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) Re-figuring 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 1/3rd,
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 3’s, 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 math 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 answer 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%ilesPart IPart IITOTALSGrades
Excellent98-9926-3021-2443-54A
Superior91-9724-2518-2040-42A-
Well-Adjusted75-9022-2315-1736-39B
NORMAL26-7418-2110-1428-35C
Below Normal10-2516-17 7-924-27D
Help Needed 3-9 15 4-621-23D-
Help Urgent 1-2 0-14 0-3 0-20E
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 = 54MeanSDSEMSkewKurtosis
Part I19.62.8.38.122.7
Part II11.94.4.59.052.9
TOTAL31.55.8.78.042.6
Biserial Item Analysis
Part I vs. Total TestPart II vs. Total Test
Item 1.16Item 1.36
Item 2.48Item 2.42
Item 3.31Item 3.62
Item 4.35Item 4.44
Item 5.35Item 5.43
Item 6.55Item 6.45
TOTAL.66TOTAL.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 to another group of college age students (N=26) yielded .92.
Part II
Grade Equivalents
RawG.E.RawG.E.RawG.E.RawG.E.
12.67 6.51310.81914.8
23.28 7.31411.62015.6
33.89 8.11512.42116.2
44.610 8.71613.02217.0
55.211 9.31713.62317.8
66.01210.41814.22418.4