# Presentation: 072918

## The NAEP Mathematics Exam

- The Nations Report Card

## Problems with the NAEP

- The NAEP is unfocused
- There are far too many mathematical errors
- The level of the exam is far below the levels in high achieving countries

## Number of Grade 4 Learning Expectations per State by Content Strand

|  | 
Number
&
Operation | Geometry   | Measurement | Algebra | Data Analysis, Probability & Statistics | Total Number of 
Learning Expectations |
| --- | --- | --- | --- | --- | --- | --- |
| California | 16 | 11 | 4 | 7 | 5 | 43 |
| Texas | 15 | 7 | 3 | 4 | 3 | 32 |
| New York | 27 | 8 | 10 | 5 | 6 | 56 |
| Florida | 31 | 11 | 17 | 10 | 20 | 89 |
| Ohio | 15 | 8 | 6 | 6 | 13 | 48 |
| Michigan | 37 | 5 | 11 | 0 | 3 | 56 |
| New Jersey | 21 | 10 | 8 | 6 | 11 | 56 |
| North Carolina | 14 | 3 | 2 | 3 | 4 | 26 |
| Georgia | 23 | 10 | 5 | 3 | 4 | 45 |
| Virginia | 17 | 8 | 11 | 2 | 3 | 41 |

- Reys, et al., 2006

## And for NAEP

| Grade | Num | Meas | Geom | Data | Alg | Total |
| --- | --- | --- | --- | --- | --- | --- |
| 4 | 26 | 10 | 15 | 9 | 10 | 70 |
| 8 | 34 | 20 | 21 | 22 | 18 | 115 |
| 12 | 27 | 14 | 20 | 26 | 23 | 110 |

## The Quality of the NAEP Problems

- Last year, The Brookings Institute asked me to review the algebra questions on the NAEP
- Of the 41 eighth grade NAEP algebra problems provided, 8 were incorrect and one was meaningless
- Moreover about 10 of the correct problems were just questions about vocabulary, not mathematics

- Of the 22 grade 4 questions provided, four were incorrect, four others were essentially vocabulary, only one could be judged mildly challenging at fourth grade level

## From the NAEP

## From NAEP

## What’s wrong with patterns?

## The Balance of Subjects is Way Off

- Very little attention is paid to basic operations, and essentially none to skills with fractions.

## The Balance of Subjects is Way Off

- Two typical fraction standards in grade 8 (there are none in grade 4):
- Provide a mathematical argument to explain operations with two or more fractions,
- interpret rational number operations and the relationships between them
- There is exactly one grade 8 standard that asks for operations with integers or fractions:
- Perform computations with rational numbers.

## When the Report Card is Flawed What do the Grades Mean?

## All this tracks back to a refusal to involve real math experts in test development

- A few mathematicians including two members of this distinguished panel have been members of NAGB but were not even allowed access to the exams

## High Achieving Countries Focus on Six Topics in The First Four or Five Grades

- Place Value and Basic Number Skills
- Fractions and Decimals
- Ratios, Rates Percents, Proportions
- Functions and Equations
- Beginning Algebra
- Measurement and Geometry

## As do the NCTM Focus Topics

## Focus Topics – Numbers

## Focus Topics Fractions

## Focus Topics Fractions, Ratios

## Focus Topics, Algebra, Data

## The Process of Constructing the NAEP has to be Improved

- At a minimum experts in both math and math education have to be involved in test construction and validation but even more is needed as we’ve indicated

## And the Sooner there are new NAEP Standards the Better