Success Factors of Calculus

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SUCCESS FACTORS OF CALCULUS:

HISPANICS VERSUS WHITE NON-HISPANICS

by

SHIRLEY ALLENE DAVIS, B.S.

A THESIS

IN

MATHEMATICS

Submitted to the Graduate Facultyof Texas Tech University In

Partial Fulfillment ofthe Requirements for

the Degree of

MASTER OF SCIENCE

Approved

Accepted

Dean of the Graduate School

December, 2001


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:^*^^ ACKNOWLEDGEMENTS 'f-C.

^ ^ I would like to thank Dr.Jat .es Epperson for his tinte and effort . init.attng th.s

project. I also appreciate the patience and assistance I received from D r. Benjamin Duran

and Dr. Carl S eaquist. Above all, I want to thank the chair of my comm ittee, Dr. Gary H arris

who at an inconvenient time inadam antly took the responsibility and nurture ofmy thesis. If

it was not for him, I would still be working on this thesis today. Thank you from the bottom

of my heart.

I also extend thanks to all of my friends, family, and, especially, classmates who have

supported me through this graduate school experience. I, especially, appreciate the patience,

understanding, and support from my closest friends, Leah, Traci, Richard, Ruby, and

Am anda during the numerous time s when I was certain there was no end in sight. Man>

thanks also goes to Texas Te ch's Ultimate Frisbee team for allowing me to use you all as an

emotional punching bag.

I also would like to thank Jim for re-introducing m e to Christ. Somew here along the

way, I became spiritually lost wandering aimlessly with despair, and although it occurred at

the tail end of my graduate school experience, I have found Christ again which has allowed

me to find myself Thanks Jim.

Finally, I thank G od. I know through him , I have the ability to do anything.

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http://jat.es/http://jat.es/


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TABLE OF CONTEXTS

^

ACKNOWLEDGEMENTS ii

ABSTRACT v

CHAPTER

I. INTRODUCTION 1

II . LITERARY REVIEW 3

IIL METH ODO LOGY 11

r / . RESULTS 13

4.1 Interviews from Group A 13

4.LI Student A 13

4.1.2 Father A 22

4.1.3 Teache r A 26

4.2 Interview s from Group B 31

4.2.1 Student B 31

4.2.2 Fathe r B 42

4.2.3 Teache r B 4"

V. CON CLUSION S 54

5.1 Analysis of Interviews 54

5.1.1 Student A 54

5.1.2 Student B 56

3.2 Conc lusion 58

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REFERENCES 60

APPENDIX 62

A. QUESTIONS FOR STUDENTS 63

B. QUESTIONS FOR PARENTS 66

C. QUESTIONS FOR TEACHERS 68

IV


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ABSTRACT

In this study we are interested in those social and academic factors that might

contribute to success in college level calculus for Hispanic students. In particular how do

these factors compare with success factors for white non-Hispanic students. Via in-depth

case studies we attempt to isolate and compare such factors for two students, one Hispanic

and one white non-Hispanic, who successfully completed a one year calculus sequence at a

large state comprehensive university.


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CHAPTER I

INTRODUCTION

Students who perform successfiiUy in calculus tend to have strong study habits,

adequate m ath preparation prior to college matriculation, and positive influences such as

mentors and/or supportive parents. Statistically, among these students, very few Hispanics

appear with the vast majority being white non-Hispanic. This raises an obvious question: To

what extent do the factors that contribute to success in calculus for Hispanic students differ

from those that contribute to the success in calculus for white non-Hispanics?

Prior research has explored the challenges and resources related to Hispanic culture,

language, and economic status in attempts to examine the structural phenomena that

contribu te to Hispanic marginalization w ithin the institutions and its potential effect on

academ ic performance . The research identified faculty contact and men toring, social and

academic integration, parental and sibling influence, and, of course, study habits as the main

factors that affect the achievement in calculus for Hispanic students, jus t as for non-Hispanic

students.

Among these selective factors, one ofthe more reoccurring and popular factors is

faculty involvem ent. It is felt that faculty role modeling positively affects stude nts'

attainment and retention in college. Although high school faculty is seen as an influential

factor in preparing students for college matriculation and math/science majoring, college

faculty interaction is viewed as a primary factor for college retention.

Additionally the research strongly suggests that social, as well as academic,

integration into the university are necessary for students' persistence in college through


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degree co mpletion . In this context social integration involves faculty interaction, peer

relation s, and involvem ent in extracurricular ac tivities. Again, are these factors of equal

importance for Hispanic students as for white non-Hispanic students?

In this study we are interested in those social and academic factors that might

contribute to success in college level calculus for Hispanic students. In particular how do

these factors compare with success factors for white non-Hispanic students? Via in-depth

case studies we attempt to isolate and compare such factors for two students, one Hispanic

and one white non-Hispanic, who successfully completed a one-year calculus sequence at a

large state comprehensive university.


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CHAPTER II

LITERARY REVIEW

We summarize those studies from the literature which we feel ha\e been in our study.

In a seminal paper, Treisman [1992] conducted a comparative smdy between 20

Chinese and 20 Blacks. He was interested in these two ethnic groups because the Ch inese

excelled academically in mathematics while the Blacks perpetually struggled in this area. He

discovered that the amount of time the Chinese studied was nowhere near important as how

they studied. The Ch inese devoted just a couple more hours a week studying more than the

Blacks but their most successful studying tool was that they spent some of that time stud\ ing

in groups. This discovery exp lained the minorities ' lack of success in calculus far better than

the other preconceived beliefs such as inadequate preparation, motivation gap, lack of family

support or understanding of higher education, and income . After realizing the effects of

these studying skills, Treisman's efforts turned towards constructing an anti-remedial

program for students providing not only tutoring, time management, and study skills but.

also, a challeng ing, yet emotionally supportive academic environm ent. In his attempts to

assist and help these students, he had to convince them that success in college required peer

group working and studying so as to create for them a community based on shared

intellectual interests and common professional aims.

In their 1997 study, Terenzini and Pascarella [1997] studied freshman attrition for a

random sample of 500 students in the College of Arts and Sciences at Syracuse University.

In particular, they w ere interested in patterns of social and academic integration that

contributed to studentsw ithdrawing from or rema ining in their classes. Students rem aining


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in their classes were called "stayers." They found that stayers reported more informal

contact with faculty members outside the classroom and their nonacademic li\ esw ere more

demanding than that of leavers. Also stayers were more involved in the social system of the

university. Their results tended to support Tinto's [1975] view that social and academic

integration are approximately of equal importance in students' decisions to remain or

withdraw.

Mayo, Murguia, and Padilla [1995] examined the formal and informal social

integration among 400 students from Hispanic, Black, and Native American groups and 400

White students. They found that relationships with faculty and ethnically matched role

mod els are successful in contributing to academic achievem ent. They claim that formal

social integration has a much greater significance on the effects of academic performance

than informal. How ever, this is not necessarily so with Hispanics since their social life

impedes with their studies negatively affecting their academics. Neverthele ss, Hispanics do

consider student organizations as an important necessity for their existence and success in

college so Mayo, Murguia, and Padilla suggests that the development of well-organized

ethnic-specific student groups would prove beneficial to the minority groups on campus.

Gainen [1995] examined four factors that grant some students success and not others

who posses s similar ability and interest. She claims that the most limiting factor in a

student's academic success is insufficient or inadequate preparation in mathematics. Her

claim is supported when considering that ofthe HS graduates, only approximately one-fourth

have the sufficient mathematical and science preparation to proceed into SME majors in

college and among this one-fourth, only11 % of wom en compared to 14% of men have the

appropriate background in mathematics upon HS graduation.


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Students affiliated w ith peer culture that fa\'or academic pursuits are much more

likely to succeed in challenging majors, however, in contrast, when peers are uninterested in

academics, students find it difficuU to maintain momentum in the face of academic

challenges of SME majors.

Students often find themselves uncomfortable and alienated and yet are unable to

determ ine the cause . Gainen attributes these feelings ofthe students to the professor's low

expectations of minorities and their favoritism to the non-minorities.

