what do we mean by length, area, capacity, and...

What DO We Mean by Length, Area, Capacity, and Volume?

Jia He, Rani Satyam & Eryn Stehr

©STEM @ MSU 2013 – MCTM Annual Conference

Traverse City, Michigan – Aug 2013

Strengthening Tomorrow’s Education in Measurement (STEM) Project

Introductions

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Jia He – Ph.D. student in math ed. at MSU. Four years

working with STEM Project. Taught content courses for Elementary Education majors.

Rani Satyam – 2nd year graduate student at MSU and

beginning 2nd year on STEM.

Eryn Stehr – 3rd year graduate student and beginning 3rd

year on STEM; Taught mathematics and Math for Preservice Elementary Teachers at Minnesota State, Mankato

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Session Overview

• What is STEM project?

• Session Goals & Rationale

• Tasks

• Questions & Discussion

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Who is STEM?Strengthening Tomorrow’s Education

in Measurement

Elementary Curriculum Analysis of Spatial Measurement –Length, Area, Volume &

Capacity

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Professional Development work with 33 facilitators in

23 regions

Research & Development work

with Elem. Math Methods students and

instructors at MSU

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Why we are interested in this

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Definitions play a significant role in mathematicsDefinitions vary in terms of their quality in curricula“Teachers must be able to choose or develop a definition that is mathematically appropriate and also usable by students at a particular level.” (Ball, 2003)

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Our goal for this session…

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Walk out with a better understanding of length, area, volume and capacity as well as how different definitions may affect elementary students’ understanding of measurement concepts.

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

What we are going to be doing…

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Write your own definitions of length, area, volume & capacity

Explore, analyze & discuss various definitions selected from textbooks•Elementary Curricula•Mathematics content textbooks for pre-service elementary teachers

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Task 1: Write definitionsWrite a definition for length.

Please work individually first, then briefly share with a neighbor.

Brief Discussion: What factors were important to you when you composed your definitions?

*© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Task 2: Explore & Analyze Definitions

Length • Briefly sort the length definition cards into

categories that make sense to you

• Talk with a neighbor about categories & questions

• Brief whole group discussion about categories and questions

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Task 2: Explore & Analyze Definitions

Length Sort the definitions into a few categories

• What were your sorting criteria?

• What similarities or differences do you see

with length definitions?

• If different, which differences matter?

• What are the pros and cons of definitions

that you think would affect your students’

learning of length? © STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Task 3: Choose a measurement.... Area

Volume/CapacityWrite a definition for chosen concept(s).

Please work individually first, then briefly share with a neighbor.

Brief Discussion: What factors were important to you when you composed your definitions?

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Explore & Analyze Definitions

Area vs. Volume/CapacitySort the definitions into a few categories

• What were your sorting criteria?

• What similarities or differences do you see

with the definitions?

• If different, which differences matter?

• What are the pros and cons of definitions

that you think would affect your students’

learning of area or volume/capacity? © STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Across the Concepts

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• What interesting patterns did you see across

your concept sets?

• What surprised you?

© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

REWRITE & COMPARE

Rewrite and compare definition for each of your concepts:

length, area, volume and/or capacity.

• What is the biggest change you made?

• Why did you make the change?

*© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Thank you!

We want to thank the National Science

Foundation for funding this work

We want to thank you for coming!

For more information: http://www.msu.edu/~stemproj

If you have any questions or

OTHER INTERESTING DEFINITIONS OF MEASUREMENT CONCEPTS

please e-mail us at: stemproj@msu.edu *

Other STEM Presentations

*© STEM Project @ MSU 2013 – MCTM Conference – Traverse City, MI

Supporting Spatial Measurement Tasks

with Technology

B101 Wed 1:30 - 2:30

Filling the Space in Length Measurement A110 Thurs 2:45 - 3:45