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Phil Daro presentation to lausd epo 02.14

Jul 08, 2015

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Education

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CCSS mathematicsPhil DaroEvidence, not PoliticsHigh performing countries like JapanResearchLessons learnedMile wide inch deepcauses

cures2011 New Leaders | #Mile wide inch deepcause: too little time per conceptcure: more time per topic = less topics2011 New Leaders | #Two ways to get less topicsDelete topicsCoherence:A little deeper, mathematics is a lot more coherentCoherence across conceptsCoherence in the progression across gradesSilence speaksno explicit requirement in the Standards about simplifying fractions or putting fractions into lowest terms. instead a progression of concepts and skills building to fraction equivalence. putting a fraction into lowest terms is a special case of generating equivalent fractions. Why do students have to do math problems?to get answers because Homeland Security needs them, pronto

I had to, why shouldnt they?

so they will listen in class

to learn mathematics7Why give students problems to solve?To learn mathematics.Answers are part of the process, they are not the product.The product is the students mathematical knowledge and know-how.The correctness of answers is also part of the process. Yes, an important part.8Three Responses to a Math ProblemAnswer gettingMaking sense of the problem situationMaking sense of the mathematics you can learn from working on the problem9Answers are a black hole:hard to escape the pullAnswer getting short circuits mathematics, making mathematical senseVery habituated in US teachers versus Japanese teachersDevised methods for slowing down, postponing answer getting10Answer getting vs. learning mathematicsUSA:How can I teach my kids to get the answer to this problem? Use mathematics they already know. Easy, reliable, works with bottom half, good for classroom management.Japanese:How can I use this problem to teach the mathematics of this unit?

11Butterfly method1213More examples of answer gettingset up proportion and cross multiplyInvert and multiplyFOIL method

Mnemonics can be useful, but not a substitute for understanding the mathematicsProblemJason ran 40 meters in 4.5 secondsThree kinds of questions can be answered:Jason ran 40 meters in 4.5 secondsHow far in a given timeHow long to go a given distanceHow fast is he goingA single relationship between time and distance, three questionsUnderstanding how these three questions are related mathematically is central to the understanding of proportionality called for by CCSS in 6th and 7th grade, and to prepare for the start of algebra in 8thGiven 40 meters in 4.5 secondsPose a question that prompts students to formulate a function

Functions vs. solving How is work with functions different from solving equations?

Fastest point on earthMt.Chimborazo is 20,564 ft high. It sits very near the equator. The circumfrance at sea level at the equator is 25,000 miles. How much faster does the peak of Mt. Chimborazo travel than a point at sea level on the equator?SOLOPARTNERSMALL GROUPWHOLE CLASSTwo major design principles, based on evidence:

Focus Coherence

The Importance of Focus

TIMSS and other international comparisons suggest that the U.S. curriculum is a mile wide and an inch deep.

On average, the U.S. curriculum omits only 17 percent of the TIMSS grade 4 topics compared with an average omission rate of 40 percent for the 11 comparison countries. The United States covers all but 2 percent of the TIMSS topics through grade 8 compared with a 25 percent non coverage rate in the other countries. High-scoring Hong Kongs curriculum omits 48 percent of the TIMSS items through grade 4, and 18 percent through grade 8. Less topic coverage can be associated with higher scores on those topics covered because students have more time to master the content that is taught. Ginsburg et al., 2005

Grain size is a major issueMathematics is simplest at the right grain size. Strands are too big, vague e.g. numberLessons are too small: too many small pieces scattered over the floor, what if some are missing or broken?Units or chapters are about the right size (8-12 per year)Districts:STOP managing lessons, START managing unitsWhat mathematics do we want students to walk away with from this chapter?Content Focus of professional learning communities should be at the chapter levelWhen working with standards, focus on clusters. Standards are ingredients of clusters. Coherence exists at the cluster level across gradesEach lesson within a chapter or unit has the same objectives.the chapter objectivesWhat does good instruction look like?The 8 standards for Mathematical Practice describe student practices. Good instruction bears fruit in what you see students doing. Teachers have different ways of making this happen.Mathematical Practices StandardsMake sense of complex problems and persevere in solving them. Reason abstractly and quantitativelyConstruct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.Attend to precisionLook for and make use of structure8. Look for and express regularity in repeated reasoning.