In addition to these o\erbearing obstacles, students also complained of unstimulating

introductory SME cou rses, bad teaching, poor advising, and unhelpful faculty. Again.

Gainen has shown that faculty plays an important role in the attraction and retainment of

students in SME majors, and proclaims that success of these students depends at least in part

on the willingness of faculty to resist cultural norms of competition.

In the secondary analysis study of Hedges and Nowell [1995]. six large data sets were

collected between 1960-1992. They found that although average sex differences are small,

females perform better in reading and writing whereas the males perform better in science

and math, and concluded, that the differences in ability arise because of differences in

experiences and socialization and not necessarily due to differences in sexes.

Rendon and Triana [1989] were interested in factors that impede Hispanic students

progress in science and mathem atics at the high school level. Am ong the factors they

isolated are the following:

1. Low socio-economic status

2. Poor academic performance

3. Nonparticipation in HS academic programs


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4. Academic related problems

5. Enrollment in remedial courses

6. Discriminatory practices

7. Mathem atics fear, anxiety, and avoidance

8. Curricu lar deficiencies

9. Teacher shortages

10. Low transfer from 2-year colleges to 4-year colleges.

Attinasi [1989] analyzed interviews with 18 Hispanic students from a single entering

class of a large public southwestern university 8 to 11 months following the end of their

freshman year. His intent was to identify, from the studen ts' point-of-view, factors that

affected their decisions to persist or not to persist in their university progra ms. He grouped

these factors into two categories: factors involved with getting ready to go to college and

factors involved with getting in. Getting ready involved initial expec tation, fraternal

influence, mentor influence, and direct and indirect simulation. Getting in involved physical,

social, and academ ic concerns. Being able to deal with the latter three was shown as a

positive relation to persistence.

Bennett and O kinak a's [1989] study was a revision ofa 1982 quesfionnaire

administered to an ethnically mixed sample in 1986 so as to compare characteristics of

persisters and nonpe rsisters and their attitudes and perceptions. Persisters pertain to students

who rem ained in college upon degree completion whereas nonpersisters are those who

withdrew before degree completion. They found that persisters, especially the Hispanics,

experienced more interracial contact prior to college and had more positive attitudestow ards

their college instructors than nonpersisters, and that involvement in ethnic organizations.


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accumulation of college friends, adjustment to college life, and openness to equity policies

were show n as predictors of college satisfaction among the persisters. Of all these factors,

students that felt the most positive about their college instructors were the m ost satisfied with

the university's social environment, administration, and classes.

In the case study paper, Galindo and Escamilla [1995] examined two Chicanos, one

male and one fem ale, through autobiographies, biographical sketches, and interviews in order

to analyze their educational experiences and the sociocultural factors that influenced those

experiences. The female, L inda contributes her good grades to her early foundation in learning

established in her home and at church and reports that her family highly supported her efforts

in education. Although she had the support of her family and church, she struggled w ith her

ethnic identity in HS and college. Due to her different cultural background and social

antagonism , she felt alienated in school and eventually in church. She contributes this

alienation to the lack of role models who could have provided an example of how other

minorities had negotiated the system. On the other hand, the male, Richard, was ridiculed in

HS for being culturally different making him feel alienated and socially outcasted. He learned

to overcome this in college and succeeded academically and socially. Although his father's

occupation w as not conducive to educational success, which alienated him from students and

teachers, his parents supported his education by allowing time for school and homew ork. They

also had all the children serve as tutors to one another including Richard. Besides the support

of his family, Richard also attributed his educational success to the impact that his pre-college

teachers had on his and his sibling's schooling. He mentions that these teachers were not just

exceptional but were ex traordinary since they were constantly going out of their way to help

educate Richard and his family.

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A sa mple of 100 Mexican-A merican undergraduate students that were divided into

two divisions: lower (age 18-21 ) and upper (age 20-30 ) were examined by Lopez [1995] in

this statistical pape r. He is particularly concerned with the age and gender patterns in the

perceptions of challenges and resources that stem from the family, peer relationships, and the

university. Upp er division males reported more challenges fi-om domestic responsibilities,

perceived m ore racial discrimination, and received more academic encouragement from

siblings and from m ale friends than lower division students. There were no age-related

differences found between the two divisions in their perceptions of challenges and resources.

Hilton and Lee [1988] studied the data obtained from two studies: one w hich

surveyed 23 ,500 high school seniors with follow up surveys every 2 years for 6 years, the

second a similar study begirming with high school sophomores. They found that most

students who choose to major in mathematics, science, or engineering (MS E) do so prior to

entering co llege. And by the first year of college H ispanic students are less likely to be

interested in majoring in MSE than either blacks or whites, while showing m ore interest in

MSE as high school sophomores.

Jay and D 'A ug elh 's [1991] study focused on assessing patterns of social support of

AA and W hite freshmen attending a predominantly W hite university and their adjustment to

university life. The ir participants included81 W hite and 84 African A merican freshmen

attending a 4-year institution. They found that predictors of adjustment were based on first

year college GPA, psychological well-being, and physical well-being.

Sax [1992] samples 15,050 students from 392 different 4-year universities. She was

interested in mathem atical self-concept development and its relation to institutional

selectivity. In her discoveries, men exhibited greater initial mathem atical self-confidence

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achievement orientation, disregard of sex role stereotyping, a development of better stud)

skills, and, mostly, encouragement in the exploration of nontradidonal interests.

Anderson [1990] summarized the efforts ofthe National Research Council's

Mathematical Sciences Education Board (MSEB) in eliminating the underachie\ement and

underreprese ntation of minorities in ma thematics. She found that the le\'el of parental

education is directly related to student performance, and poverty is directly related to

academic achievement.

Boli, Allen, and Payne [1983] looked at students in introductory mathematics and

chemistry courses at Stanford University in the fall of1997. They were interested in gender

related factors that migh t contribute to success or failure in such course. They found no

direct gender factors related to course performance; however, female students did appear to

perform somewhat better if they had female mathematics instructors.

Erekson [1989] studied 544 undergraduate students from a random sample of 100

students at Miami University to determine factors related to students grade point average

(GP A). He found that library effort and course selection did not significantly affect GPA,

but male students had significantly lower average GPA than did female students.

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Once the two students were chosen, personal and phone interviews were conducted

with the students, their fathers and their high school mathematics teache rs. All interviews w ere

audio recorded w ith the full know ledge and permission of each participant. The audio

recordings w ere later transcribed for future analysis. The students were interviewed in person

with both researche rs participating in the questioning of each student. These interviews lasted

approximately one hour each. The students were first asked for information regarding their HS

experience and then for information about their college experience. Information such as time

spent studying, me thods of studying, and external and internal influences towards education

was obtained. The student interview questions are included in Appendix A .

The interviews with the fathers were conducted over the phone by one researcher only.

They also lasted approximately one hour each and were audio recorded for later transcription.

The fathers w ere asked to discuss their prior knowledge and/or observation of their son 's

studying habits and behaviors w hile in HS, their contribution to their son 's education, and their

attitude towards math as well as education. Both fathers elaborated on most of the questions

and contributed additional comm ents outside the realm of our originally prepared questions.

The interview questions for the fathers are included as Appendix B.

Interviews with the teachers also were audio-recorded phone interviews conducted

solely one resea rcher and lasting approximately one hour each. The information obtained

from the teachers w as almost identical to that from the fathers. Questions focused on the

teachers' prior knowledge and observation ofthe their student's studying habits and

behaviors while in HS, their contribution to the student's education, what factors they think

lead to the success of that particular student and factors they believe contribute to the success

of students in genera l. The teacher interview questions are included in Appendix C.

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CHAPTER IV

RESULTS

4.1 Interview s from Group A

4.1.1 Results from Interview : Student A

Student A attended a large high school in which a majorit\ of the studentsw ere

Hispan ic; he graduated ranked 2 out of his class of527. He took AlgebraI in the 8* grade

followed by A lgebraII. geometr}.Trigonometry, and AP (Honors) Calculus in high school.

