Moving Ahead with the Common Core Learning Standards for Mathematics

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Moving Ahead with the Common Core Learning Standards for Mathematics. CFN 602 Professional Development | February 17, 2012 RONALD SCHWARZ Math Specialist, Americas Choice,| Pearson School Achievement Services. Block Stack. - PowerPoint PPT Presentation

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CFN 602Professional Development | February 17, 2012

RONALD SCHWARZMath Specialist, Americas Choice,| Pearson School Achievement Services

Moving Ahead with the Common Core Learning Standards for Mathematics

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Copyright 2010 Pearson Education, Inc.or its affiliate(s). All rights reserved.

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Post a parking lot; have a chart ready with norms

(have k w l prepped and ready for later)

Review schedule for today, materials,

Lunch, breaks, restrooms.

set context and expectations for today as a train the trainer workshop

-ask participants to take notes, use post-its to record questions/observations,etc for debrief. If general questions, not particularly linked to a module come up, put them on a post-it and add to the parking lot.

Block Stack

25 layers of blocks are stacked; the top four layers are shown. Each layer has two fewer blocks than the layer below it. How many blocks are in all 25 layers?

Math Olympiad for Elementary and Middle Schools

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AGENDA

Standards for Math Content: Conceptual Shifts

Whats Different

Math Performance Tasks

Formative assessment

Resources

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What are Standards?

Standards define what students should understand and be able to do.

The US has been a jumble of 50 different state standards. Race to the bottom or the top?

Any countrys standards are subject to periodic revision.

But math is more than a list of topics.

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NAEP & NY STATE TEST RESULTS

NYC MATH PERFORMANCE

PERCENT AT OR ABOVE PROFICIENT

NAEP

NY State Test

NAEP

NY State Test

2003 2009 2003 2009 2003 2009 2003 2009

4th Grade

8th Grade

DESPITE GAINS, ONLY 39% OF NYC 4TH GRADERS AND 26% OF

8TH GRADERS ARE PROFICIENT ON NATIONAL MATH TESTS

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What Does Higher Standards Mean?

More Topics? But the U.S. curriculum is already cluttered with too many topics.

Earlier grades? But this does not follow from the evidence. In Singapore, division of fractions: grade 6 whereas in the U.S.: grade 5 (or 4)

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Lessons Learned

TIMSS: math performance is being compromised by a lack of focus and coherence in the mile wide. Inch deep curriculum

Hong Kong students outscore US students in the grade 4 TIMSS, even though Hong Kong only teaches about half the tested topics. US covers over 80% of the tested topics.

High-performing countries spend more time on mathematically central concepts: greater depth and coherence. Singapore: Teach less, learn more.

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Common Core State Standards Evidence Base

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For example: Standards from individual high-performing countries and provinces were used to inform content, structure, and language.

Mathematics

Belgium (Flemish)

Canada (Alberta)

China

Chinese Taipei

England

Finland

Hong Kong

India

Ireland

Japan

Korea

Singapore

English language arts

Australia

New South Wales

Victoria

Canada

Alberta

British Columbia

Ontario

England

Finland

Hong Kong

Ireland

Singapore

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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 mathematics

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Answer Getting vs. Learning Mathematics

United States

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.

Japan

How can I use this problem to teach mathematics they dont already know?

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Three Responses to a Math Problem

Answer getting

Making sense of the problem situation

Making sense of the mathematics you can learn from working on the problem

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Answer Getting

Getting the answer one way or another and then stopping

Learning a specific method for solving a specific kind of problem (100 kinds a year)

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Butterfly method

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Use butterflies on this TIMSS item

1/2 + 1/3 +1/4 =

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Foil FOIL

(a + b)(c +d) = ac + bc + ad + bd

Use the distributive property

This IS the distributive property when a is a sum: a(x + y) = ax + ay

Sum of products = product of sums

It works for trinomials and polynomials in general

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On the high school level, FOIL serves the same purpose as the butterfly method: a way of getting the answer by purely mechanical means, without requiring any understanding of what one is doing.

Facilitator Ask someone to explain what the FOIL method is, for the benefit of anyone who may not know. (It stands for First, Outer, Inner Last, an acronym for the four multiplications that must be done when a binomial is multiplied by another binomial).

Another similarity to the butterfly method: students who know only the FOIL method are lost when asked to multiply a binomial by a trinomial, for example.

Answers are a black hole:hard to escape the pull

Answer getting short circuits mathematics, especially making mathematical sense

High-achieving countries devise methods for slowing down, postponing answer getting

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A dragonfly can fly 50 meters in 2 seconds.

What question can we ask?

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Rate Time = Distance

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Posing the problem

Whole class: pose problem, make sure students understand the language, no hints at solution

Focus students on the problem situation, not the question/answer game. Hide question and ask them to formulate questions that make the situation into a word problem

Ask 3-6 questions about the same problem situation; ramp questions up toward key mathematics that transfers to other problems

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Bob, Jim and Cathy each have some money. The sum of Bob's and Jim's money is $18.00. The sum of Jim's and Cathy's money is $21.00. The sum of Bob's and Cathy's money is $23.00.

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What problem to use?

Problems that draw thinking toward the mathematics you want to teach. NOT too routine, right after learning how to solve

Ask about a chapter: what is the most important mathematics students should take with them? Find problems that draw attention to this math

Near end of chapter, external problems needed, e.g. Shell Centre

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What do we mean by conceptual coherence?

Apply one important concept in 100 situations rather than memorizing 100 procedures that do not transfer to other situations:

Typical practice is to opt for short-term efficiencies, rather than teach for general application throughout mathematics.

Result: typical students do OK on unit tests, but dont remember what they learned later when they need to learn more mathematics

Use basic rules of arithmetic (same as algebra) instead of clutter of specific named methods

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