Mathematics anxiety has been defined as “feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems” (Richardson and Suinn, 1972, p. 551).

High mathematical anxiety in students hinders their ability to perform in the college environment by causing poor academic achievement (Woodard, 2004).

One of the most extensively used mathematics anxiety instruments is the Mathematics Anxiety Rating Scale (MARS; Richardson and Suinn, 1972).

The MARS has two major shortcomings:1) Is time consuming to administer and score2) Assumes a unidimensional construct (Richardson

& Suinn, 1972; Suinn, Edie, Nicoletti, & Spinelli, 1972).

Length of the MARS Several studies shortened the original 98-item MARS (e.g., Levitt & Hutton, 1984; Rounds & Hendel, 1980; Plake & Parker, 1982; Alexander & Martray, 1989).

The three most widely used shortened scales are the Revised Mathematics Anxiety Rating Scale (RMARS; Alexander & Martray, 1989), the Mathematics Anxiety Questionnaire (MAQ; Wigfield & Meece, 1988), and the Mathematics Anxiety Scale (MAS; Fennema & Sherman, 1976).

Unidimensionality of the MARS Several studies revealed that there may be more than one underlying construct in mathematics anxiety as measured by the MARS (e.g., Alexander & Martray, 1989; Brush, 1981; Ferguson, 1986; Plake & Parker, 1982; Rounds & Hendel, 1980; Satake & Amato, 1995).

The RMARS assumes multidimensionality of the construct (Alexander & Martray, 1989; Bowd & Brady, 2002) and has been shown to contain three subscales: Mathematics Test Anxiety subscale assesses

student reactions to evaluative situations in mathematics (items 1 – 15).

Mathematics Course Anxiety subscale measures student reactions to being in a mathematics class (items 16 – 20).

Numerical Task Anxiety subscale measures anxiety due to basic math activities such as multiplication and division (items 21 – 25).

The principal aims of this study are to: Explore the psychometric properties of the RMARS

within the framework of Item Response Theory (IRT); Identify the items that elicit the highest/lowest levels

of mathematics anxiety; and Investigate the fit of the data to the model and

pinpoint any items that deviate from reasonable fit statistic values.

Participants 346 college students enrolled in several sections of

same Developmental Mathematics course.

Instrument RMARS 25 items; shared 5-point rating scale: Not at

All, A Little, A Fair Amount, Much, Very Much.

Model Rating Scale Model (RSM; Andrich, 1978) is part of

the Rasch (1960) family of measurement models.

𝒍𝒐𝒈𝑷𝒏𝒊𝒌

𝑷𝒏𝒊(𝒌−𝟏)= 𝜷𝒏 − 𝜹𝒊 − 𝝉𝒌

→ 𝑷𝒏𝒊𝒌 = probability that student 𝑛 will choose category 𝑘 when responding to item 𝑖

→ 𝑷𝒏𝒊(𝒌−𝟏) = probability that student 𝑛 will choose

category 𝑘 − 1 when responding to item 𝑖→ 𝜷𝒏 = student 𝑛’s measure of mathematics anxiety→ 𝜹𝒊 = difficulty of endorsing item 𝑖; −𝜹𝒊 = easiness of

endorsing item 𝑖→ 𝝉𝒌 = difficulty threshold b/w category 𝑘 − 1 and 𝑘 Data analysis: Winsteps 3.92.0 (Linacre, 2016)

Mean-square Fit Statistics• Chi-square statistics divided by their degree of

freedom. Expected value = 1.0, range [0, ∞].• Values > 1.0 unpredictability (the data underfit

the model; unmodeled noise present in the data)• Values < 1.0 observations are too predictable

(data overfit the model; redundancy in the data)• Reasonable values: 0.8 – 1.2 (Linacre et al., 1994)• Infit Mean-Square sensitive to the pattern of

responses to items targeted to the person• Outfit Mean-Square Sensitive to responses to

items with difficulty far from a person.

Alexander, L. & Martray, C. (1989). The development of an abbreviated version of the Mathematics Anxiety Rating Scale. Measurement and Evaluation in Counseling and Development, 22,143-150.

