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The response to low graduation rates can't be to further dumb down the degree. Every functioning adult should understand algebra. I'd actually argue that trig

The response to low graduation rates can't be to further dumb down the degree. Every functioning adult should understand algebra. I'd actually argue that trigonometry should also be included in this list, but that's probably only useful for adults who build things, and sadly, not very many adults do build things these days. Instead of removing Algebra, we need to consider better ways to teach this subject to people who do not have a lot of the fundamentals in place already. One of the biggest problems with College Algebra is that it assumes a certain level of math literacy that isn't universal. Algebra simply isn't that hard of a subject to master, but it is something that requires a different sort of teaching strategy than is used at the average community college. Give me a motivated adult who understands basic arithmetic, and I can help him or her master algebra in six to eight weeks. We can go from zero to FOIL, and quadratic to partial fraction decomposition in that amount of time. The key is to listen and to instill a level of confidence as early as possible in this process. Many adults consider math to be "hard" -- not from the perspective of it actually being hard, which it is -- but from the perspective of "this is too hard for me to do, because I'm not a math person." Break this mental block, and anyone can do algebra.

plandis 9y ago
Why do you think that every functioning adult should understand algebra?
- trendia 9y ago
  Is it cheaper to buy 1 case of water for $2.50 or 3 cases of water for $9.00 ? If you get a $1,000 loan at 1% interest each month, how much will you owe in 1 year? You can buy a phone for $500 or pay Verizon $16.70 / month for 36 months. Which is cheaper?
  - deleted 9y ago
    [deleted]
  - bcruddy 9y ago
    > If you get a $1,000 loan at 1% interest each month, how much will you owe in 1 year? Pe = nRT is actually the first thing taught in calc 1.
  - vmarsy 9y ago
    > Is it cheaper to buy 1 case of water for $2.50 or 3 cases of water for $9.00 Slightly off topic as I don't think this is college level algebra, in supermarkets in Europe they are required by law to put the "€/liter" price in small on the side, so you can compare easily. In the US it doesn't seem mandatory, or at least the unit is not mandatory because sometimes they use fl oz, sometimes gallons, or for pieces of meat sometimes oz, sometimes lbs, so when you want to compare the prices of 2 similar items, what would just take you 0.5 sec in Europe takes you much longer in the US since you need to add unit conversion in the mix. For example here your "cases" could be of different sizes, that 1 case of water could be 2L ,while those 3 cases could be a gallon each...
    - dozzie 9y ago
      > [...] in supermarkets in Europe they are required by law to put the "€/liter" price in small on the side, so you can compare easily. Yeah, and then you get aggregate price in "€/package", except that packages are of different size.
      - majewsky 9y ago
        Or they switch between "€/kg", "€/100 g", "€/liter", and "€/package" seemingly randomly.
  - bsder 9y ago
    I don't need algebra for 2 of those. I need the ability to do fast mental arithmetic. And a shop math class would be far more useful for that. As for compound interest, you need WAY more than algebra ...
    - throwawayjava 9y ago
      > I don't need algebra for 2 of those. All of these are literally the sorts of things you'd find on homework assignments and final exams in a community college algebra course... You do need algebra, and don't realize how difficult this "trivial" algebra is for some students because you can do it without even realizing you're doing it. I mean, there will be some FOIL and quadratic equation examples as well. And a bunch of stuff in-between like identifying graphs of functions. But CC Algebra is super bimodal, so it's probably not the case that students are nailing these word problems and only failing with the other stuff.
- nanolith 9y ago
  I think that trendia already touched on a lot of these, but consider the typical every day problems that require algebra to solve: An item at the store is listed for $4.99 each, but under a promotion, the item is buy two, get one free. What is the net cost of each item? If I am driving at 20 miles per hour, it takes my vehicle 20 feet to stop. If I am driving at 40 miles per hour, how much distance will it take my vehicle to stop? I have a 20 foot ladder. It is leaning against a wall such that the tip of the ladder is touching the top of the wall. The distance between the bottom of the ladder to the bottom of the wall measures 10 feet. What is the height of the wall? You and three office mates decide to purchase fast food for lunch. Each of you order the same item, and your three office mates give you $10 each. The cashier rings up $35.17 as the total. How much change do you owe each of your office mates? You are traveling by bus and wish to estimate your time of arrival. You notice that it takes one minute and 25 seconds for the bus to travel from one mile marker to the next. Your destination is fifty miles away. Assuming the bus stays at the same speed, how long until you reach your destination? If these seem contrived, then consider that just about every college educated adult, at one time or another, will need to know his or her way around a spreadsheet. Even basic spreadsheet formulas make little sense unless one can reason algebraically. Just trying to learn how to use a spreadsheet program without understanding algebra is a painful process.
