MATH ANXIETY AT NNMC 1

Establishing a Baseline of Math Anxiety among Northern New Mexico Students Enrolled during Fall Semester,

2015

By Dr. Stephanie Amedeo Marquez

With research assistance from:

JoRonda AbeytaCharles BrackenHardev Khalsa

Peter LynnBrigitte MadoryPatrice MarshallJohn MartinezAlana Naranjo

Alexandria OrtizShayna Porter

Danielle Yingling-Archuleta

Northern New Mexico College

MATH ANXIETY AT NNMC 2Abstract

The purpose of this survey was to examine math anxiety in Northern New Mexico students, Fall, 2015, and to

establish a baseline, using the AMAS or Math Anxiety Scale: Math Anxiety Self-Test as developed by Hopko

et. al., 2003. The method used is the baseline "Before" (Traditional) and "After" (Redesign), in which the aim

is to establish baseline information about student outcomes in math anxiety from an offering of the traditional

format "before". That is, during regular courses being taught in the established way. Then, given information

from the data collected, perhaps a redesign begins to address math anxiety as an impediment to math retention

and success. Last, data would be compared, the outcomes achieved in a subsequent ("after") offering of the

course in its redesigned format, to see if the changes were effective. Individuals with anxiety disorders usually

have recurring intrusive thoughts or concerns, and may avoid certain situations out of worry, or out of a desire

to avoid the negatively experienced physical changes (www.apa.org). Such feelings of anxiety in regards to

math can interfere with the student’s ability to acquire skills in, to manipulate and/or to understand numbers. An

implication of the research is that stereotypes which impact competency beliefs may have a deleterious effect on

actual performance. In a psychological study of stereotype threat effects, Steele and colleagues examined

whether gender did affect actual performance in math (Steele, 1997; Steele & Aronson, 1995). For this data,

gender had no significant results. The sample was a random selection of classes from Fall, 2015 with an N of

108 out of 243 students enrolled. Findings from correlational and regression analysis suggested that STEM

major was the most influential factor affecting lowered math anxiety, and that Native American ethnicity was

the most influential factor affecting higher math anxiety.

Keywords: math anxiety, gender and math, ethnicity and math anxiety

MATH ANXIETY AT NNMC 3

Exploring Math Anxiety among Northern New Mexico Students Enrolled during Fall Semester, 2015

The purpose of this exploratory survey was to examine math anxiety in Northern New Mexico students,

Fall, 2015, and to establish a baseline, using the AMAS or Math Anxiety Scale: Math Anxiety Self-Test as

developed by Hopko et. al., 2003 (see Appendix A). The method used is the baseline "Before" (Traditional) and

"After" (Redesign), in which the aim is to establish baseline information about student outcomes in math

anxiety from an offering of the traditional format "before". That is, during regular courses being taught in the

established way. Then, given information from the data collected, perhaps a redesign begins to address math

anxiety as an impediment to math retention and success. Last, data would be compared, the outcomes achieved

in a subsequent ("after") offering of the course in its redesigned format, to see if the changes were effective.

Literature Review

‘Anxiety' defined by the American Psychological Association (APA), is an emotion characterized by

feelings of tension, and worried thoughts. Such thoughts are often accompanied by physical changes such as

adrenalin increases or heightened blood pressure. According to the APA, individuals with anxiety disorders

usually have recurring intrusive thoughts or concerns, and may avoid certain situations out of worry, or out of a

desire to avoid the negatively experienced physical changes (www.apa.org). This avoidance would pertain to

math anxiety.

Such feelings of anxiety in regards to math can interfere with the student’s ability to acquire skills in, to

manipulate and/or to understand numbers. This would involve the solving of mathematical problems in a wide

variety of settings including daily living as well as academic situations. According to one scholar, such math

anxiety impacts student success and performance in math classes because it can cause the student to forget

major concepts, to lose one's self-confidence, and thus to fail (Tobias, S., 1993).  Mark H. Ashcraft defines

math anxiety thus: “a feeling of tension, apprehension, or fear that interferes with math performance” (2002, p.

MATH ANXIETY AT NNMC 41). Math anxiety can occur because math is often associated with negative emotions such as pain and

frustration. For instance, thinking about unpaid bills, unforeseen debts, unbalanced checkbooks, IRS forms are a

few of the negative experiences associated with numbers in daily life. The consequences of math anxiety in a

college setting include: attrition, lower retention rates, dropping out, fewer students seeking majors in Science,

Technology, Engineering, and Math (STEM), changes of major from STEM to non-STEM. Larger

consequences for the society are implied: that there will be fewer science and technology teachers, workforce

members, and that may impact the United States’ ability to be competitive in a global economy. At Northern

New Mexico, in a community with high levels of poverty, a severely under-educated population, and multiple

family problems such as alcoholism, drug abuse, and family violence, the existence of math anxiety may be

even more crucial to blocking a young person’s ability to get ahead in life as he or she starts or returns to

college. According to FBI statistics reported in 2015, while the violent crime rate in New Mexico decreased

slightly during 2014, rates in New Mexico exceed national norms, and the figures released identified Española

as the New Mexico city with the highest violent crime rate ( Associated Press Thursday, October 1st, 2015 at

2:59pm http://www.abqjournal.com/652435/abqnewsseeker/fbi-statistics-nm-violent-crime-down-espanola-

tops-state.html).

“It may not be surprising that well-known urban centers like New Orleans, Baltimore, and San Francisco appear on the Forbes list of cities dealing with the worst drug problems in the nation. But some smaller communities are also facing epic battles with drugs, including tiny Española, N.M. Española is a small city in rural Rio Arriba county, north of Santa Fe. Its population of roughly 10,000 includes a large Hispanic community, relies largely on Los Alamos National Lab for employment and struggles with a high poverty rate. This is the U.S. city that consistently ranks among the top in the nation in drug overdoses, according to federal statistics. It is tough to find another American city that records 42.5 drug-related deaths per 100,000, compared with a national average of 7.3.” (Forbes, 2009)

Several researchers (Bouchey & Harter, 2005; Frome & Eccles, 1998; Keller, 2001; Tiedemann, 2000)

have examined gender stereotypes that “females are no good in math”. Stereotypes are examined because

cognitive social learning theory suggests such stereotypes influence competency beliefs. It is thought that

competency beliefs, in turn, affect one’s self-efficacy or ability. Correlational research has demonstrated

MATH ANXIETY AT NNMC 5parents' and teachers' stereotypes about gender and mathematics do predict children's perceptions of their own

abilities. The results hold, even with actual mathematics performance controlled (Bouchey & Harter,

2005; Frome & Eccles, 1998; Keller, 2001; Tiedemann, 2000). Competency beliefs, in turn, effect an

individuals' selection of activities and environments (Bandura, 1997; Bussey & Bandura, 1999), such that some

activities and environments will be avoided. According to meta-analysis of prior research on gender and

mathematics, girls report lower competence than boys do, although the difference is not large (d = +.16, Hyde et

al., 1990b). In recent studies, elementary-school boys still report significantly higher mathematics competency

beliefs than girls do (Else-Quest, Hyde, & Linn, 2010; Fredrick & Eccles, 2002;Lindberg, Hyde, & Hirsch,

2008; Watt, 2004).

An implication of the research is that stereotypes which impact competency beliefs may have a

deleterious effect on actual performance. In a psychological study of stereotype threat effects, Steele and

colleagues examined whether gender did affect actual performance in math (Steele, 1997; Steele & Aronson,

1995). Using a pretest posttest condition, half the participants (college students) were told that the math test

they were about to take typically shows gender differences (introducing the threat condition). The other half

(the non-threat group) were told that the math test is gender-fair and does not show gender differences (control).

