developing powerful measurers

DEVELOPING DEVELOPING POWERFUL MEASURERSPOWERFUL MEASURERS

MICHIGAN’S PROFESSIONAL DEVELOPMENT IN THEMICHIGAN’S PROFESSIONAL DEVELOPMENT IN THE

TEACHING & LEARNING OF SPATIAL MEASUREMENTTEACHING & LEARNING OF SPATIAL MEASUREMENT

APRIL 12APRIL 12THTH & 13 & 13THTH, 2010, 2010

JAMES B. HENRY CENTER FOR EXECUTIVE DEVELOPMENTJAMES B. HENRY CENTER FOR EXECUTIVE DEVELOPMENT

MICHIGAN STATE UNIVERSITYMICHIGAN STATE UNIVERSITY

EAST LANSING, MIEAST LANSING, MI

Tasks & TasksTasks & Tasks

• Different types of measurement tasksDifferent types of measurement tasks• ““Do it” tasksDo it” tasks• ““Enrich it” tasks—not everything is invented hereEnrich it” tasks—not everything is invented here

• We worked on length and area together this We worked on length and area together this morningmorning

• Shift leader and content to focus on lengthShift leader and content to focus on length

• Need help with time management: How to balance Need help with time management: How to balance mining more from the discussion and moving on?mining more from the discussion and moving on?

• Lorraine’s introLorraine’s intro

04/20/2304/20/2322Measurement PD, April 2010Measurement PD, April 2010

ButtonsButtons

• Everyday MathEveryday Math, Grade 1, Grade 1

• Why STEM likes this taskWhy STEM likes this task

• Enhancing the impact: what other questions Enhancing the impact: what other questions do we want to ask students?do we want to ask students?


Crazy RulersCrazy Rulers

• Another “violations” taskAnother “violations” task

• Working on the knowledge that is embedded Working on the knowledge that is embedded in rulersin rulers

• Experience at MiCTM this yearExperience at MiCTM this year

• How to sequence with work with “regular” How to sequence with work with “regular” rulers?rulers?

• What questions do we want to askWhat questions do we want to ask


Worms & RulersWorms & Rulers

• Scott-Foresman/Addison-Wesley, Grade 1Scott-Foresman/Addison-Wesley, Grade 1

• One of the few tasks presenting the challenge One of the few tasks presenting the challenge of broken rulersof broken rulers

• Includes both standard and non-standard Includes both standard and non-standard alignment of objectsalignment of objects

• Like Buttons, enhancement possibleLike Buttons, enhancement possible

• What to ask?What to ask?


Jagged PathJagged Path

• Background: paths present challenges that single Background: paths present challenges that single segments and “long” objects don’tsegments 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 Problem goes away with rulers; becomes an addition taskaddition task


Sum Up Sum Up (length tasks)(length tasks)


Intro to STEMIntro to STEM

• Problem was recognized; no explanation => Problem was recognized; no explanation => no idea about where to invest in “solution”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 Central question: Do current US elementary mathematics provide sufficient “opportunity mathematics provide sufficient “opportunity to learn” spatial measurementto learn” spatial measurement

• Our view of OTLOur view of OTL

• Painstaking & micrograinedPainstaking & micrograined


STEM methodsSTEM 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 We err on the inclusive side (don’t ignore

opportunities)opportunities)• Two independent codersTwo independent coders

• Step 2: Code the resulting spatial measurement Step 2: Code the resulting spatial measurement contentcontent• 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


STEM Methods STEM Methods (CCS)(CCS)

• Began with a focus on Began with a focus on Conceptual knowledge Conceptual knowledge for for measurement (first with length)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 Quickly saw that we needed a complementary list of Procedural knowledge Procedural knowledge (to code the content of (to code the content of curricula)curricula)• Even longer listEven longer list

• Saw that there is measurement knowledge that is Saw that there is measurement knowledge that is neither; cultural decisions about tools, notations, & neither; cultural decisions about tools, notations, & systemssystems

• Called this Called this Conventional knowledgeConventional knowledge


STEM Methods STEM Methods (CCS, II)(CCS, II)

• Also decided to code HOW measurement knowledge is Also decided to code HOW measurement knowledge is expressed in text in written curriculaexpressed in text in written curricula

