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Thursday 3 September 2009
Sunday 30 August 2009
Math Teachers are not being taught math adequately
Math Teachers are not being taught math adequately
Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an “expert” has known for years: Teachers are not being taught math adequately, and generally fail to teach it well to their students. (Do tell…)
Isn’t it funny that the “establishment” will never admit that? It takes an expensive academic “study” to show what is already known, yet Universities (in general) will not do anything about the way they teach teacher how to teach math. They will try some new, expensive methods that some textbook company has lobbied for, of course. But they won’t try anything that might actually work.
That’s why homeschooling and afterschooling are becoming more and more important. Taking an interest in your own child’s education is more important than ever, as public schools tank in their ability to actually teach, thanks to the natural entropy of society, and the idiotically simple-minded ways some people like to deal with it, as with the subtly(?) sardonically named “No Child Left Behind” act.
According to the AP article:
Author Julie Greenberg said education students should be taking courses that give them a deeper understanding of arithmetic and multiplication. She said the courses should explain how math concepts build upon each other and why certain ideas need to be emphasized in the classroom.
Teacher candidates know their multiplication tables, but “they don’t come to us knowing why multiplication works the way it does,” said Denise Mewborn, who heads the University of Georgia department of math and science education.
This is the key to most of what every student needs to know – how multiplication works. Addition is almost intuitive. It is an extension of counting. Once you extend addition to multiplication, though, you need a good understanding of how the base ten system works, and the commutative, associative, and distributive laws. You don’t need to know the names of those laws, of course, but you need to understand how to use them in order to understand multiplication. You also need to know that multiplication is not just repeated addition – a misrepresentation that is prevalent in education. (I should know, I only recently “saw the light” about this.)
That’s the big issue. Just being able to recite multiplication tables is not actually being able to understand multiplication. And just going through the motions and repeating math steps that a teacher has “taught” you by show-and-tell methods, so you can prove that you can jump through the hoops for the big test at the end of the year usually does more damage to your understanding that anything.
So what is there to do about it? First, as a truly concerned parent or teacher, make sure you, yourself understand some of the nuances of multiplication. Like why when you multiply by a fraction, the product is smaller than the multiplicand. (Did I get you with that one? Leave a comment below requesting the Math Mojo take on that one, and I’ll cover it in a new post).
Second, make sure you have at least two ways of explaining to your students how multiplication works. Not just how to do it, but how it actually works. I’m working on a video series about this now. Send me a nudge (again, in a comment below) to make it a higher priority to get it done and available to you faster.
Third, make sure you have a way to assess if your child or students understand what you taught them. The assessment doesn’t have to be a test. Tests are more about beating kids over the head. Asking questions and asking to demonstrate, in a non-threatening way would be my first strategy. If you must beat someone over the head, start with someone in an administrative position.
Here’s one of the reasons why:
According to the AP article:
Since states oversee the preparation of the nation’s school teachers, the report recommends they set tougher coursework and testing standards.
Why is does the solution always involve browbeating the learners? Why are the words “tough” and “testing” so often involved? How on earth does that teach or inspire? The problem isn’t that, “those who can’t do, teach.” The people who run those studies and teach university level education courses usually can do the math they are supposed to teach quite well.
The problem is that “those that can’t teach, teach.” Then they “train” teachers, instead of teaching them. No wonder those teachers have problems teaching.
As I always say, look up when you look for where the problem lies. You can’t blame a third grader for not learning (unless there is neurological damage, of course). If it’s behavior problems, there might be an issue beyond the teacher’s scope, but most behavior problems are dealt with by good teachers.
But beyond those things, start looking up the chain for someone who needs the butt-kicking. If the teacher can’t teach, were they taught well? (Are they even allowed to teach well in that school?) If the teacher’s teacher can’t teach, were they taught well? Is their administrator constantly putting monkey-wrenches in their teaching techniques? Is something going on at the School Board mucking up the school? Is the State requiring more tests, but providing less resources for teachers and students?
Keep looking up. Here’s a hint: Besides the handicapped, who’s got the parking spot closest to the school entrance? Start with him/her.
Remember, when things are looking bad, begin to look up.
