In Their Own Words: Getting Pumped for Calculus

This article was downloaded by: [UOV University of Oviedo]On: 27 October 2014, At: 05:41Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK

PRIMUS: Problems, Resources,and Issues in MathematicsUndergraduate StudiesPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/upri20

In Their Own Words: GettingPumped for CalculusFabiana Cardetti & P. J. McKennaPublished online: 29 Apr 2011.

To cite this article: Fabiana Cardetti & P. J. McKenna (2011) In Their Own Words:Getting Pumped for Calculus, PRIMUS: Problems, Resources, and Issues in MathematicsUndergraduate Studies, 21:4, 351-363, DOI: 10.1080/10511970903228984

To link to this article: http://dx.doi.org/10.1080/10511970903228984

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all theinformation (the “Content”) contained in the publications on our platform.However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness,or suitability for any purpose of the Content. Any opinions and viewsexpressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of theContent should not be relied upon and should be independently verified withprimary sources of information. Taylor and Francis shall not be liable for anylosses, actions, claims, proceedings, demands, costs, expenses, damages,and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of theContent.

http://www.tandfonline.com/loi/upri20

http://www.tandfonline.com/action/showCitFormats?doi=10.1080/10511970903228984

http://dx.doi.org/10.1080/10511970903228984

This article may be used for research, teaching, and private study purposes.Any substantial or systematic reproduction, redistribution, reselling, loan,sub-licensing, systematic supply, or distribution in any form to anyone isexpressly forbidden. Terms & Conditions of access and use can be found athttp://www.tandfonline.com/page/terms-and-conditions

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4

http://www.tandfonline.com/page/terms-and-conditions

PRIMUS, 21(4): 351–363, 2011Copyright © Taylor & Francis Group, LLCISSN: 1051-1970 print / 1935-4053 onlineDOI: 10.1080/10511970903228984

In Their Own Words: Getting Pumpedfor Calculus

Fabiana Cardetti and P. J. McKenna

Abstract: By understanding what motivates students to learn mathematics, instructorscan adapt their teaching strategies to help students achieve a level of engagement con-ducive to learning mathematics. There is a substantial body of research on motivationsand academic achievement at the elementary and high school levels, but less is knownat the college level. This article is a first step toward filling this gap by discussing col-lege students’ perceptions of what motivates them to learn mathematics. Our findingsare based on the analysis of the students’ journal writings about this topic. The analysisrevealed the following six main motivation themes: (a) intrinsic satisfaction, (b) bribery,(c) competition, (d) fear and the adrenaline surge, (e) learning through sharing, and (f)approval from family and peers. The article includes a discussion of the findings, as wellas recommendations for instructional practices that promote the different motivationsdescribed by the students. Areas for further research are also suggested.

Keywords: Motivations, students’ perceptions, calculus learning.

1. INTRODUCTION

Many mathematics instructors, and instructors in other disciplines, have a dif-ficult time finding ways to increase or even attain a level of motivation thatwould make a positive impact on the student’s attitude toward the class, on thelearning environment in the classroom, and ultimately on students’ academicachievement. What typically happens is that when instructors plan and developteaching strategies, they follow their own beliefs about what motivates stu-dents. It is apparent that this way of handling student engagement is not alwaysefficient.

The purpose of this article is to uncover students’ beliefs about what moti-vates them to learn mathematics. By understanding what the students report

Address correspondence to Fabiana Cardetti, Department of Mathematics, Universityof Connecticut, U-3009, 196 Auditorium Rd., Storrs, CT 06269, USA. E-mail: [email protected]

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4

352 Cardetti and McKenna

as motivating, instructors can adjust or modify their teaching to achieve theintended level of engagement that promotes mathematics learning. We baseour findings on the analysis of the students’ journal writings. These writingsare generated as part of a popular writing course offered by the Department ofMathematics at the University of Connecticut.

The writing course was created in the fall semester of 2005 shortly afterthe university was designated a Teachers for a New Era (TNE) institution by theBoard of Trustees of the Carnegie Corporation of New York. The TNE initiativestimulated the creation of this course for students enrolled in the multivariablecalculus sections. The idea was that every time a mathematics class is taught itcan be looked at as a training ground for future teachers, since future teachingstyles will probably be influenced by the actual learning experiences of thestudents in their basic courses.

