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Preparing for the NJ Math Assessments in the Middle Grades

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Dr. Eric Milou

Rowan University

Department of Mathematics

856-256-4500 x3876

- Conceptual vs. Procedural Debate
- National Math Panel

- Number Sense & Computation Proficiency
- NJ mathematics assessments

- In traditional math, children learn multiplication tables and specific techniques for calculating.
- In constructivist math, the process by which students explore the question can be more important than getting the right answer, and the early use of calculators is welcomed.

- September 12 Wall Street Journal article did not represent the substance or intent of the focal points.
- The focal points are not about the basics; they are about important foundational topics. NCTM has always supported learning the basics. Students should learn and be able to recall basic facts and become computationally fluent, but such knowledge and skills should be acquired with understanding.

- We cannot afford to waste time on polarization. What is important is that we pragmatically address critical target areas to improve mathematics education. We cannot be distracted from our primary mission—to match tactical initiatives in other, newly technological societies that are snatching our competitive advantage in innovation—while we bicker over modest differences in approach. (Jere Confrey)

- Society’s hate for mathematics that is prevalent and acceptable
- 4 out of 10 adults hate mathematics* (twice as many people said they hated math as said that about any other subject)

- International test scores
- Industry concerns (no problem solving skills)
- National Council of Teachers of Mathematics (NCTM) Standards

*2005 AP-AOL News poll

4 x 9 x 25

900 - 201

50 ÷ 1/2

Proceduresvs. Concepts

- Demonstrates a procedure
- Assigns similar problems to students as exercises
- Homework assignment

- Presents a problem without first demonstrating how to solve it
- Individual or group problem solving
- Compare and discuss multiple solution methods
- Summary, exercises and homework assignment

- Traditional text with conceptual supplement
- Conceptual text (EM, CMP, Core-Plus) with computational supplement

- 24 ÷ 4 = 6
- 24 ÷ 3 = 8
- 24 ÷ 2 =12
- 24 ÷ 1 = 24
- 24 ÷ 1/2 = ??

The F word

More than 1 or Less than 1

Explain your reasoning

- 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

- 2.43 x 5.1 = 12393
- 4.85 x 4.954 = 240269
- 21.25 x 1.08 = 2295
- 1.25 x 64 = 80
- 4.688 x 1.355 = 635224
- 46.88 x 1.355 = 635224
- 4.688 x 135.5 = 635224
- 46.88 x 13.55 = 635224

- 1000 ÷ 1.49
- Torture

- Big Macs Sell for $1.49, how many Big Macs can I buy for $10.00?
- 1 is $1.50
- 2 are $3
- 4 are $6
- 6 are $9

Mental Mathematics

is a vital skill

- Engaging & Active
- Less passive worksheets
- Creative!
- More thinking & reasoning

Target #: 6

3

3

17

1

8

- Fifty (1, 2, 3, 4, 5, 6 and addition)
- Buzz (3)
- Product Game
- Wipe Out
- Software: Math Arena

0

9

1

8

2

7

3

6

4

5

- 8+ 7 = ?
- How do we teach this?

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

0

17

/

/

1 7

- 8

2 7

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

279

+1 = 280

+ 20 = 300

+700 = 1000

- 13 x 17 = ?

10 7

2

10

3

1 3

x 1 7

1 0 0

7 0

-------

3 0

2 1

9

1

1

3

0

-------

2 2 1

221

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

x 7

x

3

x2

7x

3x

21

- Not more traditional word problems
- Placing mathematical lessons into settings
- Giving students a reason to learn the skill
- Motivating students

- You must select one spinner. Both spinners above will be spun once.
- The spinner with the higher number showing wins $1,000,000 for that person.
- Which spinner will you select?

4

5

6

5

8

5

4

9

6

9

8

9

- 8 adults and 2 children need to cross a river and they have one small boat only available. The boat can hold ONLY:
- One adult
- One or two children

- How many one-way trips does it take for all 8 adults and 2 children to cross?

- NJASK3
- 6 non-calculator items (1/2 pt each)
- 21 MC - calculator allowed - 1 pt each
- 3 Open-ended - 3 pts each
- 14 out of 33 points is a passing score

- NJASK4
- 8 non-calculator items (1/2 pt each)
- 24 MC - calculator allowed - 1 pt each
- 5 Open-ended - 3 pts each
- 17.5 out of 43 points is a passing score

- NJASK5 JPM was 18/39 (46%)
- NJASK 6 JPM was 17/39 (44%)
- NJASK 7 JPM was 13/39 (33%)
- 10 pts per cluster (one cluster with 9 pts)

- GEPA
- All items allow a calculator
- 30 Multiple choice items - 1 pt each
- 6 Open-ended - 3 pts each
- 25 out of 48 points is a passing score

- HSPA
- All items allow a calculator
- 30 Multiple choice items - 1 pt each
- 6 Open-ended - 3 pts each
- 20.5 out of 48 points is a passing score

- NJ Assessments are rigorous and conceptual
- NJ Math Standards are well aligned with NJ assessments
- Most districts have a well aligned curriculum
- Then, what’s wrong?

- Districts should not encourage all students to take Algebra I in grade 8; students should be taking Algebra I in grade 8 only if they are highly motivated, have a strong foundation in middle school mathematics, receive high grades in previous courses, intend to study calculus in high school, and only if the Algebra I courses are taught by teachers with mathematics certification.

A

B

C

D

E

F

G

H

I

F A C E

C

A

B

F

D

E

I

G

H

D E C A D E

Isolated Facts

Less likely to retain information

Connected Facts, Patterns, Fact in Context

More likely to retain information

- CONCEPTUAL
- CONTEXTUAL
- CONSTUCTIVISM
- COMPUTATION
- TEST-PREP