College and Career Readiness Standards for Mathematics26Expertise and CharacterDevelopment of expertise from novice to apprentice to expert Schoolwide enterprise: school leadershipDepartment wide enterprise: department taking responsibilityThe Content of their mathematical CharacterDevelop characterWhat does good instruction look like?Students explaining so others can understandStudents listening to each other, working to understand the thinking of othersTeachers listening, working to understand thinking of studentsTeachers and students quoting and citing each other

motivationMathematical practices develop character: the pluck and persistence needed to learn difficult content. We need a classroom culture that focuses on learninga try, try again culture. We need a culture of patience while the children learn, not impatience for the right answer. Patience, not haste and hurry, is the character of mathematics and of learning.Students Job: Explain your thinkingWhy (and how) it makes sense to you (MP 1,2,4,8)What confuses you (MP 1,2,3,4,5,6,7,8)Why you think it is true ( MP 3, 6, 7)How it relates to the thinking of others (MP 1,2,3,6,8)

What questions do you askWhen you really want to understand someone elses way of thinking?Those are the questions that will work.The secret is to really want to understand their way of thinking.Model this interest in others thinking for studentsBeing listened to is critical for learningExplain the mathematics when students are readyToward the end of the lessonPrepare the 3-5 minute summary in advance,Spend the period getting the students ready,Get students talking about each others thinking,Quote student work during summary at lessons endStudents Explaining their reasoning develops academic language and their reasoning skills

Need to pull opinions and intuitions into the open: make reasoning explicitMake reasoning publicCore task: prepare explanations the other students can understandThe more sophisticated your thinking, the more challenging it is to explain so others understandTeach at the speed of learningNot fasterMore time per conceptMore time per problemMore time per student talking= less problems per lessonSchool Leaders and CCSSDevelop the Mathematics Department as an organizational unit that takes responsibility for solving problems and learning more mathematicsPeer + observation of instructionCollaboration centered on student workSummarize the mathematics at the end of the lessonWhat to look for Students are talking about each others thinkingStudents say second sentencesAudience for student explanations: the other students. Cold calls, not hands, so all prepare to explain their thinkingStudent writing reflects student talkLook for: Who participatesEL students say second sentencesAfrican American males are encouraged to argue Girls are encouraged to engage in productive struggleStudents listen to each otherCold calls, not hands, so no one shies away from mathematicsShift1.From explaining to the teacher to convince her you are paying attention To explaining so the others understand

2.From just answer gettingTo the mathematics students need as a foundation for learning more mathematics

Step out of the peculiar world that never worked This whole thing is a shift from a peculiar world that failed large numbers of students. We got used to something peculiar.

To a world that is more normal, more like life outside the mathematics classroom, more like good teaching in other subjects.Personalization and Differences among studentsThe tension: personal (unique) vs. standard (same)Why Standards? Social JusticeMain motive for standardsGet good curriculum to all studentsStart each unit with the variety of thinking and knowledge students bring to itClose each unit with on-grade learning in the cluster of standardsSome students will need extra time and attention beyond classtimeStandards are a peculiar genre We write as though students have learned approximately 100% of what is in preceding standards. This is never even approximately true anywhere in the world. Variety among students in what they bring to each days lesson is the condition of teaching, not a breakdown in the system. We need to teach accordingly.Tools for teachersinstructional and assessmentshould help them manage the variety2011 New Leaders | #Unit architecture

Four levels of learningUnderstand well enough to explain to othersGood enough to learn the next related conceptsCan get the answers NoiseFour levels of learningThe truth is triage, but all can prosperUnderstand well enough to explain to othersAs many as possible, at least 1/3Good enough to learn the next related conceptsMost of the rest Can get the answers At least this muc