Brian (a.k.a. Professor Homunculus)
Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an “expert” has known for years: Teachers are not being taught math adequately, and generally fail to teach it well to their students. (Do tell…)
Isn’t it funny that the “establishment” will never admit that? It takes an expensive academic “study” to show what is already known, yet Universities (in general) will not do anything about the way they teach teacher how to teach math. They will try some new, expensive methods that some textbook company has lobbied for, of course. But they won’t try anything that might actually work.
That’s why homeschooling and afterschooling are becoming more and more important. Taking an interest in your own child’s education is more important than ever, as public schools tank in their ability to actually teach, thanks to the natural entropy of society, and the idiotically simple-minded ways some people like to deal with it, as with the subtly(?) sardonically named “No Child Left Behind” act.
According to the AP article:
Author Julie Greenberg said education students should be taking courses that give them a deeper understanding of arithmetic and multiplication. She said the courses should explain how math concepts build upon each other and why certain ideas need to be emphasized in the classroom.
Teacher candidates know their multiplication tables, but “they don’t come to us knowing why multiplication works the way it does,” said Denise Mewborn, who heads the University of Georgia department of math and science education.
This is the key to most of what every student needs to know – how multiplication works. Addition is almost intuitive. It is an extension of counting. Once you extend addition to multiplication, though, you need a good understanding of how the base ten system works, and the commutative, associative, and distributive laws. You don’t need to know the names of those laws, of course, but you need to understand how to use them in order to understand multiplication. You also need to know that multiplication is not just repeated addition – a misrepresentation that is prevalent in education. (I should know, I only recently “saw the light” about this.)
That’s the big issue. Just being able to recite multiplication tables is not actually being able to understand multiplication. And just going through the motions and repeating math steps that a teacher has “taught” you by show-and-tell methods, so you can prove that you can jump through the hoops for the big test at the end of the year usually does more damage to your understanding that anything.
So what is there to do about it? First, as a truly concerned parent or teacher, make sure you, yourself understand some of the nuances of multiplication. Like why when you multiply by a fraction, the product is smaller than the multiplicand. (Did I get you with that one? Leave a comment below requesting the Math Mojo take on that one, and I’ll cover it in a new post).
Second, make sure you have at least two ways of explaining to your students how multiplication works. Not just how to do it, but how it actually works. I’m working on a video series about this now. Send me a nudge (again, in a comment below) to make it a higher priority to get it done and available to you faster.
Third, make sure you have a way to assess if your child or students understand what you taught them. The assessment doesn’t have to be a test. Tests are more about beating kids over the head. Asking questions and asking to demonstrate, in a non-threatening way would be my first strategy. If you must beat someone over the head, start with someone in an administrative position.
Here’s one of the reasons why:
According to the AP article:
Since states oversee the preparation of the nation’s school teachers, the report recommends they set tougher coursework and testing standards.
Why is does the solution always involve browbeating the learners? Why are the words “tough” and “testing” so often involved? How on earth does that teach or inspire? The problem isn’t that, “those who can’t do, teach.” The people who run those studies and teach university level education courses usually can do the math they are supposed to teach quite well.
The problem is that “those that can’t teach, teach.” Then they “train” teachers, instead of teaching them. No wonder those teachers have problems teaching.
As I always say, look up when you look for where the problem lies. You can’t blame a third grader for not learning (unless there is neurological damage, of course). If it’s behavior problems, there might be an issue beyond the teacher’s scope, but most behavior problems are dealt with by good teachers.
But beyond those things, start looking up the chain for someone who needs the butt-kicking. If the teacher can’t teach, were they taught well? (Are they even allowed to teach well in that school?) If the teacher’s teacher can’t teach, were they taught well? Is their administrator constantly putting monkey-wrenches in their teaching techniques? Is something going on at the School Board mucking up the school? Is the State requiring more tests, but providing less resources for teachers and students?
Keep looking up. Here’s a hint: Besides the handicapped, who’s got the parking spot closest to the school entrance? Start with him/her.
Remember, when things are looking bad, begin to look up.
Brian (a.k.a. Professor Homunculus)
Math facts vs. Math concepts
Math facts vs. Math concepts
There are MANY kids like this out there. Dyscalculia is another LD that is little known and commonly misunderstood. Though like most "definitions" - our kids don't fit the cookie cutter stereotype. Symptoms, causality, descriptions will vary.
