Thank you! I don't know the answer to that question, teacher training isn't really my expertise, but from the outside I would love to see cognitive science be a much bigger focus. I don't think it would solve all the problems but it would be a start.
Dylan, thanks for an interesting post. There is a lot in here that I agree with, and I think you bring up some good points that I don't see coming up other places.
I have noticed something about word problems, though. Some students seem to be better at them, and some seem to be stymied every time. And this seems to be unrelated to whether or not they know the math content needed to solve them. In fact, some students can solve word problems, but can't "do the math," like a student who knows that 5 cups of dog food at 1/2 cup per day will last 10 days, but they can't tell you what 5 divided by 1/2 is. Now, I agree with you that the difference is not teaching vocab or getting students to circle the numbers, etc. But there is much too much consistency in each student's performance for me to think that "each type of word problem is its own skill."
When I teach word problems, I teach students to draw pictures. I teach them to read each sentence or clause, and then stop, and try to make sense out of what they have read. (Often drawing a picture helps them make sense of it.) I teach them to focus on WHO does WHAT and then pull in the numbers later, after they know what's going on in the situation. Just being willing to make sense out of the problem makes a big difference.
Sometimes the problem is that they want to have a complete plan, and confirmation that their plan is correct, before they are willing to start putting pencil to paper. This can really get in the way of the thinking process. I teach them to write "I wish" statements -- "I wish I knew ____" or "If I knew how to ____, then I'd be able to find the answer." Often, these steps are enough to get students thinking.
This isn't to stay that there aren't different types of word problems. For goodness sake, it's been 15 years since I last taught AP Calc, but I could still tell you exactly how I go about teaching Related Rates problems. That is a definite "type". And when kids first see the Pythagorean Theorem, they need to get accustomed to the type of diagrams they are going to need to draw now. There are certainly other examples like that. But I have seen and taught word problem skills enough to believe that there are skills for solving word problems, and they are connected to EF skills and reading skills.
I think you're right. Maybe a better way to say it is this: there are separate skills for different types of word problems, and there are also a bunch of other skills that you described above that are useful across word problems. I think the same logic applies: if I want students to get good at word problems I need to teach specific types of word problems, and also teach the specific skills that are useful across word problems. Does that fit with what you're saying?
Hmm, I think that we have mutual respect, but not alignment. I think that you are partially right, and you think that I am partially right. But I don't think we actually agree with each other.
I think that 70% of word problems involves teaching students the type of reading and executive functioning skills that they need for any word problem. And then, from time to time, there are also specific skills that are worth bringing up for particular types. And we certainly want to expose students to different types so that they are not looking at a new word problem for the first time when taking a test, but that really, the important thing is being able to understand situations presented in short paragraphs, and find the math inside those situations.
I think that you think that 70% of what you need to do is to teach specific skills for specific types of word problems, and 30% is other general skills. I don't know if I did a really good job of explaining the types of skills that I would want to teach. Maybe you mostly have exposure to techniques like CUBES (circle the numbers, underline the question, box the key words, etc). I think that type of system for solving word problems can, at best, moderately help about 1/3 of students. Some students didn't need it anyway, and the ones who really struggle aren't helped at all. If that's where you are coming from, then I don't blame you for being wishy-washy about the effectiveness of these techniques.
I think that's a fair assessment. It might just be the case that I haven't figured out the right general skills. You're right that I have seen a lot of CUBES-type stuff and feel jaded by it. I appreciate your perspective!
Great post - totally agree!
The challenge is about changing how teachers provide instruction in classrooms!
And the BIGGER question is how to change initial teacher training to enable this!
Your statements are ALL evidence-based - yet nothing changes? Why?
Again - I totally agree with your post! 👍👍
Thank you! I don't know the answer to that question, teacher training isn't really my expertise, but from the outside I would love to see cognitive science be a much bigger focus. I don't think it would solve all the problems but it would be a start.
Dylan, thanks for an interesting post. There is a lot in here that I agree with, and I think you bring up some good points that I don't see coming up other places.
I have noticed something about word problems, though. Some students seem to be better at them, and some seem to be stymied every time. And this seems to be unrelated to whether or not they know the math content needed to solve them. In fact, some students can solve word problems, but can't "do the math," like a student who knows that 5 cups of dog food at 1/2 cup per day will last 10 days, but they can't tell you what 5 divided by 1/2 is. Now, I agree with you that the difference is not teaching vocab or getting students to circle the numbers, etc. But there is much too much consistency in each student's performance for me to think that "each type of word problem is its own skill."
When I teach word problems, I teach students to draw pictures. I teach them to read each sentence or clause, and then stop, and try to make sense out of what they have read. (Often drawing a picture helps them make sense of it.) I teach them to focus on WHO does WHAT and then pull in the numbers later, after they know what's going on in the situation. Just being willing to make sense out of the problem makes a big difference.
Sometimes the problem is that they want to have a complete plan, and confirmation that their plan is correct, before they are willing to start putting pencil to paper. This can really get in the way of the thinking process. I teach them to write "I wish" statements -- "I wish I knew ____" or "If I knew how to ____, then I'd be able to find the answer." Often, these steps are enough to get students thinking.
This isn't to stay that there aren't different types of word problems. For goodness sake, it's been 15 years since I last taught AP Calc, but I could still tell you exactly how I go about teaching Related Rates problems. That is a definite "type". And when kids first see the Pythagorean Theorem, they need to get accustomed to the type of diagrams they are going to need to draw now. There are certainly other examples like that. But I have seen and taught word problem skills enough to believe that there are skills for solving word problems, and they are connected to EF skills and reading skills.
Thanks again for an interesting post.
--Debbie
I think you're right. Maybe a better way to say it is this: there are separate skills for different types of word problems, and there are also a bunch of other skills that you described above that are useful across word problems. I think the same logic applies: if I want students to get good at word problems I need to teach specific types of word problems, and also teach the specific skills that are useful across word problems. Does that fit with what you're saying?
Hmm, I think that we have mutual respect, but not alignment. I think that you are partially right, and you think that I am partially right. But I don't think we actually agree with each other.
I think that 70% of word problems involves teaching students the type of reading and executive functioning skills that they need for any word problem. And then, from time to time, there are also specific skills that are worth bringing up for particular types. And we certainly want to expose students to different types so that they are not looking at a new word problem for the first time when taking a test, but that really, the important thing is being able to understand situations presented in short paragraphs, and find the math inside those situations.
I think that you think that 70% of what you need to do is to teach specific skills for specific types of word problems, and 30% is other general skills. I don't know if I did a really good job of explaining the types of skills that I would want to teach. Maybe you mostly have exposure to techniques like CUBES (circle the numbers, underline the question, box the key words, etc). I think that type of system for solving word problems can, at best, moderately help about 1/3 of students. Some students didn't need it anyway, and the ones who really struggle aren't helped at all. If that's where you are coming from, then I don't blame you for being wishy-washy about the effectiveness of these techniques.
I think that's a fair assessment. It might just be the case that I haven't figured out the right general skills. You're right that I have seen a lot of CUBES-type stuff and feel jaded by it. I appreciate your perspective!