The goal of the writing course is for students to become more fullyengaged in their own learning and develop into better teachers in the futureby reflecting on and writing about their teaching and learning experiences. Thewriting course has allowed us to see the teaching and learning process from thestudent’s perspective. In particular, we have tried to capture the students’ viewsof what motivates them to learn mathematics.

In this article, we first discuss why understanding students’ motivationmatters. Then, we describe the writing course in more detail. Next, we presentthe different themes that emerge from students’ writings. Following eachtheme, we discuss recommendations for instructional practices that promotethe different motivations. We conclude with a summary of the findings andsome final remarks.

2. WHY MOTIVATION MATTERS?

When preparing a lesson, a typical instructor concentrates on providing stu-dents with the necessary elements to understand the mathematical topic athand. Regardless of whether it is procedural or conceptual understanding thatwe are aiming at, we want all students to eventually master the material. Thereare many variables that influence how successful we are at delivering such alesson. Among those variables is one that is very difficult to control: studentmotivation to learn the material we are presenting. Clearly, motivation alonedoes not guarantee understanding, but without some level of motivation fromthe students, no learning would be possible.

Understanding the motivational beliefs of students can help us adapt ourteaching practice to achieve the engagement level we want our students to have.James Middleton conducted a study comparing the teachers’ and students’ per-sonal beliefs with regard to motivation in the mathematics classroom [6]. Hefound that teachers are poor at predicting their students’ motivational beliefs,but the results of his study indicated that when these predictions are correct,teachers were able to adjust their lessons to turn students on to mathematics.

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4

Getting Pumped for Calculus 353

Research has also shown a positive correlation between motivation andacademic achievement. Recently, Aunola, Leskinen, and Nurmi, [1], studiedthis correlation at the elementary school level and found that motivation, asreported by the students, was a good predictor of their mathematics academicachievement. Specifically, they found that the higher the motivation studentsreported by the end of first grade, the higher the level of mathematics achieve-ment they showed in second grade. The results obtained by Aunola et al. wereconsistent with earlier studies that showed that motivation is positively relatedto school achievement from primary grades through high school [3–5]. Indeed,Gottfried [3], found that mathematics motivation was a specific component ofmathematics achievement in three different studies with students from fourththrough eighth grades. The results by Ma [5] indicate that high school studentswho enjoyed learning mathematics achieved higher scores in that subject thantheir counterparts.

These studies do not clearly demonstrate motivation as a cause of highacademic achievement. In fact, it is not our intention to imply that motivationalone improves student learning of mathematics, but rather to point out thevalue of hearing the voices of our students as to what motivates them to learnmathematics.

It is natural to assume that some of the same motivations carry over fromhigh school to the university setting, although we were unable to find com-parable studies at the higher level. Our literature review included searchingfor key terms on online databases, searching within results, and searching ofworks citing those results. We also consulted with colleagues in the School ofEducation. From the point of view of this study, we decided to focus on whattypically would be second-year college students. The reason for this is that wefeel that freshmen students have to make too many other adjustments in termsof new learning and living experiences. By comparison, students in their sec-ond year have acquired some experience and successfully negotiated the firsttwo semesters of calculus. The specific question that guided this study was:What motivates second-year college students to learn mathematics?

3. WRITING COURSE DESCRIPTION

In this section we describe our writing course in more detail. Hopefully, thiswill help the reader understand the particular context on which our findings arebased.

The authors have taught the course jointly for four consecutive years atthe time this article is being written. The students come from different sec-tions of the multivariable calculus course which they have to take concurrently.The writing course is optional and because of university regulations on writ-ing courses, it is limited to 19 students enrolled in a first-come first-servebasis. Typically, they take the course because it helps them satisfy a “writingcredit” that is part of their graduation requirements. These students are mostly

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


science-minded students pursuing degrees in mathematics, engineering, andsecondary education. Although each semester they are a small percentage ofall those taking multivariable calculus, they have been a fairly representativegroup over the last four years.

Neither one of us has taught the multivariable calculus course since westarted teaching the writing course. We feel this eliminates the uncomfort-able situation in which students would have to discuss our teaching in theiressays. Additionally, at the beginning of the semester, students choose individ-ual pseudonyms to refer to their instructors in their writings. This allows themto write more openly about their experiences.

During each weekly class meeting, a new topic is given. The students areasked to write one to two pages on this topic. The topics can range from reflect-ing on one aspect of their learning experience for a particular week of thesemester, to solving a mathematical problem using the concepts covered inthe multivariable calculus course. (For those readers interested in teaching asimilar course, we have included a list of topics that would make up a typicalsemester’s material in the Appendix.)