WTien asked to describe his high school prepara tion in mathem atics, he responded:

I wen t all thew ay through calculus I in high school. Ba sic alh . the mathpreparationI had was through UIL math. So starting in the 6 grade andthrough high school, I w as in the UIL m ath and science competition. Thatbasically prepared me through high school. My calculus professor in highschool was \e r\ good preparing us for college and calculus courses.

W hen asked if he wasalw ays good at mathem atics growing up, he responded with

"M ath has always been m y strong point. I like that subject."

One objective of the interviews with the students was to assess factors dealing with

their motivations for stud>ing mathematics and factors contributing to their confidence levels

with regard to mathem atics. We consider two types of such factors, internal and external.

Internal factors involve the students" personality types, learning styles, personal goals, etc.

External factors relate to the influence of mentors, family, peer groups, etc.

The following excerpts from the inter\iew with Student A relate prim arih with

internal factors. Personalit> traits are presented first followed by his learning and studying

habits.

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In regards to Student A's personality, the following quotes are presented.

Question: If I asked you how would you describe your moti\'ation level instudying mathematics in high school, would you describe as "high,""moderate," or "below average"? Why?

Response: Moderate in the amount that they wanted me to know but abo \ eaverage in the amount I wanted to know. I don 't think that in the high schoolsthat I have known or that I have been to or that I have competed that theyactually demand much ofyou. But in the competition like UIL, you shouldknow m ore. You are expected to know more.In just the mathematicsitself, itis intriguing study, and I like it so I delved into it further.

Question: If I were to ask you about your motivation level and said, "Wereyou motivated by your teachers, by your family, internally, or externally?"

Response: It was just basically just me. My motivation is self-induced.

Question: Would you describe your motivation level now in studyingmathem atics (in college) as "high," "moderate," or "below average"? Why?

Response: As a few months ago, above average.

Question: So last year, you would have considered it above average? Why?

Response: I was considered about moderate. For the past couple of monthsor several weeks, I would say above average.I just see the compelling needto do so. It's part of my field. Th at's what it is - mathem atics, appliedmathematics.

Question: So it is motivating you now because you want to understand it foryour career?

Response: Right.

Question: Would you describe yourself now as being internally m oti\ate d orexternally motivated?

Response: I say a little bit of both but more internal than anything else.

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Question: So you have a strong sense of competition?

Response: My dad tells me I do.

Question: Did you have any ideas about what mathematics in collegew ouldbe like?

Response: No I hadn 't really thought about it. When I was in the 6th grade, Inever thought about taking calculus.I just saw a book and saw all thesesymbols and never thought I would get there. ButI just took one course afteranother, and it just kind of snowballed, and I was just ready for the nextcourse.

Wh en asked what it is about mathematics that intrigues him and make him p ersevere,

he com mented, "I think I can do it. I know I can do anyone of these subjects. I don't think it

is beyond me to do anyone of these math problem s. Calculus III now I understand it. I

unde rstand pretty well now. It should be ok. Linear algebra, I don't know . The way it is

taught, it jus t seem s to be so abstract so theoretical. It seems to be beyond the scope of the

class of what it is suppose to be like."

In regards to Student A's learning style, the following quotes are presented.

Question: Did you feel any kind of pressure in high school to do well inmathematics that being from friends, teachers, or from parents, brothers, orsisters? Why or why not?

Response: I just basically saw everything as a little bit ofa competitionthrough out all the way we did it the valedictorian through like the 10th rank inour class. It was all very competitive. We all tried to outdo each other so wekept each other in check.

Question: Why do you say it was UIL that prepared m ore so than your highschool courses or than your mathematic courses?

Response: Because it was a competition. It was me against somebody else. 1like to do better than whoever else I am competing against.

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Question: There is something that satisfies you to know that on the test youbeat everybody else?

Response: In the begirming, I take the test or whatever as it com es. I get oneback, and it looks bad. I say that is not the grade I like, and it's m e against thetest now. It usually does better after that.

Question: You think of it as a competition with the material rather than acompetition with others?

Response: Yea.

Question: So, in other words, if you understand it than you are victorious?

Response: Right

Question: And that allows you to explain it others and that makes yo u...?

Response: Even better.

Question: W ould you describe the exams and homew ork assignments in highschool as challenging? W hy or why not?

Response: Not really. It just seemed like .... We did n't really put all oureffort into anything . I think that most of the effort or like many just about 20or 30% . It was adequate enough to go through all the tests. Through collegeso far, it has been the same way.

Question: Now , at the presence, do you feel some pressure to do well inmathem atics from your teachers, or instructors, or your parents?

Response: Again, from me and my grades.

Question: Did your confidence come from having done well or did it comefrom....?

Response: I think it comes from having done well m the past and expectingmyself to do w ell in the fiiture as w ell as the compe titive nature of the class:It's me v s. the class.

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Question: Do you have high expectafions of yourself?

Response: I think I do a little bit but it' s only at the point that I see it as acompetition. IfI don't see it as a competition then I don't put as much effortinto it.

Student A's studying style revolved around an individual effort with minor group

involvement both in high school and college. While in college in his calculus class. Student A

studied approximately 2 hours a week, however, this time was reserved only for exams. He did

not consider homew ork part of studying. He committed an hour to each homework assignment

and an hour and a half to group studying. His studying method involved working extra

problems concentrating on the conceptual problems. He would also read the sections in the

book and write formulas although he didn't particulariy appreciate the textbook due to the

excessive errors found and its literal construction. He preferred working/studying with

students who possessed the same intellectual ability as he or better, and he did not discriminate

among these intellectuals. How ever, he also tutored the mathematically underdeveloped

students because it reinforced his own knowledge and comprehension of the material. He

considered tutoring a better studying skill than individual studying. When engaged in group

studying, the group, which consisted of himself and his social group friends, would study in a

relaxed and casual atmosphere.

The following excerpts from the interview with Student A relate primarily with

external factors. The following interchange expands on the initial reference to his high

school calculus teacher:

Question: Who w as your favorite teacher and why in m athematics?

Response: I would have to say my calculus professor .. .(Teacher A below, amale H ispanic teacher who began his teaching career as a football and

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basketball co ac h) .. .He would assign homew ork but never take it up. Onlyquizzes and tests count so it kind of forced you to do your homew ork. Sothat's basically hke college.

Question: If you had to name a particular teacher/person who influenced youto pursue m athematics at the college level, who would it be? W hy?Response: .. .(Teacher A )... He just brings about the subject in the bestpossible way. He likes to show you more than what you need at the time. Heencourages you to think. He also is one of those where everyone should dobetter than the past generation. He reinforced family ideas.

Question: Somehow he comm unicated to you, that he had this hope that youwould go on do something more? Is that what you felt from him ?

Response: Right. I felt the same thing from him as my parents.

Question: W hat was it about him you liked other than that method?

Response: You could ask him any question, and he would hav e the answerfor you. It would n't matter what section, why, or the reasoning, proofs orwhatever. He had the answer for everything. He explained it quite clearly.

Question: So .. .(Teacher A ). .. inspired you to continue to study math?

Response: He did in a way he brought mathematics about. So for the mostpart, he made it a little bit more fim than any the other teachers have. Hecould answ er questions relevant to the things I talked about. He furthered theknowledge.

Question: How do you think your high school teacher became so good atmath? What theories did you have?

Response: I never really thought about it.I just thought it was pretty coolthat he knew so much math. I could ask him anything, and he would know theanswer. My other teachers could n't do that. Some of them if you took themout of the book, they got lost a httle bit but he could answer any question. Ithought that was very interesting.

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Question: Is your motivation level in college influenced by your instructors?Let 's talk about last year. Your motivation last year. Why or why not?

Response: I can't think ofa professor in college who has motivated meanym ore than I already am. It just seems to be icons just like giving out factsand figures.

Question: How is that different from high school?

Response: In high school, they give practical applications and show you whyyou might need it. It just seems like all the courses here are theoretical, youmigh t need this, you might not. W e'll teach you this just because. It justseems like that.

Student A w as curious about his HS teacher's decision to study m athematics, but he

chose not to ask his him since he felt it inappropriate. How ever, he was not at all curious

about his college professo rs' decision to major in mathematics. It did not seem to matter to

him nor make a difference. To him, they chose what they wanted as he has chosen what he

wanted for his own reasons.

