Here's a great and interesting thread on X including educators and researchers on how to help kids with math practice to build fluency. Such a great read because all the ideas about practice are in there, plus some interesting research nuggets and practical ideas: https://twitter.com/CoreyJPeltier/status/1773731496345370728
I worked in the schools for 45 years and served as a school psychologist for 27 of those. I always used sports and music to describe the importance of practice but teachers were so brainwashed that I could never break through the barrier.
Hey Dylan, hi Holly. Two of my favorite writers on this.
Perhaps useful to separate:
1. What is payoff of actual practice outside of school, closely led by reasonably well informed parent or tutor, "inherently 1-1," where you can stipulate good choice and good follow-thru.
2. What is payoff of "solo" practice actually completed by motivated median kid, reasonably willing to do Khan exercises or go thru flash cards? Here we subtract the adult helper. Often practicing the "wrong thing" or getting stuck?
3. What is payoff of "assigned" practice to typical kid? Here I'm confident low math motivation, often literally not trying. Probably easiest to answer - near zero.
4. What is payoff of "assigned" practice during math class led by reasonably well-informed teacher, but targeted to ~25 kids. The effect is likely to mix 1, 2, 3 above. Some of our guesses about payoff are really guesses about 1, 2, 3.
You're making a good point but I think there are a lot of complexities teachers have to deal with that make practice hard.
1. Practice has to be doable. If you give students a bunch of practice and they all stare at you and say "I don't know how to do this" you're not doing much good. In my experience this type of thing is a much bigger cause of math anxiety/negative feelings about math than anything else.
2. Practice is a lot of prep. I played lacrosse as a kid and spent a lot of time practicing my throwing against the wall of my garage. I could do that with no prep; my lacrosse coach could have us do throwing drills without spending much time preparing the drill. Throwing is a skill that I can work on for hours and hours and keep getting better at. In math it's not helpful to practice the same thing for hours and hours; you move on to the next thing. Preparing all that practice and making sure it's at an appropriate level isn't easy and is a lot of work for teachers.
3. Curricula have deemphasized practice. It's hard to find good practice in most curricula today. Too many don't have enough, or it gets too hard too quickly and we're back at problem 1. Teachers end up using garbage online programs like IXL that aren't designed well and end up just being busywork.
4. Repetitive practice was much more common in the past and it didn't work very well. For practice to be helpful students need to be thinking about what we want them to learn. Too much practice was 30 questions finding the circumference of a circle. Students aren't thinking about circumference, they're just thinking "ok I multiply by pi here." Lots of teachers have given this kind of practice, seen that it doesn't help very much, and feel like practice doesn't work. This plays into the drill-and-kill rhetoric you mention.
My larger point is that yes, practice is important, and in most schools today kids aren't getting enough practice. But there are a bunch of different problems we need to solve to get practice right -- curricula that offer more practice and build in difficulty gradually, resources to provide extra instruction and practice with foundational skills that actually work (there are plenty of websites that claim they do this but don't do a good job), and a better understanding of spacing/interleaving. Practice is important, but it's not an easy thing to fix.
Absolutely agree. Also, framing the practice in academics, as in sports, is effective in explaining the time limits and parameters prior to the practice. For example, fifteen minutes on this topic, or ten sentences to correct for errors.
Football practice is venerated because success in football is venerated. A few years ago my younger son attended a math camp at Texas State where many of the participants came from a particular community in a Houston suburb. This was a group among whom success in the state Math Olympiad carried the same social status that being the star quarterback carries in most Texas communities. I am guessing that their parents had no problem with their children practicing math.
So how do we get math practice valued among parents of students who are not the stars? Looking back to sports as an example, in the neighborhood where my sons grew up, parents regularly signed up their kids to play recreational sports whether or not they expected them to be competitive athletes later on. Children’s sports were valued because they were viewed as generally good for kids, and also as an experience the kids would enjoy. Now, if we could get parents thinking not only that knowing math is generally good for kids, but that the experience of practicing math is not a bad one…but that goes back to the details of structuring practice right. And persuading the parents whose own school experience with math was not a good one.
Reading these comments by experienced teachers makes me think about the amount of detail involved in getting this right – detail that is probably not known by most teachers, let alone taught in their teacher preparation programs. That is why there is interest in getting high-quality curriculum materials into teachers’ hands to give them more guidance on the details. See, for example, https://www.educationnext.org/sharp-critique-standards-based-reform-beyond-standards-polikoff-book-review/.
Great article! Made me think: Isn't homework some form of practice as well? But not only do kids never do it anymore, but it almost seems discouraged for the same dumb reasons as in school practice: it might be traumatizing!
In both of my major teaching roles, homework was NEVER a thing, although as an ELA teacher I really needed these kids reading way more than they ever did.
