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Body Uses in Mathematics – Becoming Aware: Book | Intermediate Lesson Plan 1

Link to Book

Lesson Objectives

By the end of this lesson students will start to have discussions and think about how some methods and ideas they were taught as students are not always necessarily ‘right’ or ‘better than’ other methods. The objective is to build this thinking up enough to use it throughout the next two lessons.

Lesson Outline

First discussion: How do we use our bodies in our lives naturally to measure the world around us? (5 mins)
  • Have you ever had to measure distance along a large field by counting the strides you take?
  • In a game like Bochy, how do you measure which ball is closer to the target?
  • When is it useful and when is it bad to use our body to measure things?
    For example: It is useful for measuring in a game, or the length of supplies you need for a project, but it is bad to use it to measure in a chemistry lab when you shouldn’t be approximate.
Measurement activity: Individual work (10 mins)
  • Ask students to pick four objects around the classroom to measure, and have them measure those objects themselves.
  • Have them write down how long it is in body measurements (for example: one hand width to measure a desk).
  • They will then measure that against a ruler at their desk to get an approximation (for example: if they measured one hand width, at their desk they would measure their one hand width and see how long that is on a ruler to approximate the size of the object).
Measurement activity: Partner work (5 mins)
  • Instruct students to pair up. Students will share 2 of the objects they measured (without saying the way they measured each object).
  • The students will then measure the objects shared by their partner.
  • As with activity 1, each student will write down the body measurement for each object, and then use a ruler to approximate that body measurement.
Second Discussion: Comparison (10 mins)
  • In pairs: Ask the students to compare the measurements they used on their body
  • Some leading questions you can provide:
    • How close were they with the ruler measurements?
    • Did they use the same body parts to measure? Why or why not?
  • As a class: Hold a discussion about the comparison in measurements.
  • Some leading questions to facilitate the discussion:
    • Were some pairs closer to each other than others? Why might that be?
    • Did some students try to be more precise?
    • Was it close enough? Does it matter how accurate the measurements were?
    • Why might it be better to measure things with our bodies rather than with rulers every time?
    • When might it be bad to use our bodies to measure things?
Third Discussion: How else do we use our bodies for math? (5 mins)

Leading questions:

  • Is it ever bad to use your fingers when doing math?
    Why or why not?
  • Is there ever a time we shouldn’t use our hands to count or multiply?
  • How does it make you feel when people tell you not to use your hands to count or multiply?

Making an Equation for the Finger Trick: Book | High School Lesson Plan 2

Link to Book

Lesson Objective

By the end of this lesson, students will have an algebraic and cultural understanding of the finger multiplication method. Students will also create an informal proof and have exposure to what modules are.

Materials Needed

  • Finger multiplication method- history, equation and proof.
    The first page of this document can be distributed to the students
  • Resource for teachers: Cajun Multiplication: A History, Description, and Algebraic Verification of a Peasant Algorithm (Elizabeth D. Gray)
    http://www.lamath.org/journal/Vol1/cajunmultiplicationfinal.pdf

Links to pdf resources, etc.

Lesson Introduction

Briefly explain to the students that the goal for the lesson today is to follow the steps a mathematician takes in creating and checking an algorithm.

Introduce the finger method with a story-like explanation of its historical significance. This is to engage the students in the lesson, and to connect it to the cultural objectives in the next lesson.

Lesson Outline

First part of lesson: Teaching the algorithm (10 minutes)

Introduce the finger trick method with its history and teach the algorithm of the finger trick. After showing the algorithm, go through some examples with the students, following along with the algorithm for each example.

  • How teacher and students will work in this portion.
First discussion: Why use this method? (10 minutes)

Either in small groups, or as a class, discuss how using this method might be useful to younger students.

To tie this into the next lesson:

  • Finish with a quick class lead discussion, and, if not already brought up by students, prompt the idea that for some young students, this may be the method their parents taught them.
Individual/group work: Create the general algorithm (20-30 minutes)

Ask the students to describe the algorithm as an equation in terms of x and y. Once they have an equation, they should show it works.

(Prove their equation equals x*y).

Prompts to help students start:

  • “How can you make an equation to describe multiplying x by y in terms of the algorithm?”
  • “What is the domain and range/restriction of x and y?” (This is to prompt the recognition of using 5’s in the equation)
Differentiation: Extra Challenge

Ask the students to recreate the algorithm and equation for someone with 4 fingers on each hand.

They can also make it with a partner, creating an algorithm and formula for someone with 20 fingers.

Final Discussion: Sharing ideas (5-10 minutes)

Finish the lesson going over the common equation for the algorithm:

xy=10(x+y-10)+(x-5)(y-5)

Lesson Conclusion

Conclude in reviewing the equation, and also tying it back to the discussion from the beginning of the class.

