A. Sierpinska, G. Bobos, Ch. Knipping

**Research on students’ frustration in prerequisite mathematics courses**

Data from 2003-2004

RESPONSES TO QUESTIONNAIRE ITEM 76.* Complete the sentence, ‘Math is…”*

Responses 1-63 were provided by mature students (i.e. 21+ years old and having spent some time away from formal education)

Responses 64-96 were provided by non-mature students.

1.No answer

2.very hard and time consuming

3.interesting

4.No answer

5.a practical and objective way of thinking

6.sometimes requires a lot of thinking and time, not always easy, satisfying when a correct solution is found

7.a subject to practice or you'll never get it.

8.…challenging and difficult for me but if I practice at home it becames easy and fun.

9.fun

10.interesting but I think the teacher needs to be very helpful and students have to understand him (his accent)

11.I took math in high school and did very poorly which gave me a fear of having to take another math course. Last semester I tried taking math 202 but dropped it because I found it too difficult. This summer, I took math 200 and found it to be better than I thought. I ended up with an A but I worked really hard for it. This class gave me more confidence in my math skills. The professor was understanding of our situation, that being that there were many mature students in the class.

12.fun, when I'm not having my performance graded. Then I can just have fun.

13.Math is necessary, despite whether it is liked or not.

14.…a subject which can complicated, but with a teacher who is patient and articulate, math can enjoyable and marks can be obtained.

15.…like sports. The more you practice the better you get.

16.very useful but not everyone can get deep into it

17.Obviously Math can be an emotional course to take and our self-perception play an important role in how well we do. However, I have to admit that this was the worse academic experience that I had a Concordia. I first enrolled in the course last Winter and dropped it. I enrolled a second time during the Summer and to my surprise I got the same instructor. She was very kind and pleasant, however, had very poor teaching and language skills. Which make it very difficult to obtain answers to precise questions in class. I often saw the instructor out of class to clarify any questions. I end up having to hire a Math tutor whose skills, patience and knowledge saved my semester. I wish I had done it earlier during the course, maybe I would got a better mark than a D+, which brought my GPA to under 2.50, not enabling me to be accepted at the Psy. program. So I guess, today I'm little resentful of Concordia's Math department and their lack of accountability towards the students.

18.a beautiful, natural science. It is amazing how these geniuses through history created with logical thinking something like this.

19.a hard subject that you can succeed in if you try

20.time consuming

21.a complete waste of time unless it is specifically geared towards the field you are going into. (Please know, I have nothing against people who have made math their career and life choice - but understand for some of us, the subject gives us nightmares, heart palpitations and cold sweats just thinking about it)

22.a method of thinking… it is logic.

23.difficult

24.very technical and I am only taking it because it is a prerequisite for my program.

25.…one possible way to find out how the world works:)…and how far the constructive capacity of human's brain can go… and to find out systematic rules for the physical phenomena in the world

26.Too rational for my irrational brain, but I still would like to understand and find it easy. I'd say that I have other talent I 'm proud of, but math is not one of them. I could also say that it take one and a half times more than an average student to understand, probably because my brain haven't been trained often and in a long time to solve problem. I think I need to start my learning at the very beginning.

27.the purest form of truth and its existence transcends man, earth and the whole of the universe. It is the one logical argument that there is a superior order of things

28.a different kind of language that explains our world. The more languages you know, the better you can understand things. NOTE: One comment I'd like to make… I think a lot of people's problems in MATH201 is that they lack the background in things like factoring and addition/subtraction/multiplying/dividing fractions. Perhaps in the course outline, you should recommend learning those things before taking the course? They could take a summer course on it or something. A lot of people understand the new stuff, but without knowing the old stuff they still get questions wrong. Just an idea...

29.logical.

30.Math is not my subject of interest but somehow an environmentalist needs it

31.math is like love: a simple idea, but it can get complicated

32.…very interesting and can be fun to learn if the teacher cares about the students and tries to help them understand the concepts.

33.Lovely if you know it.