Each week, we, the instructors, analyze the essays independently, and thenmeet to compare what each of us noticed with respect to issues with writ-ing (e.g., poor grammar or vocabulary), as well as issues with content (e.g.,common and unique thoughts found in the reports). Based on our discus-sions, constructive feedback is written on the students’ essays so they can berevised to produce a more polished final version on which course grades arebased.

During the next class meeting, instructors hand back the essays with thewritten feedback on them and a discussion takes place regarding the similar-ities and differences of students’ reflections. Sometimes students volunteer totalk about their perceptions, other times the instructors lead the conversationbased on what they observed on the reports. One of our goals with this prac-tice is to expose students not only to the similarities of the reflections offeredby others, but also to the uncommon views that surfaced. The discussions pro-vide an opportunity for them to express their agreement or disagreement withthose uncommon thoughts. The diversity of the students’ sections make the dis-cussions very lively as students discover how different things can be in othersections of the same multivariable calculus course.

4. DATA COLLECTION AND ANALYSIS

We focus on the essays students wrote on the topic about what motivated themto learn mathematics. Essays on this topic from across all semesters werebrought together and analyzed anonymously. Our observations from the in-class discussions provided confirmatory data for our analysis; however, theanonymous essays were the primary source of data for this study.

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


We analyzed the data in several steps. First, we focused on organizing intolabels the different thoughts expressed by the students. Then, we coded the dataaccording to those labels. Next, we examined the codes to reduce overlap andredundancy. This process continued until no new information about students’motivations surfaced from re-reading the essays. Finally, from the list of codes,we developed a set of more abstract themes that captured the main motivationsdescribed by the students. The six themes that emerged from the data analysisare discussed on the next section.

5. FINDINGS AND DISCUSSION

In this section we describe the main motivational themes that seemed to arisenaturally from the students’ essays. We classified the different motivations intothe following themes: (a) intrinsic satisfaction, (b) bribery, (c) competition, (d)fear and the adrenaline surge, (e) learning through sharing, and (f) approvalfrom family and peers. All six themes appeared on the students’ essays with(a) and (b) occurring more frequently. The themes are explained in greaterdetail in the subsections below. Each subsection includes selected excerpts,from students’ essays, that illustrate the theme.

A discussion of the instructional implications drawn from the findings ispresented for each theme. Our discussion is in the form of practical suggestionsto help engage diversely motivated students in mathematics classrooms. Wealso include practices that the instructor should avoid in order to keep thesestudents motivated. These ideas should be used carefully and in a balancedway, since the ultimate goal is to create a learning environment that wouldhave a positive impact on all students in the class.

5.1. Intrinsic Satisfaction

Students described getting a feeling of inner satisfaction when they were ableto solve a difficult problem. As mathematicians, we know about that innerjoy one feels when finally understanding a concept or conquering a problem.As Perelman explained shortly after declining the Fields Medal, “It was com-pletely irrelevant for me. Everybody understood that if the proof is correct thenno other recognition is needed.” [7, p. 2] Students motivated by intrinsic satis-faction were stimulated when faced with a demanding mathematical problem.One of the students wrote,

Most people cringe when they look at a double integral, but I actuallyenjoy computing them. There is a certain sense of satisfaction I get fromsolving a hard problem, and the challenge sometimes makes it fun. On

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


another course the material can be mindless busy work, and I wouldrather do work that challenges my brain.

The following excerpt illustrates how a student motivated by intrinsic sat-isfaction expressed feelings of joy from the process of working on and solvinga challenging problem:

When there is a tough problem I have to solve, I work on my white boarduntil I figure it out. It’s a great feeling when I come to the right answer,and get a laugh from looking at the mess that was once in my board whenI’m finished.

Motivation for these students came not only from being able to solve chal-lenging problems but also from understanding difficult concepts. A studentreflected upon the cumulative nature of mathematics and explained how thismotivates him/her to master the concepts before moving on.

In mathematics, . . . the rules are rigid and there are no exceptions. Thisis motivating to me since I always know that I can understand why orhow something works in mathematics. As long as I know the rules thatsupport something, I can figure out how it works. You can always buildnew knowledge from the rules that have already been established. Thisthought motivates me to master as many rules of mathematics as I can inorder to better understand [mathematics].

