1 Montana Mathematics Education Forum September 21, 2009 Dr. Eric Milou Rowan University Department of Mathematics [email protected] 856-256-4500 x3876 K-12.

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Montana Mathematics Education Forum September 21, 2009

Dr. Eric MilouRowan University

Department of [email protected]

856-256-4500 x3876

K-12 Standards Based Mathematics: Debate, Dialogue, and Direction

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OverviewMajor issues & debates in mathematics education

Reports/ResearchCommon core standards initiativeNational Math Panel reportNCTM focal points

DebateConcepts vs. Skills DebateWhy Don’t My Students Have Number Sense?The Role of Technology

Common Core Standards http://www.CoreStandards.org/Standards/index.htm The Council of Chief State School Officers and The National Governors

Association Center for Best Practices Fewer, clearer, and higher, to best drive effective policy and

practice; Aligned with college and work expectations, so that all students are

prepared for success upon graduating from high school; Inclusive of rigorous content and application of knowledge through

high-order skills, so that all students are prepared for the 21 st century; Internationally benchmarked, so that all students are prepared for

succeeding in our global economy and society; and Research and evidence-based.

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The Process Develop End-of-High-School Expectations

30 day public comment period starting today National Validation Committee

Develop K-12 Standards in Language Arts and Math Adoption

Each state adopting the common core either directly or by fully aligning its state standards may do so in accordance with current state timelines for standards adoption not to exceed three (3) years.

States that choose to align their standards to the common core standards agree to ensure that the common core represents at least 85 percent of the state’s standards in English language arts and mathematics.

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Race to the Top Fund

States will soon have a strong incentive to take the Common Core standards process seriously.

The Obama administration has proposed giving states that adopt common standards a competitive advantage in seeking federal aid, as part of the $4 billion Race to the Top Fund, a pool of economic-stimulus money.

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Mathematical Principles

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Equations Core Concepts An equation is a statement that two expressions are equal. The solutions of an equation are the values of the variables that

make the resulting numerical statement true. The steps in solving an equation are guided by understanding and

justified by logical reasoning. Equations not solvable in one number system might be solvable in

a larger system.

Core Skills Understand a problem and formulate an equation to solve it. Solve equations in one variable using manipulations guided by the

rules of arithmetic and the properties of equality. Rearrange formulas to isolate a quantity of interest. Solve systems of equations. Solve linear inequalities in one variable and graph the solution set

on a number line. Graph the solution set of a linear inequality in two variables on the

coordinate plane. 7

Common Core Concerns “Career/workplace readiness” = “College

readiness” ? The role of technology Missing is the math used in finance, medicine, and

other areas. Zalman Usiskin: “Completely missing is the whole

notion of literacy and citizenship and solving problems you see in life, rather than just mathematical problems. Everyday math applications are just not there.”

My greatest concern resides in the next step—the development of assessments based on these standards

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Core Skill? Which of (i)–(iv) would be the most productive first step

in factoring expressions (a)–(f)? (i) Finding a common factor (ii) Expressing as a difference of two squares (iii) Expressing as a perfect square (iv) None of the above.

(a) 4x2 + 5x (b) 36x2 – 25y2

(c) x4 – y4

(d) x2 + 6xy + 9y2

(e) x2 + 5x + 4 (f) 0.5x2 – 2.5x - 7

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National Math Panel (NMP)

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A NMP train…

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NCTM Focal Points

The Curriculum Focal Points are the most important mathematical topics for each grade level. They comprise related ideas, concepts, skills, and procedures that form the foundation for understanding and lasting learning.

The focal points are not about the basics; they are about important foundational topics. 

Students should learn and be able to recall basic facts and become computationally fluent, but such knowledge and skills should be acquired with understanding.

Teaching Gap, Stigler and Hiebert, 1999

Stated vs Developed

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We need a BALANCE

BalanceDirect InstructionConstructivism

BalanceConceptual UnderstandingAlgorithmic Proficiency

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Your Test!

4 x 9 x 25

How many ounces are in a gallon?

50 ÷ 1/2

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Conceptual Understanding

24 ÷ 4 = 624 ÷ 3 = 824 ÷ 2 =1224 ÷ 1 = 2424 ÷ 1/2 = ??

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Fractions - Conceptually

1

2

1

3

1

2

1

3 More than 1 or Less than 1

Explain your reasoning

3

6

2

6

5

6

2

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The F word

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Which is larger?

(2/3 + 3/4 + 4/5 + 5/6) OR 4 12.5 x 45 OR 4.5 x 125 (1/3 + 2/4 + 2/4 + 5/11) OR 2

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Computation

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Active Computation

Fifty (1, 2, 3, 4, 5, 6 and addition)Buzz (3)Product Game

http://illuminations.nctm.org/ActivityDetail.aspx?id=29

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Conceptual & Contextual

8 + 7 = ?How do we teach this?

xx xx x x

xx

xx

xx

xx

xxx

Best Friends

1 2 3 4 5 6 7 8 9

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8 + 7 = ?

8 + 7 = ?

2 5

10 + 5 = 15

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17 - 8 =

1 7

- 8

//0 17

2 7

8 --> --> 10 --> --> --> --> --> --> --> 17

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How Many Circles?

50

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1000 - 279 = ?

1000

279

279 +1 = 280 + 20 = 300 +700 = 1000

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High School Example

Not more traditional word problemsPlacing mathematical lessons into

settingsGiving students a reason to learn the

skill

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Drug Steady State

10 mg Zrytec daily50% of Zrytec is eliminated dailyWhat % is in the body

after 7 days10 daysn days?

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10mg Daily of Zrytec

Day Mg. of Zyrtec

1

234

56

10

1517.518.75

19.37519.6875

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Representations

Technology Teachers are able to engage and motivate

students with technology.A review of 11 studies that met the National Math

Panel’s rigorous criteria found limited or no impact of calculators on calculation skills, problem solving, or conceptual development.

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Polygons

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Engage Students to Use Technology

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Fact #1

A

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Fact #2

B

36

Fact #3

C

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Fact #4

D

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Fact #5

E

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Fact #6

F

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Fact #7

G

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Fact #8

H

42

Fact #9

I

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What is this?

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What is this?

F A C E

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What If?

A B C

D E F

G H I

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Try Again

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Try Again

D E C A D E

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What’s the Point?

Isolated Basic SkillsLess likely to retain information

Connected Facts, Use of Patterns, Facts in ContextMore likely to retain information

Standards Based Standards Based Mathematics Mathematics

All students have a chance to succeed and be based on a conception of mathematics that:balances the development of skills and concepts that empower

students to solve practical and real-world problems;makes judicious use of technology, like every other productive

segment of our society, to enhance learning and preclude the waste of precious time devoted to pencil and paper skills that are no longer used in the workplace;

builds coherently over time when students are confronted with interesting and complex problems and expected to struggle as part of the learning process.

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Thank You

Dr. Eric Milou

Rowan University

[email protected]

http://sites.google.com/site/montanamathforum/