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As a person with math degrees, I cannot agree with this more. I'm fighting this battle at home now with my first grader. There is way too much focus on the me

As a person with math degrees, I cannot agree with this more. I'm fighting this battle at home now with my first grader. There is way too much focus on the mechanics of grinding out arithmetic and way too little in teaching kids how to think about numbers and mathematical operations. You can't teach kids how to think about math when the focus is on mechanical mathematical operation. When I work with him on his homework I have to undo a lot of stuff before we can make progress. Then he goes to school and they undo all the stuff we did at home. Rinse, repeat, it can really drive you insane. Furthermore, he's already terrified about getting the wrong answer. He's so worried about doing it wrong that he is afraid to think. When he thinks he does just fine.

Jtsummers 11y ago
> There is way too much focus on the mechanics of grinding out arithmetic and way too little in teaching kids how to think about numbers and mathematical operations. As I posted to a friend on Facebook: arithmetic : Math :: spelling : English It's a critical component, but it's not the entirety of the subject. But we drill, drill, drill it, and when people have trouble with it they say they're "bad at math". I know plenty of mathematicians (also have a math degree) that were horrible at arithmetic, but mathematics (whether for the particular person this meant some field of algebra or geometry or topology or whatever) itself was easy for them. I tried to help my last girlfriend out with this. She is a teacher and a severe mathphobic person. It was incredibly frustrating, because she did get higher concepts when they were separate from numbers, but introduce numbers and her mind would shutdown. This attitude will be passed on to her (future) children and her students if she's not careful.
- Mz 11y ago
  Unless she genuinely gets over it, it will almost certainly be passed on even if she is careful.
Lawtonfogle 11y ago
I just had a talk with my brother about this Sunday night as he did his homework at my parent's home. He wasn't able to find his sheet of rules on how to simply some math expressions, so I sat down and showed him how I would simplify them without rules. He had been given rules, but never actually taught why these rules worked. (Not to mention at least one of these rules I would not count as simplification, though it would be useful in simplification.) Like you mention, he was scared of getting it wrong instead of understanding it. An hour before that, I was talking with another brother why 'oh, I don't need help with that because we are no longer on that chapter' is a horrible way to think about math, especially at a grade school level where you are building up the core foundation.
voltagex_ 11y ago
Got any tips for people who are much older who might have been taught the wrong way to think about maths in school?
- Mz 11y ago
  First, if you have a lot of baggage about numbers, realize math is not "numbers" anymore than speaking English is "the alphabet." Second, look for "normal" books filled with words instead of numbers that talk about math and read those. When I was homeschooling my oldest son, I spent about four years picking up books of that sort. I got a lot of them off the clearance table for as little as a dollar. After I finally got my husband on board with my plan, I handed the stack of books to my son and said "Here, read these." For the next few months, there were no tests, no quizes, no written work of any kind. I periodically asked if he was still reading them. He periodically gave me a book back that he had finished. After six weeks, he began bouncing into my presence joyously announcing "I finally understand why you can't divide by zero! I knew it was a rule, but I never understood why!" Third, look for fun ways to explore math. There are entertaining math books like "The Number Devil" that are a fun read and will likely introduce you to new concepts if you do not have a strong math background. I also bought games for my sons to play instead of doing arithmetic drill. Last, don't let anyone intimidate you with jargon or with their failure to explain it effectively. (Write them off as "stupid" and move on. :-p) My oldest is still incredibly bitter about learning that "x" in algebra is basically the same thing as the empty space in basic arithmetic, it is just easier to move it around and lets you have more than one "empty space" by giving it a name. So that let's you have two or more mystery numbers instead of just one. After I explained to him that X was the same as the empty space in more familiar problems, he realized he had been doing algebra in his head for years while playing video games in order to infer, for example, how many hit points of damage a particular attack did so he would know how many hits it took to kill something. He is still bitter at the system convincing him algebra was hard and something he could not do when he had been doing it competently for years. Also, consider jumping in at the top end and working backwards. I read about half of "A tour of the calculus" with my son to help win him over and convince him math is your friend. Think of it this way: Just because you can't spell doesn't mean you won't fall in love with writing poetry. Once you are thrilling to the pursuit of writing a good poem, you will have motive to look up the correct spelling and spelling might start sticking. Last, if you went through the standard algebra-geometry-trig track and have baggage about that, consider pursuing a statistics track. There are some very approachable stats books for laymen, such as "How to lie with statistics," and it shouldn't trip your "oh, god, I hate math and am bad at it" switch if you haven't previously been exposed to stats. Statistics is very serious math, yet many people do not realize that. I think the first chapter or two of "The cartoon guide to statistics" is the rough equivalent of my entire college intro to stats class. It is a deep subject, yet we hear statistics every day in the news, so it can feel a lot more approachable and familiar and relevant for some people.