Andrich, D. (1978). Scaling attitude items constructed and scored in the Likert tradition. Educational and Psychological Measurement, 38(3), 665-680.Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 357-374.Bowd, A. D., & Brady, P. H. (2002). Factorial structure of the Revised Mathematics Anxiety Rating Scale for undergraduate education majors.Psychological reports, 91(1), 199-200.Brush, L. R. (1981). Some Thoughts for Teachers on Mathematics Anxiety.Arithmetic Teacher, 29(4), 37-39.Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman mathematics attitudes scales: Instruments designed to measure attitudes toward the learning of mathematics by females and

males. Journal for Research in Mathematics Education, 7(5), 324-326.Ferguson, R. D. (1986). Abstraction anxiety: A factor of mathematics anxiety.Journal for research in mathematics education, 17(2), 145-150.Levitt, E. E., & Hutton, L. H. (1984). A psychometric assessment of the Mathematics Anxiety Rating Scale3. Applied Psychology, 33(2), 233-242.Linacre, J.M. (2016). Winsteps® (Version 3.92.0) [Computer Software]. Beaverton, Oregon: Winsteps.com. Retrieved January 1, 2016.

Plake, B. S., & Parker, C. S. (1982). The development and validation of a revised version of the Mathematics Anxiety Rating Scale. Educational and Psychological Measurement, 42(2), 551-557.Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests (Reprint, with Foreword and Afterword by B. D. Wright, Chicago: University of Chicago Press, 1980).

Copenhagen, Denmark: Danmarks Paedogogiske Institut.Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale: psychometric data. Journal of counseling Psychology, 19(6), 551-554.Rounds, J. B., & Hendel, D. D. (1980). Measurement and dimensionality of mathematics anxiety. Journal of Counseling Psychology, 27(2), 138.Satake, E., & Amato, P. P. (1995). Mathematics anxiety and achievement among Japanese elementary school students. Educational and Psychological Measurement, 55(6), 1000-1007.Suinn, R. M., Edie, C. A., Nicoletti, J., & Spinelli, P. R. (1972). The MARS, a measure of mathematics anxiety: Psychometric data. Journal of clinical psychology.Wigfield, A., & Meece, J. L. (1988). Math anxiety in elementary and secondary school students. Journal of Educational Psychology, 80(2), 210.Woodard, T. (2004). The Effects of Math Anxiety on Post-Secondary Developmental Students as Related to Achievement, Gender, and Age. Inquiry, 9(1), n1.Wright, B. D., Linacre, J. M., Gustafson, J. E., & Martin-Lof, P. (1994). Reasonable mean-square fit values. Rasch Measurement Transactions, 8(3), 370.

Item response theory provides a rich framework for analyzing the psychometric properties of the RMARS. Students are most anxious about 1) taking a final exam, 2) receiving their final grade, and 3) thinking about a test

one hour beforehand. They are least anxious about 1) solving numerical problems involving addition, 2) reading a cash receipt register, and 3) solving numerical problems involving subtraction.

Two of the underfiting items are tied to financial aspects of anxiety (having to spend money to buy a math book and reading a receipt). Students with otherwise low math anxiety levels give these items high scores.

Responses to several items (#3, #14, #19, #20) are flagged as overfitting the model, indicating that they are possibly redundant and could be removed without much loss of information.

Item Easiness to Endorse Measures• Range: – 0.79 to 1.25 logits• Item Reliability = .99Student Math Anxiety Measures• Range: – 5.55 to 5.75 logits• Mean = – 0.44 logits

- Most Anxious Students

3— w

-

-

- w

- w

2— w

- w

- w

- uu 4. Taking a final exam in a math course

- wuu 12. Receiving your final math grade

1— wuuuuu 9. Thinking about an upcoming math test one hour before

- wuuu

- wuuuuu 2. Math entrance exam 8. Thinking about math test one day before

- wuuu 3. Taking a test in a math course 10. Math requirements for graduation

- wuuuuuuuuu 15. Pop Quiz 13. Page full of problems 1. Studying for test

0— wuuuuuuuuuu M 6. Difficult homework 7. Thinking about math test one week before