Enriching Geometric Understanding through the Early STEM Pedagogy

Enriching Geometric Understanding through the Early STEM Pedagogy

Authors: Nicole Langevin, Miwa A Takeuchi, Jenny Yuen and Shayla Jaques

Abstract

The current agenda of STEM education research is implicitly focused on preparing students as future workers for STEM industries (Takeuchi et al, 2020). Incorporating an aesthetic vision in STEM gives students an ownership of their work and encourages them to see more and see the complex (Farris and Sengupta, 2016). What happens when early age STEM education centralizes on that aesthetic vision? This article follows two grade 2 boys in one such classroom where students were asked to use technology to explore what makes a mathematical shape without the traditionally defined rules. With this project and setting, the boys were able to push themselves to see more in complex shapes and show pride in the discoveries they made.

References

Alberta Education. 1985. Art (Elementary). Edmonton, Alta: Alberta Education. Also available at https://education.alberta.ca/media/482114/elemart.pdf (accessed October 20, 2021).

———. 2007. Mathematics Kindergarten to Grade 9. Edmonton, Alta: Alberta Education. Also available at https://education.alberta.ca/media/3115252/2016_k_to_9_math_pos.pdf (accessed October 20, 2021).

Davis, B, K Francis and S Friesen. 2019. STEM Education by Design: Opening Horizons of Possibility. New York: Routledge.

Farris, A V, and P Sengupta. 2016. “Democratizing Children’s Computation: Learning Computational Science as Aesthetic Experience.” Educational Theory 66, no 1–2: 279–96. Piaget, J. 1970. Genetic Epistemology. Trans E Duckworth. New York: Norton.

Sengupta, P, M-C Shanahan and B Kim, eds. 2019. Critical, Transdisciplinary and Embodied Approaches in STEM Education. New York: Springer.

Takeuchi, M A, and S Dadkhahfard. 2019. “Rethinking Bodies of Learners Through STEM Education.” In Critical, Transdisciplinary and Embodied Approaches in STEM Education, ed P Sengupta, M-C Shanahan and B Kim, 199–216. New York: Springer.

Takeuchi, M A, P Sengupta, M-C Shanahan, J D Adams and M Hachem. 2020. “Transdisciplinarity in STEM Education: A Critical Review.” Studies in Science Education 56, no 2: 213–53.

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An Exploration into Ethnomathematics in Education: Book | High School Lesson Plan 1 

Link to Book

Lesson Outline

By the end of this lesson students will start to have discussions and think about how some methods and ideas they were taught as students are not always necessarily ‘right’ or ‘better than’ other methods. The objective is to build this thinking up enough to use it throughout the next two lessons.

Materials Needed

  • Illustrated book on website
  • Document for Teacher: Finger multiplication method explanation.

Lesson Introduction

Talk about the history of ancient cultures using measurement with the body as their first form of math. For example, the length of a foot, the length of a stride, the span of a hand, and the breadth of a thumb were all classified as measurements used by multiple cultures. The foot is said to have been measure off King Henry’s foot, and the width of the thumb was used to create the measurement of an inch.

Lesson Outline

First discussion: How do we use our bodies in our lives naturally to measure the world around us? (10 minutes)

Potential leading questions for discussion:

  • Have you ever had to measure distance along a large field by counting the strides you take?
  • In a game like the lawn game Bocce, how do you measure which ball is closer to the target?
  • When is it useful and when is it bad to use our body to measure things?
    For example: It is useful for measuring in a game, or the length of supplies you need for a project, but it is bad to use it to measure in a chemistry lab when you shouldn’t be approximate.
Second discussion: What are other ways, besides measurement that we use our body for math? (10 minutes)

Some ideas:

  • Counting
    • Can also talk about multiple cultures that count with their hands differently:
    • Chisanbop method (used in China)
  • Multiplying (using the 9-multiplication finger trick, and the other finger trick as described later)
Third discussion: The stigmatization of using the body in math. (10 minutes)

Leading question: Is it bad to use your fingers when doing math for anything? Why or why not?

Did you ever have a time in school when you were no longer allowed to use your body to do math? Or did you ever feel shame for using your body for math?

Lead the discussion into why students might be shamed to use their hands and fingers in math, and if there is good reason to think that way. Is there truly a reason not to use our hands? Who does it affect the most when teachers tell students not to count with their hands? What does that tell students about the way they understand math?

Hopefully, finish this discussion with the understanding that sometimes using your hands to do math is extremely beneficial.

Lesson: The finger trick for multiplication. (15 mins)

Teach the finger trick method with its history and teach the algorithm of the finger trick. (Lesson shown in first page of the attached document – Finger multiplication method- history, equation, and proof.