  - bryanlarsen 9y ago
    What a great illustration of the one of the problems with math education: Q: If I am driving at 20 miles per hour, it takes my vehicle 20 feet to stop. If I am driving at 40 miles per hour, how much distance will it take my vehicle to stop? A: This can only be answered experimentally for a given car, tire condition & road condition, but a rough estimate would be to apply the square law naively, giving an answer of 80 feet, but of course that's very approximate. The only correct answer that can be given is "more than 40 feet".
    - nanolith 9y ago
      Yes. It can only be answered experimentally, but the Square Law still applies, with constants to account for reaction time and friction. The point is that someone who has studied Algebra would be able to recognize a polynomial in the data and could match the data to a reasonable function just by taking measurements. That is the power of Algebra, and it is something that all adults should possess.
unabridged 9y ago
>Give me a motivated adult who understands basic arithmetic, and I can help him or her master algebra in six to eight weeks. We can go from zero to FOIL, and quadratic to partial fraction decomposition in that amount of time. The key is to listen and to instill a level of confidence as early as possible in this process. Many adults consider math to be "hard" -- not from the perspective of it actually being hard, which it is -- but from the perspective of "this is too hard for me to do, because I'm not a math person." Break this mental block, and anyone can do algebra. I used to believe this until I actually tried. Maybe they lied about how much studying they really did, but I've seen people putting in many hours a week and still unable to grasp the basics of algebra. I think many of us have never really been exposed to the thinking power of people at the bottom 10-20% (IQs below 80-87) , they weren't in our classes in high school. And now these people are going to college.
- nanolith 9y ago
  I've tutored students in algebra and remedial math in the past. I agree that it is more challenging to work with adults on the lower end of the intelligence curve, but even these adults can be taught enough algebra to pass the final exam. Different teaching techniques are required for different students. For the students at the upper edge of the curve, the homework assignments and lectures are more than enough. For the students near the middle of the curve, some additional exercises and confidence building may be required. For students near the bottom of the curve, it will be necessary to break problems into parts and reinforce smaller parts before building back up to the overall problems. These students must be taught how to break problems into discrete steps, and a lot of emphasis needs to be placed in teaching them how to recognize the patterns. Mnemonics, rhymes, and other catchy phrases can help to reinforce both the pattern recognition and the execution of steps. Bear in mind that we can teach computers to perform algebra. There is a heuristic involved. This heuristic can be memorized by anyone who can memorize a bible verse, a song, or a poem. You would be surprised what someone with a low IQ can do when time is spent to organize a heuristic in terms that this person can memorize, and enough time is spent to reinforce both this learning and the confidence of this individual.
- dvfjsdhgfv 9y ago
  I'd say say the truth is somewhere in between. There are many people who think math is hard, but they can be taught quite easily with a skillful teacher if they're motivated. However, there is a group of people who simply can't grasp it. No matter how you explain, they stare blankly at you and say they don't understand. It looks like they know what you mean if you use a simple example "You have 3 apples but want to have 13 apples; how many are you missing", but make it just a bit harder and you get back to square one. It's just a kind of people. They're otherwise nice to get along with, they seem to understand many things about life in general etc., it's just this aspect that is somewhat blocked. I hope one day we discover a safe way to somewhat activate the neurons in the related area of the brain to break this barrier.
knappa 9y ago
>Give me a motivated adult who understands basic arithmetic, and I can help him or her master algebra in six to eight weeks. Well, teaching _motivated_ students is easy and fun. The question is, though, what about the semi-motivated students and do either still understand algebra after they are done with you and in their next class?

