Getting Down to the Basics with Length Measurement

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

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

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

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

5. Some Results • 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

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

7. The Toothpick Problem Data [Grade 4, large national sample]

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

9. Come Potentially Useful Activities 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

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

11. Footprint 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.

12. Funny Rulers 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.  

13. Reflecting on Activities 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?

14. Key Ideas • 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

15. Percentages of Selected Conceptual Knowledge Elements Across Grades

16. Percentages of Selected Procedural Knowledge Elements Across Grades

17. Overall 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

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

19. Closing 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)