This research demonstrated that college women underperformed compared to the college men in the threat

condition. However, women performed equal to men in the control condition. The results indicate that priming

(gender stereotypes) for gender differences in mathematics indeed impairs girls' math performance (e.g., Ben-

Zeev, Fein, & Inzlicht, 2005; Cadinu, Maass, Rosabianca, & Kiesner, 2005; Johns, Schmader, & Martens,

2005; Quinn & Spencer, 2001; Spencer, Steele, & Quinn, 1999). Other researchers also measuring stereotypes

held by college students regarding gender and math, found that stereotypes predicted performance in a calculus

course (Kiefer & Sekaquaptewa, 2007).

Further research on whether math ability is independent of skill includes studies of whether math

anxiety negatively affects the student’s ability to succeed in mathematics. For example, in the case of the much

researched gender gap in math scores, ability, and majors, the so-called gender gap may not be due to skill

MATH ANXIETY AT NNMC 6alone. One area of research has looked at competition or competitiveness to explain the gender gap in math.

“We provide evidence of a significant and substantial gender difference in the extent to which skills are

reflected in a competitive performance” (Niederle and Vesterlund, 2010: 130). The effects in mixed-sex settings

range from women failing to perform well in competitions within mixed-sex settings (Gneezy, Niederle, and

Rustichini, 2003) to women shying away from environments to women shying away from environments in

which they have to compete (Niederle and Vesterlund, 2007). Niederle et all have found that the response to

competition differs for men and women, and therefore that observed gender differences are not differences in

skill or native ability but responses to competitive performance environments. This suggests one reason why

gender has been found to be a strong prediction of poorer math ability, beyond the mere idea that taking more

math classes predicts greater math ability. According to one study, gender patterns in taking math classes in

High School have changed since the beginning of the 21st century. Girls are now taking calculus in high school

at the same rate as boys, although they still lag behind boys in taking physics (12), suggesting that physics may

be the key course. (National Science Foundation (2006), in Science and Engineering Indicators 2006. Available

at www.nsf.gov/ statistics/seind06.)

One comprehensive study looked at a meta-analysis of existing research on gender and gender

differences in recent studies of mathematics performance. The meta-analysis included 242 studies (all published

between 1990 and 2007) and had a sample size representing the testing of 1,286,350 people. The results were

that overall there were no significant results, indicating no gender difference, and a subsequent analysis

indicated that male and female variances were roughly equal (Lindberg, et. al., 2010).

Data from large data sets based on probability sampling of U.S. adolescents over the past 20 years,

including the NLSY, NELS88, LSAY, and NAEP were analyzed for the effect sizes for gender difference. The

gender differences found ranged between −0.15 and +0.22. Variance ratios ranged from 0.88 to 1.34. Taken

together these findings support the view that males and females perform similarly in mathematics (ibid).

In another study of math and gender, Hyde and Mertz (2009) found that data from several studies

indicated that greater male variability with respect to mathematics is not culturally “ubiquitous” (2009: 1). The

researchers found, instead, that male superiority in math was highly correlated with several measures of gender

MATH ANXIETY AT NNMC 7inequality in a cross cultural study. They argued that math superiority for one gender was an effect of

sociocultural factors, not biological differences between the sexes. They suggest strongly that such factors are

changeable: “we document the existence of females who possess profound mathematical talent. Finally, we

review mounting evidence that both the magnitude of mean math gender differences and the frequency of

identification of gifted and profoundly gifted females significantly correlate with sociocultural factors,

including measures of gender equality across nations” (2009: 6). This suggests that our study should look at

cultural factors, particularly in view of the fact that the location of Northern is in a unique cultural community,

composed of Spanish, Pueblo, and Anglo descendants sharing a 400 year history of isolation and agriculture in

a small Northern New Mexico valley surrounded by mountains.

Thus, it is important in this research to look at the influences of culture. At Northern New Mexico

college, there are a significant percentage of students that emerge from Native American pueblos in the area.

Since cultural factors have been shown to impact success in math, it is important to look at this aspect, which,

so far, has not been studied, for this particular tribal group. “Empirical research on Native American

achievement has mainly been small scale, non-experimental, non-longitudinal and methodologically

problematic. This research rarely involves sample sizes larger than 500 and is usually confined to specific tribes

or subgroups of Native Americans.” (Journal of American Indian Education - Volume 45, Issue 3, 2006 A

Review and Analysis of the Research on Native American Students, William G. Demmert, David Grissmer, and

John Towner)

Demmert and Towner (2003) in their critical publication “Education in Traditional Language and

Culture Northwest Regional Education Laboratory (NWRL)” propose looking at three established educational

theories regarding Native peoples. Use of these educational theories creates a close alignment with "Culturally

Based Education" or CBE. Implications include limited research evidence that shows a direct relationship

between CBE and improved academic performance among Native students. The proposed theories are:

Cultural Compatibility Theory Cognitive Theory Cultural-Historical-Activity Theory

MATH ANXIETY AT NNMC 8In Cultural Compatibility theory, it is argued, that the more closely the human interactions in the school

and in the classroom are aligned with those of the community, the more likely are the goals of the school to be

reached. Use of Cognitive Theory would introduce new knowledge through an association with prior

knowledge, again, based on cultural aspects of its meaning, as related to or associated with personal and social

relevance, or relationships to prior knowledge and experience. Cognitive theory argues this as a means of

improving learning and recall. Issues of culture, language, cognition, community and socialization are central to

learning in Cultural-Historical-Activity Theory. Based upon the primary socialization of infants and young

children (as well as all later socialization into new communities of practice) is accomplished through joint,

meaningful activity. The idea is to use hands on active learning, and to allow guidance by more accomplished

participants, such as mentor based teaching and learning.

Based upon these theoretical concepts, in order to reject the null hypothesis, our hypotheses to be tested

were as follows:

Ho1: Females will express higher anxiety than males

Ho2: Native Americans will express higher anxiety than Hispanics or Whites

Ho3: Students in lower level math classes, such as developmental math, will express higher anxiety than

students in later math classes.

Ho4: Students who are taking their first math class will have higher math anxiety than students who

have taken more than one math class.

Ho5: Students seeking STEM majors will express lower math anxiety than students seeking Non-STEM

majors.

Data Collection, Analysis, and Findings

Data Collection

Data collection was accomplished during Fall, 2015 at Northern New Mexico college. Teams of

Psychology Research Design students were assigned to specific, randomly selected courses (N=. The population

MATH ANXIETY AT NNMC 9was all math courses (N=38) being offered at Northern in Fall, 2015. These courses contained an estimated

student population of 243. The sample size is 108, which represents 44.4% of the total. There was limited risk

regarding double counting as most or all of the math classes are sequenced, such that, a student would have to

pass the one class in order to take the next. Additionally, the classes chosen represent a nice cross-section of

math levels, from the developmental courses (Math 100N), including education (ED 322 Math for Educators),

through to Trigonometry and Calculus. The surveys were administered in a standardized manner; all teams first

introduced themselves, and then read the informed consent at the top of the survey. All surveys were

anonymous, except for when the students themselves chose to self-identify in order to be contacted later for an

in-depth narrative interview (see Freedman’s AMAS Math Anxiety Survey, Appendix A). Table 1 provides

information on the classes from which data were collected.

Table 1. What class did this survey come from?

CLASS TITLE AND LEVEL PERCENT (N=108)

Math 100N Fundamentals 27.78%

Math 130 Intermediate Algebra 13.89%

Math 150 College Algebra 2.78%

Math 145 Intro to Probability and Statistics 29.63%

Math 155 Trigonometry and Pre-Calculus 9.26%

Math 162E Calculus I for Engineers 9.26%

Math 311 Vector Analysis 2.78%

Education 322 Math for Educators 4.63%

Sample Selection

Sample Size. For this data, there were a total of N=108 respondents. The total enrollments for math

classes at Northern during Fall, 2015, were estimated at 243. This means our randomly selected sample

MATH ANXIETY AT NNMC 10represents 44.4%. As far as math courses goes, there were a total of 27 offered in Teacher Education,

Developmental, and General math departments. Excluding WEB-based classes, we surveyed 10, which means

data were collected from 37.03% of classes offered. The results appear to be a good cross-section of math

classes taught at Northern in Fall, 2015. The developmental math class and the Probability and Statistics

courses carry the highest numbers of students. There was one Education course sampled, which is not offered

by the math department. There was Engineering and a junior-level math course (Vector Analysis), which helps

to round out the sample.

