1 / 17

DEVELOPING POWERFUL MEASURERS

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

sadie
Download Presentation

DEVELOPING POWERFUL MEASURERS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related