**California Math Scale ~ **

by Greg A. Grove, Ph.D.

Copyright © 1992

**PART I**

Directions: Some people experience anxiety
in math-related situations. Use the numbers below to indicate
how much anxiety you would probably experience throughout each
of the following events. Write your answers on the lines
provided.

1 =
Very High Anxiety

2 = High Anxiety

3 = MODERATE ANXIETY

4 = Low Anxiety

5 = Very Low Anxiety

_____ (1) Taking a college math placement test.

_____ (2) Learning to figure a new math
problem.

_____ (3) Refiguring incorrectly answered
problems.

_____ (4) Asking the teacher to repeat the
explanation of an equation.

_____ (5) Answering questions based on
statistical tables, charts, or graphs.

_____ (6) Solving story problems similar to
this one:

A train ran 2/5ths
of the distance between A and B

at an average speed of 24 miles an
hour. For the

remainder of the trip, its speed was
increased 1/3^{rd},

requiring 12 hours to complete the
trip. What was

the distance between A and B?

**PART II**

Sample: ____ 3 6 9 12 15 18 ____ ____ ____

Directions: Look at the sample problem
above. The row has six numbers arranged in some order. Figure
out the numbers that begin and end the series. Write your
answers on the lines provided.

Since the numbers in the Sample increase by
3s, the series begins with 0 and ends with 21, 24, 27.

You have **5 minutes** to fill in the
missing numbers below, just as you did the Sample. Use space on
your paper to figure answers. BEGIN!

____ 512 256 128 64 32 16 ____ ____ ____

____ 75 57 74 47 73 37 ____
____ ____

____ 9 3 25 5 49 7 ____
____ ____

____ 89 17 85 13 87 15 ____
____ ____

____ 842 2y 428 5x 284 8w
____ ____ ____

____ 31 34 33 36 34 37
____ ____ ____

This concludes the California Math Scale

The purpose of the California Math Scale
(CMS) is to provide a brief screen of math anxiety and numerical
reasoning in adults ages 16 and older.

Math anxiety is defined as a persistent and
irrational fear of numbers or computing problems; of learning
terms, concepts, and processes, of taking tests; of interacting
with the math teacher relative to math instruction, and so
forth, that results in physical discomfort such as tension,
fatigability, heart pounding, upset stomach, high resting pulse,
worry, difficulty in concentrating, and diarrhea. Numerical
reasoning pertains to figuring number sequences using addition,
subtraction, multiplication, and division.

Scoring Procedures: Part I is scored by
summing the numbers written to the left of each event. Items
not rated receive no points. If more than one response to an
item is indicated, the lower value is used. Record your total
here: _______ (Range 0-30 points.)

Part II is scored by referring to the
answer key below. Each correct answers receives 1 point. Wrong
answers, or problems not answered, receive no credit. Sum the
number of correctly answered items and record your total here:
________ (Range 0-24 points.)

**Answer Key**

Row 1: 1024
8, 4, 2

Row
2: 67
72, 27, 71

Row
3: 1
81, 9, 121

Row
4: 15
83, 11, 85

Row
5: -1z
842, 11v, 428

Row
6: 31
34, 37, 33

**COMPOSITE SCORE:** Now add both part
scores and record your answer here: _______ (Range 0-54
points.) Refer to the table below to determine your level of
performance.

**Levels** **%iles**
**Part I** **Part II** **
TOTALS** **Grades**

Excellent 98-99
26-30 21-24 43-54 A

Superior 91-97 24-25
18-20 40-42 A-

Well-Adjusted 75-90 22-23
15-17 36-39 B

NORMAL 26-74 18-21
10-14 28-35 C

Below Normal 10-25 16-17 7-9
24-27 D

Help Needed 3-9 15
4-6 21-23 D-

Help Urgent 1-2 0-14
0-3 0-20 E

**Psychometric Data:**

The above norms were based on 54 students
enrolled in a general education course at a community college in
northern California. The average age was 22. The average IQ as
measured by the Vocabulary subtest of the *California Test of
Mental Maturity *(1963 edition) was IQ 105. Further
statistics follow:

__N = 54__
**Mean ** **SD** __
SEM __ **Skew** **Kurtosis**

Part I 19.6 2.8
.38 .12 2.7

Part II 11.9 4.4
.59 .05 2.9

TOTAL 31.5
5.8 .78 .04 2.6

**Biserial Item Analysis**

__Part I vs. Total Tes__t
**Part II vs. Total Test**

Item 1
.16 Item
1 .36

Item 2
.48 Item
2 .42

Item 3
.31 Item
3 .62

Item 4
.35 Item
4 .44

Item 5
.35 Item
5 .43

Item 6
.55 Item
6 .45

TOTAL
.66
TOTAL .87

The average item correlation for Part I is
.37 and .45 for Part II. The Pearson correlation between Parts
I and II is .23 (*p* < .09), which suggests that each part
is testing a different domain (anxiety vs. computation). The
internal consistency of the Total Test on the sample norming
population was .79. Another administration of the test (N=26)
yielded .92.

**Part II **

**Grade Equivalents**

**Raw**
**G.E.** **Raw **
**G.E.** **Raw**
**G.E.**

1 2.6 7
6.5 19 14.8

2
3.2 8
7.3 20 15.6

3
3.8 9
8.1 21 16.2

4
4.6 10
8.7 22 17.0

5
5.2 11
9.3 23 17.8

6
6.0 12
10.4 24 18.4