaningful learning experiences through language arts and mathematical connections
Examining the Evidence
For centuries, traditional American schooling has taken place in isolated silos of math, language arts, science, and social studies. However, once entering the workforce, students find that the increasingly global and interconnected world does not discriminate between disciplines. Artists, athletes, and authors require problem-solving and computational skills as much as engineers, entrepreneurs, and electricians depend on the skills of strong and effective communication. To develop citizens who are well-equipped to consider and analyze current world issues, we draw upon interdisciplinary learning to " ... expand student understanding and achievement between all disciplines [and] enhance communication skills" (Jones, 2009).
Current educational research has given rise to STEM and STEAM initiatives across the nation. Along with these initiatives, project-based learning and service learning are essential components of a middle school student's education. However, language arts and mathematics have historically been areas with little overlap. As middle school educators, we must find meaningful connections between disciplines to emphasize the truly integrated nature of our world. Unfortunately, little to no training is provided for a language arts and mathematics (LAM) program.
This article combines research-proven concepts of project-based learning with new collaborations between two disciplines whose partnership is typically overlooked. Ultimately, our goal is to create, implement, measure, and sustain a math and language arts interdisciplinary program that meets these goals.
How to Start
The easiest way to begin a cross-curricular collaboration is by examining the school's vision, grade-level themes, and current projects teachers have already developed within their disciplines. Through purposeful reflection, common themes and areas of overlap can be determined. A math project may have communication, reading, and writing components, whereas a language arts project may have the potential for rich mathematical understanding. In our case, the math teacher engaged the students in an annual budgeting project while the language arts teacher conducted a business-themed unit. These two projects showed clear overlap.
During the initial implementation at our school, we connected a study of Hoot by Carl Hiaasen with an analysis of environmental issues using ratios and proportions. The students read the novel and completed a writing assignment that sparked interest and further discussion of statistics in math class.
As our interdisciplinary explorations evolve, projects form from many aspects of student need. While novels may be the starting point for one unit, development of student character may be the beginning for another. Some units and projects are launched with student interest in mind, while others come from a specific academic need.
Language Arts Novels
Research consistently supports the fact that successful teachers of literacy provide their students with ample time to read and write. Guthrie and Humenick (2004) found that reading volume predicted reading comprehension, and that dramatic increases in reading volume are important for literacy proficiency. It is paramount that language arts students not only receive explicit reading instruction, but spend lots of time actually reading. According to Lucy Calkins and Mary Ehrenworth (2017) in A Guide to the Reading Workshop: Middle School Grades, by the time students are in middle school, two-thirds or more of their curriculum will be in content classes. Because language arts teachers carry the responsibility of supporting students in their transition from learning-to-read to reading-to-learn, we use class novels and nonfiction as the foundation for cross-curricular planning.
Once class novels are determined, we identify themes. During our study of The Mighty Miss Malone by Christopher Paul Curtis and No Place by Todd Strasser, students analyzed the factors that influence poverty and homelessness. More subtle themes included an understanding of identity and finding one's own path and place of belonging. Once themes are identified, teachers can begin to think about how content can be taught through these big ideas.
The world of mathematics learning is changing. Gone are the days when timed tests, memorization, and quick recall are valued above all else. According to Jo Boaler (2015), "Real mathematics is about inquiry, communication, connections, and visual ideas. We don't need students to calculate quickly in math. We need students who can ask good questions, map out pathways, reason about complex solutions, set up models, and communicate in different forms."
Math topics at the middle school level are inherently connected to all other disciplines. Recognizing these connections within the classroom not only increases student engagement in the task, but also creates real-life connections that provide opportunities for students to solve problems.
Once themes of study are identified in the language arts classroom, we take inventory of which mathematical concepts connect to those themes. Percentages easily connect when studying poverty rates. Fractions can be practiced through baking for a homeless shelter. Geometry skills naturally connect to discussions and designs of dream homes. Integers and functions can be explored through a budgeting project. Integrating the themes into the math classroom connects learning between classes while providing experiences and simulations for student engagement.
Kids are surprisingly similar across the globe. Nonetheless, the social and emotional needs of students can vary depending on the school community, home and family support, socio-economic status, and other factors. Berkowitz and Bier note that, "(m)any of the American founders understood that education is vital for self-governance and the success of our form of representative democracy. Schools simply have to contribute to the formation of civic character if the nation is to survive" (2005). The incorporation of character development through an analysis of various perspectives and exposure to a variety of content is not only essential to developing global citizens but promotes academic learning.
Evaluate what the kids need. Consider the experiences they do not encounter on a regular basis and formulate projects that expose them to these life moments. For example, while poverty and homelessness is a relatively unfamiliar experience for many students, it is an issue to which they must be exposed in order to be agents of change in the future. Do the students need leadership development? Consider a partnership with younger students. Do the students need a lesson in kindness and compassion? Perhaps a partnership with a local organization or a trip to a food pantry could open their eyes to an unseen world.
Pokemon Go, SnapMap, bottle flipping, fidget spinners, escape rooms, and basketball. The games and activities our students are interested in can connect to curriculum with some foresight and planning. We use these activities as a vehicle for learning deeper concepts. For example, through a study of identity, students created personal Pokemon characters and used math review concepts to capture each other's Pokemon across the school's campus. Students enjoyed a school basketball game as they studied percentages and wrote feature articles about the players and coaches. If teachers can capitalize on current fads and transfer them to the classroom, learning engagement will skyrocket.
We would be remiss if we did not address the fact that student interests change year to year, month to month, and sometimes day to day. The nature of student interests, along with the fluctuation in emotional, social, and academic needs, requires that projects, simulations, and experiences change, or be adjusted, with each new group of students.