Math Level. Next, taking a look at the levels of math ability represented in the sample of 108 students,

Table 2 below shows us the breakdown of math levels, such that roughly equal numbers of students were

enrolled in Low and Mid-level math classes (41.7% and 37.0% respectively). 21.3% were enrolled in the high

level math classes at Northern.

Table 2. What level of Math is Represented in the sample?

Frequency

(N)

Percent

%

Valid

Percent

Cumulative

Percent

Low (45) 41.7% 41.7 41.7

Mid (40) 37.0% 37.0 78.7

High (23) 21.3% 21.3 100.0

Total 108 100.0 100.0

Table 2 above portrays that 45 students were at the low/developmental level, or rather that they were

taking Math 100N=1 or Math 130=1. A nearly equal number of students (N=40), were at the mid-level for

college math, taking Math 145 Probability and Statistics, Math 150 College Algebra, or Ed 322 Math for

Educators. Students at the high college level courses were enrolled in Math 155, Math 162E and Math 311.

MATH ANXIETY AT NNMC 11

The random sample above provided a strong cross-section of the population of courses offered. We were

assured that there was little or no double counting because students must complete each one of the required

courses in the sequence in order to take the next course; thus, it was unlikely that students would be enrolled in

two math courses during the same semester.

Univariate Descriptives

Gender. Out of 105 who answered the gender question, 49 or 46.67% were male, while women counted

for 53.33% of the sample (N=56). This means that, while the math department can be deservedly proud that the

female proportion is higher than the male proportion, yet the students enrolled in math classes are much more

highly male than the general population of the college. From the most recent Student Fact Book, 2014

(http://nnmc.edu/wordpress/wp-content/uploads/2010/10/Northern-New-Mexico-College-Fact-Book-2014.pdf)

the gender make-up of the college as a whole is as follows. Out of credit enrollment, Fall of 2014, the total

student count was said to be 1348, while the gender make-up was 60% female and 40% male. The gender

makeup of our sample is demonstrated below in Figure 1.

MATH ANXIETY AT NNMC 12

Figure 1. Gender as Reported by 108 NNMC Students Enrolled in Math Classes at NNMC, Fall, 2015.

Representativeness. The T-test difference for gender within our math sample compared to the gender

makeup of the overall student population was not significant, so the sample is representative. Differences were

inconclusive: the independent T-value for the means is 0. The P-Value is .5. The result is not significant at p

< .10. Therefore we can proceed with the assumption that the null hypothesis for effects of gender on math

anxiety if not rejected, will hold for findings between gender and math anxiety, and not be based upon strong

differences in proportions of gender within the math classes. We will proceed to examine gender issues within

this sample of the overall math student population.

Ethnically, the sample represents the total NNMC college population (see Table 2). According to Table

2, the results from the math anxiety survey reveal similar ethnic distributions to the campus as a whole. It may

reflect validity issues that we did not get responses to “Anglo” and perhaps should have labelled it “White” or

perhaps those students refrained from answering the question at all. Yet, the math classes contain higher

percentages of Hispanic than those reported in the prior year as enrolled at Northern total. It appears that Native

MATH ANXIETY AT NNMC 13Americans enrolled in math classes in fewer numbers than the totals for the campus would expect, which is

perhaps suggestive in regards to the research on Native American culture and education cited above.

TABLE 2. Ethnic Representativeness

Ethnicity/Race Sample Results, Fall 2015

SAMPLE (N=108)

NNMC Fall 2014*

NORTHERN (N=1384)

Hispanic/Spanish 79.44% 71%

Mexican 7.48% *

Native American 5.06% 8%

Anglo/White/Caucasian 1.09% 12%

Asian 0% *

African-American .49% *

Other/Biracial 6.54% 9%

*Not reported by Northern.

(Source for NNMC: http://nnmc.edu/wordpress/wp-content/uploads/2010/10/Northern-New-Mexico-College-Fact- Book-2014.pdf )

STEM major. For those declaring a major, the results were as follows, categorizing as STEM;

Information Technology, Engineering, Biology, Environmental Science, Psychology, there were 43.5% or 47

out of 108 declaring a STEM major. Categorizing the following as Non-STEM: Education, Nursing, Business,

Humanities, Liberal Arts, Art, Music, we found 48 of the 103, or 44.4% declaring they were a Non-STEM

majors, and approximately 12% undecided or undeclared (see Table 3).

For this data, 47 or 43.3% of the sample were declaring non-STEM majors, out of those enrolled in math

classes in the sample for Fall, 2015, 48 out of 108, or 44.4% were majoring in STEM. And, 13, or 12% were

undecided or had left the question blank (missing data).

MATH ANXIETY AT NNMC 14

Table 3. Students Declaring a STEM or Non-STEM major

Declared Major Frequency

(N)

Percent

%

Non-STEM 47 43.5%

STEM 48 44.4%

Undeclared or

Undecided 13 12.0%

Total 108 100.0

Bivariate Analysis

One of the major questions in this study is whether those pursuing STEM majors would be more or less

anxious regarding math. A correlational analysis was used to determine the relationship between math anxiety

and STEM versus Non-STEM majors. The results show (Table 4) that the STEM majors are significantly (at .02

level) less likely to express math anxiety than non-STEM (Pearson’s correlation coefficient=-.233).

Table 4. Correlation Between Math Anxiety and STEM or Non-STEM Majors

Overall, how anxious do you feel about math?

Stem Major

Overall, how anxious do you feel about math?

Pearson Correlation

1 -.233*

Sig. (2-tailed) .023N 108 95

Stem Major

Pearson Correlation

-.233* 1

Sig. (2-tailed) .023N 95 95

*. Correlation is significant at the 0.05 level (2-tailed).

MATH ANXIETY AT NNMC 15

One variable thought to impact math anxiety is the number of math classes the person has taken, such

that, math being an extremely sequenced curriculum, perhaps those with more math classes would have less

anxiety, because of greater preparation and positive experience making gains in math skills. Alternatively,

perhaps those in higher level math classes have greater anxiety due to the complexity of the content.

Accordingly we looked at whether the student was taking a first math class, or had taken more than one, in

order to later examine the hypotheses in a bivariate equation. For this data, 36 or 33.96% were taking their first

math class, out of an N of 106 respondents who answered the question (see Table 5).

Table 5. Responses to “Is this your first math class?”

Frequency

(N)

Percen

t

%

Valid

Percent

Cumulative

Percent

Missin

g

(2) 1.9% 1.9 1.9

No (36) 33.3% 33.3 35.2

Yes (70) 64.8% 64.8 100.0

Total 108 100.0 100.0

Out of 106 who answered the question, only 36 or 33.3% were not taking their first math class at Northern,

and 64.8% or 70 students were enrolled in their first math class at Northern. To explore this potential issue of

attrition and retention, the study utilized a narrative interview. The students’ plans to take more math classes is

perhaps explained by the qualitative comments gathered, in which, except for a very few math or engineering

majors, most students take exactly the number of math classes needed, and few students take math as an

elective.

MATH ANXIETY AT NNMC 16Qualitative Answers Regarding Plans to Take Another Math Class. In order to further investigate the

reasons students have for taking/not taking another math class, as perhaps connected with math anxiety, see the

collected qualitative analyses of students’ answers to whether or not they were planning to take another math

class next semester. For virtually all of those who responded, the reasons provided were not math anxiety, nor

the rigors of the math courses, but rather centered on the requirements of their degree program. Those who

answered “no” typically stated they were done with required math classes. Such common examples are:

“This is the last of my AS requirement” “all done with math courses” “I am done with math after this semester (math requirements)” “because I don't need any more maths” “because cal I, is my stopping point for my major” “because I have completed all the necessary math courses needed for my degree”

Out of the ordinary “No” respondents gave some interesting feedback: “No, because its not offered at the time I need.” “No No, busy next semster, senior season of base ball. will take Cal 2 at NM tech” “No No!!”