34.Math is truth preservation through mathematical inference (I'm kidding). Math is not not math (kidding again). Math is the tool of science. If one learns math, one can go about reading physics without much trouble (and other sciences with a little bit more work, that is learning definitions of jargon), but math can be seen as a Swiss army knife in this case. But math can also be seen as a theoretical investigation of the most powerful formal system that man has created/discovered. However, math is being presented to students like a set of fixed rules. In a way I am surprised that most people don't care to ask what the axioms are (even if math is not a purely axiomatic system), but what I mean is that I am surprised that most people don't care to ask why these rules hold. But the reason why I am not surprised is part of the answer to my previous question. People are massively fallacious. A few good instances will convince most people that a rule works (confirmation bias). In psychological experiment, people were told that there is a rule: "on the opposite side of a card with a vowel is the color red". The subject is presented with 4 card: a blue, a red, an 'A' and a 'B'. They had to choose one card to test the rule. A majority of people chose the 'A' to test (verify) the rule, instead of trying to falsify it. (I think that's how the story goes). Of course, no one would try to falsify a mathematical rule in that way, like observing triangles to see if the sum of the angle equals the sum of two right angles. But what is forgotten is that there are presuppositions about the status of the Euclidian space. All this I am babbling about is really to illustrate that the way mathematics is being in though is in a 'rule-giving' fashion (as logic is being thought). The goal is to form specialists/technicians, at least in the branch of mathematics I took this course. I don't think math class should be taught like history classes, but I seriously don't know how. I don't think people are fools and only care to learn the formulas, I am sure that if the class had a tiny bit of contextual content, it might be more interesting. Just a bit. I haven't taken calculus, and don't intend to (i'd rather learn it on my own, and learn what I need), but I wonder how the concept of limit and infinity is generally being taught. As a matter of fact, I was reading this paper by Michel Baranger ( http://necsi.org/projects/baranger/cce.pdf ), and he is actually hold the view that in physics department, analysis is presented as the ultimate tool to understand the world, and that with enough effort and computing power, it could solve everything. That is to say that there is a way in wish math is seen as a problem solving tool within a certain scope/domain, no one ever mentions the results from chaos theory, because the generation of people teaching these thing don't really know or don't really care. So maybe a bit more of context about the application and limitation of some mathematical branch might be appropriate. Now I am really far from the question of completing the sentence. If you've read up until now, you probably think I'm crazy, or maybe not. I will just go back to the original question. So, math is so profound, that unless students are engaged in theoretical problems of mathematics, I doubt that the educational system will ever give them greater insights on the very tools they will be using everyday. (Except maybe statistician who reflect on the limits of their models.) I hope you're research will be fruitful and that you'll get some results to improve the teaching methods of mathematics. Also, I hope my input was of some interest to you.

35.essential in this world to solve daily problems.

36.everywhere and relates to almost every aspect of our lives.

37.FANTASTIC

38.Extremely discouraging when you are forced to take it as a prerequisite. If I was going into Arts program with a major in math, then I would understand that the course is necessary. However, in the commerce program, there is nowhere near as much or as difficult math as I have just taken. I also have another year of math prerequisites to take in order to get into the program I want. If I fail math, I don't get into commerce. So I feel math is the only thing that's stopping me from getting into the program I want. I can't imagine the number of people who have dropped out of their dream just because of one subject that got in their way. I am currently spending 20 hours of studying math outside of class and I got 30% on my midterm. I'm starting to think that I'm the problem, and that's very discouraging. Hopefully math 208 and 209 will be a little less stressful.

39.not for everyone and wonder really if the pre-requisite classes are really well demanded… Many people in marketing at my job, tell me they don't understand why we have to go through algebra… Stats yes, but not algebra…

40.the universal language

41.boring. Especially in university. The only teacher that I've had who is interesting and engages the students is [*name concealed by researcher*].

42.a course which requires a lot of work to succeed in.

43.interesting, and important

44.…fun but demands a lot of reasoning and time for practice.

45.…a subject which I intend to comprehend more feel more comfortable with. It is an invaluable tool for my future goals. Financial and career.

46.Math is good to develop our analytic skills. However, in my case, I am taking up bachelor's degree in commerce, major in accountancy and is already an accountant from another country, I think MATH 209 - Calculus is no longer useful to this program. But I really work hard to it because I need to proceed with my accountancy. There are some who failed and get discouraged and will rather not proceed with the program which is not really reasonable because calculus is not helpful for accountancy. I'd rather spend my time studying to something that is related or in preparation to accounting courses. Calculus is good for engineering and math major, I think. But that's the university requirements, so I just have to abide in order for me to have a diploma in accountancy.

47.interesting but hard.

48.very complicated if you don't understand the rules.

49.very interesting

50.fascinating and challenging

51.… a very interesting study because if you follow the steps, you'll get the answers eventually.

52.for nerds

53.not for me.

54.perfection in the abstract form

55.necessary but tedious

56.part of our everyday life, but not in the way it is taught to us. I'm a future commerce student, and I can't/ see how I will need the course material (except for interest, which is part of the Finance class).