- wuuuuuuuuuu 14. Prepare to study for test 11. Difficult reading assignment

- wuuuuuuuuu M 23. Signing up for math course 5. Open textbook to do homework

- uuuuuuuu 24. Student explanation 22. Teacher solution 25. Walking into math class

- wuuuuuuuuu 20. Division 21. Buying textbook 19. Multiplication

-1— uuuuu 18. Subtraction 16. Reading receipt 17. Addition

- wuuuuu

- wuuuu

- wuuuu

- wuu

-2— wuuu

- u

- wu

- w

- wu

-3— u

- w

-

-

-

-4—

-

- w

-

- Least Anxious Students

-5— u

-

A

Fair

Amount

A

Little

Not

at

All

Most Difficult Items to Endorse

(Low Raw Score Totals)

Each u represents 3 students; Each w represents 1 to 2 students.

Very

Much

Much

Figure 1: Map of Student and Item Measures on RMARS Logit Scale

Logit

ScaleStudents Items

Rating

Scale

Easiest Items to Endorse

(High Raw Score Totals)

Students report this item as causing the

most anxiety.

Students report these items as causing the

least anxiety.

RMARS Items

Item

Easiness

(logits)

S.E.

Infit

Mean

Square

Outfit

Mean

Square

4. Taking a final exam in a math course. 1.25 0.06 1.20 1.43

12. Receiving your final math grade. 1.09 0.06 1.11 1.14

9. Thinking about an upcoming math test one hour

before.0.91 0.06 1.32** 1.99**

2. Taking the math section of the college entrance

exam.0.64 0.06 1.13 1.32

8. Thinking about an upcoming math test one day

before.0.63 0.06 1.03 1.40

3. Taking a test in a math course. 0.61 0.06 0.76* 0.80*

10. Realizing you have to take a certain number of

math classes to fulfill graduation requirements.0.56 0.06 1.09 1.11

15. Being given a "pop" quiz in a math class. 0.34 0.06 1.19 1.23

13. Opening a math or stats book and seeing a page

full of problems.0.21 0.06 0.85 0.86

1. Studying for a math test. 0.15 0.06 0.83 0.90

6. Being given homework assignments that include

many difficult problems that are due the next class

meeting.

0.08 0.06 0.95 1.01

7. Thinking about an upcoming math test one week

before.0.05 0.06 0.80 0.86

14. Getting ready to study for a math test. -0.01 0.06 0.72* 0.71*

11. Picking up a math textbook to begin a difficult

reading assignments.-0.10 0.06 0.93 0.95

5. Picking up a math textbook to begin working on

a homework assignment.-0.38 0.06 0.85 0.80

23. Signing up for a math course. -0.36 0.06 0.82 0.80

24. Listening to another student explain how to use

a math formula.-0.47 0.06 0.93 0.89

22. Watching a teacher solve an algebraic equation

on the board.-0.49 0.06 0.98 0.88

25. Walking into a math class. -0.49 0.06 1.24 1.09

21. Buying a math textbook. -0.60 0.06 1.68** 1.94**

20. Being given a set of numerical problems

involving division to solve on paper.-0.58 0.06 0.76* 0.73*

19. Being given a set of numerical problems

involving multiplication to solve on paper.-0.68 0.06 0.78* 0.69*

18. Being given a set of numerical problems

involving subtraction to solve on paper.-0.77 0.06 0.83 0.72

16. Reading a cash register receipt after your

purchase.-0.78 0.06 1.56* 1.63**

17. Being given a set of numerical problems

involving addition to solve on paper.-0.79 0.06 0.93 0.77

*Overfitting item, Mean Square Statistic < .08; **Underfitting Item, Mean Square Statistic > 1.2

Test

An

xie

tyM

ath

em

atic

s C

ou

rse

An

xie

tyN

um

eri

cal T

ask

An

xie

ty

Table 1: Item Measures and Fit Statistics