What seems truly common is the "inability" with Math Facts and the "ability" to practically intuit higher level math concepts. It also seems - to me - to be a tad more common amongst kids who are also dysgraphic. Also amongst "visual spatial" thinkers (which is also seems tied to dysgraphia - hmmmm...... anyways)
For my son - and quite a number of other kids I know - in person or via parent/cyberspace - the "solution" is NOT drill drill drill (an anathema to these kids!), but to just stop worrying about it, let them go on to more challenging math problems. They will have to USE computational skills to solve them but they will also be getting the mental challenge/stimulus they NEED.
For many, letting them use a grid or (in our case) a calculator - to SOLVE the problems is perfectly fine! What happened (s) is: they get the PICTURE they need to retrieve quickly (you know they know and understand the concept - because they constantly refigure - so the PICTURE is ok here). And - over time, you see them access the calculator/chart less and less.
Do NOT "hold them back" for silly things like math facts. (Do you stop your kid from reading more interesting books because they can't spell??) It will make them bored and resentful, and they will come to HATE MATH and question that wonderfully intuitive skill they have.
And for (whatever diety you wish)'s sake - DO NOT GIVE THEM TIMED TESTS!!!!!!!!!!!!!!!!!!!!!!!!!!
This will only increase TEST ANXIETY which can - and does (BTDT) - spill over into every OTHER test they ever take.
FWIW - Timed "math facts" tests were a large part of what drove my son out of PS. The teacher knew he "knew" them, but he absolutely could not - between dyscalculia, dysgraphia, and test anxiety - legibly complete the test in the time alloted!
As my son has advanced to more complex Algebraic problems, he's figured out that he HAS to "show his work" (aaaggh!) in order to work through the problems. He also has to "proof" his work (so he's doing mostly self-checking.) He still wants the calculator there, but he doesn't use it very often for basic calculations.
Although, on his recent yearly test (we do ours in January) - he again - scored about 50% on Math Calculations and 99% on Math Concepts. Even though they were basically the "same problems" - whereas the Math Calc problem was "just numbers" - and the Math Concept problem was buried in a "word problem".
http://www.dyscalculia.org /
http://www.ldonline.org/ld_indepth/math_skills/math-ski ...
=================================
By definition, math must be UNDERSTOOD. It CANNOT be memorized. Memorizing is not math. Memorization is a surface-level, short-term memory task. Math involves deep thinking and understanding - real brain work - and your 7-yo may or may not be ready to do it.
Math is not about memorizing algorithms or facts. It's about understanding the reality that the world is made of numbers.
Really. I am deadly serious about this. My kids are all really, really good at math, at least according to their standardized test scores, and none of them have ever once cracked a math book or a flashcard (and Mr. Unschooler and I both suck at math, so there is no inherited talent at work). And, yes, they can answer quickly if you ask them one of those "math facts" questions such as what is 7 times 8. The great thing is that if they forget what 7 times 8 is, it's not big deal, because they can very quickly and easily figure out a strategy to solve the problem.
100% of our arithmetic consisted either of figuring out "real world" problems (how many giraffes would you have to stack up to reach the top of mommy's office building? how would you go about doubling that recipe?) or in math games we invent. To learn times tables, we did a lot of counting by tens, fives, sevens, eights, elevens and so on. To learn division, we played a game where we imagined there were a set number of cookies to be divided amont a set number of children, with the leftovers (remainder) going to the dog. We also figure out the area of all kinds of things. Another favorite is the "number machine" wherein one person puts a number into the "machine" (the other player), which spits back an answer. The first person continues to "insert" numbers into the "machine" until he can figure out what the machine did to the "input" number in order to generate the "output" (the machine can do something as simple as adding one or two or as complicated as algebra).
Sometimes, I'll throw out a problem for one of the kids and let them think about it for minutes, hours or days. There's no rush. I'd rather they think deeply about it and figure out a way to solve the problem than memorize an algorithm and not understand what they are doing.
The National Council of Teachers of Mathematics has embraced a pedgagogical approach based on deep understanding of numbers rather than memorization of facts. I'd encourage you to look at their ideas and also those in John Holt's excellent book "Learning All the Time."
There are MANY kids like this out there. Dyscalculia is another LD that is little known and commonly misunderstood. Though like most "definitions" - our kids don't fit the cookie cutter stereotype. Symptoms, causality, descriptions will vary.
