Exploring Spatial Measurement Through a Conceptual Lens Lorraine Males, Funda Gonulates, Shannon...

Exploring Spatial Measurement Through a Conceptual Lens

Lorraine Males, Funda Gonulates, Shannon Sweeny, Nic Gilbertson

©STEM @ MSU 2011 – Math in Action, Grand Valley State University

Strengthening Tomorrow’s Education in Measurement (STEM) Project

IntroductionsLorraine – 4th yr doctoral student, working on the STEM project

all 4 years, taught secondary methods, currently supervising interns, taught middle/high school mathematics for 8 years

2©STEM @ MSU 2011 – Math in Action, Grand Valley State University

Funda – 3th yr doctoral student, working on the STEM project all 3 years, formerly taught middle school mathematics for 4 years

Shannon – 4th yr doctoral student, taught elementary & middle school for 8 years (2 years as a math specialist), taught elementary math methods & currently supervise elementary interns @ MSU

Nic – 2nd year doctoral student, taught middle school & high school math for 6 years, currently teaching elementary methods courses at MSU

Agenda


• Introductions• Reflections on Measurement• A Look at Some National Data• Introduction to the STEM Project• Measurement Tasks• A Look at STEMS’s Curriculum Data• Evaluation

Reflections on MeasurementTake some time to think about and share your answer with a partner to the following:

4

What are the key ideas you want your students to know about measurement?

What do you find challenging about teaching length, area and/or volume?

©STEM @ MSU 2011 – Math in Action, Grand Valley State University

The Toothpick (Broken Ruler) Problem

“What is the length of the toothpick?”

[NAEP, Grade 4, 2003, Open response]

©STEM @ MSU 2011 – Math in Action, Grand Valley State University 5

Toothpick Performance Data[Grade 4, 2003, open response]

Response % Responding

2 ½ inches (correct)

10 ½ inches

3 ½ inches

Other

Omitted


20

14

23

42

2

Toothpick Performance Data



58

10 ½ inches 13

3 ½ inches 20

8 ½ inches 7




20

10 ½ inches 14

3 ½ inches 23

Other 42

Omitted 2

[Grade 8, 2003, multiple choice][Grade 4, 2003, open response]

Toothpick Results Over Time


Percent Correct

Assessment Year 4th Grade 8th Grade

1996 24 64

2000 25 64

2003 20* 58*

* Statistically lower than 1996 and 2000.

NAEP results across three assessments

The STEM Project• Initial situation

– Problem was recognized; no explanation – So no idea about where to invest in a “solution”

• STEM I: Examine the curricular contribution (elementary curricula)– Two years (Fall 2007- Fall 2009)– Do current US elementary mathematics provide

sufficient “opportunity to learn” (OTL) spatial measurement

• STEM II: Put what we have learned to work– Three years (August 2009 – July 2012)– PD is one project component


STEM – Three Curricula

The three carefully chosen curricula are:Scott Foresman-

Addison Wesley Mathematics

UCSMP’s Everyday Mathematics

Saxon Math


STEM – Our AnalysisIn our analysis we are looking at every lesson, problem, and activity of teaching curricula for two important aspects:Knowledge elements - Spatial measurement

knowledge (conceptual, procedural, conventional)[What content is in the textbook]

Textual elements - The ways in which this knowledge is expressed (statements, demonstrations, worked examples, questions, problems, games)[How the content is presented in the textbook]


Measurement Tasks – Part I

• Length– Strange Rulers – original STEM task

• Area – Crazy Cakes – Investigations, grade 4/Developing

Mathematical Ideas (DMI)• Volume

– The Wet Box Task – adapted from Dr. Michael Steele

Pick one of these measures (length, area, or volume) and complete the task


Measurement Tasks – Part II

What would a student need to understand about measurement

in order to successfully complete this task?

[Record on your poster paper]


Some Results (LENGTH)• All three curricula are heavily procedural

(more than 75% of all codes, all curricula, Grades K–3)

• Common procedures– Direct Comparison– Visual & Indirect Comparison– Measure with Rulers– Draw line segments of given lengths– Calculate perimeter


More Results (LENGTH)Some conceptual knowledge is addressed

Element Frequency

Definition of length Uncommon; hard to do

Greater means longer Very common

Unit-measure compensation Fairly common

Unit Iteration Uncommon; gaps & overlaps


Some Results (AREA)• All three curricula are even more procedural

with area than with length (more than 88% in grade K-4)

• Common procedures– Visual Comparison

– Covering and counting to find area

– Computing area with formulas (starting with rectangles)


K-1

K-2

2-3

More Results (AREA)• Very little conceptual knowledge

Element Frequency

Definition of area Uncommon

Unit Iteration Uncommon

Unit-measure compensation Uncommon

Area remains the same when partitioned (gr. 3 & 4)

Very uncommon (1 in each curricula)

Composition/Decomposition of Regular Polygons (gr. Gr. 4)

Very uncommon (2 in EM)


Some Results (VOLUME)• All three curricula are heavily procedural

(more than 75% of all codes, all curricula, Grades K–1)

• Common procedures– Visual Comparison– Measure capacity/volume with standards and

non-standard units– Estimating Capacity/Volume


More Results (VOLUME)Some conceptual knowledge is addressed

Element Frequency

Greater means larger Uncommon

Definition of volume/capacity Very Uncommon

Unit-measure compensation Very Uncommon

Unit Iteration Very Uncommon

Only units of vol/cap can be used to measure volume/capacity

Uncommon

The spatial structure of rectangular prisms

Uncommon


Major Lessons

• Conceptual foundations of measurement are weakly developed

• Weak attention to Unit Iteration (length, area, volume)

• Conjecture: The sheer extent of visual content on the page (esp. for EM & SFAW) may make it hard for teachers to find and focus on the conceptual content

• Implication: Teachers will need to enrich the written curriculum


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 :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]

Exploring Spatial Measurement Through a Conceptual Lens Lorraine Males, Funda Gonulates, Shannon...

Documents

Transcript of Exploring Spatial Measurement Through a Conceptual Lens Lorraine Males, Funda Gonulates, Shannon...