5.1.1. Instructional Implications

Motivation of these students can be achieved by carefully selecting problemsto be worked by students either in class or as homework. The key is to selectproblems that are non-trivial, yet doable. The instructor should avoid giv-ing too many routine plug-and-chug problems, or perhaps, problems that areunrealistically hard.

5.2. Bribery

The expectation of a tangible reward as a result of their efforts was often men-tioned as motivating. The most common rewards mentioned by these studentsincluded obtaining a good grade in the class and landing a high-paying job.Nonetheless, the rewards varied widely, covering a range of different students’interests. Here are three different variations on this theme.

Sometimes the rewards mentioned were very specific and material. Onestudent wrote,

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


Perhaps the easiest way to motivate me is to include incentives. Forinstance, I am getting my first car after this semester. Although it wasnever actually stated, I am sure that my grades are directly related to theamount of input I get into which car my dad buys. Obviously I am goingto work a bit harder to make sure I get a CD player, power windows, andan automatic car starter for those cold mornings in Storrs.

For another student, the motivation came from a barely missed opportu-nity. The student’s reflection read,

After getting into the University of Connecticut, I discovered thatI missed getting a scholarship by one percentage point. If I had workedharder I would have gotten the scholarship. I think about this and use itto help motivate me in college.

Finishing their careers is the short-term reward expected by any collegestudent. For many bribery-motivated students, the college degree kept themmotivated, as explained by the following student:

It is hard to motivate myself to spend hours on the homework, especiallywhen you have friend asking you if you want to go play some soccer, oryou want to go out to a party. But one thing is certain: I have to finish mydegree in engineering. If I practice one day of my life in the field, or if Idecide to be a fisherman, I need a degree to succeed in this life.


To help motivate these students, the instructor could occasionally tell stories ofsuccessful mathematicians like that of James Simons, former chairman of theMathematics Department at SUNY Stony Brook, whose work involved min-imizing multi-dimensional surfaces. In 1982 he founded his hedge fund. In2007, he earned $1.7 billion, topping the list of highest-paid hedge fund man-agers for the second year in a row. A way to discourage this type of studentwould be to have unpredictable exams with a large random amount of partialcredit or too-low standards.

5.3. Competition

These students felt motivated to understand mathematics so that they could usetheir knowledge to show they were better than others. Winning a competition,getting awards, and receiving public recognition, all fall under this motiva-tional theme. The idea of showing better mathematical skills than other studentsseemed to keep many motivated to learn more mathematics. Many students

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


had fond memories from their elementary school experience of mathematicsclassroom competitions. One such student wrote,

When I was in fifth grade we would have a math quiz every week andmy friends and I would race to see who finished first. We would get allpumped up and say phrases to each other like “you can’t beat me, I’m thebest.” We were always anxious and whenever I lost I made sure I cameready to win next week’s challenge. My teacher liked how we showedinterest in math by competing and never interfered but just smiled.

The following excerpt provides evidence that still in college, some studentsfeel motivated by competing with others:

I do not enjoy learning some material in calculus. I am extremely com-petitive, however, and found that if I make it a competition with one ofmy friends in the class it helps. My friend John and I will bet ten dollarson who will get a better grade on our exam.


One suggestion for motivating this type of students is to embed challengingquestions in the lecture and homework and invite students to share the solutionwith the class. Of course, the challenge here is that for every three or four win-ners in the class, there are a lot more losers unless this is handled sensitively.And of course, most professional mathematicians have ended up on the los-ing side themselves at times in their careers, so one should not emphasize the“winning is the only thing.”

5.4. Fear and the Adrenaline Surge

This theme can best be illustrated by the words of the English author SamuelJohnson: “Depend upon it, Sir, when a man knows he is to be hanged in afortnight, it concentrates his mind wonderfully” [2, p. 238]. For these students,the power of an imminent deadline, like an upcoming test, was a source ofmotivation. Any form of graded examination counted for these students, aswas clearly expressed by the following student:

I have definitely found that fear is a good way to get motivated to studyfor me. I am very afraid of doing poorly so that helps me a lot in pushingme to learn and understand all of the necessary material. Quizzes, andespecially tests, are a very effective incentive for me.

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


Another student described the adrenaline surge generated by exams asfollows:

There is nothing that can compare to the feeling you have while taking amath exam! Your heart is pounding and your mind is racing with thought.For me, there is a definite rush I experience when I take a math exam notonly because my intelligence is put to a test, but also because my gradesare on the line. What excites me is that if I do well on the exam thenI have beaten quite a formidable opponent. With math exams it truly iseither “do or die.”

