exploring spatial measurement through a...

Exploring Spatial Measurement through a

Conceptual Lense Lorraine Males, Funda Gonulates, Shannon

Sweeny, & Nic Gilbertson

Strengthening Tomorrow’s Education in Measurement (STEM) Project

Michigan State University

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

Introductions Lorraine – 4th yr doctoral student, working on the STEM

project all 4 years, formerly taught middle school/high school mathematics for 8 years

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

Funda –

Shannon –

Nic –

Agenda


• Introductions

• Reflection on Measurement

• Introduction to the STEM Project

• Data from the STEM project

• National Data

• Working with some tasks

• Sharing/Summarizing

• Evaluation

Measurement Take 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?


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 methods

Step 1: Find the spatial measurement content

– Should be easy: look at measurement lessons & units

– More complicated

– Err on the inclusive side (don’t ignore opportunities)

– Two independent coders

Step 2: Code the resulting spatial measurement content

– All pages with L, or A, or V content

– List of measurement knowledge in small bits

– Code each bit of text on all pages with measurement content

– Two independent coders


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)


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 segments

– Find perimeter


More Results (LENGTH)

• Conceptual knowledge is addressed, but with gaps

Element Frequency

Definition of length Uncommon; hard to do

Greater <=> Longer Very common

Unit-measure compensation Pretty common

Unit Iteration Uncommon; gaps & overlaps


Some Results (AREA)

• Even more procedural, across curricula and grades (K–4); 88% or more of all codes

• Common procedural sequence – Focus on Visual Comparison (which 2-D shape is

larger/bigger?) in primary grades – Next, covering shapes with same units and counting

them – Finally, computational procedures, beginning with

rectangles • Area is defined as a quantity in Grade 2 (all curricula) • Weaker attention to Unit Iteration for area than length


Some Preliminary Results (VOLUME)

• Hard work (problems of conceptual clarity & duration)

• Capacity (property of containers, continuous quantity) is interleafed with volume (filling and counting, discrete quantity)

• Introduced in K, present throughout elementary grades, slow development

• Primary focus (K & 1): Capacity

• Gradual shift from Capacity to Volume across the grades

• Thus far, only Grades K–3; will code Grade 4 in early 2011


Major Lessons

• Conceptual foundations of measurement are weakly developed

• Weak attention to Unit Iteration (length & area)

• 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 curriculum as written


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 14

Toothpick Performance Data [Grade 4, large national sample]

Response % Responding

2.5 inches (correct) 20

10.5 inches 14

3.5 inches 23

Other 42

Omitted 2


Lessons from Toothpick

• We are not doing so well nationally

• Too many kids don’t understand length measurement, rulers, or both

• Some errors are sensible; some remain mysterious

• Not obvious what we are doing wrong

• => Not obvious what we should change


Some Measurement Tasks

• Crazy Rulers (Length) – original STEM task

• Crazy Cakes (Area) – Investigations, grade 4?/DMI

• Finding the Volume (Volume) – Everyday Mathematics, grade 4?

Your task:

• Pick one of these tasks

• Complete the task

• With your group members answer the following question: What would a student need to understand about measurement in order to successfully complete this task? [Record on your poster paper]


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]

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