The following interchange expands on the initial reference to his family:

Question: What are your parent's wishes for your future career?

Response: They always said whatever makes me happy soI just go with that.I always felt like I need to something good for me so I picked engineering.

Question: So they kind of told you that you can do what makes you happyand you feel like pursuing an engineer degree makes you happy right now?Response: Right.

Question: What role, if any, did your family play in supporting your decisionto come to college?

Response: They support my decision w ith everything they have.

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Question: Did they encourage you to go on to college or say do whatever youwant to do?

Response: No. They definitely encouraged college.

Question: In what way did they encourage it?

Response: It's basically like a culture type idea. It' s like further culture in ourfamily. I think it is good for all ofus .

Question: Could you explain that to me about "culture idea"?

Response: Like each generation should do better than the previous one sosince the majority of my family mem bers didn't go college. Some graduated,some have degrees; I should also have a degree and do better.

Question: Grow ing up did they ever say since maybe you were in 1 ^ gradethat you were going to college or did they say...?

Response: They never did put that type of pressure. My dad said I put toomuch pressure on myse lf I think itis just me. I am naturally competitive.

Question: This confidence that you have academically, do you feel like it hasalways been or do you feel like it was something that was built up over theyears from you like your parents rewarding, always telling you goodjob, andthat you were always working hard and being competitive? Do you feel like itwas always there, orit just got stronger through your course of life andacademics?

Response: I think it was always there. My parents never rewarded me fordoing good . If you do your best then that is what you are suppose to do. Ifyou earn a C, and it was hard fought then it is all right but if you could havegotten an A then you slacked off then you know what the problem is.

Question: What kinds of responsibilities did you have in high school? Didyou have to work or did you have to take care of your sister?

Response: No. I was just like a mentor to my sister and tha t's about it. Ihelped my other friends in their subjects. Other than that, I did n't have muchmore to do

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The following interchange expands on the initial reference to his high school and

college peers.

Question: If I asked you did you study with others in high school, what wouldyou say?

Response: I basically studied by my self Th at's basically how itw orked.

Question: Describe your social group in high school like who did you hangaround with?

Response: I don't know ifI had a certain chck. I pretty much just hungaround w ith everyone. We had our own group but it was quite di\ erse.

Question: In what way was it diverse?

Response: We had people that were more into like the liberal arts or Englishand type of stuff to math or just regular peop le. We just hung out witheveryone.

Question: What w as the common thread?

Response: Just personality I suppose.

Question: You all kind of like to do the same things?

Response: Yea, we all kind of did the same thing beside from studying.

Question: If you had to pinpoint a number of people in your social group saywou ld it be less than 10 or less than 5?

Response: It wou ld be close to 20. We hung out quite frequently.

Question: Why were they from your circle of friends and not from outsideyour circle of friends?

Response: My circle of friends usually included the brightest to theoutspoken. Th at's how it worked in high school. We w ere all very' close.

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Question: How important were your friends' opinions when you werechoosing a place to go like a university ... when you w eretr> ing to decidewhat university to attend, how important were your friends opinion aboutthat?

Response: I basically wanted to go to a college they weren t going to. Ididn 't want that social distraction. I didn't want to go to a place where I hadall the same friends again. I wanted to interact with different peop le. I wantto branch out a little bit. I did n't want the same competition from them . Iwan ted to see different people. I keep close fies with them but I like me ownspace too.

Question: Would you care to explain a little bit what you mean b \ that?

Response: You always have the socialistic type of friends who go out and

party or do something else other than studying.

4.1.2 Results from Student A 's Father - Father A

Father A is a self-motivated and self-driven educated man with a Ma ster's degree in

the social sciences. Bo m into an uneducated and working class family that strongly values

education, he chose "the military shortly after high school graduation (since) Vietnam was at

its height" and he thought it better to serve first then pursue an education. He has a high

regard for education and the hard sciences and encourages the pursuance of the mathematical

disciplines although he is not very confident in his ability to perform and comprehend

ma them atics. After spend ing a lifetime w orking and raising a family, he still entertains the

idea of returning to college for a PhD, if not in the social sciences then, alternatively, in law.

Question: Are there other ways that have not been mentioned that you think tthat your high school could better prepare students for college?

Response: High school itself Oh yea, high school could a lot betterjob. Alot of people go out there. You sh ouldn 't have asked m e that question. In ourhigh schools, a lot of educators and even the counselors, I am sorrv to say, I'mnot sorry that's why I am saying it. Seriously , they go up there and they are

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interested in doing what they do and tha t's it. They do n't publicize enough.They don't tell the kids look if you are going to do this then you should do.They more or less let the kid and his parents, ifhe had the help at home, figureit out mosfly. They give you the degree plan for four\ears, and if you ha\ eques tions, come ask. They don't. Here ask if you want but tha t's it. I think Iwou ld take a different approach to that. Th at's my opinion. They could do a

lot better. I think a lot ofkids are not prepared for college because somebodydid not tell them this is what you need to do because we ha\ea jr. collegehere. I know some kids come back from universities because theyw eren'tprepa red. Tha t's to me , although the student has a responsibility, the schoolbears a lot of the responsibility. That is what they are there for. Yea, theycould do a lot better.

Question: Would you encourage a degree/career in the mathematicaldisciplines compared to any other degree or career or is there not really adifference there; is it whateve r the kid desires?

Response: Yea but if you are going for a math major, that's fine and fantastic,but you almost have to want to teach. Either you want to be a teacher o r...Tha t's fine. There is nothing wrong with that. If that is what the person wantsto do. If you don 't want to be a teacher then you need to do something else.Once they tell me,I just try to put into perspective for him. Th at's all. Youchoose what you want to do. Tha t's it. Easy!

Question: You said teachers did not encourage you?

Response: No, no. Heck no ! I am serious. I don't w ant to sound mean oranything . The teache rs, I guess it is still the sam e that's how I see it. Forexamp le, when I was in high school, I didn't know that they were doing me adisservice by not encourag ing me to take algebra. I thought fantastic. I don 'thave to go to algebra. I don't have to take algebra in order to graduate. So Idid n't. Nob ody w ould say that if you are going to go or if you are going to dothis then ... nobody w ould say anything. We thought we were getting awaywith som ething. I went to college after, and I realized that I had to passcollege algebra before I could graduate from any major university. I saidwell, that is where I am going to start because ifI don 't then I am not going to

graduate. So I jus t started with the basic algebra. The very first one. Noteacher.. .1 can honestly say they did not. I am not saying that I am upsetbecause really it is a pe rso n's responsibility to find out. If you care then youare going to or if you have someone who cares then they are going to helpyou. Everybody else, sometimes, they have their own issues, their own thingto do.

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Question: You w ished that you were a little bit more well informed?

Response: I wish people, educators especially, do more thanw hat they arepaid to do. I think that would go a long ways in helping people sometimeswho come from families who are not well educated or not in tunedw ith the

system or the consequences. Educators sometime disappoint me. They don'tshare the informafion they have. I wish educators would take m ore interest indoing what they are supposed to do.

Question: So they valued education?

Response: Oh yea, yea absolutely! I am tired of hearing people say that somepeople do n't value education and stuff and this and that. I think that is bunkand uncool. I have never met any parent who did not value education. Theproblem is that people don't see that factors and things get in the way ofeducation and sometimes people have to eat and it is more pressing theimm ediate. The immediate need is more pressing than going to school. Thatis why you have people who w ere migrants w ho leave and go off even toLubbock and to the fields andstuff. It is not that they don't value education,it's because they got to eat. One time I had to I said the same thing.Teachers, for example, they get their undergraduate degree and then they go towork. If you ask them, I know a lot of educators, how come th ose .. .whyhav en't you got your Ma ster's degree. Well, it's because I have bills to pay, Ihave this to pay. Well, that is the same thing with people who go out andwork...to eat. The have priorities. The same reason why you are not gettingyour Ma ster's degree immediately is the same reason they don 't. They havebills to pay and they have to eat. It is not because they do n't value education.

Question: You don't think that it could have been the teachers in college whoturned you off?

