The 10 Instructional Shifts That Raise Student Achievment

The 10 Instructional Shifts That Raise Student Achievement(From the book Accessible Mathematics by Steven Leinwand, Principle Research Analyst at the American Institutes for Research and former president of the National Council of Supervisors of Mathematics.)

NWSC Cohort WorkshopsFebruary 1-3, 2011Factors Impacting Student AchievementCoherent Curriculum GuidesAligned AssessmentsAccess to Viable Print MaterialsAccess to TechnologyAdministrative Leadership and SupportSupportive Parents/GuardiansQuality of Instruction#1 Incorporate ongoing cumulative review into every days lessonTodays Mini-MathWhat is 1/10 of 450?Draw a Quadrilateral and all of its diagonals.The cost of a substance is directly proportional to its weight. If 30 grams of the substance costs $45, what is the cost of 6 grams of the substance?A population P increases by 5% each year for 2 years. Write an expression for the population in terms of P after 2 years.What number is 1000 less than 18,294# 1 Incorporate ongoing cumulative review into every days lessonYour Task:Make a record of concepts covered during first semester that need to be consistently reviewed.List by Strand# 1 Incorporate ongoing cumulative review into every days lessonWhats seen in an Effective Classroom:Ongoing, cumulative review of key skills and conceptsStudents given the opportunity to clarify their understandingsClasses that waste no time and begin with substantive mathematics at the very start of every class.Classes that end with summarizing questions and/or exit slipsThe use of a brief review and discussion of mini-math questions

#2 Adapt what we know works in our reading programs . . .Jane went to the storeCan you read the sentence aloud?Can you tell me where Jane went?Can you tell me who went to the store?Can you tell me why Jane might have gone to the store?Do you think it made sense for Jane to go to the store?

Differentiation Through Questioning#2 Adapt what we know works in our reading programs . . .Your Task:Write three open-ended questions that you will use within the next two weeks of instruction.#2 Adapt what we know works in our reading programs . . .Whats seen in an Effective Classroom:Consistent parallels between the types of questions that require inferential and evaluative comprehensions in reading instruction and the probing for ways in which the answers were found, alternative approaches, and reasonableness in mathematics instruction.Open-ended Questions and Parallel Tasks for purposes of differentiating the mathematicsAnswers greeted with a request for justificationReasonable homework assignments with the focus on explanation and understanding

#3 Use multiple representations of mathematical entities.Draw at least 3 representations of 3 quartersDraw at least 3 representations/models for adding integersSystems of equationsX + Z = YY + Z = 9Y X = 2X + 1 = 6#3 Use multiple representations of mathematical entities.Systems of equationsNumber Shapes 2 + = 9

- = 2

+ =

+ 1 = 6#3 Use multiple representations of mathematical entities.Systems of equations using 3-Bean SaladsSalad #1 contains2 Lima beansTwice as many Red beans as Lima beans 10 beans in all

Salad #2 contains3 times as many Red beans as Black-eyed PeasOne more Lima bean than Red beans8 beans in all

#3 Use multiple representations of mathematical entities.Systems of equations using BarsJulie packs her clothes into a backpack and it weighs 29 kg.Xavier packs his clothes into an identical backpack and it weights 11 kg.Julies clothes are three times as heavy as Xaviers.What is the weight of the Xaviers clothes?What is the weight of the backpack?

Xavier: Julie:#3 Use multiple representations of mathematical entities.Your Task:Look at the skills and concepts youll be teaching over the next 3 weeks.Determine where you can provide multiple representations for at least 3 of these skills/concepts.#3 Use multiple representations of mathematical entities.Whats seen in an Effective Classroom:Frequent use of pictorial representations to help students visualize the mathematicsFrequent use of the number line and bar models to represent numbers and word problemsFrequent opportunities for students to draw or show and then describe what is drawn or show

#4 Create language-rich routinesTell the person next to you three things you see and/or know about the numbers 73 and 63.Vocabulary strategies Wordles (handout in workshop packet)Math Reflections

#4 Create language-rich routinesYour Task: List 30 key vocabulary words that need to be reviewed/used this second semesterCreate at least one writing assignment where students are asked to explain their understanding of a concept.

#4 Create language-rich routinesWhats seen in an Effective Classroom:An ongoing emphasis on the use and meaning of mathematical terms, including their definitions and their connections to real-world entities and/or picturesStudent and teacher explanations that make frequent and precise use of mathematics terms, vocabulary, and notationAn extensive use of words walls that capture the key terms and vocabulary with pictures when appropriate

#5 Take every available opportunity to support the development of number senseNumber Sense is a comfort with numbers that includes estimation, mental math, numerical equivalents, a use of referents like and 50%, a sense of order and magnitude, and a well-developed understanding of place value.Number Sense is one of the overarching goals of mathematics learning.How can we work to develop number sense?#5 Take every available opportunity to support the development of number senseBy asking questions like Which is most or greatest? How do you know?Which is least or smallest? How do you know?What else can you tell me about those numbers?How else can we express that number? Is there still another way?About how much would that be? How did you get that?

And by having students estimate the answer first!#5 Take every available opportunity to support the development of number senseYour Task:If you began class one day with the statement provided below, what are ten number sense questions you could use to help develop number sense?

The statement: As of this morning, my age is 28,935,285.

