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How to FAIL a Math Course

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Many students fail math because they don't do the work or don't show up to class. But some students do the work, show up to class, and still manage to fail. We'll look at some of the reasons why they fail, and what can be done about it.

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How to FAIL a Math Course

  1. 1. How to FAIL A Math Course Jeff Suzuki Department of Mathematics Brooklyn College Brooklyn NY 11210 jeff suzuki@yahoo.com J. Suzuki (CUNY) How to Fail Math 1 / 7
  2. 2. How To Fail Math (the Easy Way) The easy way to fail a math class: J. Suzuki (CUNY) How to Fail Math 2 / 7
  3. 3. How To Fail Math (the Easy Way) The easy way to fail a math class: Not being prepared for the class. J. Suzuki (CUNY) How to Fail Math 2 / 7
  4. 4. How To Fail Math (the Easy Way) The easy way to fail a math class: Not being prepared for the class. If you haven’t passed algebra, you probably shouldn’t take calculus. J. Suzuki (CUNY) How to Fail Math 2 / 7
  5. 5. How To Fail Math (the Easy Way) The easy way to fail a math class: Not being prepared for the class. If you haven’t passed algebra, you probably shouldn’t take calculus. Not going to class. J. Suzuki (CUNY) How to Fail Math 2 / 7
  6. 6. How To Fail Math (the Easy Way) The easy way to fail a math class: Not being prepared for the class. If you haven’t passed algebra, you probably shouldn’t take calculus. Not going to class. Registering for a course and not showing up to class is like buying lunch and leaving it on the counter: you’ve paid for it, but it won’t feed you. J. Suzuki (CUNY) How to Fail Math 2 / 7
  7. 7. How To Fail Math (the Easy Way) The easy way to fail a math class: Not being prepared for the class. If you haven’t passed algebra, you probably shouldn’t take calculus. Not going to class. Registering for a course and not showing up to class is like buying lunch and leaving it on the counter: you’ve paid for it, but it won’t feed you. Not doing the work. J. Suzuki (CUNY) How to Fail Math 2 / 7
  8. 8. How To Fail Math (the Easy Way) The easy way to fail a math class: Not being prepared for the class. If you haven’t passed algebra, you probably shouldn’t take calculus. Not going to class. Registering for a course and not showing up to class is like buying lunch and leaving it on the counter: you’ve paid for it, but it won’t feed you. Not doing the work. Since your grade depends on the work you’ve done, not doing the work is a guaranteed way to fail the course. J. Suzuki (CUNY) How to Fail Math 2 / 7
  9. 9. How To Fail Math (the Hard way) The hard way to fail a math class is to J. Suzuki (CUNY) How to Fail Math 3 / 7
  10. 10. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, J. Suzuki (CUNY) How to Fail Math 3 / 7
  11. 11. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, go to every class, J. Suzuki (CUNY) How to Fail Math 3 / 7
  12. 12. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, go to every class, and do all the work, J. Suzuki (CUNY) How to Fail Math 3 / 7
  13. 13. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, go to every class, and do all the work, then fail the class. J. Suzuki (CUNY) How to Fail Math 3 / 7
  14. 14. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, go to every class, and do all the work, then fail the class. How can you do this? J. Suzuki (CUNY) How to Fail Math 3 / 7
  15. 15. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, go to every class, and do all the work, then fail the class. How can you do this? I’ve been teaching math for 3413yearsfeet15.351 years, J. Suzuki (CUNY) How to Fail Math 3 / 7
  16. 16. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, go to every class, and do all the work, then fail the class. How can you do this? I’ve been teaching math for 3413yearsfeet15.351 years, but I’m still a math student, and still learning new things in mathematics. J. Suzuki (CUNY) How to Fail Math 3 / 7
  17. 17. How To Fail Math (the Hard way) The hard way to fail a math class is to be prepared for the course, go to every class, and do all the work, then fail the class. How can you do this? I’ve been teaching math for 3413yearsfeet15.351 years, but I’m still a math student, and still learning new things in mathematics. So I know how to fail math. J. Suzuki (CUNY) How to Fail Math 3 / 7
  18. 18. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. J. Suzuki (CUNY) How to Fail Math 4 / 7
  19. 19. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. J. Suzuki (CUNY) How to Fail Math 4 / 7
  20. 20. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. J. Suzuki (CUNY) How to Fail Math 4 / 7
