Social stigma and mathematical ignorance.

Abstract

Although excelling in mathematics can be socially stigmatizing, is it a social stigma to be deficient in mathematics? Over 1000 undergraduate students were questioned as to the embarrassment level they would feel for various deficiencies (including mathematical and nonmathematical situations). Results reveal that most students (including mathematics majors) do not find it embarrassing to make a mathematical mistake, but do find it embarrassing to make nonmathematical mistakes. Implications include the difficulty of teaching K-12 mathematics if the discipline is not valued.

Introduction

Research has shown that excelling in mathematics can cause students to feel socially stigmatized (Manor-Bullock, Look, & Dixon, 1995). However, might the opposite also be true? That is: Do students also feel socially stigmatized for being deficient in mathematics? It has been suggested that students do feel stigmatized if they are illiterate (Beder, 1991), but what happens if they are innumerate? Stigma is a strong word. Sociologists use the word to mean some characteristic of a person that causes the person to hold an inferior social position or social standing. For example, people who are honest have a higher social standing than people who are dishonest. Dishonesty can cause a social stigma. If the stigma is not extensive, one might call it a failing, a shortcoming, or a handicap (Goffman, 1963). The stigmatized person tends to accept the stigma.

As mentioned, research has shown a social stigma for excelling in mathematics. Is there a social stigma for being deficient in mathematics? Mathematics education is undergoing reform, mostly because of the view that traditional mathematics education has not been successful, but also due to the changing nature of technology, and the increasing volume of mathematics education research (National Council of Teachers of Mathematics, 2000). However, no matter what reforms are introduced, mathematics education will not improve if society does not truly care that mathematics knowledge improves. Research has shown that attitudes and beliefs are formed by social forces and predict academic performance (Kloosterman, Raymond, & Emenaker, 1996; Lester, 2002; Singh, Granville, & Dika, 2002). If there is no societal pressure against mathematical ignorance, there will not be sufficient motivation for some K-12 grade students to learn mathematics (Day, Borkowski, Dietmeyer, Howsepian, & Saenz, 1992).

Related Research

Researchers have examined student and teacher attitudes, beliefs, and perceptions about the school subject of mathematics. Although teachers' beliefs are very important for the teaching and learning of mathematics, they are not necessarily reflective of society's beliefs about mathematics (Cooney & Shealy, 1997). In particular, examining mathematics teachers' beliefs about mathematics will not tell us what society thinks about mathematical ignorance. McLeod (1992) writes about students' beliefs, attitudes, and emotions. He outlines the belief domain in terms of beliefs about mathematics, the sell; mathematics teaching, and the social context. Researchers are recognizing that students' (and teachers', for that matter) beliefs about mathematics are embedded in the school setting, the educational system, and in society (Greer, Verschaffel, & De Corte, 2002). Yet, research into society's influence on students' attitudes about mathematics is only in the beginning stages (Boaler, 1999).

Recent research has demonstrated the positive changes in student attitudes under National Council of Teachers of Mathematics aligned curricula (Senk & Thompson, 2003). The Third International Mathematics and Science Study data reveal that most secondary students feel it is important to do well in mathematics. However, not very many students wanted a future job that used mathematics, nor thought that doing well in mathematics was important for their future employment. Tapia and Marsh (2004) state that "students may find math to be simply unappealing or socially unacceptable, although they may actually have high aptitude." These two issues are quite different. If students find the subject matter of mathematics to be unappealing, then teachers (and mathematics education researchers) need to explore methods for making mathematics more appealing. However, if students find the doing of mathematics itself socially unacceptable, that poses a much greater challenge.

In fact, research has found that students' peers are influential in causing students not to pursue mathematics in school (Day et al., 1992; Kindermann, 1993). Eccles and Jacobs suggest that "social and attitudinal factors have a greater influence on junior and senior high school students' grades and enrollment in mathematics courses than do variations in mathematical aptitude" (1986, p. 370). However, other research has shown that school mathematics and everyday mathematics have various differences, even including some people's ability to do one type and not the other (Lave, 1988).