Project One: A Study of Poverty
This interdisciplinary LAM unit project begins with the theme of "poverty and homelessness" derived from the novels The Mighty Miss Malone and No Place. Studying this topic gives the students a chance to dive into an important social issue. Connections to ratios and proportions in mathematics allow students to analyze data and statistics that connect to the stories being read in language arts class. This study spans two and a half weeks of math class and four weeks of language arts.
Language Arts Assignments
- The Mighty Miss Malone by Christopher Paul Curtis, novel study
- No Place by Todd Strasser, novel study
- Comparison of novels to current events - nonfiction reading strategies
- Definition of poverty and minimum wage
- Annotations, readings, discussions, and writing assignments concerning the following:
- Social, economic, and political factors that make up a novel's setting (and our own environment)
- The connection between poverty and unemployment
- Race and poverty
- Factors that perpetuate poverty
- Cost-of-living for basic needs and the implications
Analysis of graphic representations of poverty by location
- Study of local median annual incomes
- Calculations of minimum wage
- Finding unit rates to compare income by race
- Proportional reasoning to determine number of people in poverty
- Fractional modeling to bake cookies for a food pantry
- Scale drawings to build a home for those in need
Project Two: Business and Budgets
This simulation is a quarter-long experience in which students use design thinking, collaboration, and experimentation to budget for a family, adopt an egg baby, obtain a "job," create a product, pitch their idea to "sharks," market their products, and produce and "sell" their creations. Unlike the poverty simulation, this experience begins with student interest, the social need to expose students to the difficulties of budgeting, and the need to connect learning to real-world experiences. This connection allows students to see possible applications of their learning that could be useful in their future. In math, students explore functions, percentages, and integers, while they utilize non-fiction writing, presentation skills, marketing techniques, and research skills in language arts.
Language Arts Assignments
- Cover letter and resume
- Business proposal
- Poetry for "egg baby"
- Comic strip story
- Shark tank presentation
- Commercial script
- Business and economics articles - nonfiction reading strategies
- Mission statement
- Letter of thanks
- Press release
- Response to complaint
- Calculation of salary and taxes
- Calculation of car payment, rent, monthly loan charges
- Calculation of cost of a child
- Coupon creation
- Cost analysis of business
- Comparison to minimum wage from poverty study
- Graphing daily balances on coordinate plane
- Find line of best fit
- Creation of circle graph to compare spending
- Analysis of profits and losses
Building connections across disciplines takes time and planning. One cannot only plan for the needs of their class; one must place an equal focus on the other teacher's class and curriculum as well. Additionally, as unit projects or simulations occur, consistent check-ins, updates, and adjustments keep the experience both rich in academic value and implemented smoothly.
Tips and Tricks
Math teacher reads novels. It is vital that the mathematics teacher
be aware of and well-versed in the novels and themes being discussed and
studied in the language arts classroom. This allows for authentic
communication and more clarity in the planning process.
Be flexible and communicate. To stay on track and adjust due to
student ideas, we update a Google Doc each day with what was
accomplished and where we need to go next. This allows each teacher to
be aware of the status of the other discipline and make adjustments
Set deadlines. Prior to beginning the project, teachers need to
decide which assignments have strict deadlines and which are more
flexible. Prioritizing the assignments that have a direct effect on the
other discipline allows each teacher to continue progressing through the
Use math content to guide pacing. To authentically connect projects
to curriculum, the language arts teacher must allow the math content to
guide the pace. Students need time to explore math content prior to
diving into tough discussions that require analysis.
Kids take the lead. It's important to allow students to guide the
experience. If a student takes the project in a new direction, let him
or her. We often find that these are the most valuable moments within a
Introduce projects together. Introducing projects as a team tells the students that the teachers value
this collaboration and builds the connection from day one.
Communicate with parents. Emphasizing that parents can contact both
teachers with questions or concerns is helpful when dealing with any
issues that arise. This also allows parents to feel connected as their
child experiences learning in a way that may be different than what the
parent is used to.
Be sure to differentiate. With projects, simulations, and the use of
design thinking and iteration, students' needs can be met through
individualized studies and depth of analysis.
Don't force it. If it doesn't fit, it's ok. Not all units connect well. Aim for authentic experiences.
Keep anecdotal records of student discussion and "aha" moments. These
reminders will help with planning and adjusting of projects in future
Berkowitz, M. W., & Bier, M. (2005, February). What works in character education. Retrieved from http://www.character.org/uploads/PDFs/
Boaler, J. (2015, May 7). Memorizers are the lowest achievers and other Common Core math surprises. Retrieved from http://hechingerreport.org/memorizers-are-the-lowest-
Calkins, L., & Ehrenworth, M. (2017). A guide to the reading workshop: Middle school grades. Portsmouth, NH: Heinemann.
Guthrie, J., & Humenick, N. (2004). Motivating students to read: Evidence for classroom practices that increase reading motivation and achievement. In P. McCardle & V. Chhabra (Eds.), The voice of evidence in reading research (pp. 329-354). Baltimore, MD: Brookes.
Jones, C. (2009). Interdisciplinary approach - advantages, disadvantages, and the future benefits of interdisciplinary studies. ESSAI, 7 (Article 26), 76-81. Retrieved from http://dc.cod.edu/cgi/
Sonam Shahani is a sixth grade language arts teacher at Columbus Academy, Gahanna, Ohio.
Katie Castle is a sixth grade mathematics teacher at Columbus Academy, Gahanna, Ohio.
The authors wish to thank middle school librarian Stacy Nockowitz for advising on this article.
Published in AMLE Magazine
, August 2018.