Students’ Reasoning for Fleeing MathematicsRelated Fields
Greta Flaaten
I. Introduction and Reasoning for the Study
After Sputnik, it was the mission of the United States to improve the mathematics and science programs in order to become the international leader of technology and science. The government did not have the authority to directly change the mathematics curricula, so it gave incentives to modify mathematics in the schools in order to better prepare students for further mathematics courses. The changes were in the content and pedagogy of mathematics, as well as in the other sciences.
This concern continued, so President George Bush in 1990 challenged the US schools to be number one in mathematics by the year 2000 (3). However, in 1999, the Third International Mathematics and Science Study found that US 12^{th} graders ranked 19 out of 21 countries in mathematics (2). Evidently, Bush’s goal was not achieved.
The fact that students are unprepared in mathematics will dramatically show its face in due time because the true crisis at hand is that 2 million engineers, scientists, and technologists will retire in 2009. There will not be enough graduates with a strong mathematics background to replace these retirees and to fill new positions as a result of a growing society, both technologically and populationwise. It has been suggested that students do not pursue mathematicsrelated careers because they are not well prepared in mathematics when they enter college (1).
If the demand is clearly there, then why are college students not viewing these fields as windows of opportunity and instead choosing to steer clear of plentiful mathematicsrelated career choices? The purpose of this research is to better understand the factors before college, beyond being unprepared, that influence students’ college course taking and career choices.
II. Gathering the Data
The study included a sample of 39 students attending the University of Arizona pursuing mathrelated fields and 55 students pursuing non mathrelated fields. The following report will refer to “students of mathrelated fields” by the abbreviation smf and “students of nonmathrelated fields” by snmf. A comparison between perceived experiences of smf and of snmf is of interest in order to better understand the reasons behind students’ decisions to opt out of mathematicsrelated careers.
The criteria for categorizing fields as math related is if the major for the career goal requires at least Vector Calculus. Therefore, it was logical to administer the questionnaire in Vector Calculus and in Calculus I classes, for Calculus I consisted of many students on track for mathrelated fields. From the above criteria of mathrelated fields, nonmathrelated fields consisted of all other career goals. Other logical mathematics courses for administering the questionnaire that generally do not consist of smf were Elementary Mathematics and College Algebra. College Algebra is a requirement to all majors for graduation and solely students of Elementary Education take Elementary Mathematics.
Students of Vector Calculus, Calculus I, Elementary Mathematics, and College Algebra volunteered to complete a multiplechoice questionnaire (Appendix A) that was designed to determine the type of experiences they had in high school mathematics. The questions more specifically involved students’ confidence level (Appendix A: questions12), preference level (Appendix A: questions 3), experiences (Appendix A: questions 46), influences (Appendix A: questions 7, 1217), and level of understanding of mathematics and study of mathematics (Appendix A: questions 811).
The questionnaires completed were separated by smf and by snmf based on the career goal indicated by the student, and the responses were tallied and displayed in a table. See Appendix B for smf and Appendix C for snmf. To make sense of the data, the tallies were converted into percentages. The percentages helped to compare the separate findings and to then make insightful conclusions.
One obvious indicator of students’ level of preparation in mathematics is to inquire about their perceived understanding of mathematics and method of studying mathematics. It is no secret that smf generally grasp mathematics with less effort than snmf. The results of the survey show that 36% of smf reported that they always understood mathematics concepts without working hard. On the other hand, only 5% of snmf felt the same. Obviously the responses of time spent on homework reflect a similar theme. 39% of smf suggested math homework took very little time, even less than homework of other content areas. Only 7% of snmf reported the same experience. It seems trivial to point out that students who understand mathematics and are privileged to spend less time on homework are more likely to select a mathematicsrelated field.
A less obvious factor that directly relates to students choosing a certain career is their confidence level in mathematics. Snmf have an overall low confidence in their ability to understand mathematics compared to smf. 34% of nonmathematics students expressed nervousness or lack of emotion when confronted with a mathematics problem because of previous failures. In comparison, only 3% of smf are nervous when confronted with a math problem. Initial feeling indicates how one perceives his/her mathematical ability. A difference of 31% reflects that snmf generally perceive themselves with a low ability in mathematics, and this selfcriticism definitely affects their decision to not choose a career that involves more mathematics.