In summary, the vast research on teachers' attitudes about mathematics does not transfer to society's attitudes about mathematics ignorance, nor does the vast research on students' attitudes about school mathematics transfer to their attitudes about mathematical ignorance. Recent research (Tapia & Marsh, 2004) demonstrating social pressure on students to not learn mathematics is quite related to the current study, which proposes to further the body of research by examining the question: Do undergraduate students find it more embarrassing to make a mathematical or a nonmathematical mistake?

Sample and Methods

A survey was constructed and administrated to undergraduate students at a Midwest university. The survey consisted of eight situations; four in which the person found him or herself lacking mathematical skills and four in which the person found him or herself lacking language skills. The four mathematical situations involve real-life situations (i.e., figuring out tips, making change, finding a sale price, and figuring out interest) that involve fairly simple mathematics (i.e., subtracting, adding, and multiplying). The involved mathematical concepts are very easy on three of the four situations (with the most difficult being finding a percent) and a little more difficult in one situation (finding interest).

The four non-mathematical situations involve real-life situations (i.e., visiting with friends, writing a letter, reading a passage at a meeting, and talking with a business acquaintance) that involve fairly simple language/communication skills (i.e., vocabulary, grammar, written skills, and verbal skills). The involved language concepts are very easy on three of the four situations (with the most difficult being grammatical) and a little more difficult in one situation (writing a formal letter). The survey was created for the purpose of this study and tested for validity and reliability. Full validity and reliability results are available from the author. A short summary is given here. A survey with nearly 100 situations (50 mathematical and 50 non-mathematical) was given to professors of mathematics, professors of language, and professors of disciplines not related to either mathematics or language (n=30). A short-answer question was placed on the survey simply asking the professors if they would feel a social stigma if they lacked mathematics or language skills. The professors were also asked to rate the difficulties of the involved situations. The attempt was not to have all situations of equal difficulty, but to allow for enough easy situations that students were not selecting based solely on difficulty. In addition, it was desired that each mathematical situation had a parallel language situation. A similar process was followed using a student sample (n=50), but the students were not asked about social stigma. However, the students were interviewed after taking the survey, and the investigator made a judgment as to whether the survey had accurately represented the students' views. Adjustments were made, including all but 8 items eliminated. The final version was then given to a subgroup of students (n=203) twice (one month apart) and a test-retest measure of reliability was calculated at .73. In addition, this final subgroup was asked to comment on the survey, given that its objective was to measure whether students found mathematical or non-mathematical situations more embarrassing.

The surveys were evaluated by tallying the number of first, second, and third place votes for each item. Chi-square analysis was run to determine whether the data was significant or obtained by chance selection. Survey responses were also separated by gender and major. All large lecture sections across the campus were targeted. All students present in these classes were asked to complete the survey, although numerous people turned in a blank survey or turned in nonsense results (e.g., circling all answers). Those responses (n=15) were eliminated. The process resulted in 1004 completed (and not eliminated) surveys, with slightly over fifty percent (n=504) female respondents and slightly under fifty percent (n=500) male respondents. The campus had an enrollment at that time of 10,127 students of whom 49.7% were female and 50.3% were male.

In addition to asking students their gender, they were asked to indicate their major. The majors followed fairly close to the campus distribution of majors, with 55 percent from humanities, 22 percent from science, 16 percent from business, 4 percent from mathematics/teaching mathematics, and 3 percent from communication. The actual campus distribution is 55 percent from humanities, 18 percent from science, 20 percent from business, 3 percent from mathematics/teaching mathematics, and 4 percent from communication (this data was taken from an internal campus data book). Thus, the gender and majors in this study are consistent with university-wide gender and majors, and the assumption that the sample fairly represents the campus is well met.

