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AMTNJOctober 2008

Dr. Eric MilouRowan University

Department of Mathematicsmilou@rowan.edu

856-256-4500 x3876

What are Basic Skills in Mathematics in 2008

(and Why Don't My Students Have Them)?

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Overview

National Math Panel Recommendations

Number Sense & Computation Proficiency

NJ State Assessments

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National Math Panel (NMP)

A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided.

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NMP

Instructional practice should be informed by high-quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers. High-quality research does not support the contention that instruction should be either entirely “student centered” or “teacher directed.”

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NMP

A major goal for K–8 mathematics education should be proficiency with

fractions (including decimals, percents, and negative fractions).

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A NMP train…

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Response by Peppermint Patty

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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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What’s “Typical?” in US

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Third International Math & Science Study (TIMSS)

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8

16

52

18

46

20

48

19

37

59

00

10

20

30

40

50

60

70

80

Australia

Czech RepublicHong Kong

Japan

NetherlandsUnited States

Procedures vs. Concepts

STATED vs. DEVELOPED

Teaching Gap, Stigler and Hiebert, 1999

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We need a BALANCE

BalanceDirect InstructionConstructivism

BalanceConceptual UnderstandingAlgorithmic Proficiency

These are NOT Dichotomous

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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

5

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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Conceptual Fraction task

Kim’s teacher asked her class to design a flag using four colors, dividing a square into parts, and to color the parts as follows:1/2 is colored red1/4 is colored blue1/8 is colored greenAny other part is to be left white

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Flags

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Decimals

1000 ÷ 1.49= 671.1409396

= Torture!Big Macs Sell for $1.49, how many Big Macs can

I buy for $10.00?1 is $1.502 are $34 are $66 are $9

Number Sense

is a vital skill

1.49 1000

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Computation is Important

Engaging & ActiveLess passive worksheetsMore thinking & reasoning

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Computation

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Active Computation

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

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

Web Applets

NCTM Illuminations http://illuminations.nctm.org

National Library of Virtual Manipulatives (NLVM) http://www.nlvm.usu.edu/

Shodor Interactivate http://www.shodor.org/interactivate/activities/

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Conceptual & Contextual

8 + 7 = ?How do we teach this?

xx xx x x

xx

xx

xx

xx

xxx

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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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1000 - 279 = ?

1000 - 1 = 999

999-278

721

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Multiplication

13 x 17 = ?

1 3

x 1 7

1

2

9031

2 2 1

-------

-------

10 7 10

3

1 0 0

3 0

7 0

2 1

221

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Conceptual approach leads to ?

x 7 x

3

x2

3x

7x

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Algebra: (x + 3) (x + 7) =

NJ ASK 5, 6, 7, & 8

  Proficient Advanced Proficient

2008Cut Score Cut Score

  Raw Score 2008

% Correct

2007

% Correct

2008

Raw Score

% Correct

Math 5 25 46 50 40 80Math 6 25 44 50 41 82Math 7 27 33 52 42 81Math 8 29 50 56 43 83

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The Effect

  Math5 Math6 Math7 Math82008 77 74 66 68

2007 84 79 66 68

2008 LS 82 81 89 75

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Why?

“In 2008 we propose raising the standard for student achievement resulting in fewer students being deemed proficient. The impact of this decision will lead to identifying students for intervention and assistance earlier in their school careers, which has long been a goal of the State Board. Our hope is that this will better prepare all students for success in high school and beyond.”

Lucille E. Davy, NJDOE Commissioner

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NJ STEPS proposal

End of course Alg I assessment will replace HSPA math beginning with graduating class of 2012 (08-09)

End of course Geometry assessment will be required beginning with graduating class of 2014 (10-11)

End of course Alg II assessment will be required beginning with graduating class of 2016 (12-13)

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Proposed Amendments to N.J.A.C. 6A:8, Standards and Assessment for Student

Achievement (Sept 17, 2008) to State Board

The biology competency assessment has replaced the science portion of the HSPA.

For language arts literacy and mathematics, the intent is to implement the assessments first and then to review the results and consider the impact on students, schools, and districts of possibly phasing out the traditional HSPA.

These amendments do not include a proposed schedule for eliminating the HSPA in mathematics or language arts literacy.

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Algebra II field test results

Total possible points (76)46 points from MC items30 points from Constructed response items

88,344 students participated nationwideAverage number of points correct was 20 out of

76 or 26.9%Average number of points correct on constructed

response items was 3 out of 30 (10.2%)

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NJ Algebra II results

9,813 students were testedApproximately 43,000 students are enrolled

in Alg II in NJAverage score was 21/76 or 27.5%Average score on constructed response

items was 3/30 or 10.7%

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Fact #1

A

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Fact #2

B

40

Fact #3

C

41

Fact #4

D

42

Fact #5

E

43

Fact #6

F

44

Fact #7

G

45

Fact #8

H

46

Fact #9

I

47

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

50

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

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Characteristics of a good mathematics program

CONCEPTUALand COMPUTATION

CONTEXTUALCONSTRUCTIVISM

and direct instruction

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Thank You

Dr. Eric Milou

Rowan University

milou@rowan.edu

http://www.rowan.edu/colleges/las/departments/math/facultystaff/milou/eric.html