Response: Let me tell you this. This is my experience. I told Jose the samestory. My experience in college was the teacher or professor or whatever hewas .. .he would stand there and interact with the brightest. The questionswou ld be directed at the brightest. Interaction was between that student and

the teacher.

Question: So he discriminated against the non-brightest?

Response: The non-brightest. The non-brightest were not challenged. Theywere not because the teacher liked 'this is what we did and how we did it

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and.. .the quadratic equa tion.' Th at's it. Ifhe had a question to share, hewou ld direct at the brightest. He would not direct an\ thing at an>bod} else. Isuppose. Now m e. I am thinking. I am not sure. I couldn 't say anything butI imagine that was because this guy doesn't know then Lll ha\e to explain itagain. Maybe I'll I have to lower how I explain this stuff We went throughit pretty fast. The guys that were the brightest would of course be like this and

this and this.. ..would you share your homework, how did you do thisproblem , and how did you do this, this, and that. Sometimes we would get ingroups and get by that way.

Question: What factors contributed to your child's success in high schoolma thematics courses? (i.e. social group, amount of time studying, parentalinvolvement, etc.)

Response: He took the higher-level courses. The honor courses, the hardcore mathem atic courses. He went through calculus. I had an influence onlyup to 7 ^ grade. After that, he lost me. I helped h im up to 7^ maybe 8 ^ butnot much more than that. H e's a pretty bright guy. I don't know how he gotthrough. I helped him the early years but not in high school.Question: Would you describe your child's motivation level in studying(ma thematics) as "high", "moderate", or "below average"? Why?

Response: High because he is a self-starter and very competiti\e. He likes toexplore . You give him a task and the tougher it is, the more he likes it. I'mnot sure. But he is self-driven.

Question: You said you didn't have to do too much; did you ever pressureJose to do well academically?

Response: In my opinion, no. The only thing I tell my kids is to do theabsolute best and to seek and find.

Question: Do you reward them for a good performance?

Response: No, I always told them that doing their best is what they are

suppose to do. I go to work, my wife goes to work, we get paid for doingwhat we are suppose to do. I always tell them everybody hasa job. Your jobis to do well in school as well as you can. Th at's the most I can ask. Th at's it.I didn't holler and scream if they didn 't bring an A home.I just tell them ifthat is the best you can do then that is the best you can do . If you need help,let me know, and w e'll do something.

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Question: Do you feel that your child's high school adequately preparesstudents for college?

Response: Yea but let me say this. Yes but it was mostly he. I don 't want tosay me but it wa s mosfly him . If there was anybody else, telling him

anything, it was me. His teachers were there. He had very good mathteache rs in high school at the higher levels. But the school, if \o u decided togo the vocational way, they d on't do anything or sayan> thing. So it is up toyou as the student to meander your way through whatever it is you want to do.He knew what he wanted to do. He did have all those courses. He wasw ellprepared. I have to give him a lot of credit Jose himse lf

Question: Based on the inadequateness ofthe counseling in high school,would you say that you had a large amount of influence as far as helping Joseleam about the colleges and universities?

Response: Yea, I think I may have contributed there because1 alwa> s put thestuff in front of him. I always told him. The only concern I had in that regardwas if he was not ready to go out, leave home. I didn't tell him that way. Imade it plain to him that he could go to the jr. college and take his basics thenprece de. I mad e the offer if he wanted to do that before he went on. He waswell aware about all the academic opportunities, and I left it up to him.

4.1.3 Results from Student A 's Teacher - Teacher A

Although Teacher A was a dedicated and devoted HS m athematics teacher for 33

years, teaching was unintentional career choice. His first career inclination was coaching

baseball. Since a coaching job w as contingent upon him teaching mathematics concurrentK.

he chose the dual career, and as years passed, transferred his love from coaching to teaching.

After the cessation of his coaching career, he sought UIL participation in mathematics in

order to fill the void of competition. In an overview of his career, he comm ents, "IfI had to

do my life over again, I would still want to be a teacher.''

The following excerpts from the interview w ith Teacher A relate to his philosophy

and teaching style.

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Question: Did you encourage academic competition in your class among yourstudents or academic cooperation?

Response: I was teaching mainly honors. I didn't have to encourage it. Inmost cases, it was already there.

Question: Did you encourage academic cooperation orw as that alread>' there?

Response: I did encourage that but see I was an UIL sponsor. Most of thekids were in UIL also. Especially because I wanted them to help each othernot only for that but also for competition. But then there are some kids whodo n't w ant to do it. If they know how to do something then they don 't workwith nobody else.

In regards to Teacher A 's perspective of his own classes, he comm ents. "My classes

were very competitive against each other.. .Everybody would compete against each other. 1

didn 't make it that way. They made it."

In Teacher A's interaction with his students, he never volunteered his rationalization

for m ajoring in mathem atics losing the opportunity to elaborate of his struggles and triumphs

in mathematics because he assumed that they already knew everything about him since he

had most of their parents and older siblings as students.

Question: What w as your role in Jose's performance in math?

Response: I came from a poor family myself but I see these kids and try tohelp them as much as I could. I wo uldn 't trade it for any pay. I would spendhours after school. I would stay late until 5:00 in the e\en ing . I would alwaystell them, 'If you can win here at the local level then you can win at regionaland at the state .' That is something that you can put on your resum e.W henever you apply somew here, people are going to look at you ofa sudden.Not that you just one in district but you also went to the state level. To be

perfectly honest, at our high school, I was the Calculator coach for fifteenyears. Actually 16 but one year, I had cancer. Out of those 16, we wondistrict 14 times in a row. In the Number Sense, we won half the time ormore.

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Question: What qualities do you feel that students must possess in order topursue a career in a mathematics-based discipline?

Response: I feel like for a student to pursue this career, they must first ha\e alove for math cause if you don't have a love for math then you are going to bebored. Nex t, I think you have to have a lot of patience to sohe problems.

You ca n't give up too easily. And the next thing, you must be willing towork. If you don 't have those qualities then you wo n't getan> where.

Question: How do you encourage/model these qualities?

Response: I usually let them model them selves. I start off easy and let themwork. I had only honors classes so they were fighting for grades for rank inthe class so they would have to stay up. I didn 't physically threaten any ofthem. I might once in while scare some of them. That was part of it.

Question: If a student lacks theses qualities, what advice do you give thestudent?

Response: I have never discouraged anybody. That is one thing I think a lotof math teache rs do wrong . I've known a lot of math teachers to do thatespecially teachers at Jr. colleges. I teach at a Jr. College also. There areteachers where the students come and there and they put some problems onthe board and they say, 'Oh, you can 't work this problem cause you do n'tbelong in this class.'

Question: So you think a lot of teach ers...

Response: I think that we can alw ays bring a kid that is down low up to acertain level.

Question: Do you think that the high school teachers discourage students frommajoring in math?

Response: Yes

Question: What suggestions do you usually give your students on how tostudy for mathematics courses?

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Response: I ask them to keep a notebook. Something that they canw ritedown the formulas in. I could get them to do anything because they like me.It didn't matter how hard I worked them, they enjoyed it cause they liked me.It took me about five years to become a good math teacher. If they like youthen you can do anything with them. I think in my case that was the mostsuccessful thing I did. A lot ofthe things I taught them, I learned from other

teachers.

When asked if Teacher A encouraged cooperative learning, he responded,

"Co opera tive learning is great. I do feel so that cooperative learning in calculus is not as

good as it is for developm ental. In calculus, they need to think on theirow n. Somebody

needs to lead them a litfle." Besides cooperative learning, he encourages students to take

calculus because they may need it depending on their major.

He responded with "I don't like to push any universities but I do tell them this, "Go to

an university that has what you need .' An example I use. Le t's say you get in the car with

your friend and here you are thinking about getting some enchiladas. On the way over, you

stop at M cD on ald 's.... This is also what I tell them. What is the one thing that they can 't

take away from you? Money, car,.. .what is the one thing that they can 't take away from

you? Your education. No matter where they put you, they cannot take they away from you.

