WHAT STUDENTS THINK ABOUT A



WHAT STUDENTS THINK ABOUT A

CONSORTIUM’S APPROACH CALCULUS I CLASS

Kathleen Cage Mittag

University of Texas at San Antonio

210-458-5851

kmittag@lonestar.jpl.utsa.edu

Abstract

This paper presents results of a survey and a questionnaire that were given in a Calculus class which was taught using the Calculus Consortium’s Approach. The textbook Calculus (Hughes-Hallett, Gleason, et al., 1994) was used along with cooperative learning, extensive graphing calculator applications, and laboratories. The survey was a mathematics attitude survey given the first class meeting and the last class meeting. Pre and post results of the surveys were tabulated and compared. Attitudes of the students improved in most of the categories. The questionnaire was given the last class meeting and included questions about students’ previous calculus experience, thoughts about the teaching method and textbook, and opinions of the graphing calculator. The majority (89%) of the students liked the method and all the students think the graphing calculator is a good tool to use for calculus. Hopefully, calculus reform will evolve into a methodology which improves student comprehension and attitudes.

Introduction

The Calculus Consortium based at Harvard and funded by the National Science Foundation created a calculus textbook, Calculus, which was guided by two principals (Hughes-Hallett, Gleason, et al., 1994):

The Rule of Three: Every topic should be presented geometrically, numerically, and algebraically.

The Way of Archimedes: Formal definitions and procedures evolve from the investigation of practical problems.

The author used this textbook for the first time in Calculus I during the Spring 1996. During the first class meeting students were asked to complete a mathematics attitude survey. The survey was given again during the last class meeting and also included a questionnaire about the students’ previous calculus experiences, thoughts about the teaching method and textbook, and opinions of the graphing calculator. The survey and questionnaire are included in Appendix A. All surveys and questionnaires were anonymous. Students chose some identification mark to put on each survey in order for individual pre and post scores to be tabulated. Results of the surveys and questionnaire will be discussed in this paper.

Calculus I Course

Graphing calculators are essential for this course. They were used for teacher and student demonstrations, inquiry lessons, cooperative learning, homework, laboratories, and on tests. Group work and laboratories were also utilized extensively. Laboratories and daily grades counted 30% of the semester grade. The students attended class three hours per week and lab one hour per week. The lab was taught by a teaching assistant. Two unit tests and a comprehensive final counted for 70% of the grade.

Mathematics Attitude Survey

A mathematics attitude survey titled, Mathematics and Me, by Dr. Ralph Anttonen was administered the first and last class meetings. Sixteen students completed both surveys. The survey was a Lickert type which contained eighteen word pairs. The students had to put an X near the word indicating very strong feelings or in the middle of the pair indicated neutrality. An example is:

A B C D E

enjoyable __X__:_____:_____:_____:_____ distasteful

which shows the student finds mathematics very enjoyable.

Numerical values were assigned to the letters as follows:

A - 1 point; B - 2 points; C - 3 points; D - 4 points; and E - 5 points

A class score was tabulated for each word pair on both surveys. Differences in the scores from the pre and post surveys were calculated. Complete results of the surveys are included in Appendix B.

The results indicate that the students’ scores improved for the following word pairs:

1. enjoyable-distasteful

4. relaxed-tense

5. strange-familiar

9. high-low

11. cruel-kind

12. easy-hard

13. good-bad

15. unpleasant-pleasant

The student scores differed by only one point for the following word pairs:

2. active-passive

6. negative-positive

7. sharp-dull

10. valuable-worthless

17. weak-strong

The student scores went down for the following word pairs:

8. worst-best

18. unfair-fair

The following word pairs did not measure improvement or no improvement:

3. heavy-light

14. unusual-usual

16. fast-slow

As the scores indicate, the majority of student attitudes improved since the differences for only two word pairs did not indicate improvement.

Questionnaire

A calculus questionnaire was given to the students during the last class meeting. Nineteen students completed the questionnaire. Seven students had previously taken calculus in high school and one in college. All but two of these students had taken calculus in the last two years. Five of the eight students had used graphing calculators in the previous calculus course but none had used computers.

Two open-ended questions were asked. The first question for students who had taken calculus previously was:

How does this method (textbook) compare to previous method?

Comments for this question were as follow:

1. All the calculators are different to operate so it was hard to figure out what buttons to use and I had never used a graphing calculator before. Also, some calculators did not do certain functions.

2. More flexible and average to fair.

3. Tries too hard to be “modern”. I preferred learning by “classical method”. (this student had last taken calculus ten years ago.)

4. I did not really look at this book a whole lot, but what I did came across as “user friendly.”

5. Sucks. Completely different order. Out of order to me.

6. Nothing especially helpful, seemed similar to the past methods.

7. Easier. More practical. Easier to apply.

8. Easier to comprehend.

The first question for students who had not previously taken calculus was:

If no, what did you think of the method (textbook) used to teach this course?

Comments for this question were as follow:

1. It was OK. Fun.

2. The method in the book helped because it started out with material that was familiar to me.

3. I think there should be more examples before the problems.

4. I think it was pretty cool but it should show more of the traditional way to better help us out.

5. I liked it because it showed me how to work with graphing calculators and taught me a inductive way of studying calculus.