Here's a great and interesting thread on X including educators and researchers on how to help kids with math practice to build fluency. Such a great read because all the ideas about practice are in there, plus some interesting research nuggets and practical ideas: https://twitter.com/CoreyJPeltier/status/1773731496345370728
I worked in the schools for 45 years and served as a school psychologist for 27 of those. I always used sports and music to describe the importance of practice but teachers were so brainwashed that I could never break through the barrier.
Hey Dylan, hi Holly. Two of my favorite writers on this.
Perhaps useful to separate:
1. What is payoff of actual practice outside of school, closely led by reasonably well informed parent or tutor, "inherently 1-1," where you can stipulate good choice and good follow-thru.
2. What is payoff of "solo" practice actually completed by motivated median kid, reasonably willing to do Khan exercises or go thru flash cards? Here we subtract the adult helper. Often practicing the "wrong thing" or getting stuck?
3. What is payoff of "assigned" practice to typical kid? Here I'm confident low math motivation, often literally not trying. Probably easiest to answer - near zero.
4. What is payoff of "assigned" practice during math class led by reasonably well-informed teacher, but targeted to ~25 kids. The effect is likely to mix 1, 2, 3 above. Some of our guesses about payoff are really guesses about 1, 2, 3.
You're making a good point but I think there are a lot of complexities teachers have to deal with that make practice hard.
1. Practice has to be doable. If you give students a bunch of practice and they all stare at you and say "I don't know how to do this" you're not doing much good. In my experience this type of thing is a much bigger cause of math anxiety/negative feelings about math than anything else.
2. Practice is a lot of prep. I played lacrosse as a kid and spent a lot of time practicing my throwing against the wall of my garage. I could do that with no prep; my lacrosse coach could have us do throwing drills without spending much time preparing the drill. Throwing is a skill that I can work on for hours and hours and keep getting better at. In math it's not helpful to practice the same thing for hours and hours; you move on to the next thing. Preparing all that practice and making sure it's at an appropriate level isn't easy and is a lot of work for teachers.
3. Curricula have deemphasized practice. It's hard to find good practice in most curricula today. Too many don't have enough, or it gets too hard too quickly and we're back at problem 1. Teachers end up using garbage online programs like IXL that aren't designed well and end up just being busywork.
4. Repetitive practice was much more common in the past and it didn't work very well. For practice to be helpful students need to be thinking about what we want them to learn. Too much practice was 30 questions finding the circumference of a circle. Students aren't thinking about circumference, they're just thinking "ok I multiply by pi here." Lots of teachers have given this kind of practice, seen that it doesn't help very much, and feel like practice doesn't work. This plays into the drill-and-kill rhetoric you mention.
My larger point is that yes, practice is important, and in most schools today kids aren't getting enough practice. But there are a bunch of different problems we need to solve to get practice right -- curricula that offer more practice and build in difficulty gradually, resources to provide extra instruction and practice with foundational skills that actually work (there are plenty of websites that claim they do this but don't do a good job), and a better understanding of spacing/interleaving. Practice is important, but it's not an easy thing to fix.
Absolutely agree. Also, framing the practice in academics, as in sports, is effective in explaining the time limits and parameters prior to the practice. For example, fifteen minutes on this topic, or ten sentences to correct for errors.
Some more thoughts on this subject:
Football practice is venerated because success in football is venerated. A few years ago my younger son attended a math camp at Texas State where many of the participants came from a particular community in a Houston suburb. This was a group among whom success in the state Math Olympiad carried the same social status that being the star quarterback carries in most Texas communities. I am guessing that their parents had no problem with their children practicing math.
So how do we get math practice valued among parents of students who are not the stars? Looking back to sports as an example, in the neighborhood where my sons grew up, parents regularly signed up their kids to play recreational sports whether or not they expected them to be competitive athletes later on. Children’s sports were valued because they were viewed as generally good for kids, and also as an experience the kids would enjoy. Now, if we could get parents thinking not only that knowing math is generally good for kids, but that the experience of practicing math is not a bad one…but that goes back to the details of structuring practice right. And persuading the parents whose own school experience with math was not a good one.
Reading these comments by experienced teachers makes me think about the amount of detail involved in getting this right – detail that is probably not known by most teachers, let alone taught in their teacher preparation programs. That is why there is interest in getting high-quality curriculum materials into teachers’ hands to give them more guidance on the details. See, for example, https://www.educationnext.org/sharp-critique-standards-based-reform-beyond-standards-polikoff-book-review/.
Great article! Made me think: Isn't homework some form of practice as well? But not only do kids never do it anymore, but it almost seems discouraged for the same dumb reasons as in school practice: it might be traumatizing!
In both of my major teaching roles, homework was NEVER a thing, although as an ELA teacher I really needed these kids reading way more than they ever did.
Looking forward to your next post.