I also tell them that that little piece of paper that you get opens a lot of doors. I won 't tell

them in class but if they ask and they start talking about it. I tell them that you don't have to

belong to a fraternity. All you have to do is get the most education you can out of school. If

your grades are good enough, somebody will find you. You don 't need anybody else 's. That

is wha t I try to encourage. I try to encourage them to get the most they can out ofthis and

that they need all the education you can get. That is the one thing that they cannot take away

from you," when asked ifhe encouraged (Student A) to attend a particular university.

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The following excerpts from the interview with Teacher A relate to his perspecti\e of

Student A.

Question: Describe Jose's performance in your mathematics course(s)?

Response: I knew Jose before my mathematics classes. First course he tookfrom me was either a trigonometry/analytic or a pre-calculus cla ss. He likesto compete with other people.

Question: Did you encourage Jose to pursue more mathematical courses andpossibly a mathematical career?

Response: I didn't pursue him to do that. I think he made up his mind.

Question: Do you think there was any contributions from extra-curricularactivities or social group?

Response: I think the extra-curricular activities helped more than the socialgroup. He was more of an individual. He didn't like to socialize that much.He wan ted to socialize but then he didn't want to socialize. He would onlyhave certain people hanging him.Question: What extra-curricular activities was he in?

Response: French, Chem., Mathematics for a while, I don't know . Maybe,calculator.

Question: Did you think that maybe extracurricular actixities and the socialgroup distracted Jose from his work in school at all?

Response: Nothing distracted him from his work. He would be the type ofstudent who would come in after school and do his work. You know afterschool in my classroom. Ifhe couldn't do something, he would ask for helpon it. He was very dedicated.

When asked what role did the parents have in Student A 's success, he commented, "I

do n't think his father really helped him I don't think his father helped a who le lot

although I don't think his father discouraged him either."

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Question: Name (and rank) three factors that contributed to J ose 'sperformance in your course(s)? (e.g. mofivation level, aptitude formathem atics, smdy habits, etc.)

Response: I think proba bh' the biggest part w as that he wanted to besomebodv in that class.

Question: He wanted to make his presence know n?

Response: He wanted to beat other people although the\' were better peoplethan he was. It was still there. It wo uldn't go away for some of those people.Those peop le probably drove in more than I did. It was not a com petition typething. We were all going to go to the same contest.

Question: Name the factors that contribute to Jose's success?

Response: He would do his work. He was not the lazy t\p e. He wouldalwavs ha\e his work.

Question: Would \ ou sa\ he his internally motivated?

Response: Yes. I think so. He may not have had the best ability of all thekids that I had but intem alh he was motivated. Not only did he ha\e thatability but also he overachieved.

Teacher A's additional comment relating to Smdent A s success is the following.

"The only thing that helped Sm dent A is that he never became girl crazy. He ne \ er had any

girlfriends."

4.2 Interviews from Group B

4.2T Resu lts from the Interview : Student B

Student B attended a 5A high school (HS) in Dallas. TX. With the completion of

algebra I in junio r high, he had the liberty to take geom etrv. algebra II. pre-calculus, and

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calculus I in HS. He received A 's in all his mathematical courses with the exception of

geom etry, in which he received a B. His father and older brother hold a degree in

engineering and his mother and older sister have a degree in education. Student B chose to

major in computer science.

In regards to Student B's personality, the following quotes are presented.

Question: Would you describe the exams and hom ework assignments in highschool as challenging? Why or why not?

Response: Exams w ere challenging; the homework was not becausehomew ork w as straight out ofthe book. The book problems were not easy butthey are not challenging either.

Question: How was it that the exam problems w ere challenging and thehomework wasn't?

Response: The exams had more ofa conceptual focus other than justcalculating problems whereas the homework problems m ainly focused oncalculation.

Question: Would you describe your motivation level in studying mathematicsin high school as "high", "moderate", or "below average"? Why?

Response: Below average in high school. I did the work but I really didn'tstrive to go beyond doing the work. I didn't try to leam anything on my ownor anything like that.

Question: W ould you describe your motivation level in studying mathem aticsin college as "high", "mo derate",or "below average"? Why?

Response: I wou ld say it is very high right now. Probably because of the

major I chose and to see how m ath plays an integral role in that. Also , justbeing more aware that math is a part of everyday life like my teachers told mein high school. I understood that but I did n't actually really look at how itgoes whether you're counting money or pay somebody with money, you ha\ eto know how to count in order to know how m uch change y ou 're going to get.I understood that but I really didn 't understand how the upper level of math

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goes. 1 want to get a better understanding of that included in my major Ichose and technology is really important as a foundation for my major.

Question: Would you describe yourselfas internally motivated (motivatedfrom within) or externally motivated (motivated from without)? Why or why

not?

Response: Internally motivated cause I have set high standards for myself andI like to succeed at anything I do, and I don't like to do anything that I'm not

But I'm willing to do stuffI may not succeed at but ifI do decide to do it,I'm going to try to succeed. Maybe, I can succeed at something I thought Icou ldn't do. I don't really know. I think it's just the type of personality that Ihave.

Question: In your college courses last year, do you feel like you gained anyconceptual knowledge of calculus or its applications?

Response: Yes very much so. I find it very easy to memorize form ulas. I canlook at a problem, and I may not understand the conceptual applications but Ican solve it because in my leaming process, it is something very easy for me.So in high school that's what I did with calculus but it is something that isharde r for me to do. I feel like with the classes in college I'm getting a betterbackground.

Question: You said you were below average in high school, do you feel like inhigh school, there is a tendency to experience external pressure or internal?

Response: It was part of it. I knew high in school that the teachers, if you arenot mo tivated yourself then they will push you to do it. I think also a part of itwas in high school if you didn't push yourselfto do the work, generally thereis going to be a way you can get out ofit. If you don't perform as well as youlike then there is going to be a way you can make it up. You can m ake bettergrades, or you can make up your grades. In high school, the big emphasis wasgrade s. W here college, the professors care to a certain extent beyond that, it isyour responsibility, and you push yourself in the class cause they are not

going to push you. You have to push yourself in college whereas in highschool.

Question: Did you leam to push yourself by being pushed by your teachers inhigh school?

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Response: Yes and no. I did leam a lot from my teachers in high school but 1also knew in high school, I wa sn't going to ha \e to push myself I think allalong I knew I could m otivate myself and have the motivation within me but Ialso knew in high school, I didn't have to use it.

Question: So in other words, high school could have been a little bit morechallenging?

Response: Yes, it could have been.

Question: It seems as though now, you have a lot of confidence in yourselfbased on what your parents that they have an occupation now but not dealingwith their major, do you feel that the reason that you don't receive anypressure is because you think that given this like high school, if it doesn'twork out, there is always that outlet?

Response: Th at's a nice question! I think that can be a part ofit. I think itcan. Even with what I am interested in now, there is many different options Ican take if engineering doesn 't work, or I decide I don 't w ant to be anenginee r, there is many different things I can with that degree .

Question: Besides engineering, what other occupation would you be interestedin?

Response: I am very interested in teaching on the secondary teaching leve l. Ienjoy teaching people things. I enjoy engineering, and the degree I ampursuing but I also do not necessarily enjoy a classical, typical engineer likethe material I am leaming. I don 't just wan t to work for a big corporation anddesign new things and stuff like that. So teaching is an option or a differentcareer I have looked at.

Question: Are you competitive at all? Do you have a competitive nature?

Response: Very much so.

Question: When you take an exam, do you feel that you compete internally ordo you compete with the rest ofthe class, or do you like to know what theaverage was?

Response: I like to know what the a verage w as to see where I stand againstthat but I think that is more for just m y know ledge . My friends, I like to knowhow they did on the exam and then talk about why d idn't you do this problem

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right or what was missing, can you help out, andw hy 1 didn 't do this one. Ido like to know that but it's more for my knowledge. I do definitely competewithin myself on each exam that I take.

In regards to Student B's leaming style, the following quotes are presented.

Question: When you were in high school did you need any help on thematerial and how did you get help?

Response: After school hours, my math and all other teachers stayed at least30 minutes after school so you could talk them m ore or you could set up atime where you could stay longer after school to get extra help.

Question: Did you do that very often?