This last respondent does suggest math anxiety without mentioning it specifically. In examining “yes”

responses, respondents had similar reactions, that the math was required:

“need to” “so I can get my associates” “because I need to do math in engineering” “calc is part of my degree” “to get my basic out of the way” “continue towards my major” “because my degree requires” “ I need to graduate” “Yes, simly because I have to. Not because i Not because i want to “physics is a requirement” “because it is required” “because I need math for my degree” “yes I do, because I need it to finish my degree”

Interesting ‘yes’ responses were few but telling: “to gain more knowledge” “to expand my knowledge of math” “to learn more” “because I feel tat I need to conquer math” “because I feel like I need it”

MATH ANXIETY AT NNMC 17These respondents suggest they are in the group of students pursuing math from interest and perhaps, skill, or

prior positive experiences in math classes. For instance, here are two contrasting responses to, ‘will you take

another math class next semester? Compare “Yes, because I have to” to this respondent who said, “Yes yeah, i

think math is really intresting and i really like to work with numbers, and solve things, to know what the

number says”. Finally, one student linked up success in math with job attainment, “Yes, because I know I'll

need them for me to get my major and ultimately get the job I want.”

Significant Correlations. An examination of the correlations between various variables and overall math

anxiety showed no significant association for anything other than STEM versus Non-STEM majors (see Table

6).

Table 6. Correlations for Variables Thought to Explain Overall Math Anxiety

Overall, how anxious do you feel about math?Pearson Correlation Sig. (2-tailed) N

Stem Major -.233* .023 95Is this your first math class? -.159 .102 106

About how many math classes have you taken at Northern?

-.056 .630 76

Do you plan to take another math class next semester?

-.134 .192 96

Respondents who were taking their first math class, the number of math classes taken, or planning to

take another math class had no significant relationship with overall math anxiety, significances were,

respectively, p=.102, p=.630, p=.192. The significance level for the question: “is this your first math class”, at

p=.102 approaches significance. The analysis proceeds to look more closely at math anxiety items. In the

analysis above, the math anxiety measure was one question: “overall, how anxious do you feel about math?”

Perhaps disentangling aspects of math anxiety that contribute to the overall anxiety about math will yield

interesting results. Declaring a STEM major was the only variable significantly correlated with math anxiety, at

-.233, it is significant at the level of p<.05.

MATH ANXIETY AT NNMC 18

Measurement and Instrumentation: Measuring Math Anxiety

Presented below in Table 7 are the univariate results for the dependent variable, the AMAS Abbreviated

Math Anxiety Scale (Hopko, 2003). We selected this particular math anxiety scale for its reliability, validity,

and because it was brief enough to be administered during class sessions. Hopko, et. al. (2003) assessed and

reported on a brief version of Freedman’s originally developed measure. Using a large sample size (N =

1,239), the authors developed an abbreviated math anxiety measure, examined its psychometric properties, and

assessed the generalizability of the model across samples. Exploratory factor analysis yielded a nine-item

measure and strong internal consistency, test-retest reliability, and good convergent/divergent validity was

demonstrated with an independent sample. When administered to a replication sample, indexes suggested an

excellent model fit. The authors proposed that the Abbreviated Math Anxiety Scale (AMAS) was a more

parsimonious and valid approach to assess mathematics anxiety. In this study, a brief measure was required by

time constraints and resources. Thus, we adopted the AMAS to look at math anxiety in Northern New Mexico

college students.

The scale was pre-tested by the psychology research students for face validity, in case the questions were

perhaps not well-stated for our unique cultures and populations at the school. The instrument was also pretested

for timing, ease of completion, and construct validity or flow of questions. Results showed that the one of the

questions, located in between qualitative response boxes, regarding family concerns that might impact math

anxiety due to scheduling and other conflicts with studying and attending class was not well-completed, and

perhaps construct validity may be an issue for that particular question. However, the univariate results of the

AMAS match those in other studies, as follows.

There was a tie between items most endorsed for high anxiety, both featuring an average rating on a 5 point

Likert Scale of 3.39: “Being given a homework assignment of many difficult problems which is due the next

class meeting”, and “Taking an examination in a math course”.

The item least endorsed for high anxiety was “Having to use the tables in the back of a math book” with an

average rating on a 5 point Likert Scale of 1.66.

MATH ANXIETY AT NNMC 19

Table 7. AMAS Math Anxiety Scale Ranked in Order of Weighted Averages

 How anxious do you typically feel when:

Low Some Moderate Quite a

bit

A lot (N) Weighte

d

Average

Taking an examination in a math course.

11.32%

12

14.15%

15

31.13%

33

20.75%

22

22.64%

24 (106) 3.29

Being given a homework assignment of many difficult problems which is due the next class meeting.

8.49%

9

17.92%

19

28.30%

30

26.42%

28

18.87%

20 (106) 3.29

Thinking about an upcoming math test one day before.

11.11%

12

18.52%

20

27.78%

30

25.93%

28

16.67%

18 (108) 3.19

Being given a “pop” quiz in a math class.

13.46%

14

19.23%

20

30.77%

32

14.42%

15

22.12%

23 (104) 3.13

Overall, How anxious are you about math?

15.74%

17

26.85%

29

25.93%

28

15.74%

17

15.74%

17 (108) 2.89

Watching a teacher work an algebraic equation on the blackboard.

37.38%

40

18.69%

20

21.50%

23

11.21%

12

11.21%

12 (107) 2.40

Starting a new chapter in a math book.

37.74%

40

15.09%

16

27.36%

29

9.43%

10

10.38%

11 (106) 2.40

Listening to another student explain a math formula.

46.23%

49

25.47%

27

10.38%

11

10.38%

11

7.55%

8 (106) 2.08

Listening to a lecture in math class.

52.34%

56

16.82%

18

19.63%

21

2.80%

3

8.41%

9 (107) 1.98

Having to use the tables in the back of a math

55.88% 27.45% 12.75% 2.94% 0.98%

MATH ANXIETY AT NNMC 20book. 57 28 13 3 1 (102) 1.66

Items that involve the most anxiety (as measured by the weighted average) are items that are associated

with testing, where the emphasis is on getting the answers right, suggesting that competitiveness may play a

role, at least for our sample:

Being given a “pop” quiz in a math class. Thinking about an upcoming math test one day before. Taking an examination in a math course. Being given a homework assignment of many difficult problems which is due the next class meeting.

Analyzing the items on the basis of their learning activity, anxieties were expressed less for items that were

passive: that involved using visual aids such as using the tables in the back of a math book or that involved

listening (e.g. items “Listening to a lecture in math class” and “Listening to another student explain a math

formula”).

Dispersions are mostly nicely distributed, and move from higher percentages on the left for the items with

higher weighting averages, as you would expect, to lower for the items that were scored low by students. It is

interesting that the overall has a lower weighted average, meaning lower endorsement than the highest three

items. The pattern of dispersion also suggests that there is lower math anxiety than high math anxiety, taken as a

whole, as shown by the high percentages in the lowest three items, ranging between 46.23% for “Listening to

another student explain a math formula” to 55.88% for the lowest weighted average item of “Having to use the

tables in the back of a math book”. Compare this to the highest percentages for those items with high anxiety

ratings in terms of weighted averages, such as 22.64% for “Taking an examination in a math course”.

Measurement Validity. The AMAS is a 9 item questionnaire, but an “overall, how anxious are you about

math?” item was added in order to run an analysis of internal consistency using Cronbach’s alpha to see which

items contributed most or least to their overall anxiety, as shown in Table 7, and to compare overall scale

reliabilities to reliabilities reported for the scale. The Cronbach’s alpha statistic for the overall reliability of the

entire scale was estimated to be .856, for the N of 10 items.