Jtsummers 11y ago

> There is way too much focus on the mechanics of grinding out arithmetic and way too little in teaching kids how to think about numbers and mathematical operations. As I posted to a friend on Facebook: arithmetic : Math :: spelling : English It's a critical component, but it's not the entirety of the subject. But we drill, drill, drill it, and when people have trouble with it they say they're "bad at math". I know plenty of mathematicians (also have a math degree) that were horrible at arithmetic, but mathematics (whether for the particular person this meant some field of algebra or geometry or topology or whatever) itself was easy for them. I tried to help my last girlfriend out with this. She is a teacher and a severe mathphobic person. It was incredibly frustrating, because she did get higher concepts when they were separate from numbers, but introduce numbers and her mind would shutdown. This attitude will be passed on to her (future) children and her students if she's not careful.

Mz 11y ago
Unless she genuinely gets over it, it will almost certainly be passed on even if she is careful.

Lawtonfogle 11y ago

I just had a talk with my brother about this Sunday night as he did his homework at my parent's home. He wasn't able to find his sheet of rules on how to simply some math expressions, so I sat down and showed him how I would simplify them without rules. He had been given rules, but never actually taught why these rules worked. (Not to mention at least one of these rules I would not count as simplification, though it would be useful in simplification.) Like you mention, he was scared of getting it wrong instead of understanding it. An hour before that, I was talking with another brother why 'oh, I don't need help with that because we are no longer on that chapter' is a horrible way to think about math, especially at a grade school level where you are building up the core foundation.

voltagex_ 11y ago

Got any tips for people who are much older who might have been taught the wrong way to think about maths in school?

Mz 11y ago
First, if you have a lot of baggage about numbers, realize math is not "numbers" anymore than speaking English is "the alphabet." Second, look for "normal" books filled with words instead of numbers that talk about math and read those. When I was homeschooling my oldest son, I spent about four years picking up books of that sort. I got a lot of them off the clearance table for as little as a dollar. After I finally got my husband on board with my plan, I handed the stack of books to my son and said "Here, read these." For the next few months, there were no tests, no quizes, no written work of any kind. I periodically asked if he was still reading them. He periodically gave me a book back that he had finished. After six weeks, he began bouncing into my presence joyously announcing "I finally understand why you can't divide by zero! I knew it was a rule, but I never understood why!" Third, look for fun ways to explore math. There are entertaining math books like "The Number Devil" that are a fun read and will likely introduce you to new concepts if you do not have a strong math background. I also bought games for my sons to play instead of doing arithmetic drill. Last, don't let anyone intimidate you with jargon or with their failure to explain it effectively. (Write them off as "stupid" and move on. :-p) My oldest is still incredibly bitter about learning that "x" in algebra is basically the same thing as the empty space in basic arithmetic, it is just easier to move it around and lets you have more than one "empty space" by giving it a name. So that let's you have two or more mystery numbers instead of just one. After I explained to him that X was the same as the empty space in more familiar problems, he realized he had been doing algebra in his head for years while playing video games in order to infer, for example, how many hit points of damage a particular attack did so he would know how many hits it took to kill something. He is still bitter at the system convincing him algebra was hard and something he could not do when he had been doing it competently for years. Also, consider jumping in at the top end and working backwards. I read about half of "A tour of the calculus" with my son to help win him over and convince him math is your friend. Think of it this way: Just because you can't spell doesn't mean you won't fall in love with writing poetry. Once you are thrilling to the pursuit of writing a good poem, you will have motive to look up the correct spelling and spelling might start sticking. Last, if you went through the standard algebra-geometry-trig track and have baggage about that, consider pursuing a statistics track. There are some very approachable stats books for laymen, such as "How to lie with statistics," and it shouldn't trip your "oh, god, I hate math and am bad at it" switch if you haven't previously been exposed to stats. Statistics is very serious math, yet many people do not realize that. I think the first chapter or two of "The cartoon guide to statistics" is the rough equivalent of my entire college intro to stats class. It is a deep subject, yet we hear statistics every day in the news, so it can feel a lot more approachable and familiar and relevant for some people.