Response: More often in the later years, my junior and senior years.Sometimes it was to get a little extra help, sometimes itw as just to do thehomew ork w hile the teacher was around. We had several students whow oulddo the same.

Question: When you do work in groups with other people, who did you feelmore comfortable with? (i.e. others of your ability le\el. others from yoursocial background, others from high schools similar to your own, etc.)

Response: I feel more comfortable with people with the same ability le\ el.The people with the same ability level, somebody will have a different ideathan I did. Th ey'r e going to see a different way to sohe a problem than I did.But they are not very out of my league such that they are understandingeveryth ing, and I'm trying to play catch up. Somebody on the lower level, Ifind it hard to study with because they may not be understanding the conceptsand rather than studying, I'd be going back and helping them understand howto do something. Which in a way is studying but I don't mind helping peoplebecause I generally leam something when I'm trying to help someoneunderstand the sam e thing. But if it's actually studying for a test or quiz thenI feel like I'm missing out in the time where I need to focus on what I need towork on so generally, somebody at the same ability level.

Question: Describe your experiences in your college calculus course, (i.e.did you like the professor, the textbook, the structure ofthe class, etc.)

Response: Calculus 1,1 like my professor, and I like the idea of projects but Ifelt the projects w e were doing were a lot of busy work with not as muchreturn on the actually leam ing the conce pts. I did n't really follow the way shetaught as well. She didn't have a problem teaching;I just wasn't following

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the way she taught. I like the way the class was set up in that we had quizzesand we had projects where you could work with other people in understandingthe material and there was n't a big focus on doing the homework. Iunderstand the point of doing homework but I don't like to feel that I have tohave it done every single time completely completed because sometimes lifegets busy, and 1 don't get it done.

Question: When you did study for calculus classes, how did you study? Didyou use the book?

Response: I like to review the sections in the book that were covered, look atthe homework especially if it had been graded to see what part ofthe sectionsI was m issing the most problems on. If it wasn 't graded then I would justreview some ofthe problems that I had done to see ifI remembered and to seeif I could still do them. Right before the test, I would review the notes takenin class.

Student B studied majority of the time alone with an occasional group study session.

In college, he studied approxim ately 3- 4 hours a week outside of class alone. For the entire

semester, S tudent B spent close to 25% of the time studying with other people.

The following exchanges expands on the initial references to his high school teacher:

Question: If you had to name a particular teacher/person who influenced youto pursue mathematics at the college level, who would it be? Why? [e.g. Werethey interested in mathematics and tell you about their own story of how theybecame interested in mathematics]

Response: Algebra II / Calculus I teacher in high school. Her name w as..(Teacher B).. . She was my trainer my freshman/sophomore year. Myjunior/senior year, she wa sn't a trainer but she still taught math; taught mathall the time. She focused on her relationship with her students. She keptencouraging me to stay with math and some sort of field that would requireme to continue to take math in college.

Question: How did your teacher foster these relationships you talked abouther getting to personally know the students; what did she do exactly?

Response: Sh e's the type of teacher in class who doesn't keep necessarilystrict rules. She keeps the class lively and encourages us to talk about thetopics w e're lea ming. She 's just a real fun teacher. She has a reputation forbeing fun. I remem ber when I had her for algebra II as a sophomore, Iw ould

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see upperclassmen, and people who had graduated came back to see her justbecau se she really is a very caring teacher. So we got that before we met herand then w hen we talked to her, she was a lot of fun and very helpful evenoutside of mathemadcs.

Question: How did she convey to you that she cared?

Response: She 's very open and would joke around with you. If you w eren'tan open person, she'd tried to get you to open up and enjoy the class and notjus t the m athematics that she was teaching but also just to enjoy life as it was.

Question: Did the teachers encourage you to get together outside of class orwere they hands off?

Response: My teacher w as laid back about it. She realized it was helping usout so she made her classroom available after school. She suggested that wedo it if we were having problems but she wasn't real pushy about it.

Question: Did you feel that your high school preparation in mathematics wasadequate for college?

Response: Yes, because the teachers were aware what we needed as far aswhat kind of mathematics or how to prepare us for the math classes in college.They not only taught us to the concepts that we needed for our high schoolclasses but they also taught us how to leam it on our own, and taught us tounderstand what we w ere leaming and how it would be in college. They stilldid high school grading but talked about that in college you wouldn't have allthese homew ork grades so focus more on the tests.

Question: Was your motivation level in high school influenced by yourteachers? Why or why not?

Response: Ye s, my teachers pushed me to raise the mofivation level. I thinkthat kept me still going in math.

Question: How would they motivate you?

Response: By encouraging me that I didn't just have to do the basics to get bywith math. I could go further w ith that. They design some projects that hadsome challenges to them but were also fun which try to keep you interested.That was building a relafionship with their students to help keep peoplemofivated as well.

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Question: Is your mofivafion level in college influenced by your instructors?Why or why not?

Response: Yes it is. Some classes seem boring at times. I may revert backand highlight some classes in high school and realize I can leam just as muchand I'll be jus t fine cause I'm understanding the stuff Most instmctors that

I've had, I don't think I have n't had an instmctor who do esn't try to show youhow much further you can go with the material.

Once I see that that then I can go farther than I am letting my self It's just kind of

natural for me to ingrain that. IfI can go further, why not go further because I am paying for

the class. If an instructor is willing to show me how much fiarther I can go then I should take

the chance and see what I can actually leam.

The following interchange expands on the initial reference to his family.

Question: Would you describe your motivafion level in studying mathematicsin high school as "high", "moderate", or "below average"? Why?

Response: Not really. My parents would encourage me to do well. Thewanted me to do well and keep my standards high as far as achieving goals inmath as well as all my classes. They didn't pressure me into math. Thatw asmy choice.

Question: Are your parents' occupations related at all to your careerchoice/future occupation goals? If yes, why? Ifno, why not?

Response: Yes and no, my mother has physical education degree for teachingelementary physical education. My father has an electrical engineeringdegre e. They both were working within their degree right out of college butare now with a Christian organization. That is something, I am also looking at.Even though I am in the engineer degree, I'm not sure I will stick with it onceI graduate.

Question: What are your parent's wishes for your future career? [may want topursue this with why?] How do they compare with your own career goals?

Response: Their main wish is I choose som ething I'm happy and that I enjoydoing for life. My dad knows about enginee ring so they don't w ish for me to

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do engineering vs. something else. They just w ant me to choose som ething 1enjoy doing.

Question: What role, if any, did your family play in supporting your decisionto come to college?

Response: Yes, I think they did in that they encouraged me to go to college. Ireally never had any thoughts about going to college just because, for one, ithelps you choose a career eariy and prepares you for a career. If you don 't goto college then it's harder to choose a career and, I really don't know what I'mthat interested in so I think that's why my family encouraged me to go tocollege.

Question: What family and peer relationships empower you in your academicpursuits? How?

Response: My relafionship with my enfire family empowers me in myacademic pur suits. My entire family is very supportive whether what I chooseto do. I'm the youngest in the family. I have my oldest brother and sister tolook up to and see what they have chosen and be able to talk to them aboutwhy did you choose this, what if you didn't choose this. That helps me in mydecision to be able to choose my own path that I want to follow.

The following interchange expands on the initial reference to his high school and

college peers:

Question: So the other times you studied by yourself?

Response: Yes

Question: How/What did you study with other people in calculus?

Response: It was my senior year and was more fun to study with others. Lesswork on my part. Generally, most ofus had the same types of questions so

when we studied together, we could narrow it down to a few main questionsof a concept we stm ggled w ith then the teacher had to answer those questionswe had.

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Question: Describe your social group in high school, (i.e. what interests didyou have in comm on?, are they now attending college?, how m any of yourclose friends were in your mathematics courses?, etc.)

Response: Most of my friends were in math classes. Most ofus were inmarching band in high school so we had that as general interest. Some of m\

friends and I were interested in engineering and then just good ole goofing offand sports.

Question: How did ya'U meet each other either marching band or classes?

Response: Both of those, largely due to marching band and then themathemafics classes as a freshman being in geom etry. Most ofus within thatgroup started algebra in middle school and then had the same math classesfrom geometry through calculus.