The preference level of snmf is generally low compared to smf. 80% of snmf express a low preference of mathematics compared to other content areas, of which 23% claimed they preferred mathematics the least compared to other subjects. In comparison, 39% of smf express some level of low preference. Preference level is important because it reflects how students enjoy and appreciate mathematics; it does not express the success of a student. If it is a preferred subject, then it is common knowledge that students are more likely to pursue a career that is mathematics related.
Another factor that could affect one’s career choice is his/her experience with learning mathematics, i.e., how students were taught mathematics. Since Sputnik, the US has concentrated on changing the pedagogy of mathematics, so this data interestingly reflect the studentperceived impact of the change. 86% of snmf believed the experiences they had in mathematics were effective at least more than half the time. Likewise, a high percentage, 97%, of smf believed similarly. This implies that teachers generally use an appropriate type of presentation to meet the needs of snmf and smf alike. As far as implementation, teachers meet the needs of most of their students, so this is not the key to students selecting mathematicsrelated fields.
Finally, students in adolescence are in the process of being molded, and influences in a general sense play a large role because students are in the middle of selfdiscovery and examining possible life paths. The biggest overall influence to adolescent students is their peers. However, according to the data, peers do not have an apparent, significant role with respect to the learning of mathematics.
Another role in the school setting is the guidance counselor, the individual who organizes a student’s coursework. According to student responses, he/she plays a small role with respect to actually influencing a student’s coursework. The questionnaires of both subject groups express the same notion that the guidance counselor does not play a role. Even more surprising, less than 9% of both groups suggest that their guidance counselor encouraged them to take mathematics all four years of high school and to continue taking mathematics in college. That small percentage is shocking because universities require four years of mathematics for admittance. Furthermore, without those four years of mathematics credit, students are not well prepared to take further courses in mathematics. Here is one possible reason why students are not well prepared in mathematics and so do not pursue mathrelated fields. Because both subject groups expressed similar experiences, it could be that was by chance that students chose mathematicsrelated fields. This negative influence suggests that more work needs to be done with guidance counselors to help them guide students into taking mathematics.
Another expected influence on adolescent students is their parents. However, the questionnaires reflect that snmf and smf received a similar level of parent involvement. This was unexpected because it is believed that parents have a strong role in the education and the future of a student. Parents do have a strong role in sense that they are supportive and expect their child to do equally well in all content areas. The little difference of parent involvement does indicate that parents do not have an influence in persuading their child to specifically enter in a mathematicsrelated field.
However, a powerful influence, both positive and negative, is one’s teacher in the pursuing of mathematics. 49% of snmf believe that their teachers had a negative impact on their attitude towards mathematics. In contrast, 23% of smf believe their teachers made a negative impact. The attitude of a student towards a content area is vital because no person in the right mind would choose a career to which they possess a negative attitude. It would not be an enjoyable experience. On the contrary, 1/3 of mathematics students expressed that their teachers personally influenced them to pursue mathematics. This indicates that teachers do have a profound impact. It was previously reported above that teachers’ pedagogy might not be the factor that persuades one to a math field because both groups had a majority claim the right type of implementation met their needs. Other factors besides pedagogy seem to be in play, but this questionnaire was not constructed to uncover those.
V. Concluding Thoughts
The purpose of this study was not to find means to encourage all students to enter mathematicsrelated fields, but rather to find factors that might contribute to the shortage of students entering mathrelated fields. These factors will hopefully inform educators so that students are soon given the preparation and encouragement to strongly consider selecting a mathematicsrelated career. The data without analysis have the potential to present different meanings to each individual, just like a song. Thus, the following paragraphs are my interpretations and suggestions to educators on how to attack this serious shortage.
Cooperative learning is a teaching tool that increases the chance of students receiving oneonone interaction with their teacher. Also, the teacher takes many roles in this teaching style because students play the role of teacher with each other. The grouped students work together in order to accomplish a proposed task and, so, are more likely to experience success. It is evident that the level of success relates to one’s confidence level, which is a determinant of students entering paths to mathrelated fields.
Guidance counselors must support and verbally encourage students to take four years of mathematics credit in high school. Teachers understand the vitality of taking mathematics throughout high school, so the constant communication between teacher and guidance counselor could benefit the students by having two forces of encouragement. It is a simple task that will brighten more students’ futures only because they have the preparation and meet the criteria for more opportunities.