• Six major categories of Textual elements: Six major categories of Textual elements: StatementsStatements, , QuestionsQuestions, , DemonstrationsDemonstrations, , Worked ExamplesWorked Examples, , ProblemsProblems, & , & GamesGames

• Code whether the presenter was the teacher (common Code whether the presenter was the teacher (common in primary grades) or the students’ textin primary grades) or the students’ text

• Also code if Questions/Problems require activity away Also code if Questions/Problems require activity away from the students’ desks and if they require Explanation from the students’ desks and if they require Explanation

• Typical situation: One sentence in the text is coded as Typical situation: One sentence in the text is coded as an ordered pair (Textual Element; Knowledge Element)an ordered pair (Textual Element; Knowledge Element)


Some Results Some Results (length)(length)

• Approach: Discuss all three; focus on Approach: Discuss all three; focus on Everyday Everyday MathMath

• All three curricula are heavily Procedural (more All three curricula are heavily Procedural (more than 75% of all codes, all curricula, Grades K–3)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


More Results More Results (length)(length)

• Conceptual knowledge is addressed in EM but Conceptual knowledge is addressed in EM but with gapswith gaps

Element Frequency

Definition of length Uncommon; hard to do

Greater <=> Longer Very common

Unit-measure compensation

Pretty common

Unit Iteration Uncommon; gaps & overlaps


Some Results Some Results (AREa)(AREa)

• Even more procedural, across curricula and grades (K–4); Even more procedural, across curricula and grades (K–4); 88% or more of all codes88% or more of all codes

• Primary content is largely based on visual comparisons Primary content is largely based on visual comparisons (which 2-D shape is larger/bigger)(which 2-D shape is larger/bigger)

• Next we have covering and countingNext we have covering and counting

• Finally, computational procedures, beginning with Finally, computational procedures, beginning with rectanglesrectangles

• Area is defined as a quantity in Grade 2 (all curricula)Area is defined as a quantity in Grade 2 (all curricula)

• Everyday Math Everyday Math spends a lot of time on rectangular arrays spends a lot of time on rectangular arrays (both “contiguous” and not) in the service of whole (both “contiguous” and not) in the service of whole number multiplication and area (Grades 3, 4)number multiplication and area (Grades 3, 4)

• Weaker attention to Unit Iteration for area than lengthWeaker attention to Unit Iteration for area than length04/20/2304/20/231414Measurement PD, April 2010Measurement PD, April 2010

Initial Take on VolumeInitial Take on Volume

• Hard (conceptual clarity & duration)Hard (conceptual clarity & duration)

• Capacity (property of containers, continuous Capacity (property of containers, continuous quantity) is interleafed with volume (filling quantity) is interleafed with volume (filling and counting, discrete quantity)and counting, discrete quantity)

• Introduced in K, present throughout Introduced in K, present throughout elementary grades, slow developmentelementary grades, slow development

• Our question: Where is the foundational Our question: Where is the foundational content?content?

• Thus far, only examined Grades K–3; will need Thus far, only examined Grades K–3; will need to examine moreto examine more


Lessons to Take AwayLessons to Take Away

• No strong case that conceptual foundations of No strong case that conceptual foundations of measurement are faring well in written curriculameasurement are faring well in written curricula

• Everyday Math Everyday Math attends to conceptual knowledge attends to conceptual knowledge but can easily do morebut can easily do more• Buttons Buttons is a good exampleis a good example

• Weak attention to Weak attention to Unit Iteration Unit Iteration (length & area)(length & area)

• ConjectureConjecture: The sheer extent of visual content on : The sheer extent of visual content on the page (EM & SFAW) make it hard for teachers to the page (EM & SFAW) make it hard for teachers to find and focus on the conceptual contentfind and focus on the conceptual content

• ImplicationImplication: Teachers will need help to enrich the : Teachers will need help to enrich the curriculum as written curriculum as written


Your Questions Your Questions (for STEM)(for STEM)

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developing powerful measurers

Documents

list of measurement

mimeasurement pd

measurement lessons

conceptual knowledge

conventional knowledge

length tasks

stem methodschoose

stem methods ccsbegan