Question: If you studied with other people, how many of them were fromyour social group (i.e. friends)? Why were they the same? Or why were theydifferent?

Response: Studied with same people.

Question: How important were your friends' opinions when it came tochoosing a university to attend? [Why were they important? Why weren't theyimportant?]

Response: My friends' opinions were something I definitely thought about butI knew even though we had been in high school, most of us for 4 years weretogether. We were close friends but we were probably going to choosedifferent universities just because of our different interests. There was somemerit to it but I knew I couldn't base my enfire decision off of that.

Question: What family and peer relationships empower you in your academicpursuits? How?

Response: My relationship with my entire family empow ers me in myacadem ic pursuits. My entire family is very supportive whe ther what I chooseto do. I'm the youngest in the family. I have my oldest brother and sister tolook up to and see what they have chosen and be able to talk to them aboutwhy did you choose this, what if you didn 't choose this. That helps me in mydecision to be able to choose my own path that I want to follow.

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Response: I had a couple of jobs . They went into my school once classesstarted but I really didn 't have a job that I kept the entire school year because Iwa s in the marching band and was really hard to work during practice sogenerally I would n't have a job during the fall semester of the year. I didn 'thave a job until the end of the spring semester.

Question: So you worked at the end of the spring and in the summer?

Response: Yes

Question: What kinds of responsibilities (housework, child care, job, etc.) didyou have in high school? Do you think that these responsibilities enhanced ordetracted from your educational experiences?

Response: I think it enhanced it. When I hada job, I had to manage my time

better because I ha set a schedule; I couldn 't just goof off and play all thetime because I had the responsibility of being somewhere at a certain time. Itreally helped me understand that with taking classes I had to work at it but Icould still have fun. I had to make sure to manage my time to do the workand have fun. Holdinga job helped me that way.

Question: How much do you think that helped you in your classes, havingdescribed as though you'v e had a pretty good background? So how wouldyou say that helped you?

Response: I thought it helped quite a bit especially that I had calculus in highschool but I retook it my freshman year in collegeso just the fact that thebackground that I had in math was already a strong background. It was easierfor me to get into, as a freshman, college classes and not to worry as muchthat I'd be struggling as much in the area of math. I knew that1 already had agood understanding ofit. That just kind of helped me just kind of take it andleam to sit in as a freshman and leam what was required of me in college.

4.2.2 Results from Student B 's Father - Father B

Father B received a BS in electrical engineering (EE) in college then retumed for his

MS degree in EE for reasons of diversity and m arketability. Once as an engineer and.

presently, as a m issionary, he has had the experience of changing his career along the w ay

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Question: Did it adequateh prepare your child, particularly, in mathematics?

Response: Yes , I do. Again, I think the teachers were ver> enthusiastic. Bythat. I mean not just by teaching lessons in the book, how to sohe problems,

or w hate \ er but tying it to real life type stuff

Question: Are there other ways that have not been mentioned that you thinkthat your (son's) high school could better prepare students for college?

Response: No . I don't think so We actually switched Jonathan to a largerhigh school so he would ha\e the opportunity to take ad\anced classes inmultiple subjects without a conflict. The high school did a real good job ofmaking sure there was an opportunity for all that and for staffing it withpeople who w ere good at their job .

Even though Father B encouraged ad\'anced mathematical courses, he was also leer\

of trying to speed up the proce ss" of Student B 's education. He elaborates about this idea

w ith the following comment, "Universities put together their curriculum based on some

assum ptions that might not be tme. If you take those classes some other way. I never said

no don't do that but I would have been a little leery of it because I wouldn't want him to get

to college and start the2" ^ semester of math and science courses."

Question: In what ways, do you promote pursuing a higher education amongyour child(ren)?

Response: Basically, it was a given. Non-negotiable. Form nately. we nevergot into a test of will over you 'll do this. It wa sn't that way. and it worked outsmoothly. Both my w ife and I have degrees. We w ork in a Chrisfianorganiza tion where e\ ervbody there has a degree. I think that they justthought that the world is a much broader place if you have a degree. I think it

was kind of osmosis, I guess, but it was non-negofiable. They were go ing togo away and at least try. It never cam e to a test of will of ordering that youwere going to do it.

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Question: Do you have definite ideas about the career path your child shouldfollow? Why or why not? (Do you encourage them to dow hatever theydesire?)

Response: No. I think they should choose what they want to do.

With the experience of career change and geographically relocating. Father B

strongly advises a degree in the mathemafical disciplines simply because it allows for

ma rketab ility. The following excerpts reveal his reasoning:

Question: Are your ideas about your child's career path the same as yourch ild 's goals? I'm not saying you would direct his career path but have youever thought about him taking a certain career or mentioned it to him?

Response: Jonathan was bom in Africa while we there as missionaries, and1have real strong feelings that there is a likelihood that he may want to go backand live overseas. He was a3' ' culture kid. Children who grow up in a3' ^culture tend to want to move back into a3"^ culture but not necessarily thesame one. There is a real high probability of that happening. We have talkedto them and said if you are going to want to have the op tion, you are going tohave to have a degree that's , in American terminology, it 's called amark etable skill. You have to have a degree that the country sees as reason togrant you a VISA to live there. That tends to mean som ething in teaching,medicine, or some type of degree that you can do where the country thinks it'svaluable We were pleased, and I don't know how much pressure weexerted or how m uch of an influence we were but we w ere pleased that eachof our children including Jonathan has chosen a degree that is marketable; oneyou can get a job w ith. It's not that I expect them to geta job but because Ilike to expec t them to consider full-time Christian w ork but it is still a veryimportant criteria in that department. As opposed to, picking on theologians,doing an undergraduate degree in religion education and seminary degree intheology and trying to go to another country, they are not going to look at thatacademic qualification say, "How are you going to help us?

Question: You w ould consider (a degree in mathematics) marketable?

Response: Yes, it would be marketable in a sense of that it would be a basisfor education or something. Probab ly, teaching not education.

Father B's perspective of Student B is reflected in the following quotafions.

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Question: Would you describe your child's motivation level in studying(mathemafics) in high school as "high ," "m oderate," or "below average"?Why?

Response: Above average

Question: Why do you think this is?

Response: Probably, natural apfitude. Enthusiastic paren ts.

Question: Would you say Student B's motivation is within?

Response: Yes, definitely.

Question: Why do you think this is? Do you think he inherited it from one ofyou or...?

Response: Yea , it transcends math. He's an achievem ent-oriented person.

Question: Have you ever pressured your child to perform well academically?(i.e. punishment for poor performance, reward for good performance, etc.)

Response: No, but, of course, he probably feels different. We are not trying tolive out our lives through our children but don't settle less for what we knowthey are capable of giving.

Question: Did you reward for good performance?Response: No

Question: So did you punish for bad performance?

Response: N o, we did n't punish either but it depends on what you mean by

reward. If you mean extemal reward then no. We feel like praise andcheering them on and going out having a meal and celebrating good grades;well, I guess, those are rewards too, but we did that each semester. It was nottied to monetary or a car or anything like that.

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Question: Besides helping and tutoring Student B to excel in math, how elsedid you assist him to excel in ma th? Did you provide other tutors or did heget help from teachers after school?

Response: I'm not sure about talking to teachers. We did n't find other tutors.We done things like, again, because part ofit is just my interest too, done

things like tour Cape Canaveral, toured the Soviet Space Exhibitw hen it wasin Fort Worth during his high school years. Kind of tied it to the real world ofhow people accomplish what they've done.

4.2.3 Results from Student B 's Teacher - Teacher B

Teacher B decided to becom e a HS m athemafics teacher after "teaching a m iserable

semester of Health and P.E ." She realized that she abhorred teaching these two subjects and

preferred to teach mathem atics. An interesting situation when considering that she had not

always liked mathem atics until her experience with trigonometry. For some unknown

ration ale, the course jus t clicked for her. Thus, trigonometry convinced her to minor in

mathem atics since a major in mathematics seemed unattainable due to its demanding mental

challenge. She thought that she was real good at mathematics unfil a couple of upper le\e l

mathem afics co ur

Success Factors of Calculus

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