57.difficult but necessary

58.Challenging and fun if you understand the theories and know how to apply them (applications) or can be frustrating if you miss out on the understanding (comprehension) of basic theories

59.OK

60.interesting

61.analytical study

62.…hard, complicated but very interesting.

63.easy to learn, extremely difficult to remember

64.for those who are pursuing a career in mathematics

65.…something that can be used to explain almost everything; …international language

66.challenging

67.a necessity.

68.never easy

69.an important course and always helpful, but not necessarily for everyone. It is sometimes hard and needs a lot of studying and motivation. (I hope that my answers will help you. Please do not hesitate to e-mail me again if you have any other questions !)

70.interesting to learn if the theory can be applied to everyday situations.

71.a subject I am not interested in

72.really interesting subject which needs a lot of knowledge , specially is necessary to have a really good background of it so it wouldn't be so hard

73.I have no choice

74.interesting to learn

75.fun

76.A subject that is not only about calculation and rules. It forces U to use your background knowledge of math and the rules U have remembered in order to be able to solve a mathematical problem. And most importantly, it requires patience and accuracy.

77.great if you understand it but horrible if you don't.

78.not difficult if you just do the homework

79.Hell. No…it's for some people, but not for me…I'm lucky that I can do it if I need to, but I'd rather pretend it doesn't exist.

80.quite the stressful subject!!!

81.No answer

82.not fun and takes lots of time

83.strange, frustrating, exhilarating and terrific.

84.everywhere

85.no answer

86.fun if you understand it, when you don't it's confusing and stressful. It has to click if it doesn't you will never understand what you are learning.

87.beautiful once understood.

88.OKAY

89.a necessary course

90.complicated and requires a lot of time to study to get a good grade

91.fun when I understand it. When I understand my homework and get the problems right, I love it. It gives me a lot of motivation to pursue. I guess this is why I never missed a class. I enjoyed math this semester, even though it was challenging at times. I always used to think people are either good, or either bad in math. and I used to think I was simply bad, but I can see now how hard work and dedication pays off and I am really liking it.

92.learning how to think and solve problems given to you (either in math or in the outside world)

93.challenging and interesting

94.trying to discover the logic behind all the numbers, rules and formulas

95.boring when you have to take the same course over and over and over, just because of a computer error, or previously poor marks (especially when more advanced courses were given good marks)

96.… fun! (when you understand) otherwise, it gives headaches!

Data from 2003-2004

RESPONSES TO QUESTIONNAIRE ITEM 76.

Responses 1-63 were provided by mature students (i.e. 21+ years old and having spent some time away from formal education)

Responses 64-96 were provided by non-mature students.

1.No answer

2.very hard and time consuming

3.interesting

4.No answer

5.a practical and objective way of thinking

6.sometimes requires a lot of thinking and time, not always easy, satisfying when a correct solution is found

7.a subject to practice or you'll never get it.

8.…challenging and difficult for me but if I practice at home it becames easy and fun.

9.fun

10.interesting but I think the teacher needs to be very helpful and students have to understand him (his accent)

11.I took math in high school and did very poorly which gave me a fear of having to take another math course. Last semester I tried taking math 202 but dropped it because I found it too difficult. This summer, I took math 200 and found it to be better than I thought. I ended up with an A but I worked really hard for it. This class gave me more confidence in my math skills. The professor was understanding of our situation, that being that there were many mature students in the class.

12.fun, when I'm not having my performance graded. Then I can just have fun.

13.Math is necessary, despite whether it is liked or not.

14.…a subject which can complicated, but with a teacher who is patient and articulate, math can enjoyable and marks can be obtained.

15.…like sports. The more you practice the better you get.

16.very useful but not everyone can get deep into it

17.Obviously Math can be an emotional course to take and our self-perception play an important role in how well we do. However, I have to admit that this was the worse academic experience that I had a Concordia. I first enrolled in the course last Winter and dropped it. I enrolled a second time during the Summer and to my surprise I got the same instructor. She was very kind and pleasant, however, had very poor teaching and language skills. Which make it very difficult to obtain answers to precise questions in class. I often saw the instructor out of class to clarify any questions. I end up having to hire a Math tutor whose skills, patience and knowledge saved my semester. I wish I had done it earlier during the course, maybe I would got a better mark than a D+, which brought my GPA to under 2.50, not enabling me to be accepted at the Psy. program. So I guess, today I'm little resentful of Concordia's Math department and their lack of accountability towards the students.

18.a beautiful, natural science. It is amazing how these geniuses through history created with logical thinking something like this.