MATH ANXIETY AT NNMC 21As a measure of mathematics anxiety, the Mathematics Anxiety Rating Scale or MARS (Suinn &

Winston, 2003) was originally developed and has been widely used for research and clinical studies. Despite the

validity and usefulness of the original scale, a shorter version of the scale was needed. There was an unwieldly

administration time for their original scale, which contained 98-items. Hopko, et. al. (2003) created a shorter

version of the MARS and analyzed the reliability and validity information for the new version. The Cronbach

alpha of .96 indicated high internal consistency. The validity data confirm that the MARS 30-item test is

comparable to the original MARS 98-item scale. According to Hopko, et. al. (2003), who then examined the

psychometric properties of the newer, shorter MARS mathematics anxiety measures using a large sample size

(N = 1,239), psychometric properties suggested generalizability of the model across samples. Exploratory factor

analysis yielded a nine-item measure and strong internal consistency, test-retest reliability, and good

convergent/divergent validity was demonstrated with an independent sample. When administered to a

replication sample, indexes suggested an excellent model fit. The new Abbreviated Math Anxiety Scale

(AMAS) Hopko and others developed, is said to represent a more parsimonious, yet still valid approach to

assess mathematics anxiety. We used this 9-item AMAS scale, and subjected it to a Cronbach’s alpha to

examine its comparability to the normed samples in the previous studies. For our data, the internal consistency

as measured by Cronbach’s alpha was: .856, while Hopko found a Cronbach’s alpha of .96 which indicated that

our administration had less high internal consistency, which may be due to the small sample size, or may be due

to the differences in the make-up of our student samples as our college is a majority minority. The validity data

confirmed that the AMAS administration for our study is somewhat comparable to the original scale.

Test Re-test Reliabilities. The test-retest reliability for the MARS 30-item was .90 (p<.001). Given time

constraints in the term, we were unable to re-administer the survey. On the other hand, educational tests are

often not suitable, because students will learn much more information over the intervening period and show

better results in the second test. If, for instance the test (math anxiety survey) was taken beginning of the

semester, and again post-tested at the end of the semester, it can be assumed that the intervening lessons may

have improved the ability of the students, and perhaps affected their math anxiety. Thus, test-retest reliability

will be compromised and other methods, such as split testing, are better. Since we were unable to re-administer

MATH ANXIETY AT NNMC 22the survey, given time constraints in the term, to take a look at test-retest reliability, we divided the sample

randomly into two groups, using SPSS’ random select cases function, to find split testing reliabilities. The

correlation between the two parts of the test was estimated to be .819, and the Guttman Split-Half Coefficient

was .892. These reliabilities are very close to the overall, at .856, which means the Split Test Reliabilities were

comparable to the overall. In interpreting the split test reliabilities it can be seen that in split-half reliability we

randomly divide all items that purport to measure the same construct into two sets. Then, since the entire

instrument was administered to the same sample of students, it is necessary to calculate the total score for each

randomly divided half. You can interpret the split-half reliability estimate, as shown in the figure, as equivalent

to the correlation between these two total scores (.819). As compared to the original alpha for the entire 10

items, which was at .856, it is possible to conclude, given the measure of consistency where the test is split in

two and the scores for each half of the test are comparable with each other and with the overall, that the test was

consistent. This consistency is nicely summarized in Table 8.

Table 8. Split half test statisticsMean Variance Std. Deviation N of Items

Part 1 13.87 16.266 4.033 5a

Part 2 12.32 23.569 4.855 5b

Both Parts 26.19 71.919 8.480 10

a. The items are: Feel anxious to use Tables?, Feel anxious about upcoming math test?,

Feel anxious while watching the teacher work equations?, Feel anxious about taking an

exam?, Feel anxious about getting homework with many difficult problems?.

b. The items are: Feel anxious while listening to lecture?, Feel anxious listening while

another student explains a formula?, Feel anxious about taking a pop quiz?, Feel anxious

about starting a new chapter in the math book?, Overall, how anxious do you feel about

math?.

Since the overall Cronbach's Alpha is equivalent to the average of all possible split half correlations, and

the split half correlation is comparable, the conclusion is that the scale we administered was reliable and

consistent. Therefore, the next step is to describe how each item on the scale contributes to overall math anxiety

(Table 9).

MATH ANXIETY AT NNMC 23

Table 9. Cronbach’s alpha item specific analysis of Math Anxiety scale

Scale Mean if Item Deleted

Scale Variance if Item Deleted

Corrected Item-Total Correlation

Squared Multiple Correlation

Cronbach's Alpha if Item Deleted

Feel anxious to use Tables?

24.51 64.644 .408 .262 .854

Feel anxious about upcoming math test?

22.96 59.998 .477 .415 .850

Feel anxious while watching the teacher work equations?

23.83 57.448 .604 .559 .838

Feel anxious about taking an exam?

22.95 59.356 .530 .395 .845

Feel anxious about getting homework with many difficult problems?

22.86 61.730 .403 .266 .856

Feel anxious while listening to lecture?

24.30 59.104 .666 .600 .835

Feel anxious listening while another student explains a formula?

24.10 59.088 .534 .405 .845

Feel anxious about taking a pop quiz?

23.13 57.874 .645 .515 .835

Feel anxious about starting a new chapter in the math book?

23.76 55.922 .699 .541 .829

Overall, how anxious do you feel about math?

23.35 56.710 .661 .490 .833

For this analysis, we mainly look at the alpha coefficient we earlier established as the reliability

estimated of the scale at .856, so, in order of how much each item contributes to the scale, these items are, in

order of most importance:

Feel anxious about starting a new chapter in the math book? (Cronbach’s alpha if removed at .829, amount of change= -27).

Overall, how anxious do you feel about math? (Cronbach’s alpha if removed at .833, amount of change= -23).

Feel anxious while listening to lecture? And Feel anxious about taking a pop quiz? (Cronbach’s alpha if removed at .835, amount of change=-21).

MATH ANXIETY AT NNMC 24These next items are moderate contributors to overall anxiety scale reliability:

Feel anxious while watching the teacher work equations? (Cronbach’s alpha if removed at.838, amount of change=-18).

Feel anxious about taking an exam? And, Feel anxious listening while another student explains a formula? (Cronbach’s alpha if removed at.845, amount of change=-11).

According to this analysis, four items are not important contributors to the reliability coefficient of the overall anxiety scale:

Feel anxious about upcoming math test? (Cronbach’s alpha if removed at.850, amount of change=-06). Feel anxious to use Tables? (Cronbach’s alpha if removed at .854. amount of change=-02). Feel anxious about getting homework with many difficult problems? (Cronbach’s alpha if removed

at .856, no change to overall scale reliability.

Thus, Table 9 shows the effect on the scale if each item were deleted. This can be interpreted as

demonstrating each item’s contribution to the overall scale. For instance, recall that the overall alpha coefficient

for the entire scale was calculated as .856; thus, removing item “Feel anxious to use Tables” would only move

the scale reliability coefficient to .854. The conclusion is that this item does not contribute much to the scale.

Notice that the scale reliability would remain .856 if item “Feel anxious about getting homework with many

difficult problems?” was removed, suggesting that this item contributes nothing to the scale. Concluding that

the scale is roughly reliable and valid, we proceed to test our hypotheses using bivariate and multivariate

analyses, proceeding to use items Overall Math Anxiety and Anxious About Starting a New Chapter as

dependent variables in further analyses.

Bivariate Results

The table below (Table 10) describes the Pearson’s correlation coefficients between the math anxiety

items and gender, first math class, number of math classes, STEM vs Non-Stem major, and Ethnicity: Native.

Table 10. Influences on Math Anxiety

MATH ANXIETY AT NNMC 25

Math Anxiety Items Gender First Math Class?

Math Level STEM vs Non-STEM major

Ethnicity: Native

Feel anxious about starting a new chapter in the math book?

-.051

(sig=.637)

-.145

(sig=.142)

-.163

(sig=.095)

-.106

(sig=.312)

.222*

(sig=.022)

Overall, how anxious do you feel about math?