The following is a simile written by a student who compared the motiva-tion generated by tests with a roller coaster ride.

When I know the material I get this surge to take exams. Inside my headI am saying, “Bring it on,” because I know that I am going to do well.But before I get that feeling, sometimes I go on what I call an emotionalroller coaster. I start at the bottom of the ride, and that is my studyingphase. I experience a special feeling at this stage, and it comes from menot comprehending the material, to me going ah ha! I finally understand.When everything finally makes sense is when I reach the highest point ofmy ride. The anxiety of the big drop is equivalent to waiting for the test.After the drop is over, and the test is handed out, I then relax and enjoythe ride.


Pointing out problems that are likely to appear on tests could help motivate stu-dents that fall into this category. Even inserting the word “exam” randomly inthe class can serve as a little call to arms. It would be easy to do this by finish-ing a problem on the board and then asking: “How could I ask a question likethis on an exam?” On the other hand, giving poorly designed or unpredictableexams can easily depress motivation for these students. This finding also sug-gests that frequently offering well-though-out exams would be an effectiveteaching strategy to keep these students motivated.

5.5. Learning Through Sharing

The mere fact of being able to teach mathematics to others made this type ofstudents eager to learn new concepts. These students felt not only motivatedbut also pleased to help their peers. One student summarized it as follows:

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


Another thing that gets me pumped is when I can explain a topic tosomeone else. The only way you can explain something is if you reallyunderstand it. Sometimes you don’t know you know it until you explainit. It also gives me a sense of fulfillment because I am able to helpsomeone else.


A strategy that can improve motivation in the classroom for these students isto encourage students to help each other or work in groups. This strategy hasto be dealt with carefully. Although teaching was a great motivator for manystudents, some specifically mentioned not liking it. Even working in groupsdoes not appeal to all students as explained by the following student:

When it comes to working with other people, I don’t do well in general.It’s not that I don’t get along with people, I just work much better alone.I don’t consider myself a very good teacher. Even if I know something, Iwill have trouble explaining it.

5.6. Approval from Family and Peers

Many students explained that motivation to do well in class came from theirneed to please their family and peers, especially their parents and friends. Oneof these students expressly stated,

Whenever I feel like skipping a class, not doing homework, or going outwhen I should be studying for an exam, my conscience tells me that Ishould be doing all the things that I want to avoid and I begin to feelguilty. I never want to disappoint my parents with bad grades and thatreally motivates me to stay on track at school.

The following excerpt is from a student who eloquently describes not onlyhow attaining the approval from family and friends can be motivating, but alsodescribes a particular gender perception of this motivation:

Being a female math major I often feel pressure to perform. My girl-friends always tell me that they are proud of me for sticking to math.Sometimes I feel like I am representing all of them, not just myself, whenI enter a math class . . . . Also, when I see a female mathematics professorI am always inspired . . . . I don’t work hard just for my financial statuslater in life. There are other people in my life besides me. These people

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


provide me with the motivation to crawl out from under my blankets inthe morning and drag myself to math class.


Since instructors do not have any contact with families or peers it is not clearhow we can address this motivation explicitly in the classroom. Approval fromfamily and peers plays an important role in everyday life for most people, notjust for students. Nonetheless, the need to show progress to family is intensifiedfor college students whose education is paid for by their parents.

5.7. A Final Note

Most of these motivations would be familiar to the readers from the experiencein their own departments.

6. CONCLUSION

The study described here sought to present the students’ views about whatmotivates them to learn mathematics at the sophomore level. What emergedis that students are motivated in many different (non-exclusive) ways.

The results indicate that for some students, motivation is generated withinthem as they conquer a difficult mathematical problem, while for othersmotivation comes from the rewards they may obtain as a result of learningmathematics. The results also suggest that some students consider that win-ning over their peers is motivating, while other students are motivated by thepressure of deadlines. Furthermore, some students find teaching motivating,while others find motivation in pleasing their families or friends.

Different teaching strategies were presented so that instructors can caterto a diverse group, that is, make informed decisions that would make classesinteresting and more engaging to as diverse a group of students as possible.

The reader may have noticed by now one deafening silence: although stu-dents mention grade school experience, none seem to mention the instructor ofthe section as a principal motivating factor. This is not to say that inspirationalinstructors do not exist. However, in this large multi-section service courses, itseems as if a student’s motivational orientation is more or less set by the timethey take this course.