19.a hard subject that you can succeed in if you try

20.time consuming

21.a complete waste of time unless it is specifically geared towards the field you are going into. (Please know, I have nothing against people who have made math their career and life choice - but understand for some of us, the subject gives us nightmares, heart palpitations and cold sweats just thinking about it)

22.a method of thinking… it is logic.

23.difficult

24.very technical and I am only taking it because it is a prerequisite for my program.

25.…one possible way to find out how the world works:)…and how far the constructive capacity of human's brain can go… and to find out systematic rules for the physical phenomena in the world

26.Too rational for my irrational brain, but I still would like to understand and find it easy. I'd say that I have other talent I 'm proud of, but math is not one of them. I could also say that it take one and a half times more than an average student to understand, probably because my brain haven't been trained often and in a long time to solve problem. I think I need to start my learning at the very beginning.

27.the purest form of truth and its existence transcends man, earth and the whole of the universe. It is the one logical argument that there is a superior order of things

28.a different kind of language that explains our world. The more languages you know, the better you can understand things. NOTE: One comment I'd like to make… I think a lot of people's problems in MATH201 is that they lack the background in things like factoring and addition/subtraction/multiplying/dividing fractions. Perhaps in the course outline, you should recommend learning those things before taking the course? They could take a summer course on it or something. A lot of people understand the new stuff, but without knowing the old stuff they still get questions wrong. Just an idea...

29.logical.

30.Math is not my subject of interest but somehow an environmentalist needs it

31.math is like love: a simple idea, but it can get complicated

32.…very interesting and can be fun to learn if the teacher cares about the students and tries to help them understand the concepts.

33.Lovely if you know it.

34.Math is truth preservation through mathematical inference (I'm kidding). Math is not not math (kidding again). Math is the tool of science. If one learns math, one can go about reading physics without much trouble (and other sciences with a little bit more work, that is learning definitions of jargon), but math can be seen as a Swiss army knife in this case. But math can also be seen as a theoretical investigation of the most powerful formal system that man has created/discovered. However, math is being presented to students like a set of fixed rules. In a way I am surprised that most people don't care to ask what the axioms are (even if math is not a purely axiomatic system), but what I mean is that I am surprised that most people don't care to ask why these rules hold. But the reason why I am not surprised is part of the answer to my previous question. People are massively fallacious. A few good instances will convince most people that a rule works (confirmation bias). In psychological experiment, people were told that there is a rule: "on the opposite side of a card with a vowel is the color red". The subject is presented with 4 card: a blue, a red, an 'A' and a 'B'. They had to choose one card to test the rule. A majority of people chose the 'A' to test (verify) the rule, instead of trying to falsify it. (I think that's how the story goes). Of course, no one would try to falsify a mathematical rule in that way, like observing triangles to see if the sum of the angle equals the sum of two right angles. But what is forgotten is that there are presuppositions about the status of the Euclidian space. All this I am babbling about is really to illustrate that the way mathematics is being in though is in a 'rule-giving' fashion (as logic is being thought). The goal is to form specialists/technicians, at least in the branch of mathematics I took this course. I don't think math class should be taught like history classes, but I seriously don't know how. I don't think people are fools and only care to learn the formulas, I am sure that if the class had a tiny bit of contextual content, it might be more interesting. Just a bit. I haven't taken calculus, and don't intend to (i'd rather learn it on my own, and learn what I need), but I wonder how the concept of limit and infinity is generally being taught. As a matter of fact, I was reading this paper by Michel Baranger ( http://necsi.org/projects/baranger/cce.pdf ), and he is actually hold the view that in physics department, analysis is presented as the ultimate tool to understand the world, and that with enough effort and computing power, it could solve everything. That is to say that there is a way in wish math is seen as a problem solving tool within a certain scope/domain, no one ever mentions the results from chaos theory, because the generation of people teaching these thing don't really know or don't really care. So maybe a bit more of context about the application and limitation of some mathematical branch might be appropriate. Now I am really far from the question of completing the sentence. If you've read up until now, you probably think I'm crazy, or maybe not. I will just go back to the original question. So, math is so profound, that unless students are engaged in theoretical problems of mathematics, I doubt that the educational system will ever give them greater insights on the very tools they will be using everyday. (Except maybe statistician who reflect on the limits of their models.) I hope you're research will be fruitful and that you'll get some results to improve the teaching methods of mathematics. Also, I hope my input was of some interest to you.

35.essential in this world to solve daily problems.

36.everywhere and relates to almost every aspect of our lives.

