1. Getting Down to the Basics with Length Measurement Lorraine Males, Funda Gonulates, STEM Project, Michigan State University MiCTM Conference August 6, 2009

2. Welcome! Your presenters & you A bit about the STEM project A problem & NAEP data Three Activities Putting together the key length measurement ideas Feedback 2 Introduction and Overview

3. A Bit About Our Project STEM – Strengthening Tomorrow's Education in Measurement Premise: Part of the problem may be our curriculum materials Carefully examine 3 elementary programs Everyday Mathematics Scott-Foresman/Addison-Wesley Mathematics Saxon Mathematics We are not aiming to evaluate these curricula – we are looking to provide a description of the opportunity to learn measurement 3

4. A Bit About Our Project Look for every instance of measurement content Code each as an “opportunity” to learn some bit of conceptual or procedural knowledge Length analysis is complete for K through Grade 3 4

5. Lots of different conceptual and procedural elements We found that these curricula provide tasks that mostly have a procedural focus We found some examples that may be used to introduce some key ideas related with length measurement 5 Some Results

6. The Toothpick Problem “What is the length of the toothpick?” 6 Into the Content [NAEP, Grade 4, 2003, Open response]

7. [Grade 4, large national sample] Response% Responding 2.5 inches (correct) 20 10.5 inches14 3.5 inches23 Other42 Omitted2 7 The Toothpick Problem Data

8. What lessons can we take from the toothpick problem? students teaching content curriculum 8

9. We will do three length measurement activities Buttons Footprint Funny Rulers As we do these activities think about: the key length measurement ideas possible connections between these activities and ideas 9 Come Potentially Useful Activities

10. Question: What is the width of the paper you are given in buttons? 1. Sketch possible ways that a student may solve this task. 10 Buttons

11. Question: What is the height of the desk you are sitting at? How long is it? 1. Trace you footprint on the paper provided in your bag, cut it and determine the height and length of your desk. 2. Sketch possible ways students might come up with. 11 Footprint

12. Question: How long is the paperclip provided in your bag? 1. Examine the rulers in your envelope to answer the following questions: Which rulers could give you an accurate measure? Which rulers you should not use? For each, explain why the ruler will not give an accurate measure. 12 Funny Rulers

13. Think back to the following questions: What were some of the key length measurement ideas in these activities? What are some possible connections between these activities and ideas? 13 Reflecting on Activities

14. In all those three activities there is an exhaustion of the space but If we skip tiling ………………. If we always provide sufficient materials but do not provide opportunities for unit iteration ………… If we start with measurement with ruler without providing an enough experience with tiling and unit iteration ……….. Rulers embed units 14 Key Ideas

15. 15 Percentages of Selected Conceptual Knowledge Elements Across Grades

16. 16 Percentages of Selected Procedural Knowledge Elements Across Grades

17. What happens if we don’t show strange and incorrect ways of doing something? Is it good if we just show students correct procedures? Think back to the toothpick problem Some things may be worth investing more time on than others because of the benefit these things may provide 17 Overall

18. Thank you for coming & engaging Please let us know if you are interested in free professional development around measurement ideas 18 Closing

19. Engage with us Feedback form Indicate an interest in measurement Are you using one of our target curricula? Look for us around the state, at NCTM, and in NCTM’s journals Lorraine Males (maleslor@msu.edu) Funda Gonulates (gonulate@msu.edu) Jack Smith (jsmith@msu.edu) 19 Closing