6. The class provided a better understanding of the formulas that are utilized universally. The hows and whys!

7. I think this method is suspicious. From all I’ve heard about calculus it sounded like “torture.”

8. Very good most of the time.

9. It’s pretty good for not be exposed to any other method.

The last question was for all the students and it follows:

For everyone, what do you think about graphing calculators?

The comments follow:

1. I’ve finally found use for it. I bought it for trig in high school and this is the first time I’ve used it really.

2. They are helpful in this class and simplify complicated expressions.

3. I think they rock!!

4. I like it!!

5. It showed me that even I can operate a more complicated electronic device.

6. The graphing calculator is pretty useful.

7. They can help if they are easy to use.

8. I think they are pretty useful because I had never used them before but the instruction booklet should have a little flash card or quick reference to help out a little bit.

9. I think they are useful but there are a lot of skills that can be developed without them.

10. They are complicated to learn to use, but with practice I hope I will get better at using them.

11. It was fun to play with.

12. Once you are able to use them, they are great.

13. Cool.

14. They’re nice for some problems; but for others they aren’t so good.

15. Great tool.

16. They are very useful but only if you know the material beforehand. Graphing calculators were a wonderful reinforcement, but not a good teacher.

17. It does help to visualize the problems.

18. Good but company manuals or pamphlets would be nice.

Conclusion

Results of the surveys and questionnaires indicate that the majority (89%) of the students like the Consortium’s Approach to calculus. There were only two students who questioned the method. All the students think the graphing calculator is a good tool to use in calculus. Students’ attitudes improved while taking the calculus course. Hopefully, the teaching method contributed to some of this improvement. The questionnaire will be expanded to include questions about cooperative learning and laboratories in the Fall 1996. Hopefully, calculus reform will help improve learning and attitudes for future students.

REFERENCES

Anttonen, R. Mathematics and me. A mathematics attitude survey. Stephen F. Austin State University, Nacogdoches, Texas.

Hughes-Hallett, D., Gleason, A., and others. (1994). Calculus. New York: John Wiley & Sons, Inc.

APPENDIX A

Mathematics and Me

(By Dr. Ralph Anttonen)

We are interested in how you feel about mathematics.

Below is a list of word pairs that look like this:

good _____:_____:_____:_____:_____ bad

If you feel very good about mathematics, place an X near good.

good __X__:_____:_____:_____:_____ bad

If you feel very bad about mathematics, place an X near bad.

good _____:_____:_____:_____:___X_ bad

If you do not feel either very good or very bad about mathematics, place an X closer to the middle.

IMPORTANT: Mark an X for every word pair. Mark only one X for every word pair. Remember, we want you first feeling for each work pair.

A B C D E

1. enjoyable _____:_____:_____:_____:_____ distasteful

2. active _____:_____:_____:_____:_____ passive

3. heavy _____:_____:_____:_____:_____ light

4. relaxed _____:_____:_____:_____:_____ tense

5. strange _____:_____:_____:_____:_____ familiar

6. negative _____:_____:_____:_____:_____ positive

7. sharp _____:_____:_____:_____:_____ dull

8. worst _____:_____:_____:_____:_____ best

9. high _____:_____:_____:_____:_____ low

10. valuable _____:_____:_____:_____:_____ worthless

11. cruel _____:_____:_____:_____:_____ kind

12. easy _____:_____:_____:_____:_____ hard

13. good _____:_____:_____:_____:_____ bad

14. unusual _____:_____:_____:_____:_____ usual

15. unpleasant_____:_____:_____:_____:_____ pleasant

16. fast _____:_____:_____:_____:_____ slow

17. weak _____:_____:_____:_____:_____ strong

18. unfair _____:_____:_____:_____:_____ fair

CALCULUS I SURVEY

Classification:______________

1. Have you taken calculus before this course? ___________

2. If yes,

a) when? __________

b) high school or college?_____________

c) how many semesters? ___________

d) How does this method (textbook) compare to previous method?

e) Were graphing calculators used as much as we did?_________

f) Were computers used extensively?___________

3. If no to question 1, what did you think of the method (textbook) used to teach this course?

4. For everyone, what do you think about graphing calculators?

Thanks and have a great summer!!

APPENDIX B

RESULTS OF PRE AND POST SURVEYS

Word Pair Pre-score Post-score Post - Pre Want

1. enjoyable-distasteful 36 31 -5 neg

2. active-passive 35 36 1 neg

3. heavy-light 46 44 -2 ?

4. relaxed-tense 48 46 -2 neg

5. strange-familiar 63 68 5 pos

6. negative-positive 64 63 -1 pos

7. sharp-dull 35 36 1 neg

8. worse-best 59 55 -4 pos

9. high-low 42 34 -8 neg

10. valuable-worthless 25 26 1 neg

11. cruel-kind 50 57 7 pos

12. easy-hard 54 42 -12 neg

13. good-bad 32 30 -2 neg

14. unusual-usual 64 55 -9 ?

15. unpleasant-pleasant 55 58 3 pos

16. fast-slow 39 37 -2 ?

17. weak-strong 59 60 1 pos

18. unfair-fair 68 64 -4 pos

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