plandis 9y ago

Why do you think that every functioning adult should understand algebra?

trendia 9y ago
Is it cheaper to buy 1 case of water for $2.50 or 3 cases of water for $9.00 ? If you get a $1,000 loan at 1% interest each month, how much will you owe in 1 year? You can buy a phone for $500 or pay Verizon $16.70 / month for 36 months. Which is cheaper?
- deleted 9y ago
  [deleted]
- bcruddy 9y ago
  > If you get a $1,000 loan at 1% interest each month, how much will you owe in 1 year? Pe = nRT is actually the first thing taught in calc 1.
- vmarsy 9y ago
  > Is it cheaper to buy 1 case of water for $2.50 or 3 cases of water for $9.00 Slightly off topic as I don't think this is college level algebra, in supermarkets in Europe they are required by law to put the "€/liter" price in small on the side, so you can compare easily. In the US it doesn't seem mandatory, or at least the unit is not mandatory because sometimes they use fl oz, sometimes gallons, or for pieces of meat sometimes oz, sometimes lbs, so when you want to compare the prices of 2 similar items, what would just take you 0.5 sec in Europe takes you much longer in the US since you need to add unit conversion in the mix. For example here your "cases" could be of different sizes, that 1 case of water could be 2L ,while those 3 cases could be a gallon each...
  - dozzie 9y ago
    > [...] in supermarkets in Europe they are required by law to put the "€/liter" price in small on the side, so you can compare easily. Yeah, and then you get aggregate price in "€/package", except that packages are of different size.
    - majewsky 9y ago
      Or they switch between "€/kg", "€/100 g", "€/liter", and "€/package" seemingly randomly.
- bsder 9y ago
  I don't need algebra for 2 of those. I need the ability to do fast mental arithmetic. And a shop math class would be far more useful for that. As for compound interest, you need WAY more than algebra ...
  - throwawayjava 9y ago
    > I don't need algebra for 2 of those. All of these are literally the sorts of things you'd find on homework assignments and final exams in a community college algebra course... You do need algebra, and don't realize how difficult this "trivial" algebra is for some students because you can do it without even realizing you're doing it. I mean, there will be some FOIL and quadratic equation examples as well. And a bunch of stuff in-between like identifying graphs of functions. But CC Algebra is super bimodal, so it's probably not the case that students are nailing these word problems and only failing with the other stuff.
nanolith 9y ago
I think that trendia already touched on a lot of these, but consider the typical every day problems that require algebra to solve: An item at the store is listed for $4.99 each, but under a promotion, the item is buy two, get one free. What is the net cost of each item? If I am driving at 20 miles per hour, it takes my vehicle 20 feet to stop. If I am driving at 40 miles per hour, how much distance will it take my vehicle to stop? I have a 20 foot ladder. It is leaning against a wall such that the tip of the ladder is touching the top of the wall. The distance between the bottom of the ladder to the bottom of the wall measures 10 feet. What is the height of the wall? You and three office mates decide to purchase fast food for lunch. Each of you order the same item, and your three office mates give you $10 each. The cashier rings up $35.17 as the total. How much change do you owe each of your office mates? You are traveling by bus and wish to estimate your time of arrival. You notice that it takes one minute and 25 seconds for the bus to travel from one mile marker to the next. Your destination is fifty miles away. Assuming the bus stays at the same speed, how long until you reach your destination? If these seem contrived, then consider that just about every college educated adult, at one time or another, will need to know his or her way around a spreadsheet. Even basic spreadsheet formulas make little sense unless one can reason algebraically. Just trying to learn how to use a spreadsheet program without understanding algebra is a painful process.
- bryanlarsen 9y ago
  What a great illustration of the one of the problems with math education: Q: If I am driving at 20 miles per hour, it takes my vehicle 20 feet to stop. If I am driving at 40 miles per hour, how much distance will it take my vehicle to stop? A: This can only be answered experimentally for a given car, tire condition & road condition, but a rough estimate would be to apply the square law naively, giving an answer of 80 feet, but of course that's very approximate. The only correct answer that can be given is "more than 40 feet".
  - nanolith 9y ago
    Yes. It can only be answered experimentally, but the Square Law still applies, with constants to account for reaction time and friction. The point is that someone who has studied Algebra would be able to recognize a polynomial in the data and could match the data to a reasonable function just by taking measurements. That is the power of Algebra, and it is something that all adults should possess.

unabridged 9y ago

>Give me a motivated adult who understands basic arithmetic, and I can help him or her master algebra in six to eight weeks. We can go from zero to FOIL, and quadratic to partial fraction decomposition in that amount of time. The key is to listen and to instill a level of confidence as early as possible in this process. Many adults consider math to be "hard" -- not from the perspective of it actually being hard, which it is -- but from the perspective of "this is too hard for me to do, because I'm not a math person." Break this mental block, and anyone can do algebra. I used to believe this until I actually tried. Maybe they lied about how much studying they really did, but I've seen people putting in many hours a week and still unable to grasp the basics of algebra. I think many of us have never really been exposed to the thinking power of people at the bottom 10-20% (IQs below 80-87) , they weren't in our classes in high school. And now these people are going to college.

nanolith 9y ago
I've tutored students in algebra and remedial math in the past. I agree that it is more challenging to work with adults on the lower end of the intelligence curve, but even these adults can be taught enough algebra to pass the final exam. Different teaching techniques are required for different students. For the students at the upper edge of the curve, the homework assignments and lectures are more than enough. For the students near the middle of the curve, some additional exercises and confidence building may be required. For students near the bottom of the curve, it will be necessary to break problems into parts and reinforce smaller parts before building back up to the overall problems. These students must be taught how to break problems into discrete steps, and a lot of emphasis needs to be placed in teaching them how to recognize the patterns. Mnemonics, rhymes, and other catchy phrases can help to reinforce both the pattern recognition and the execution of steps. Bear in mind that we can teach computers to perform algebra. There is a heuristic involved. This heuristic can be memorized by anyone who can memorize a bible verse, a song, or a poem. You would be surprised what someone with a low IQ can do when time is spent to organize a heuristic in terms that this person can memorize, and enough time is spent to reinforce both this learning and the confidence of this individual.
dvfjsdhgfv 9y ago
I'd say say the truth is somewhere in between. There are many people who think math is hard, but they can be taught quite easily with a skillful teacher if they're motivated. However, there is a group of people who simply can't grasp it. No matter how you explain, they stare blankly at you and say they don't understand. It looks like they know what you mean if you use a simple example "You have 3 apples but want to have 13 apples; how many are you missing", but make it just a bit harder and you get back to square one. It's just a kind of people. They're otherwise nice to get along with, they seem to understand many things about life in general etc., it's just this aspect that is somewhat blocked. I hope one day we discover a safe way to somewhat activate the neurons in the related area of the brain to break this barrier.

knappa 9y ago

>Give me a motivated adult who understands basic arithmetic, and I can help him or her master algebra in six to eight weeks. Well, teaching _motivated_ students is easy and fun. The question is, though, what about the semi-motivated students and do either still understand algebra after they are done with you and in their next class?