What's math got to do with it?
I recently read the book What's math got to do with it?. The title is a bit misleading; the book is about K-12 math education and how math education and performance in the US is very poor (when compared to other countries, esp when you take into account $$ spent).
The problem is simple and in some ways, it is getting worse. The focus has been so heavily on regular standardized assessments which have only been growing in importance in school funding, teachers' salaries, etc, that as a recent friend and teacher has told me, testing and teaching to the test is all they have time to do in school.
Teaching to the test however is the worst way to educate children, the worst way to interest them in math AND actually (according to several studies) is the worst way to get them to perform well on tests! In K-12 math, children are given a list of math equations, formulas and routines to memorize. They then quietly, individually practice applying these formulas 20 times each. In surveys taken of kids, over 75% say math is about memorization. This is HORRIBLE. Math has NOTHING to do with memorization. Math is all about recognizing and understanding patterns; applying basic logic to models to better understand their properties. You shouldn't memorize 5+8=13 and 17+5=22 and 87+52=139, you should learn how to add. You don't have to memorize formulas if you understand what they mean and where they came from. Math isn't formulas that you memorize, it's about how to logically recognize patterns and apply logical reasoning to them. No wonder people think they don't use math at all after they graduate. Of course you aren't going to figure every day the volume of a cone using the memorized appropriate formula. But most jobs and many of non-job leisure activities involve being able to recognize relationships and patterns and reason about numbers and such.
Anyhoo, in addition to studies, the author actually ran several studies and programs herself. The results were clear. When students were taught HOW to think and given time to explore and ask questions rather than drilled through memorization and repeated application of formulas they perform BETTER on standardized tests and have a greater interest in math. For example, you can tell whether someone gets a B or higher versus a C or lower in their math classes based almost entirely on a simple question: In your head, add 196 and 45.
Those that have an UNDERSTANDING of numbers easily take 45 and split it into 4 and 41 and then see that 196 + 45 = 196 + 4 + 41 = 200 + 41 = 241. They finish the test almost instantly. Those that don't have an understanding use the standard formula involving counting on your fingers & memorization with carries and cannot perform this operation in their head.
In one study, they took people who performed poorly on a standardized math assessment exam, taught them for 2 weeks about how to manipulate numbers, reason through problems and gave them time to explore through various situations in a group setting. This increased their scores greatly! No extra memorization, no explicit studying of any anticipated test questions, etc.
In conclusion, kids do better in math when we stop emphasizing tests and start emphasizing reasoning, engaging them with questions not rote repetition and allowing them to ASK questions.
The book made me somewhat interested in teaching especially in junior high & high school. I would love to do that except we overwork our teachers, pay them poorly and treat them like crap. (In fact, the book has one example of a teacher who was fired for using project-based teaching instead of standard practice and memorization despite having achieved exceptional math assessment scores in the years she was teaching - so according to the own gov't's standards, she was doing really well.)
The problem is simple and in some ways, it is getting worse. The focus has been so heavily on regular standardized assessments which have only been growing in importance in school funding, teachers' salaries, etc, that as a recent friend and teacher has told me, testing and teaching to the test is all they have time to do in school.
Teaching to the test however is the worst way to educate children, the worst way to interest them in math AND actually (according to several studies) is the worst way to get them to perform well on tests! In K-12 math, children are given a list of math equations, formulas and routines to memorize. They then quietly, individually practice applying these formulas 20 times each. In surveys taken of kids, over 75% say math is about memorization. This is HORRIBLE. Math has NOTHING to do with memorization. Math is all about recognizing and understanding patterns; applying basic logic to models to better understand their properties. You shouldn't memorize 5+8=13 and 17+5=22 and 87+52=139, you should learn how to add. You don't have to memorize formulas if you understand what they mean and where they came from. Math isn't formulas that you memorize, it's about how to logically recognize patterns and apply logical reasoning to them. No wonder people think they don't use math at all after they graduate. Of course you aren't going to figure every day the volume of a cone using the memorized appropriate formula. But most jobs and many of non-job leisure activities involve being able to recognize relationships and patterns and reason about numbers and such.
Anyhoo, in addition to studies, the author actually ran several studies and programs herself. The results were clear. When students were taught HOW to think and given time to explore and ask questions rather than drilled through memorization and repeated application of formulas they perform BETTER on standardized tests and have a greater interest in math. For example, you can tell whether someone gets a B or higher versus a C or lower in their math classes based almost entirely on a simple question: In your head, add 196 and 45.
Those that have an UNDERSTANDING of numbers easily take 45 and split it into 4 and 41 and then see that 196 + 45 = 196 + 4 + 41 = 200 + 41 = 241. They finish the test almost instantly. Those that don't have an understanding use the standard formula involving counting on your fingers & memorization with carries and cannot perform this operation in their head.
In one study, they took people who performed poorly on a standardized math assessment exam, taught them for 2 weeks about how to manipulate numbers, reason through problems and gave them time to explore through various situations in a group setting. This increased their scores greatly! No extra memorization, no explicit studying of any anticipated test questions, etc.
In conclusion, kids do better in math when we stop emphasizing tests and start emphasizing reasoning, engaging them with questions not rote repetition and allowing them to ASK questions.
The book made me somewhat interested in teaching especially in junior high & high school. I would love to do that except we overwork our teachers, pay them poorly and treat them like crap. (In fact, the book has one example of a teacher who was fired for using project-based teaching instead of standard practice and memorization despite having achieved exceptional math assessment scores in the years she was teaching - so according to the own gov't's standards, she was doing really well.)