Skills
One of the most important lessons I've learned about teaching is that there are no generic skills. I often sound off about how "critical thinking" and "problem solving" aren't things you can teach. But even skills that sound more specific, like "hit a ball with a bat as it crosses the plate," aren't specific enough. The video below is a great example, as future hall of fame baseball player Albert Pujols gets struck out by softball pitcher Jennie Finch.
(Video via Dylan Wiliam)
Maybe you agree when I say that problem solving isn't a skill we can teach. I think this mistake happens in other places where it's less obvious. Here are some more things that I don't think are skills:
Number sense
Number sense isn’t one thing, it’s lots of little things. Number sense is having some flexible strategies for subtraction, using nice numbers to estimate in multiplication, knowing a lot about divisibility, and a whole bunch more.
Test-taking
Some students are good at taking tests, absolutely but they don’t have a magical test-taking skill. They a) know a bunch of math, and b) know a bunch of different ways that tests often ask questions and how to answer them.
Word problems
Having a large vocabulary and lots of background knowledge help, but word problems aren’t one skill. Each type of word problem is its own skill, and while they’re definitely correlated they’re not one thing.
Multi-step problems
I’ve seen teachers become obsessed with multi-step problems, as if giving students a multi-step problem every day will mean great scores on a state test full of multi-step problems. Multi-step problems require a combination of patience, organization, and whatever specific mathematical skills are necessary to solve the problem.
I could go on. Metacognition. Note-taking. Sustained attention. Lots of things seem like skills at first glance but are actually collections of lots of little skills.
Be Specific
The solution isn’t “number sense is fake, I’m not going to teach it.” The solution is to be specific. Don’t teach number sense by throwing random problems at students that require number sense, pick a specific component of number sense and figure out how to help students get good at it. Don’t teach test-taking by giving students lots of tests, pick a specific way that tests phrase questions and help students understand how to answer them. Don’t teach word problems by giving students vague general strategies like circle the question or read it three times, pick a specific type of word problem and help students understand why all those different problems connect to the same mathematical idea.
I think generic skills are appealing because if they existed they would make teachers’ jobs a lot easier. Teachers work really hard. Wouldn’t it be great if instead of having to teach this type of word problem and that type and the other type we could just teach a generic word-problem-solving-skill? That would make my life easier. But it doesn’t exist. There are no shortcuts. Teaching is all about playing the long game. Wake up, head to school, put the effort in, make a bit of progress, come back tomorrow, do it again. The best way to make progress is to be as specific as I can about what I want students to learn today.
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! 👍👍
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