Most importantly, mathematics must be an enjoyable experience! The fact that students may show success in mathematics does not directly indicate that they enjoy it. An enjoyable experience simply means that the time passes at a good rate, that the classroom environment is positive, or that the students are always learning and feeling successful. It is crucial to make mathematics a preferred subject by incorporating student interests into lessons. Mathematics exists everywhere in this world, so it is achievable to bring any interest into the classroom.
References
1. Murnane, Tom. “Summit to Shine Spotlight on Academic, Industrial ‘Brain Drain.”
The
Business Review 15 Oct. 2001.
www.bizjournals.com/albany/stories/2001/10/15/story8.html
2. “SchooltoCareers Sparks Higher Student Achievement in Math and Science.”
The Employer Focus Vol. 1, Issue 2 (1999): 1.
Questionnaire
Major: ____________________________________
Career Goal: _______________________________
1. When you are confronted with a mathematics problem, what is your initial feeling?
a. Without emotion because you feel that it is likely it will be impossible to solve
b. Nervous and/or anxious because you know that you always struggle
c. Calm and willing to try, but you do not know if you are capable
d. Calm and willing to try due to successful experiences in the past
e. Eager and you perceive it as an enjoyable challenge
2. In your high school mathematics classes, generally what were your experiences most like?
a. Experienced few to no successes throughout and, therefore, did not care about mathematics
b. Experienced few to no successes but still tried to do well
c. Experienced few successes early on and then more successes later on
d. Experienced success early on and then fewer successes as math classes became more advanced
e. Experienced success throughout high school
3. How would you compare your preference for mathematics with other subjects you took in middle and high school?
a. Preferred mathematics over all other subjects
b. Mathematics was rated high with other subjects
c. Preferred mathematics some years and not other years.
d. Mathematics was rated low
e. Preferred all other subjects over mathematics
4. How were mathematical concepts presented to you in the middle and high school classroom? (select all that apply)
a. Lecture
b. Guided Discovery/Inquiry
c. Problem Solving
d. Handson i.e. use of manipulatives
e. Technology i.e. graphing calculators or computers
5. How effective were the above experiences on your learning mathematics?
a. Always effective
b. Mostly effective
c. Effective about half the time
d. Almost never effective
e. Never effective
6. Did the type of presentation of mathematics concepts cater to how you learn best?
a. Yes
b. No
7. Overall, who affected your decision to pursue or not pursue mathematics?
(select
all that apply)
a. Myself
b. My parents
c. My teachers
d. My peers
e. My guidance counselor
8. How did you grasp mathematical concepts in high school?
a. Never understood mathematics because I did not try or care
b. Rarely understood mathematics even though I tried hard
c. Sometimes understood because I always received tutoring help
d. Most of the time and with the same effort as for any other subject
e. Always understood because I never had to work hard to understand math
9. How long would it take to complete your math homework in high school?
a. Took hours every night; more than any other subject
b. Took about the same time as homework in other subjects
c. Took very little time; less time than other subjects
10. How would you describe the homework in your high school mathematics courses?
a. All busy work; problems that did not serve any purpose
b. Excessive; too many unnecessary problems
c. Manageable and almost always useful to my learning of mathematics
d. Very useful; problems served a purpose and helped my learning of mathematics
11. How did you prepare for mathematics tests?
a. Only memorized formulas
b. Memorized formulas and did practice problems
c. Only did practice problems
d. Learned how to derive the formulas if needed
e. Did not prepare for tests
12. Do you feel like some teachers personally influenced you to pursue mathematics?
a. Definitely
b. Slightly
c. Never
13. In general, what kind of impact did teachers have on your attitude towards mathematics?
a. Caused me to always feel frustrated
b. Caused me to feel that mathematics is too hard for me
c. Caused me to resent mathematics
d. Influenced me to appreciate mathematics
e. Influenced me to enjoy and pursue mathematics further
14. How were your parents involved in your learning of mathematics in high school?
a. Never involved; I worked independently on my math assignments
b. Sometimes involved; only if I asked them a question
c. Frequently involved; they volunteered to help me or to find someone that could help me so that I would succeed in learning mathematics
15. What was the level of expectation your parents had for your math classes?
a. There was no level of expectation.
b. They expected me just to pass the course.
c. They expected me to do equally well in all course areas.
d. They had high expectations; I was always to get an A or B in mathematics.
16. How did your peers in high school play a role in your learning of mathematics?
a. They did not play a role.
b. They discouraged me from taking an interest in mathematics.
c. They offered verbal encouragement.
d. They tutored me so that I could succeed in learning mathematics.
17. How did your high school guidance counselor play a role in your learning of mathematics?
a. He/she did not play a role.
b. He/she did not encourage me to take mathematics in high school.
c. He/she offered me information, but did not advise one way or the other.
d. He/she encouraged me to take four years of mathematics in high school and to continue taking mathematics in college.
? Number 
A 
B 
C 
D 
E 
Sum 