Results

Although all the analysis was run with student responses separated by gender, this was not a statistically significant factor. In addition, the student's major was never a statistically significant factor. (It seemed surprising that major was not a significant factor, as we hypothesized that mathematics majors would value mathematical situations.) However, Chi-square analysis does show statistically significant differences (with p-values less than .01) on all tallies of first, second, and third place. Recall that four of the eight items were of a numeric nature and asked students to identify their comfort when confronted with situations such as the inability to successfully calculate change or calculate the sale price of an item. The remaining four items could be placed into a linguistic category and asked students to identify their comfort when confronted with situations such as the inability to pronounce a word or to use correct grammar.

In all cases, most students chose linguistic options as their first, second, or third place choice. Sixty-nine percent of the respondents selected a language situation as the most embarrassing (with the remaining 31% selecting a numeric situation). Sixty-one percent of the respondents selected a language situation as the second most embarrassing (with the remaining 39% selecting a numeric situation). Finally, 65% selected a language situation as the third most embarrassing (with the remaining 35% selecting a numeric situation). These percents are particularly high when one realizes that the number of language situations decreases for a student who continues to select a non-mathematics situation. For example, if a student selects a non-mathematics situation for the most embarrassing and the second most embarrassing, then that student has a choice from two non-mathematics situations and four mathematics situations to select as the third most embarrassing situation. Yet, the percents remain quite high (again, they are 69% non-mathematics for first choice, 61% non-mathematics for second choice, and 65% non-mathematics for third choice). In the linguistic category, 74% of the sample selected mispronouncing a word at a meeting as their first, second, or third choice of most embarrassing. Other options were also popular, with 52%, 36%, and 33% of the students choosing the remaining three linguistic options, respectively, as one of their top three choices. Thus, even the least popular linguistic choice was chosen by 33% of the students.

Although the majority of students identified linguistic options as most embarrassing, a substantial number of students identified one of the numeric situations as embarrassing. Sixty-six percent of the students would find it embarrassing to be unable to make correct change (i.e., 66% of the students choose that situation as either first, second, or third most embarrassing). The remaining three numeric situations did not seem to strike students as embarrassing. The percent of students choosing the remaining three numeric situations as one of their top choices was only 11%, 12% and 13%, respectively.

Thus, a linguistic situation (mispronouncing a word at a meeting) was the most frequently identified choice of an embarrassing situation, being identified by 74% of the students. A mathematics situation (not being able to make change) was the second most frequently identified choice of an embarrassing situation, being identified by 66% of the students. The remaining three linguistic situations were the next most frequently identified choices (with the percents of students selecting them 52%, 36%, and 32%, respectively). At a considerable distant are the remaining numeric choices (11%, 12%, and 13% of the students selecting each).

It seems clear that the making change situation is different from the other mathematics situations. Since all eight of the situations were public in nature (others would view the mistake, thus leading to the public embarrassment), one can only surmise that it was the apparent everyday nature of working with money or the apparent easiness of making change that would lead to it being more embarrassing than the other mathematical situations. Yet, recall that the situations were paired, linguistic and numeric, through the pilot/validity study for difficulty, with three easy linguistic, one difficult linguistic, three easy numeric, and one difficult numeric. Therefore, although easiness may be an explanation for finding the making change situation embarrassing, it still does not explain why so many students choose the remaining linguistic options over the remaining numeric options.