What seems truly common is the "inability" with Math Facts and the "ability" to practically intuit higher level math concepts. It also seems - to me - to be a tad more common amongst kids who are also dysgraphic. Also amongst "visual spatial" thinkers (which is also seems tied to dysgraphia - hmmmm...... anyways)
For my son - and quite a number of other kids I know - in person or via parent/cyberspace - the "solution" is NOT drill drill drill (an anathema to these kids!), but to just stop worrying about it, let them go on to more challenging math problems. They will have to USE computational skills to solve them but they will also be getting the mental challenge/stimulus they NEED.
For many, letting them use a grid or (in our case) a calculator - to SOLVE the problems is perfectly fine! What happened (s) is: they get the PICTURE they need to retrieve quickly (you know they know and understand the concept - because they constantly refigure - so the PICTURE is ok here). And - over time, you see them access the calculator/chart less and less.
Do NOT "hold them back" for silly things like math facts. (Do you stop your kid from reading more interesting books because they can't spell??) It will make them bored and resentful, and they will come to HATE MATH and question that wonderfully intuitive skill they have.
And for (whatever diety you wish)'s sake - DO NOT GIVE THEM TIMED TESTS!!!!!!!!!!!!!!!!!!!!!!!!!!
This will only increase TEST ANXIETY which can - and does (BTDT) - spill over into every OTHER test they ever take.
FWIW - Timed "math facts" tests were a large part of what drove my son out of PS. The teacher knew he "knew" them, but he absolutely could not - between dyscalculia, dysgraphia, and test anxiety - legibly complete the test in the time alloted!
As my son has advanced to more complex Algebraic problems, he's figured out that he HAS to "show his work" (aaaggh!) in order to work through the problems. He also has to "proof" his work (so he's doing mostly self-checking.) He still wants the calculator there, but he doesn't use it very often for basic calculations.
Although, on his recent yearly test (we do ours in January) - he again - scored about 50% on Math Calculations and 99% on Math Concepts. Even though they were basically the "same problems" - whereas the Math Calc problem was "just numbers" - and the Math Concept problem was buried in a "word problem".
http://www.dyscalculia.org /
http://www.ldonline.org/ld_indepth/math_skills/math-ski ...
=================================
By definition, math must be UNDERSTOOD. It CANNOT be memorized. Memorizing is not math. Memorization is a surface-level, short-term memory task. Math involves deep thinking and understanding - real brain work - and your 7-yo may or may not be ready to do it.
Math is not about memorizing algorithms or facts. It's about understanding the reality that the world is made of numbers.
Really. I am deadly serious about this. My kids are all really, really good at math, at least according to their standardized test scores, and none of them have ever once cracked a math book or a flashcard (and Mr. Unschooler and I both suck at math, so there is no inherited talent at work). And, yes, they can answer quickly if you ask them one of those "math facts" questions such as what is 7 times 8. The great thing is that if they forget what 7 times 8 is, it's not big deal, because they can very quickly and easily figure out a strategy to solve the problem.
100% of our arithmetic consisted either of figuring out "real world" problems (how many giraffes would you have to stack up to reach the top of mommy's office building? how would you go about doubling that recipe?) or in math games we invent. To learn times tables, we did a lot of counting by tens, fives, sevens, eights, elevens and so on. To learn division, we played a game where we imagined there were a set number of cookies to be divided amont a set number of children, with the leftovers (remainder) going to the dog. We also figure out the area of all kinds of things. Another favorite is the "number machine" wherein one person puts a number into the "machine" (the other player), which spits back an answer. The first person continues to "insert" numbers into the "machine" until he can figure out what the machine did to the "input" number in order to generate the "output" (the machine can do something as simple as adding one or two or as complicated as algebra).
Sometimes, I'll throw out a problem for one of the kids and let them think about it for minutes, hours or days. There's no rush. I'd rather they think deeply about it and figure out a way to solve the problem than memorize an algorithm and not understand what they are doing.
The National Council of Teachers of Mathematics has embraced a pedgagogical approach based on deep understanding of numbers rather than memorization of facts. I'd encourage you to look at their ideas and also those in John Holt's excellent book "Learning All the Time."
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