Conceptual Development in Area Measurement Funda Gonulates, Lorraine Males, & Nic Gilbertson...

Conceptual Development in Area MeasurementFunda Gonulates, Lorraine Males, & Nic Gilbertson

Strengthening Tomorrow’s Education in Measurement (STEM) Project

Michigan State University

MCTM Conference 2010 Dakota High School

WelcomeWe’d like to take some time for everyone to introduce themselvesNamePositionGrade levelDistrict/School

2STEM 2010 - MCTM Conference

AreaTake some time to think about and share your answer to the following:


What is area?What issues or difficulties

do you think students might have with area measurement?

Pentagon Task

STEM 2010 - MCTM Conference 4

1) Find the area

2) Draw a second pentagon with the same area

Pentagon Task


With a partner, 1) Share your solutions2) What might students have difficulties with in

solving this problem?3) What would students need to know in order

to solve this problem?

Pentagon Task – NAEP results


Scoring Rubric:• Incorrect (both parts a & b incorrect)• Partial (either a or b correct)• Correct (both a & b correct)• Omitted• Off Task



Scoring Rubric:• Incorrect (both parts a & b incorrect)…48%• Partial (either a or b correct)…47%• Correct (both a & b correct)…2%• Omitted…2%• Off Task…(rounded to 0%)



Grade 8 – 2005

Scoring Rubric:• Incorrect (both parts a & b incorrect)…48%• Partial (either a or b correct)…47%• Correct (both a & b correct)…2%• Omitted…2%• Off Task…(rounded to 0%)

STEM – Who, Where, and When

Who: PI: Dr. Jack Smith Research Assistants: Dan Clark, Kuo-Liang Chang, Leslie Dietiker,

Hanna Figueras, Nic Gilbertson, Funda Gonulates, Pat Greeley, Jia He, Kosze Lee, Lorraine Males, Aaron Mosier, Matt Pahl, Gulcin Tan Sisman, Shannon Sweeny, Alexandria Theakston

When: 2007 – present

Where: Michigan State UniversityWork beginning in various districts throughout Michigan including

Eastern UP, Grand Rapids, Jackson, Kalamazoo, & Oakland9STEM 2010 - MCTM Conference

Strengthening Tomorrow’s Education in Measurement

STEM – WhatWhat:

Researchanalyzing the capacity of three written elementary

curricula to support robust learning of spatial measurement (length, area, volume)

Professional Developmentworked with pre-service teachers during their year-

long internship on measurement lesson study working with facilitators throughout Michigan who

are in turn working with teachers in their areas10STEM 2010 - MCTM Conference

STEM – Three Curricula

The three carefully chosen curricula are:Scott Foresman-

Addison Wesley Mathematics

UCSMP’s Everyday Mathematics

Saxon Math


STEM – Our Analysis

In our analysis we are looking at every lesson, problem, and activity of teach curricula for two important aspects:Knowledge elements - Spatial measurement

knowledge (conceptual, procedural, conventional)Textual elements - The ways in which this knowledge

is expressed (statements, demonstrations, worked examples, questions, problems, games)


STEM – Area Core Principles Area as a measurable quantityConservation under partitioning. Conservation under motion Identical UnitsUnit iteration TransitivitySpatial structure of rectangular arraysMultiplicative composition from lengths


STEM – Area AnalysisFlow of Area Topics


• “Grain-size perception of area”

• the ability to exploit the structure

• “Holistic perception of area”

• to understand the structure of a region

• Array of Objects (Numbers, counting)

• Arrays of Tesselating Objects

• Rectangles

• Visual Judgment

• Cover

• Measure and Cover

• Measure w/ Grid w/out Array

Structure• Measure w/

Array Structure

• Compute LxW

• Std. vs Non std. Units

• Visual Estimation of Area

• Partition

Analysis of area content in all curricula K-4 (Gonulates & Mosier, 2010)

Area Lesson Analysis: SFAW Grade 3, P.468A


Area Lesson Analysis: SFAW Grade 3, P.468



SFAW GR3 Area Lesson Analysis

Objectives of the Lesson

P. 468A P. 468Conceptual Knowledge

Procedural Knowledge

Connections

Reflection


SFAW GR3 Area Lesson Analysis

Objectives of the Lesson Estimate or find the areas of figures in square units.

P. 468A P. 468Conceptual Knowledge • Area as a

measurable quantity (Definition and meaning of area measure)

•Order/Equity•Unit Measure Compensation•Area as a measurable quantity (Definition and meaning of area measure)

Procedural Knowledge • Measure area (G, RC)• Draw a region

•Measure area (G, covering, counting, grid)•Visual estimation •Read an area•Draw a region

Connections

Reflection

Thank you!We want to thank the National Science

Foundation for funding this work

We want to thank you for coming!Please take a few minute to fill out our evaluation.

For more information starting this fall you can go to: http://www.msu.edu/~stemproj

If you have any questions please e-mail us at: [email protected]


http://www.msu.edu/~stemproj

mailto:[email protected]

Conceptual Development in Area Measurement Funda Gonulates, Lorraine Males, & Nic Gilbertson...

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