-.017

(sig=.876)

-.159

(sig=.102)

-.144

(sig=.137)

-.233*

(sig=.023)

.052

(sig=.592)

Feel anxious while listening to lecture?

-.052

(sig=.629)

-.201

(sig=.039)

-.241*

(sig=.012)

-.201

(sig=.051)

.274**

(sig=.004)

Feel anxious about taking a pop quiz?

.172

(sig=.109)

-.071

(sig=.476)

-.122

(sig=.217)

-.179

(sig=.312)

.014

(sig=.890)

Feel anxious while watching the teacher work equations?

-.093

(sig=.388)

-.118

(sig=.230)

-.196

(sig=.043)

-.227*

(sig=.027)

.210*

(sig=.030)

Feel anxious about taking an exam?

.142

(sig=.187)

-.036

(sig=.715)

-.081

(sig=.423)

-.263*

(sig=.011)

.007

(sig=.945)

Feel anxious listening while another student explains a formula?

.109

(sig=310)

-.173

(sig=.079)

-.216

(sig=.026)

-.247*

(sig=.017)

.240*

(sig=.013)

Feel anxious about upcoming math test?

.126

(sig=.243)

-.127

(sig=.195)

-.127

(sig=.192)

-.289**

(sig=.005)

-.067

(sig=.491)

Feel anxious to use Tables? -.174

(sig=106)

-.293**

(sig=.003)

-.303**

(sig=.002)

-.160

(sig=.134)

.033

(sig=.738)

Feel anxious about getting homework with many difficult problems?

.025

(sig=.814)

-.186

(sig=.059)

-.127

(sig=.193)

-.141

(sig=.179)

.045

(sig=.649)

MATH ANXIETY AT NNMC 26Correlations. Examining the correlation matrix above, it is notable that for the variable gender, which is

showing some negative Pearson’s R correlation coefficients for the math anxiety items, that none of these

relations are significant. Lack of significance means that, for our data, the male students and the female students

aren’t significantly different on math anxiety. Therefore, we must accept the null hypothesis. For this data, the

students’ gender does not affect their math anxiety.

The largest and most significant correlation exists between math level and being anxious about using tables at

the end of the book (yielding a negative correlation of -.303, which is significant at p<.01). The higher the math

level, the lower the anxiety. Other negative correlations include: math level and feeling anxious while listening

to lecture (-.241, sig=.012); first math class and feeling anxious to use tables at the end of the book (-.293,

sig=.003).

An interesting comparison exists between STEM vs Non-STEM majors and Native Ethnicity in their

respective associations with the anxiety items. STEM vs Non-STEM majors had five significant Pearson’s R

correlations, all negative, indicating less anxiety, while the Native Ethnicity variable had four significant

Pearson’s R correlations, all positive, indicating higher anxieties. An illustrative example exists for “Feel

anxious while watching the teacher work equations?” item. Compare the result for the STEM majors at -.227,

(sig=.027), while Native students correlated at .210, (sig=.030), suggesting opposite reactions. A similar result

occurred for the math anxiety item, “Feel anxious listening while another student explains a formula?” The

STEM majors were correlated negatively at -.247 with a significance level of .017, while the Native students

had nearly the exact result in a positive direction, with a correlation of .240, significant at .013. Two items,

“feeling anxious about getting homework with many difficult problems” and “feel anxious about taking a pop

quiz” yielded no significant associations for this data. Results allow us to proceed to look at our two

hypotheses, whether STEM majors have lower or higher math anxiety than non-STEM majors, and whether

Native American students have different responses to math as a result of culture, using two of the original math

anxiety items.

MATH ANXIETY AT NNMC 27

Regression Analysis

Use of ordinary least squares (OLS) regression provides us with the ability to examine the effects of one

variable with other variable controlled as a predictor of math anxiety. Regression analysis is a statistical tool for

the investigation of relationships between variables. The goal is to go beyond mere association and to ascertain

the causal effect of one variable upon another. Additionally, the effect of one variable, controlling for the other,

can be explored. Regression creates an equation to estimate the quantitative effect of the causal variables (math

level, Native ethnicity, and STEM vs Non-STEM majors) upon the math anxiety variables that they influence.

The regression analysis also typically assesses the “statistical significance” of the estimated relationships, that

is, the degree of confidence that the true relationship is close to the estimated relationship. R-squared is the

general statistical measure of how close the data are to the fitted regression line, called the coefficient of

determination. The mathematical calculation of R-squared is fairly straight-forward; it is the percentage of the

response variable variation that is explained by a linear model. Or, to say it another way, the R-squared =

represents explained variation compared to or divided by the total variation. R-squared is always between 0 and

100% and 0% indicates that the model explains none of the variability of the response data around its mean.

100% indicates that the model explains all the variability of the response data around its mean. Typically, you

would not achieve 100% unless you regressed a variable with itself. In general, the higher the R-squared, the

better the model fits the data. The regression equations run for this analysis include these independent

predictors: Native ethnicity, STEM vs Non-STEM, and Math Level. Math Anxiety items form the dependent

variables.

Model One. In examining the effect of our two predictors, that is, declaring a Stem Major, and, Are you

Native American for effects or influences on the math anxiety item as the dependent variable: “Feel anxious

while watching the teacher work equations?” We chose this dependent variable item as it was revealed in the

correlational analysis as showing significant opposite effects for the two predictors. “Feeling anxious watching

MATH ANXIETY AT NNMC 28the teacher work equations on the board”, the regression analysis reveals significant results. Looking at the

Model Summary for the regression reported in Table 11, the model fit is weak. The R square is close to zero,

at.088. The R was .297 and the adjusted R Square at .068, while the Standard Error of the Estimate was really

high at 1.327.

The ANOVA report for this model, reports that, using analysis of variance, the regression equation is

significant, at F=4.443, and significance estimated at p<.05. F as a test statistic measures the variance of the

group means as compared to the mean of the within group variances. The p-value on the other hand, is the

probability of obtaining the result. ANOVA is very helpful because of its advantage over a two-sample t-test:

ANOVA (when used instead) decreases chances of committing an error. To make sure that the results of a one-

way ANOVA can be considered reliable, assumptions must be met. The variables must be normally distributed,

independent samples, population variances are equal and group responses should be independent and identically

distributed.  For the two-way ANOVA Table, which is the extension to the one-way ANOVA, there are two

independent variables.  To consider the results as reliable, samples must be independent, groups must have

same sample size, population variance must be equal and the populations from which the samples were taken

must be normally distributed. In all cases, the residual statistics were examined to ensure that assumptions were

met. The ANOVA for Model one, predicting math anxiety between STEM majors and Native ethnicity students

on watching the teacher work equations on the board had the following findings, F=4.443, sig=.014.

Even if the overall model as reported by the R-squared value is low, as in this case, it is possible to look

for statistically significant predictors within the model. In this case, both the predictors are significant. Taking a

look at the information reported in Table 12c below, as observed above in the correlations, Native American

students significantly (p=.058) predict changes in the math anxiety scale estimated at Unstandardized B

coefficient of .855, and standardized coefficient of .192. Important conclusions about how changes in the

predictor value of Stem majors are associated with changes in the response value also, and, again, are found to

be negative changes. That is, declaring a STEM major is significant (p<.036), and predicts a decline of -.583 in

math anxiety. Regardless of the R-squared, these significant coefficients still represent the mean change in the

MATH ANXIETY AT NNMC 29response for one unit of change in the predictor while holding other predictors in the model constant.

Obviously, this type of information can be extremely valuable (Table 11).

Table 11. Regression Coefficients Testing the Fit For Model OneModel Unstandardized

CoefficientsStandardized Coefficients

t Sig.

B Std. Error Beta

1

(Constant) 2.678 .202 13.275 .000Are you Native American?

.855 .445 .192 1.922 .058

Stem Major -.583 .273 -.213 -2.134 .036a. Dependent Variable: Feel anxious while watching the teacher work equations?