1 

1 
16 
12 
10 
39 

2 

4 
4 
12 
19 
39 

3 
6 
14 
13 
5 
1 
39 

4 
26 
11 
29 
5 
19 
90 

5 
2 
27 
9 
1 

39 

6 
26 
11 



37 

7 
38 
9 
10 
2 
1 
60 

8 

1 
3 
21 
14 
39 

9 
5 
19 
15 


39 

10 
1 
13 
22 
2 

38 

11 
1 
21 
7 
3 
5 
37 

12 
13 
14 
12 


39 

13 
2 
1 
6 
23 
7 
39 

14 
15 
20 
4 


39 

15 
2 
2 
19 
16 

39 

16 
27 
1 
8 
3 

39 

17 
29 
1 
6 
3 

39 

























? Number 
A 
B 
C 
D 
E 



1 

2.56% 
41% 
30.77% 
25.64% 



2 

10.26% 
10.26% 
30.77% 
48.72% 



3 
15.38% 
35.90% 
33.33% 
12.82% 
2.56% 



4 
N/A 
N/A 
N/A 
n/A 
N/A 



5 
5.13% 
69.23% 
23.08% 
2.56% 




6 
70.27% 
29.73% 






7 
N/A 
N/A 
N/A 
N/A 
N/A 



8 

2.56% 
7.69% 
53.85% 
35.90% 



9 
12.82% 
48.72% 
38.46% 





10 
2.63% 
34.21% 
57.89% 
5.26% 




11 
2.70% 
56.76% 
18.92% 
8.11% 
13.51% 



12 
33.33% 
35.90% 
30.77% 





13 
5.13% 
2.56% 
15.38% 
58.97% 
17.94% 



14 
38.46% 
51.28% 
10.26% 





15 
5.13% 
5.13% 
48.72% 
41.03% 




16 
69.23% 
2.56% 
20.51% 
7.69% 




17 
74.36% 
2.56% 
15.38% 
7.69% 








































Appendix
C
? Number 
A 
B 
C 
D 
E 
Sum 

1 
2 
16 
17 
17 
2 
54 

2 
2 
12 
7 
16 
19 
56 

3 
3 
8 
16 
16 
13 
56 

4 
43 
17 
43 
16 
32 
151 

5 
3 
27 
18 
8 

56 

6 
35 
19 



54 

7 
52 
1 
11 


64 

8 

12 
9 
31 
3 
55 

9 
19 
32 
4 


55 

10 
5 
22 
25 
3 

55 

11 
3 
38 
4 
1 
8 
54 

12 
10 
20 
26 


56 

13 
6 
9 
12 
24 
4 
55 

14 
19 
27 
9 


55 

15 
4 
8 
30 
14 

56 

16 
30 
1 
14 
10 

55 

17 
44 

7 
5 

56 

























? Number 
A 
B 
C 
D 
E 


1 
3.70% 
30% 
31% 
32% 
4% 


2 
3.57% 
21.43% 
12.50% 
28.57% 
33.93% 


3 
5.36% 
14.29% 
28.57% 
28.57% 
23% 


4 
N/A 
N/A 
N/A 
N/A 
N/A 


5 
5.36% 
48% 
32.14% 
14.29% 



6 
64.81% 
35.18% 





7 
N/A 
N/A 
N/A 
N/A 
N/A 


8 

21.82% 
16.36% 
56.36% 
5.45% 


9 
34.55% 
58.18% 
7.27% 




10 
9.09% 
40.00% 
45% 
5.45% 



11 
6% 
70% 
7% 
2% 
15% 


12 
17.86% 
35.71% 
46% 




13 
10.91% 
16.36% 
21.82% 
43.64% 
7.27% 


14 
34.55% 
49% 
16.36% 




15 
7.14% 
14.29% 
53.57% 
25.00% 



16 
54.55% 
1.82% 
25.45% 
18.18% 



17 
78.57% 

12.50% 
8.93% 


































