Preparing for the NJ Math Assessments in the Middle Grades

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Preparing for the NJ Math Assessments in the Middle Grades. Dr. Eric Milou Rowan University Department of Mathematics milou@rowan.edu 856-256-4500 x3876. Overview. Conceptual vs. Procedural Debate National Math Panel Number Sense &amp; Computation Proficiency NJ mathematics assessments.

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Preparing for the NJ Math Assessmentsin the Middle Grades

Dr. Eric Milou

Rowan University

Department of Mathematics

milou@rowan.edu

856-256-4500 x3876

Overview
• Conceptual vs. Procedural Debate
• National Math Panel
• Number Sense & Computation Proficiency
• NJ mathematics assessments
RhetoricNY Times (5/15/06)
• 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.
NCTM Focal Points (9/12/06)
• 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.
Education Week 11/1/06
• 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)
Motivating Factors for Change
• 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

Compute the following:

4 x 9 x 25

900 - 201

50 ÷ 1/2

Lesson Study
• 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
We need a BALANCE
• Traditional text with conceptual supplement
• Conceptual text (EM, CMP, Core-Plus) with computational supplement
Conceptual Understanding
• 24 ÷ 4 = 6
• 24 ÷ 3 = 8
• 24 ÷ 2 =12
• 24 ÷ 1 = 24
• 24 ÷ 1/2 = ??
Fractions - Conceptually

The F word

More than 1 or Less than 1

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
Where’s the Point?
• 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
Computational Balance
• 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

Computation is Important
• Engaging & Active
• Less passive worksheets
• Creative!
• More thinking & reasoning
Active Computation
• 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

Patterns
Conceptual & Contextual
• 8+ 7 = ?
• How do we teach this?

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

17 - 8 =

0

17

/

/

1 7

- 8

2 7

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

1000 - 279 = ?

279

+1 = 280

+ 20 = 300

+700 = 1000

Multiplication
• 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

Contextual Problem Solving
• Not more traditional word problems
• Placing mathematical lessons into settings
• Giving students a reason to learn the skill
• Motivating students
Example
• 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?
Spinner Example

4

5

6

5

8

5

4

9

6

9

8

9

Crossing the River
• 8 adults and 2 children need to cross a river and they have one small boat only available. The boat can hold ONLY:
• One or two children
• How many one-way trips does it take for all 8 adults and 2 children to cross?
2006 NJ Assessment Data
• 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
2006 NJ Assessment Data
• 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)
2006 NJ Assessment Data
• 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
2006 NJ Assessment Data
• 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
Implications & Inferences
• 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?
Algebra Placement
• 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.
What If?

C

A

B

F

D

E

I

G

H

Try Again

D E C A D E

Isolated Facts

Less likely to retain information

Connected Facts, Patterns, Fact in Context

More likely to retain information

What’s the Point?
Characteristics of a good mathematics program
• CONCEPTUAL
• CONTEXTUAL
• CONSTUCTIVISM
• COMPUTATION
• TEST-PREP
Thank You

Dr. Eric Milou

Rowan University

milou@rowan.edu