Model Two. The same regression analysis was run for the second dependent math anxiety item, “Feel

anxious listening while another student explains a formula” with the same two independent predictor variables,

Native American and STEM major. Table 12 shows that the R square for this second model is stronger, at .106

it compares favorably to the earlier model in 12 where the model fit was weak, estimated at an R square close to

zero (.088). The R estimated as variance (dispersions) explained was found to be at .326, and the standard error

for this estimate is 1.322.

The ANOVA model for this second regression (model two) reports that, using analysis of variance, the

regression equation has a significant estimate of the variance of the group means, compared to the mean of the

within group variances, at F=5.334, and a significance of .006. In comparison to the earlier model’s F=4.443,

and significance estimated at p<.05, the second model is a more robust estimate. The predictors (STEM major

and Native American ethnicity) more strongly predict the math anxiety item, “feel anxious while another

student explains a formula”.

One way to interpret the results in Table 12 for our second model is to compare the coefficients for

Native American students versus STEM majors. That is, declaring a STEM major is a more significant (.024)

prediction of the math anxiety item and it predicts a change that represents a decline (-.632). The predictive

value of Native American ethnicity is unchanged from the former regression equation, which means that, even

controlling for whether or not the student declares a STEM major, holding Native American ethnicity still

MATH ANXIETY AT NNMC 30

predicts upward changes in the math anxiety scale estimated at Unstandardized B coefficient of .945, at

sig=.036).

Table 12. Regression Coefficients Testing the Fit For Model TwoModel Unstandardized

CoefficientsStandardized Coefficients

t Sig.

B Std. Error Beta

1

(Constant) 2.407 .206 11.700 .000Are you Native American?

.945 .444 .213 2.130 .036

Stem Major -.632 .275 -.230 -2.296 .024a. Dependent Variable: Feel anxious listening while another student explains a formula?

Conclusions

The overall alpha coefficient for the AMAS scale, for this sample, was calculated as .856, and shows

strong reliability for our dependent measure. In testing the hypothesis that gender affects this measure of math

anxiety, for our data, the variable gender, while showing some negative Pearson’s R correlation coefficients for

the math anxiety items, all of these relations were insignificant. For our data, the male students and the female

students aren’t significantly different on math anxiety. Therefore, the null hypothesis could not be rejected,

thus, the conclusion is that for this data, the students’ gender does not affect their math anxiety. On the other

hand, the STEM vs Non-STEM majors had five significant Pearson’s R correlations, all negative, indicating far

less math anxiety. Interestingly, the Native Ethnicity variable had four significant Pearson’s R correlations, all

positive, indicating higher anxieties. An illustrative example of this contrast existed for “Feel anxious while

watching the teacher work equations?” item. (Compare the result for the STEM majors at -.227, (sig=.027),

while Native students correlated at .210, (sig=.030), suggesting opposite reactions). A similar distinction

emerged for the math anxiety item, “Feel anxious listening while another student explains a formula?” On this

item, for example, the STEM majors were correlated negatively at -.247 with a significance level of .017, while

the Native students had nearly the exact result in a positive direction, with a correlation of .240, significant

at .013. Testing this finding further, the data were subjected to two regression models. The results were that

MATH ANXIETY AT NNMC 31predictive value of Native American ethnicity as showing higher positive significant math anxiety was

reproduced in both regression equations. Declaring a STEM major, in both equation models still predicted

downward changes in the math anxiety scale. The equations power to explain the variance in two of the math

anxiety items, “Feel anxious listening while another student explains a formula?”, and “Feel anxious while

watching the teacher work equations?” were both significant as estimated by the F statistic, at respectively,

F=4.443, sig=.014. and F=5.334, with a significance of .006.

Implications

Establishing a Baseline. In order to establish a baseline of math anxiety among NNMC student enrolled

in math classes during 2015, a random sample of N=108 respondents, representing 44.4% of total enrollments

for math classes at Northern during Fall, 2015. All students were administered the AMAS or Math Anxiety

Scale: Math Anxiety Self-Test as developed by Hopko et. al., 2003 (see Appendix A). This method established

a baseline measurement of the "Before" condition. The aim is to establish baseline information about student

outcomes in math anxiety. The math anxiety scale was proven to be valid and reliable for our student

population, and matched the alpha coefficients from other studies.

Limitations of the Data. Limitations of the data involve the interesting nonsignificant results for gender,

combined with the implications in prior research regarding competitiveness. Future research should measure

competitiveness as a variable used to explain math anxiety, and students’ plans to take another math class.

Because of the small numbers of students who planned to take another math class out of personal desire to

learn, we were unable to further research this aspect of math retention/attrition. Perhaps a measure such as the

‘need for cognition’ scale could also be used in the next data collection, although the need for cognition scale

hasn’t been used to determine students’ math abilities or math anxiety levels. Since the Need for Cognition

Scale is an assessment instrument that quantitatively measures "the tendency for an individual to engage in and

enjoy thinking" (Cacioppo & Petty, 1982, p. 116), this suggests that students who enjoy math may have a higher

need for cognition. A revised, brief 18-item Need for Cognition Scale has been used in several settings, and a

MATH ANXIETY AT NNMC 32pertinent one was Sadowski and others examinations of the relationship between students’ need for cognition

and their academic performance (Sadowski & Gulgoz, 1992a, 1996; Tolentino, Curry, & Leak, 1990).

In addition, suggested by our data in which analysis of the weighting by students of the math anxiety items

on the basis of their learning activity, we saw that anxieties were expressed less for items that were passive: that

involved using visual aids such as using the tables in the back of a math book or that involved listening (e.g.

items “Listening to a lecture in math class” and “Listening to another student explain a math formula”). Items

that were endorsed as having the most anxiety (as measured by the weighted average) were the items associated

with testing, where the emphasis is on getting the answers right, suggesting that competitiveness may play a

role, at least for our sample, and further arguing that future research might look at competitiveness. A

competitiveness measure such as the Competitiveness-Cooperation Scale developed by Stagel and Koonen

(2005) is strongly suggested by the findings for the Native American students. Cultural sensitivity such as that

suggested by "Culturally Based Education" or CBE should have further, and more detailed, study. Implications

include limited research evidence that shows a direct relationship between CBE and improved academic

performance among Native students, the idea that cognitive theories of how to improve the Native students’

math anxieties may involve dealing with competitiveness, given that the majority of the NNMC students are

Pueblo people, and that culturally, the social psychology would suggest cooperative learning over competitive.

This may involve focusing on the concepts rather than the right answer and letting students work on

their own and discuss their solutions before the answer is given. Emphasis is given that to be wrong is aversive,

and situations where students can be embarrassed by being wrong may contribute to math anxiety, which in,

turn, predicts whether students plan to continue in college at all, or to take further math classes, or perhaps, to

change from a STEM major.

National Council of Teachers of Mathematics (NCTM) (1989, 1995b) provided suggestions for teachers

seeking to prevent math anxiety that include:

Accommodating for different learning styles

MATH ANXIETY AT NNMC 33 Creating a variety of testing environments

Designing positive experiences in math classes

Refraining from tying self-esteem to success with math

Emphasizing that everyone makes mistakes in mathematics

Making math relevant culturally

For this data, we did not measure student’s impressions of the learning activities, except to suggest them in the

math anxiety items. Items with low anxiety were passive learning activities such as looking up tables in the

back of the book, listening, watching.

Hackworth (1992) suggested several activities that can help in reducing and mitigating mathematical

anxiety, such as to develop calming/positive ways to deal with fear of math, including visualization, positive

messages, relaxation techniques, frustration breaks. We had some indications of this in our qualitative

interviews, but more data needs to be collected. We measured Hackworth’s 1992 idea that to use gradual,

repeated success to build math confidence in students by looking at whether math anxiety was heightened or

lessened depending upon the number of math classes the student had taken, but again, there were no statistically

significant indications that this was true.

