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

Agenda 2 Introductions Reflecting on Measurement A Look at Some National Data Measurement Tasks Discussion MSU 2011 – NCTM Gallery Session, Indianapolis, IN

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 – 4th yr doctoral student, taught elementary & middle school for 8 years (2 years as a math specialist), taught elementary math methods & currently supervise elementary 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 3 MSU 2011 – NCTM Gallery Session, Indianapolis, IN

Reflecting 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? MSU 2011 – NCTM Gallery Session, Indianapolis, IN

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

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

Toothpick Performance Data Response% Responding 2 ½ inches (correct) ½ inches13 3 ½ inches20 8 ½ inches7 7 Response% Responding 2 ½ inches (correct) ½ inches14 3 ½ inches23 Other42 Omitted2 [Grade 8, 2003, multiple choice][Grade 4, 2003, open response] MSU 2011 – NCTM Gallery Session, Indianapolis, IN

Toothpick Results Over Time 8 Percent Correct Assessment Year4 th Grade8 th Grade *58* * Statistically lower than 1996 and NAEP results across three assessments MSU 2011 – NCTM Gallery Session, Indianapolis, IN

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. 9 MSU 2011 – NCTM Gallery Session, Indianapolis, IN

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

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? 11 MSU 2011 – NCTM Gallery Session, Indianapolis, IN

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 12 MSU 2011 – NCTM Gallery Session, Indianapolis, IN

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

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 : If you have any questions please us at: 14 MSU 2011 – NCTM Gallery Session, Indianapolis, IN