Activities to Support Conceptual Understanding of Spatial Measurement

Activities to Support Conceptual Understanding of Spatial Measurement Lorraine Males, Shannon Sweeny, Nic Gilbertson, Funda Gönülateş Strengthening Tomorrow’s Education in Measurement (STEM) Project ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN

Agenda • • • Introductions Reflecting on Measurement A Look at Some National Data Measurement Tasks Discussion ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 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 Shannon – 4 th 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, 2 nd year on STEM project, taught middle school & high school math for 6 years, currently teaching elementary methods courses at MSU, Funda – 3 th yr doctoral student, working on the STEM project all 3 years, formerly taught middle school mathematics for 4 years ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 3

Reflecting on Measurement Take some time to think about and share your answer with a partner to the following: v What are the key ideas you want your students to know about measurement? v What do you find challenging about teaching length, area and/or volume? ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 4

The Toothpick (Broken Ruler) Problem “What is the length of the toothpick? ” [NAEP, Grade 4, 2003, Open response] ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 5

Toothpick Performance Data [Grade 4, 2003, open response] Response 2 ½ inches (correct) 10 ½ inches % Responding 20 14 3 ½ inches 23 Other 42 Omitted 2 ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 6

Toothpick Performance Data [Grade 4, 2003, open response] [Grade 8, 2003, multiple choice] Response % Responding 2 ½ inches (correct) 10 ½ inches 20 58 14 2 ½ inches (correct) 10 ½ inches 3 ½ inches 23 3 ½ inches 20 Other 42 8 ½ inches 7 Omitted 2 ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 13 7

Toothpick Results Over Time NAEP results across three assessments Percent Correct Assessment Year 4 th Grade 8 th Grade 1996 24 64 2000 25 64 2003 20* 58* * Statistically lower than 1996 and 2000. ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 8

Measurement Tasks Skim the tasks and choose as many as you can to focus on Do the task and discuss with people near you We are always looking for good tasks and so we will also be passing out some reflection cards which we will collect to get your opinions of the tasks. ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 9

Measurement Tasks Length Strange Rulers Area Crazy Cakes Volume Packing a Truck [original STEM task] [Investigations, gr. 4] [Saxon, gr. 5/4] ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 10

Participant Thoughts on the Tasks • What key ideas about measurement might these tasks help to elicit? • How might these tasks address some of the challenges to the teaching and learning of measurement? • What features of these tasks do you find productive or helpful in teaching / learning measurement? ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 11

Why these Tasks? • Present non-conventional problems • Provide good avenues for discussions about measurement • Provide problems in which there are multiple solution paths • Highlight key conceptual ideas - Units - Additivity ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 12

Why these Tasks? Ruler construction Strange Rulers Measuring with ruler (Length) Partitioning Units Additivity Composing & Crazy Cakes Decomposing (Area) Meaning of volume a Packing Fractions Truck Finding volume w/ non-cube units (Volume) Equal area does not imply congruence Connects to divisibility 13

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: stemproj@msu. edu ©STEM @ MSU 2011 – NCTM Gallery Session, Indianapolis, IN 14