It would be interesting to pursue the ideas of this article in a more rigor-ous study. For example, it would be nice to know whether there are importantdifferences in academic achievement between students who reported differ-ent types of motivations. The categories we mentioned were certainly notexclusive so it might also be interesting to ask students to assign weights to the

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


different motivations. Research could also focus on comparing the instructors’expectations of what motivates their classes with what the students actuallyreport.

In conclusion, on the basis of what we observed the best that instructorscan do is recognize their students’ motivational orientations and carefully tailortheir teaching to the different styles of their students. It is especially easy tothink of one style as the ideal and teach to students as if all should fall in thatmold. (Most mathematicians would tend to reward the intrinsic satisfactiongroup and hold this up as the ideal for the rest.) Maybe it is worth rememberingthat these classes have many different learning and motivational styles, and weshould try to be inclusive of all, and to take advantage of any different way wecan encourage or motivate them.

APPENDIX: COURSE TOPICS

For those readers interested in teaching a similar course, we included here a listof topics that would make up a typical semester’s material. A brief explanationof each topic is provided between parentheses.

1. Introduction/first impressions (Introductions, first week experience, andexpectations for the semester)

2. Interview (Interview with a successful student from a previous semesterabout learning strategies and experiences in multivariable calculus)

3. Motivation (Motivations to learn mathematics)4. Exam Preparation (Strategies to prepare for the first exam)5. Conceptual Problem (Solving a mathematical problem using the concepts

of the calculus course. For example: a Max/Min problem)6. Post-mortem (What went right and/or wrong in preparing for and taking

the exam)7. Take Stock (Mid-semester assessment of progress and strategies for the

second half of the semester)8. Online Search (Online exploration of resources available about a mathe-

matical concept from the calculus course)9. Software Exploration (Solving a mathematical problem using special

software. For example: Mathematica)10. Bill of Rights (Bill of Rights of a calculus student)11. Conceptual Problem (Solving a mathematical problem using the concepts

of the calculus course. For example: a line integral problem)12. Final Exam Preparations (Strategies to prepare for the final exam and for

the finals week)13. Final Report (Revised collection of essays including an introduction and a

conclusion)

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4


REFERENCES

1. Aunola, K., E. Leskinen, and J.-E. Nurmi. 2006. Developmental dynamicsbetween mathematical performance, task motivation, and teachers’ goalsduring the transition to primary school. British Journal of EducationalPsychology. 76(1): 21–40.

2. Boswell, J. Life of Johnson. http://www.netlibrary.com/Details.aspx?ProductId=1085526 Accessed 8 May 2009.

3. Gottfried, A. E. 1985. Academic and intrinsic motivation in elementaryand junior high school students. Journal of Educational Psychology. 77:631–645.

4. Gottfried, A. E. 1990. Academic intrinsic motivation in young elementaryschool children. Journal of Educational Psychology. 82: 525–538.

5. Ma, X. 1997. Reciprocal relationships between attitude toward mathematicsand achievement in mathematics. The Journal of Educational Research. 90:221–229.

6. Middleton, J. 1995. A study of motivation in the mathematics classroom:A personal constructs approach. Journal for Research in MathematicsEducation. 26(3): 254–279.

7. Nasar, S., and D. Gruber. 2006. Manifold destiny: A legendary problemand the battle over who solved it. New Yorker, August 28. http://www.newyorker.com. Accessed 8 May 2009.

BIOGRAPHICAL SKETCHES

Fabiana Cardetti is an assistant professor of mathematics at the Universityof Connecticut. She is also a teacher for a New Era Fellow at the university.She earned her Ph.D in control theory at Louisiana State University where shewas awarded certificates of teaching excellence. Her current research interestsinclude undergraduate mathematics education and teacher preparation.

Joe McKenna is a professor of mathematics at the University of Connecticut.He earned his Ph.D from the University of Michigan in 1976. He won theLester Ford prize for writing in the American Mathematical Monthly in 1999,and NES/MAA Award for Distinguished College or University Teaching ofMathematics in 2004. He is also listed at ISIhighlycited.com as a highly citedresearcher (in nonlinear differential equations).

Dow

nloa

ded

by [

UO

V U

nive

rsity

of

Ovi

edo]

at 0

5:41

27

Oct

ober

201

4

Documents

In Their Own Words: Getting Pumped for Calculus