DEVELOPING POWERFUL MEASURERS

1. DEVELOPING POWERFUL MEASURERS MICHIGAN’S PROFESSIONAL DEVELOPMENT IN THE TEACHING & LEARNING OF SPATIAL MEASUREMENT APRIL 12TH & 13TH, 2010 JAMES B. HENRY CENTER FOR EXECUTIVE DEVELOPMENT MICHIGAN STATE UNIVERSITY EAST LANSING, MI

2. Tasks & Tasks • Different types of measurement tasks • “Do it” tasks • “Enrich it” tasks—not everything is invented here • We worked on length and area together this morning • Shift leader and content to focus on length • Need help with time management: How to balance mining more from the discussion and moving on? • Lorraine’s intro Measurement PD, April 2010

3. Buttons • Everyday Math, Grade 1 • Why STEM likes this task • Enhancing the impact: what other questions do we want to ask students? Measurement PD, April 2010

4. Crazy Rulers • Another “violations” task • Working on the knowledge that is embedded in rulers • Experience at MiCTM this year • How to sequence with work with “regular” rulers? • What questions do we want to ask Measurement PD, April 2010

5. Worms & Rulers • Scott-Foresman/Addison-Wesley, Grade 1 • One of the few tasks presenting the challenge of broken rulers • Includes both standard and non-standard alignment of objects • Like Buttons, enhancement possible • What to ask? Measurement PD, April 2010

6. Jagged Path • Background: paths present challenges that single segments and “long” objects don’t • Let’s do it • As before, remember your process and your result • Does it matter which side we work on? • What happens at the corners, “inside” and “out”? • Problem goes away with rulers; becomes an addition task Measurement PD, April 2010

7. Sum Up (length tasks) Measurement PD, April 2010

8. Intro to STEM • Problem was recognized; no explanation => no idea about where to invest in “solution” • STEM I: Examine the curricular contribution • Central question: Do current US elementary mathematics provide sufficient “opportunity to learn” spatial measurement • Our view of OTL • Painstaking & micrograined Measurement PD, April 2010

9. STEM methods • Choose three elementary curricula (two were easy) • Step 1: Find the spatial measurement content • Should be easy: look at measurement lessons & units • That’s not good enough • We err on the inclusive side (don’t ignore opportunities) • Two independent coders • Step 2: Code the resulting spatial measurement content • Begin with length work our way along • All pages with L, or A, or V content • Need an independent way of assessing OTL • =>List of measurement knowledge at fine-grain size Measurement PD, April 2010

10. STEM Methods (CCS) • Began with a focus on Conceptual knowledge for measurement (first with length) • Our definition • It is a long list; useful to construct it • Quickly saw that we needed a complementary list of Procedural knowledge (to code the content of curricula) • Even longer list • Saw that there is measurement knowledge that is neither; cultural decisions about tools, notations, & systems • Called this Conventional knowledge Measurement PD, April 2010

11. STEM Methods (CCS, II) • Also decided to code HOW measurement knowledge is expressed in text in written curricula • Six major categories of Textual elements: Statements, Questions, Demonstrations, Worked Examples, Problems, & Games • Code whether the presenter was the teacher (common in primary grades) or the students’ text • Also code if Questions/Problems require activity away from the students’ desks and if they require Explanation • Typical situation: One sentence in the text is coded as an ordered pair (Textual Element; Knowledge Element) Measurement PD, April 2010

12. Some Results (length) • Approach: Discuss all three; focus on Everyday Math • 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 segments • Find perimeter Measurement PD, April 2010

13. More Results (length) • Conceptual knowledge is addressed in EM but with gaps Measurement PD, April 2010

14. Some Results (AREa) • Even more procedural, across curricula and grades (K–4); 88% or more of all codes • Primary content is largely based on visual comparisons (which 2-D shape is larger/bigger) • Next we have covering and counting • Finally, computational procedures, beginning with rectangles • Area is defined as a quantity in Grade 2 (all curricula) • Everyday Math spends a lot of time on rectangular arrays (both “contiguous” and not) in the service of whole number multiplication and area (Grades 3, 4) • Weaker attention to Unit Iteration for area than length Measurement PD, April 2010

15. Initial Take on Volume • Hard (conceptual clarity & duration) • Capacity (property of containers, continuous quantity) is interleafed with volume (filling and counting, discrete quantity) • Introduced in K, present throughout elementary grades, slow development • Our question: Where is the foundational content? • Thus far, only examined Grades K–3; will need to examine more Measurement PD, April 2010

16. Lessons to Take Away • No strong case that conceptual foundations of measurement are faring well in written curricula • Everyday Math attends to conceptual knowledge but can easily do more • Buttons is a good example • Weak attention to Unit Iteration (length & area) • Conjecture: The sheer extent of visual content on the page (EM & SFAW) make it hard for teachers to find and focus on the conceptual content • Implication: Teachers will need help to enrich the curriculum as written Measurement PD, April 2010

17. Your Questions (for STEM) Measurement PD, April 2010