#5 Take every available opportunity to support the development of number senseWhats seen in an Effective Classroom:An unrelenting focus on estimation and justifying estimates to computations and to the solution of problemsAn unrelenting focus on a mature sense of place valueFrequent discussion and modeling about how to use number sense to outsmart the problemFrequent opportunities to put the calculator aside and estimate or compute mentally when appropriate

#6 Build from graphs, charts, and tablesTicket Sales for Country Music ConcertsConcertTickets SoldKenny ChesneyBrad PaisleyMartina McBrideLady Antebellum

385,204259,593285,447327,982

About how many tickets sold?Which concert was probably least popular?About how many more tickets were sold for Chesney than for Paisley?Which concert sold closest to 300,000 tickets?About what percent of the total tickets did the McBride concert sell?#6 Build from graphs, charts, and tablesYour Task:Develop 5 questions around the following data from the Federal Highway Administration:

Increasingly Crowded Roads in the United States1996Growth since 1970Miles drivenNumber of vehiclesNumber of driversPopulationMiles of roads2.5 billion206.4 million179.5 million265.3 million3.9 million123%90%61%30%7%

#6 Build from graphs, charts, and tablesUse the 4 Representations

Identify where in the next month you will have the opportunities to work the data

#6 Build from graphs, charts, and tablesWhats seen in an Effective ClassroomAn abundance of problems drawn from the data presented in tables, charts, and graphsOpportunities for students to make conjectures and draw conclusions from data presented in tables, charts, and graphsFrequent conversion, with and without technology, of data in tables and charts into various types of graphs, with discussions of their advantages, disadvantages, and appropriateness#7 Tie the math to such questions as How big? How much? and How far? to increase use of measurementRocky Rococo Pizza, with its rectangular pizzas, once had billboards displaying the following: 20% More! We Dont Cut Corners!

26#7 Tie the math to such questions as How big? How much? and How far? to increase use of measurementUsing your scope and sequence for the next couple of months, determine where there is opportunity to work with measurement before the MCAs#7 Tie the math to such questions as How big? How much? and How far? to increase use of measurementWhats seen in an Effective ClassroomLots of questions are included that ask how big? How far? How much? How many?Measurement is an ongoing part of daily instructionStudents are frequently asked to find and estimate measures, to use measuring, and to describe the relative size of measures that arise during instruction.Frequent reminders that measurement is referential#8 Minimize what is no longer important, and teach what is important. . .If we can answer WHY? (or cant answer WHY?) we teach a concept then we can determine WHAT to teach and WHAT not to teach.

Why do we teach multi-digit multiplication such as 2953 multiplied by 12.5?Why do we teach division of fractions?

#8 Minimize what is no longer important, and teach what is important. . .Your Task:Read #15 Less Can Be More in Faster Isnt SmarterNote 2 to 3 key points to discuss at your table

#8 Minimize what is no longer important, and teach what is important. . .Whats seen in an Effective ClassroomA curriculum of skills, concepts, and applications that are reasonable to expect all students to masterImplementation of a district & state curriculum that includes essential skills and understandings for a world of calculators & computersA deliberate questioning of the appropriateness of the mathematical content, regardless of what may or may not be on the high-stakes state test, in every grade and course

#9 Embed the mathematics in realistic problems and real-world contextsDan Meyers Math Class Needs a Makeover

"I teach high school math. I sell a product to a market that doesn't want it but is forced by law to buy it.Dan Meyer#9 Embed the mathematics in realistic problems and real-world contextsYour Task:Read #1 Math for a Flattening World in the Faster Isnt Smarter bookDiscuss at your table the 4th and 5th Questions in the Reflection and Discussion for Teachers section on p. 6.#9 Embed the mathematics in realistic problems and real-world contextsWhats seen in an Effective ClassroomFrequent embedding of the mathematical skills and concepts in real-world situations and contextsFrequent use of So. What questions arise from these data or this situation?Problems that emerge from teachers asking, When and where do normal human beings encounter the mathematics I need to teach?

#10 Make Why? How do you know? Can you explain? mantrasQuestioning Templates

#10 Make Why? How do you know? Can you explain? mantrasYour Task:Choose one of the Questioning Templates and make a commitment to use it throughout the rest of this school year. Make a poster or a laminated bookmark of it but use it and make it part of what you do in every class every day.#10 Make Why? How do you know? Can you explain? mantrasWhats seen in an Effective ClassroomEvery student answer is responded to with a request for justificationBoth teachers and students consistently and frequently use Why? Can you explain that? How do you know? or equivalent questionsDismissive responses such as Not, Wrong, Not quite, and their equivalents are absent from the classroom

The 10 Instructional Shifts:Incorporate ongoing cumulative review into every days lessonAdapt what we know works in our reading programs and apply it to mathematics instruction.Use multiple representations of mathematical entities.Create language-rich routines.Take every available opportunity to support the development of number sense.Build from graphs, charts, and tables.Tie the math to such questions as: How big? How much? How far? to increase the natural use of measurement throughout the curriculum.Minimize what is no longer important.Embed the mathematics in realistic problems and real-world contexts.Make Why? How do you know? Can you explain? classroom mantrasPunting Is Simply No Longer AcceptableImplementing these shifts takes time and it takes planning.We are expected to find ways to make math work for far more kids.We live in a world of calculators and computes and in a world that expects, even requires, deeper understanding and far greater problem-solving skillsPlanning TemplatesWrap UpFaster Isnt Smarter #40 Seven Steps to Becoming a Better TeacherEvaluations