1. 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

2. Tasks & Tasks Different types of measurement tasksDifferent types of measurement tasks “Do it” tasks“Do it” tasks “Enrich it” tasks—not everything is invented here“Enrich it” tasks—not everything is invented here We worked on length and area together this morningWe worked on length and area together this morning Shift leader and content to focus on lengthShift leader and content to focus on length Need help with time management: How to balance mining more from the discussion and moving on?Need help with time management: How to balance mining more from the discussion and moving on? Lorraine’s introLorraine’s intro 11/24/20152Measurement PD, April 2010

3. Buttons Everyday Math, Grade 1 Everyday Math, Grade 1 Why STEM likes this taskWhy STEM likes this task Enhancing the impact: what other questions do we want to ask students?Enhancing the impact: what other questions do we want to ask students? 11/24/20153Measurement PD, April 2010

4. Crazy Rulers Another “violations” taskAnother “violations” task Working on the knowledge that is embedded in rulersWorking on the knowledge that is embedded in rulers Experience at MiCTM this yearExperience at MiCTM this year How to sequence with work with “regular” rulers?How to sequence with work with “regular” rulers? What questions do we want to askWhat questions do we want to ask 11/24/20154Measurement PD, April 2010

5. Worms & Rulers Scott-Foresman/Addison-Wesley, Grade 1Scott-Foresman/Addison-Wesley, Grade 1 One of the few tasks presenting the challenge of broken rulersOne of the few tasks presenting the challenge of broken rulers Includes both standard and non-standard alignment of objectsIncludes both standard and non-standard alignment of objects Like Buttons, enhancement possibleLike Buttons, enhancement possible What to ask?What to ask? 11/24/20155Measurement PD, April 2010

6. Jagged Path Background: paths present challenges that single segments and “long” objects don’tBackground: paths present challenges that single segments and “long” objects don’t Let’s do itLet’s do it As before, remember your process and your resultAs before, remember your process and your result Does it matter which side we work on?Does it matter which side we work on? What happens at the corners, “inside” and “out”?What happens at the corners, “inside” and “out”? Problem goes away with rulers; becomes an addition taskProblem goes away with rulers; becomes an addition task 11/24/20156Measurement PD, April 2010

7. Sum Up (length tasks) 11/24/20157Measurement PD, April 2010

8. Intro to STEM Problem was recognized; no explanation => no idea about where to invest in “solution”Problem was recognized; no explanation => no idea about where to invest in “solution” STEM I: Examine the curricular contributionSTEM I: Examine the curricular contribution Central question: Do current US elementary mathematics provide sufficient “opportunity to learn” spatial measurementCentral question: Do current US elementary mathematics provide sufficient “opportunity to learn” spatial measurement Our view of OTLOur view of OTL Painstaking & micrograinedPainstaking & micrograined 11/24/20158Measurement PD, April 2010

9. STEM methods Choose three elementary curricula (two were easy)Choose three elementary curricula (two were easy) Step 1: Find the spatial measurement contentStep 1: Find the spatial measurement content Should be easy: look at measurement lessons & unitsShould be easy: look at measurement lessons & units That’s not good enoughThat’s not good enough We err on the inclusive side (don’t ignore opportunities)We err on the inclusive side (don’t ignore opportunities) Two independent codersTwo independent coders Step 2: Code the resulting spatial measurement contentStep 2: Code the resulting spatial measurement content Begin with length work our way alongBegin with length work our way along All pages with L, or A, or V contentAll pages with L, or A, or V content Need an independent way of assessing OTLNeed an independent way of assessing OTL =>List of measurement knowledge at fine-grain size=>List of measurement knowledge at fine-grain size 11/24/20159Measurement PD, April 2010

10. STEM Methods (CCS) Began with a focus on Conceptual knowledge for measurement (first with length)Began with a focus on Conceptual knowledge for measurement (first with length) Our definitionOur definition It is a long list; useful to construct itIt 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)Quickly saw that we needed a complementary list of Procedural knowledge (to code the content of curricula) Even longer listEven longer list Saw that there is measurement knowledge that is neither; cultural decisions about tools, notations, & systemsSaw that there is measurement knowledge that is neither; cultural decisions about tools, notations, & systems Called this Conventional knowledgeCalled this Conventional knowledge 11/24/201510Measurement PD, April 2010

11. STEM Methods (CCS, II) Also decided to code HOW measurement knowledge is expressed in text in written curriculaAlso 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, & GamesSix 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’ textCode 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 ExplanationAlso 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)Typical situation: One sentence in the text is coded as an ordered pair (Textual Element; Knowledge Element) 11/24/201511Measurement PD, April 2010

12. Some Results (length) Approach: Discuss all three; focus on Everyday MathApproach: Discuss all three; focus on Everyday Math All three curricula are heavily Procedural (more than 75% of all codes, all curricula, Grades K–3)All three curricula are heavily Procedural (more than 75% of all codes, all curricula, Grades K–3) Common proceduresCommon procedures Direct ComparisonDirect Comparison Visual & Indirect ComparisonVisual & Indirect Comparison Measure with RulersMeasure with Rulers Draw segmentsDraw segments Find perimeterFind perimeter 11/24/201512Measurement PD, April 2010

13. More Results (length) Conceptual knowledge is addressed in EM but with gapsConceptual knowledge is addressed in EM but with gaps ElementFrequency Definition of lengthUncommon; hard to do Greater LongerVery common Unit-measure compensationPretty common Unit IterationUncommon; gaps & overlaps 11/24/201513Measurement PD, April 2010

14. Some Results (AREa) Even more procedural, across curricula and grades (K–4); 88% or more of all codesEven 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)Primary content is largely based on visual comparisons (which 2-D shape is larger/bigger) Next we have covering and countingNext we have covering and counting Finally, computational procedures, beginning with rectanglesFinally, computational procedures, beginning with rectangles Area is defined as a quantity in Grade 2 (all curricula)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) 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 lengthWeaker attention to Unit Iteration for area than length 11/24/201514Measurement PD, April 2010

15. Initial Take on Volume Hard (conceptual clarity & duration)Hard (conceptual clarity & duration) Capacity (property of containers, continuous quantity) is interleafed with volume (filling and counting, discrete quantity)Capacity (property of containers, continuous quantity) is interleafed with volume (filling and counting, discrete quantity) Introduced in K, present throughout elementary grades, slow developmentIntroduced in K, present throughout elementary grades, slow development Our question: Where is the foundational content?Our question: Where is the foundational content? Thus far, only examined Grades K–3; will need to examine moreThus far, only examined Grades K–3; will need to examine more 11/24/201515Measurement PD, April 2010

16. Lessons to Take Away No strong case that conceptual foundations of measurement are faring well in written curriculaNo strong case that conceptual foundations of measurement are faring well in written curricula Everyday Math attends to conceptual knowledge but can easily do more Everyday Math attends to conceptual knowledge but can easily do more Buttons is a good example Buttons is a good example Weak attention to Unit Iteration (length & area)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 contentConjecture: 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 writtenImplication: Teachers will need help to enrich the curriculum as written 11/24/201516Measurement PD, April 2010

17. Your Questions (for STEM) 11/24/2015Measurement PD, April 201017