37.FANTASTIC

38.Extremely discouraging when you are forced to take it as a prerequisite. If I was going into Arts program with a major in math, then I would understand that the course is necessary. However, in the commerce program, there is nowhere near as much or as difficult math as I have just taken. I also have another year of math prerequisites to take in order to get into the program I want. If I fail math, I don't get into commerce. So I feel math is the only thing that's stopping me from getting into the program I want. I can't imagine the number of people who have dropped out of their dream just because of one subject that got in their way. I am currently spending 20 hours of studying math outside of class and I got 30% on my midterm. I'm starting to think that I'm the problem, and that's very discouraging. Hopefully math 208 and 209 will be a little less stressful.

39.not for everyone and wonder really if the pre-requisite classes are really well demanded… Many people in marketing at my job, tell me they don't understand why we have to go through algebra… Stats yes, but not algebra…

40.the universal language

41.boring. Especially in university. The only teacher that I've had who is interesting and engages the students is [

42.a course which requires a lot of work to succeed in.

43.interesting, and important

44.…fun but demands a lot of reasoning and time for practice.

45.…a subject which I intend to comprehend more feel more comfortable with. It is an invaluable tool for my future goals. Financial and career.

46.Math is good to develop our analytic skills. However, in my case, I am taking up bachelor's degree in commerce, major in accountancy and is already an accountant from another country, I think MATH 209 - Calculus is no longer useful to this program. But I really work hard to it because I need to proceed with my accountancy. There are some who failed and get discouraged and will rather not proceed with the program which is not really reasonable because calculus is not helpful for accountancy. I'd rather spend my time studying to something that is related or in preparation to accounting courses. Calculus is good for engineering and math major, I think. But that's the university requirements, so I just have to abide in order for me to have a diploma in accountancy.

47.interesting but hard.

48.very complicated if you don't understand the rules.

49.very interesting

50.fascinating and challenging

51.… a very interesting study because if you follow the steps, you'll get the answers eventually.

52.for nerds

53.not for me.

54.perfection in the abstract form

55.necessary but tedious

56.part of our everyday life, but not in the way it is taught to us. I'm a future commerce student, and I can't/ see how I will need the course material (except for interest, which is part of the Finance class).

57.difficult but necessary

58.Challenging and fun if you understand the theories and know how to apply them (applications) or can be frustrating if you miss out on the understanding (comprehension) of basic theories

59.OK

60.interesting

61.analytical study

62.…hard, complicated but very interesting.

63.easy to learn, extremely difficult to remember

64.for those who are pursuing a career in mathematics

65.…something that can be used to explain almost everything; …international language

66.challenging

67.a necessity.

68.never easy

69.an important course and always helpful, but not necessarily for everyone. It is sometimes hard and needs a lot of studying and motivation. (I hope that my answers will help you. Please do not hesitate to e-mail me again if you have any other questions !)

70.interesting to learn if the theory can be applied to everyday situations.

71.a subject I am not interested in

72.really interesting subject which needs a lot of knowledge , specially is necessary to have a really good background of it so it wouldn't be so hard

73.I have no choice

74.interesting to learn

75.fun

76.A subject that is not only about calculation and rules. It forces U to use your background knowledge of math and the rules U have remembered in order to be able to solve a mathematical problem. And most importantly, it requires patience and accuracy.

77.great if you understand it but horrible if you don't.

78.not difficult if you just do the homework

79.Hell. No…it's for some people, but not for me…I'm lucky that I can do it if I need to, but I'd rather pretend it doesn't exist.

80.quite the stressful subject!!!

81.No answer

82.not fun and takes lots of time

83.strange, frustrating, exhilarating and terrific.

84.everywhere

85.no answer

86.fun if you understand it, when you don't it's confusing and stressful. It has to click if it doesn't you will never understand what you are learning.

87.beautiful once understood.

88.OKAY

89.a necessary course

90.complicated and requires a lot of time to study to get a good grade

91.fun when I understand it. When I understand my homework and get the problems right, I love it. It gives me a lot of motivation to pursue. I guess this is why I never missed a class. I enjoyed math this semester, even though it was challenging at times. I always used to think people are either good, or either bad in math. and I used to think I was simply bad, but I can see now how hard work and dedication pays off and I am really liking it.

92.learning how to think and solve problems given to you (either in math or in the outside world)

93.challenging and interesting

94.trying to discover the logic behind all the numbers, rules and formulas

95.boring when you have to take the same course over and over and over, just because of a computer error, or previously poor marks (especially when more advanced courses were given good marks)

96.… fun! (when you understand) otherwise, it gives headaches!