# Kinesthetic Mathematics in the Middle Grades

## Physical movement helps students engage in, investigate, and understand mathematics concepts

#### Introduction

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 disorder (ADHD).

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.

#### Mathematics Content

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 understanding.

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 trendy handshake.

#### Angle Exercises

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.

#### Quadrilateral Stretches

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 differences.

- 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 isosceles trapezoid.
- To challenge students and accelerate the pace, gradually increase the call rate of the types of quadrilaterals.

#### Conclusion

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.

#### References

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.

DeborahMc@usca.edu

**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).

BridgetC@usca.edu

Published in

*AMLE Magazine*, April 2020.