Finally, again referencing the qualitative narrative data, students indicated that math, for them, was a

practical necessity to complete their chosen degrees. Therefore, perhaps the next research should study how

much the student perceives math as relevant to their everyday lives and to their larger goals. According to

Sheila Tobias (1993) large numbers of American adults are blocked from professional and personal

opportunities because they fear or perform poorly in mathematics. To quote one of the NNMC students in our

study about why he/she was going to take another math class, “Yes, because I know I'll need them for me to get

my major and ultimately get the job I want.” The goal would be to create a math program in which all the

students gained this realization.

For many Northern New Mexico students without this perception economic and financial opportunities may

be limited. Such opportunities which are few and far between in the Espanola valley, and the lack of which

MATH ANXIETY AT NNMC 34opportunities explains why too many residents of Northern New Mexico fail to emerge from poverty,

unemployment, and lower educational attainment.

REFERENCES

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MATH ANXIETY AT NNMC 38APPENDIX A

Anonymous Survey about Feelings and Attitudes Regarding Math

The CJ and Psychology Research class (CJ/PSY 321) is conducting a survey to learn about how to do research.

We are interested in knowing about your feelings and attitudes about math. All responses will be kept

anonymous and confidential, and not released to your instructor. The results will be aggregated, so no

individual identifying information will ever be collected or released. Your participation is strictly voluntary.

This brief survey will take about 5-10 minutes of your time.

Demographics: Are you? Please put a check or X in the space provided.

Male_____ Female____

Age: <18______ 18-25_____ 26-30______ 31-40_____ 41-50______51+

Hispanic/Spanish_______ Mexican_______Native American: Pueblo_________ which Pueblo? ___________

Navajo___________Anglo ______ Asian _______ African-American_____ Other/Biracial/please

specify______________________________

Married/in committed relationship_______ Single___________

Do you work? Yes______ No______ If yes, Fulltime___________ or Part time_____________

Do you have children? Yes ____No _____How many?____________ Are you expecting? Yes___No____

Do you have a religious affiliation? If yes, what is it? _____________________

How spiritual would you say you are? 1=not at all_____ 2=a little bit ______3=somewhat_______4=very

much______5=a great deal______

What is your major?_________________________________

How anxious do you typically feel when: 1 = 2 = 3 = 4 = 5=

MATH ANXIETY AT NNMC 39Low Some Moderate Quite

a bitA lot

Having to use the tables in the back of a math

book.

Thinking about an upcoming math test one day

before.

Watching a teacher work an algebraic equation

on the blackboard.

Taking an examination in a math course.

Being given a homework assignment of many

difficult problems which is due the

next class meeting.

Listening to a lecture in math class.

Listening to another student explain a math

formula.

Being given a “pop” quiz in a math class.

Starting a new chapter in a math book.

Overall, How anxious are you about math?

Is this your first math class? Yes______ No_____

About how many math classes have you taken at Northern? _________

MATH ANXIETY AT NNMC 40The following questions are about obstacles you might have in attending class:

What do you typically do when feeling stressed? Check all that apply:___Study harder ___do yoga

____spend time with family ___ask the instructor for help _____ study with another student/ask

another student for help ____ Other/please specify:________________________

Other strategies I use to release stress are:

Have you ever been pulled over and given a speeding ticket while driving to or from school and perhaps

running late for class or to get home? _____ YES _____NO

Do you plan to take another math class next semester? Why or Why not?

What family issues make it complicated for you to attend school?

______daycare ______personal health ________health issues of elder members of the family

______alcohol/addiction issues for family members other than yourself _______finances

______transportation _______religious holidays/feast days

Other: Please explain_____________________________________________________

Any comments you have?

THANK YOU!!! Would you be willing to be interviewed regarding how you feel about math? If yes, provide

only your first name_____________; and an email_________________ or phone number________________.

MATH ANXIETY AT NNMC 41APPENDIX B. Math Anxiety Interviews

SCRIPT:

SAY OR READ: Dear NNMC Student. We are contacting you because you took a math anxiety survey and said

you were willing to be contacted. Is this a good time? (If not, make arrangements for alternative time. If not, ask

if ok to email and verify email). If they agree, tell them the informed consent: “this information that I will be

collecting will be known only to me, and it will remain confidential. Any information that you tell me will

never be shared except anonymously or in the aggregate, do you understand? We will destroy our record of

your phone number, first name, and email when the study is completed. Are you ok to proceed? We really thank

you for helping to improve math classes at Northern.

1. Tell them your first name. Then ask: Can I ask your first name? (check correct box or write in)

First names CHECK or WRITE IN FIRST NAME ONLY!

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

MATH ANXIETY AT NNMC 42

2. READ OR SAY: Here were some comments made by members of the math classes this semester at Northern:

ok if I read you the comments? There aren’t very many. Read COMMENTS:

Math is pretty chill in my eyes. My bran likes to figure things out.

I enjoy math because there is several approaches but only one outcome.

Math is interesting, but the pressure to get the good grades is really miserable because pulling allnighters

sucks.

Math courses should accommodate more for those with anxiety

math is the sole detriment existence to my education

I Love Math

I live alone part of that makes it harder because I need to take care of alot of things.

Math sucks!!! I feel that Math is holding be back from getting my AA

The only time I have ever been stressed was in a math class

ASK: What do you think? Do you any of these comments agree with your experience? (Write in their answer

here)

3. ASK: How much do you agree with the following statements? Answer “1” if you think “ not at all” and a “5”

if you agree a great deal. (repeat this if asked)

Math Classes should focus more on the concepts rather than the right answer. (Record their answer

here____________________).

Math classes should let students work in groups and discuss their solutions before the answer is given. (Record

their answer here____________________).

MATH ANXIETY AT NNMC 43One reason people have a hard time in math classes is because emphasis is given on being wrong. (Record their

answer here____________________).

I feel embarrassed when I’m wrong. (Record their answer here____________________).

4. ASK: What do you think your best learning style is? Do you think you learn best from:

Reading the chapter? Yes___No___ Comment:

Seeing visual depictions such as figures in the book? Yes___No___ Comment:

Hearing it explained in lecture? Yes___No___ Comment:

Working out the problems by hand? Yes___No___ Comment:

Working in a group to find answers and learn skills? Yes___No___ Comment:

5. ASK: the last thing I want to talk to you about is what you think Northern and the math department could do

to help allay anxiety and improve the way students learn math?

For Instance, in class: which one of the following suggestions do you think would have helped you the most in

learning math without having anxiety?

Creating a variety of testing environments, such as some being in class, open book, or focusing on concepts

and definitions as well as solutions to problems. Yes___No___ Comment:

Designing positive experiences in math classes, such as maybe games or group work Yes___No___

Comment:

Emphasizing that everyone makes mistakes in mathematics Yes___No___ Comment:

Making math relevant to real world experiences such as doing taxes or paying bills. Yes___No___

Comment:

Letting students have some input into their own evaluations Yes___No___ Comment:

Allowing for different social approaches to learning mathematics, for instance, culturally relevant methods

or problems Yes___No___ Comment:

MATH ANXIETY AT NNMC 44 Emphasizing the importance of original, quality thinking rather than rote manipulation of formulas

Yes___No___ Comment:

6. ASK: Do you think it would help to reduce your math anxiety, if in math classes, you could:

Discuss and write about math feelings in class; Yes___No___ Comment:

Be asked to be a more active learner, and perhaps create problem-solving techniques; Yes___No___

Comment:

Be allowed to evaluate your own learning; Yes___No___ Comment:

Be asked in class to use calming/positive ways to deal with fear of math, including visualization, positive

messages, relaxation techniques, frustration breaks; Yes___No___ Comment:

7. ASK: How valuable would it be for you, if Northern should institute a study group or lab for Math and

Statistics classes? It would use a combination of coaching for material comprehension, but use counseling to

address the reasons for anxiety, and not just the mathematical skills which may be lacking.

READ AND CIRCLE: 1=not at all 2=a little bit 3=somewhat 4=very much 5= a great deal

OK WHAT ELSE! COMMENTS? IDEAS? ANYTHING? (write on back if you need more room or add

addition pages)

THANK YOU SO MUCH!! AND, GOOD LUCK IN MATH!!!