1. 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

2. Introductions Lorraine – 4 th 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 – 3 th 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 – 2 nd year doctoral student, taught middle school & high school math for 6 years, currently teaching elementary methods courses at MSU

3. Agenda 3 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University 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

4. Reflections on 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? ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

5. 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

6. Toothpick Performance Data [Grade 4, 2003, open response] Response% Responding 2 ½ inches (correct) 10 ½ inches 3 ½ inches Other Omitted ©STEM @ MSU 2011 – Math in Action, Grand Valley State University 6 20 14 23 42 2

7. Toothpick Performance Data Response% Responding 2 ½ inches (correct) 58 10 ½ inches13 3 ½ inches20 8 ½ inches7 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University 7 Response% Responding 2 ½ inches (correct) 20 10 ½ inches14 3 ½ inches23 Other42 Omitted2 [Grade 8, 2003, multiple choice][Grade 4, 2003, open response]

8. Toothpick Results Over Time ©STEM @ MSU 2011 – Math in Action, Grand Valley State University 8 Percent Correct Assessment Year4 th Grade8 th Grade 19962464 20002564 200320*58* * Statistically lower than 1996 and 2000. NAEP results across three assessments

9. 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 9 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

10. STEM – Three Curricula The three carefully chosen curricula are:  Scott Foresman- Addison Wesley Mathematics  UCSMP’s Everyday Mathematics  Saxon Math 10 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

11. STEM – Our Analysis In 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] 11 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

12. 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 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University 12

13. 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] ©STEM @ MSU 2011 – Math in Action, Grand Valley State University 13

14. 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 14 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

15. More Results (LENGTH) Some conceptual knowledge is addressed ElementFrequency Definition of lengthUncommon; hard to do Greater means longerVery common Unit-measure compensationFairly common Unit IterationUncommon; gaps & overlaps 15 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

16. 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) 16 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University K-1 K-2 2-3

17. More Results (AREA) Very little conceptual knowledge ElementFrequency Definition of areaUncommon Unit IterationUncommon Unit-measure compensationUncommon 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) 17 ©STEM @ MSU 201 – Math in Action, Grand Valley State University

18. 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 18 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

19. More Results (VOLUME) Some conceptual knowledge is addressed ElementFrequency Greater means largerUncommon Definition of volume/capacityVery Uncommon Unit-measure compensationVery Uncommon Unit IterationVery Uncommon Only units of vol/cap can be used to measure volume/capacity Uncommon The spatial structure of rectangular prisms Uncommon 19 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

20. 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 20 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University

21. 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/~stemprojhttp://www.msu.edu/~stemproj If you have any questions please e-mail us at: stemproj@msu.edu stemproj@msu.edu 21 ©STEM @ MSU 2011 – Math in Action, Grand Valley State University