  21. 21. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. Many students are taught that quadratic equations can be solved by factoring, so they factor: J. Suzuki (CUNY) How to Fail Math 4 / 7
  22. 22. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. Many students are taught that quadratic equations can be solved by factoring, so they factor: x2 − x − 6 = 10 J. Suzuki (CUNY) How to Fail Math 4 / 7
  23. 23. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. Many students are taught that quadratic equations can be solved by factoring, so they factor: x2 − x − 6 = 10 (x − 3)(x + 2) = 10 J. Suzuki (CUNY) How to Fail Math 4 / 7
  24. 24. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. Many students are taught that quadratic equations can be solved by factoring, so they factor: x2 − x − 6 = 10 (x − 3)(x + 2) = 10 This takes them quickly to the answers x = 3, x = −2. J. Suzuki (CUNY) How to Fail Math 4 / 7
  25. 25. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. Many students are taught that quadratic equations can be solved by factoring, so they factor: x2 − x − 6 = 10 (x − 3)(x + 2) = 10 This takes them quickly to the answers x = 3, x = −2. Unfortunately, these are the wrong answers. J. Suzuki (CUNY) How to Fail Math 4 / 7
  26. 26. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. Many students are taught that quadratic equations can be solved by factoring, so they factor: x2 − x − 6 = 10 (x − 3)(x + 2) = 10 This takes them quickly to the answers x = 3, x = −2. Unfortunately, these are the wrong answers. If you don’t know why, J. Suzuki (CUNY) How to Fail Math 4 / 7
  27. 27. How To Fail a Math Course: Memorizing Procedures Procedures are important time savers, and there are a few things that you should memorize. But memorizing a procedure without understanding why you’re doing it is a fast way to failure. For example: Solve x2 − x − 6 = 10. Many students are taught that quadratic equations can be solved by factoring, so they factor: x2 − x − 6 = 10 (x − 3)(x + 2) = 10 This takes them quickly to the answers x = 3, x = −2. Unfortunately, these are the wrong answers. If you don’t know why, you shouldn’t use this procedure. J. Suzuki (CUNY) How to Fail Math 4 / 7
  28. 28. How To Fail a Math Course: Following Examples Many math teachers (myself included!) give examples of how to solve problems, then assign problems based on those examples. J. Suzuki (CUNY) How to Fail Math 5 / 7
  29. 29. How To Fail a Math Course: Following Examples Many math teachers (myself included!) give examples of how to solve problems, then assign problems based on those examples. This gives the impression that the problems can be solved by following the examples. J. Suzuki (CUNY) How to Fail Math 5 / 7
  30. 30. How To Fail a Math Course: Following Examples Many math teachers (myself included!) give examples of how to solve problems, then assign problems based on those examples. This gives the impression that the problems can be solved by following the examples. However, it’s not possible to give examples of every situation that can occur, so you will ALWAYS encounter problems for which you’ve never seen an exemplar. J. Suzuki (CUNY) How to Fail Math 5 / 7
  31. 31. How To Fail a Math Course: Following Examples Many math teachers (myself included!) give examples of how to solve problems, then assign problems based on those examples. This gives the impression that the problems can be solved by following the examples. However, it’s not possible to give examples of every situation that can occur, so you will ALWAYS encounter problems for which you’ve never seen an exemplar. Focus on the reasoning behind the example, and not the details of the example itself. J. Suzuki (CUNY) How to Fail Math 5 / 7
  32. 32. How To Fail a Math Course: Working In Your Head Many math students (myself included!) practice mathematics by thinking about what they would do to solve a particular problem. J. Suzuki (CUNY) How to Fail Math 6 / 7
  33. 33. How To Fail a Math Course: Working In Your Head Many math students (myself included!) practice mathematics by thinking about what they would do to solve a particular problem. It’s a great workout, but it’s very easy to convince yourself that you know how to solve a problem, without actually being able to solve it. J. Suzuki (CUNY) How to Fail Math 6 / 7
  34. 34. How To Fail a Math Course: Working In Your Head Many math students (myself included!) practice mathematics by thinking about what they would do to solve a particular problem. It’s a great workout, but it’s very easy to convince yourself that you know how to solve a problem, without actually being able to solve it. This is because actual problems often have unexpected complications that aren’t apparent until you get to them. J. Suzuki (CUNY) How to Fail Math 6 / 7