Conclusion

The survey results seem to support that it is less embarrassing to lack mathematics skills than it is to lack language skills. When we began this study, we hypothesized that students majoring in mathematics (perhaps more so than those majoring in other fields) would report feeling embarrassment over making mathematical mistakes. However, major was not a significant factor. Our results indicate that even mathematics majors (and certainly other majors) do not find mathematical mistakes embarrassing, or at least they rank language mistakes as more embarrassing. If society does not care about mathematics ability, K-12 grade mathematics teachers certainly have their work cut out for them. Yet, the survey may reveal the direction that K-12 grade mathematics teachers and mathematics curricula directors must turn. Students did find it embarrassing to be unable to make change. Something about this situation made it important. We have hazard a guess that it was the ease and everyday nature of the situation that caused students to want to be able to make change correctly. Yet, other mathematical concepts (such as figuring a tip) were not valued (but were rated as easy in the validity study). We could continue to guess at why making change is more valued than figuring out a tip, but what is, perhaps, more constructive is to turn our attention to how mathematics could be presented to students so that it is all viewed in the same manner as making change is viewed (e.g., not only easy, but everyday). Said another way, K-12 grade mathematics should be presented in such a manner that students view it as basic life skills (making change being one such example). Until mathematics is viewed this way, there will remain little incentive for some students to master it.

Note

Readers interested in additional research details, such as from the validity study, may contact the author, Carmen M. Latterell, via e-mail ([e-mail]) or postal letter (140 Solon Campus Center, 1117 University Drive, Duluth, Minnesota, 55812).

References

Boaler, J. (1999). Participation, knowledge and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40, 259-281.

Beder, H. (1991). The stigma of illiteracy. Adult Basic Education, 1(2), 67-78.

Cooney, T. J., & Shealy, B. E. (1997). On understanding the structure of teachers' beliefs and their relationship to change. In E. Fennema & B. S. Nelson (Eds.), Mathematics teachers in transition (pp. 87-109). Mahwah, N J; Lawrence Erlbuam Associates.

Day, J. D., Borkowski, J. G., Dietmeyer, D. L., Howsepian, B. A, & Saenz, D.S. (1992). Possible selves and academic achievement. In L. T. Winegar, & J. Valsiner (Eds.), Children's development within social context: Vol. 2. Research and methodology (pp. 181-201). Hillsdale, NJ: Erlbaum.

Eccles, J., & Jacobs, J. (1986). Social forces shape math attitudes and performance. Signs: Journal of Women in Culture and Society, 11(21), 367-380.

Goffman, E. (1963). Stigma. Englewood Cliffs, NJ: Prentice-Hall.

Greer, B., Verschaffel, L., & De Corte, E. (2002). 'The answer is really 4.5': Beliefs about word problems. In G. C. Leder, E. Pehkonen, & Torner, G. (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 271-292). London: Kluwer Academic Publishers.

Kindermann, T. A. (1993). Natural peer groups as contexts for individual development: The case of children's motivation in school. Developmental Psychology, 29, 970-977.

Kloosterman, P., Raymond, A. M., & Emenaker, C. (1996). Students' beliefs about mathematics: A three-year study. The Elementary School Journal, 97(1), 39-56.

Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge, England: Cambridge University Press.

Lester, F. (2002). Implications of research on students' beliefs for classroom practice. In G. C. Leder, E. Pehkonen, & Torner, G. (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 345-353). London: Kluwer Academic Publishers.

Manor-Bullock, R., Look, C., & Dixon, D. (1995). Is giftedness socially stigmatizing? The impact of high achievement on social interactions. Journal for the Education of the Gifted, 18(3), 319-338.

McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 575- 596). New York: Simon & Schuster Macmillan.

National Council of Teachers of Mathematics. (2000). Principles and standards of school mathematics. Reston, VA: Author.

Senk, S., & Thompson, D. (2003). Standards-based school mathematics curricula: What are they? What do students learn? Mahwah, NJ: Lawrence Erlbaum Associates.

Singh, K., Granville, M., & Dika, S. (2002). Mathematics and science achievement effects of motivation, interest, and academic engagement. Journal of Educational Research, 95(6), 323-332.

Tapia, M., & Marsh, G. E. (2004). An instrument to measure mathematics attitudes. Academic Exchange Quarterly, 8(2), 16-21.

Carmen M. Latterell, University of Minnesota Duluth

Latterell, Ph.D., is Assistant Professor of Mathematics in the Department of Mathematics and Statistics.