  35. 35. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. J. Suzuki (CUNY) How to Fail Math 7 / 7
  36. 36. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Of course, if it can be reduced to a bumper sticker, it’s either very trivial . . . or very profound. J. Suzuki (CUNY) How to Fail Math 7 / 7
  37. 37. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Of course, if it can be reduced to a bumper sticker, it’s either very trivial . . . or very profound. I’m hoping for profound. J. Suzuki (CUNY) How to Fail Math 7 / 7
  38. 38. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. J. Suzuki (CUNY) How to Fail Math 7 / 7
  39. 39. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. J. Suzuki (CUNY) How to Fail Math 7 / 7
  40. 40. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. J. Suzuki (CUNY) How to Fail Math 7 / 7
  41. 41. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. J. Suzuki (CUNY) How to Fail Math 7 / 7
  42. 42. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. J. Suzuki (CUNY) How to Fail Math 7 / 7
  43. 43. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. It’s useful to know things besides the definitions, but if you don’t know the definitions, you can’t do mathematics. J. Suzuki (CUNY) How to Fail Math 7 / 7
  44. 44. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. It’s useful to know things besides the definitions, but if you don’t know the definitions, you can’t do mathematics. It doesn’t matter if you get it right at first, as long as you get it right at last. J. Suzuki (CUNY) How to Fail Math 7 / 7
  45. 45. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. It’s useful to know things besides the definitions, but if you don’t know the definitions, you can’t do mathematics. It doesn’t matter if you get it right at first, as long as you get it right at last. Once you get past the simplest arithmetic, there’s a lot of trial-and-error in mathematics, and the most important thing to remember about trial and error J. Suzuki (CUNY) How to Fail Math 7 / 7
  46. 46. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. It’s useful to know things besides the definitions, but if you don’t know the definitions, you can’t do mathematics. It doesn’t matter if you get it right at first, as long as you get it right at last. Once you get past the simplest arithmetic, there’s a lot of trial-and-error in mathematics, and the most important thing to remember about trial and error is that it involves a lot of errors and trying again. J. Suzuki (CUNY) How to Fail Math 7 / 7
  47. 47. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. It’s useful to know things besides the definitions, but if you don’t know the definitions, you can’t do mathematics. It doesn’t matter if you get it right at first, as long as you get it right at last. Once you get past the simplest arithmetic, there’s a lot of trial-and-error in mathematics, and the most important thing to remember about trial and error is that it involves a lot of errors and trying again. A little analysis goes a long ways. J. Suzuki (CUNY) How to Fail Math 7 / 7
  48. 48. Three Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. It’s useful to know things besides the definitions, but if you don’t know the definitions, you can’t do mathematics. It doesn’t matter if you get it right at first, as long as you get it right at last. Once you get past the simplest arithmetic, there’s a lot of trial-and-error in mathematics, and the most important thing to remember about trial and error is that it involves a lot of errors and trying again. A little analysis goes a long ways. Did I say three? I meant four. J. Suzuki (CUNY) How to Fail Math 7 / 7
  49. 49. Four Bumper Stickers Perhaps you don’t want to fail this math course. In that case, here are three bumper stickers you might take to heart. Paper is cheap, understanding is priceless. Write stuff down. Even if you can do several steps in your head, write them down one step at a time. Definitions are the whole of mathematics; all else is commentary. You MUST know the definitions, and understand the difference between definitions, theorems, and rules. It’s useful to know things besides the definitions, but if you don’t know the definitions, you can’t do mathematics. It doesn’t matter if you get it right at first, as long as you get it right at last. Once you get past the simplest arithmetic, there’s a lot of trial-and-error in mathematics, and the most important thing to remember about trial and error is that it involves a lot of errors and trying again. A little analysis goes a long ways. Analyze the problem before you start to write things down. J. Suzuki (CUNY) How to Fail Math 7 / 7

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