English teacher here. I like the idea of kids knowing Math facts. Multiplication tables never killed us. It's so weird when kids can't do basic calculations in their heads. Even watching them with calculators, they struggle when they don't understand what a number is. But I could ramble here.
"Student knowledge of math facts predicts lots of other outcomes later on in math class."
I don't doubt that this is true. But I also suspect that many people draw the wrong conclusion from this observation -- that student knowledge of math fact **causes** later outcomes. On the face of it, that seems plausible; for instance, students cannot perform basic single-digit arithmetic will struggle when they encounter fractions. And I'm sure that many math teachers will have experienced this phenomenon in their own practice. But this is a classic example of confusing correlation with causation, and we should also consider the possibility that the causal connection isn't quite so strong.
Instead, I think a more plausible explanation is that there is an innate ability to do math, and that varies from person to person. Thus, an inability to grasp basic math facts is simply an early indicator that that person does not have a strong innate ability, and then later on this manifests as struggling with more advanced concepts. In this view, lack of skill with basic math facts doesn't **cause** difficulties in math later on; instead, students do not have strong innate abilities at math, and this then causes struggles with math at the early stages, which are observable when trying to learn basic math facts.
Both concepts can be simultaneously true! It can be the case that not learning basic math facts leads to problems later on, and it can also be the case that struggling with basic math facts is indicative of low innate ability. So they aren't mutually exclusive possibilities. But we should think carefully about the possibility that the causal connection isn't quite as strong as we might assume at first.
It looks at a bunch of different predictors of fraction knowledge. Multiplication fact fluency is a predictor even when lots of other stuff is controlled for. I do think there is a causal relationship here. There are some people who overstate the size of the effect, but I see evidence that one causes the other.
Another factor the study looked at is working memory capacity. Working memory is one component of what we might call "innate ability." There isn't much we can do to influence working memory, and working memory impacts math learning and performance. But that actually leads me to a different conclusion than yours. We shouldn't be trying to increase students' working memory capacity, or problem solving skills, or grit -- despite a lot of research we haven't found reliable ways to influence those things. Instead, we should focus on things like fact fluency. Fact fluency is just making knowledge secure in long-term memory, and I haven't seen any convincing evidence that a significant number of students can't learn their math facts with the right instruction.
Are there some things we could refer to as "innate ability" that we can't do much to influence, and that have a causal impact on math performance? Yes. But fact fluency is not one of them, which is why I think it's worth doing right.
I had never even heard of mad minutes, after 35 years of teaching secondary maths. I may have done something similar as a quick five for starters, but they would have been from related tables e.g.2,4 and 8 or 3,6 and 9, never a random mix. even 7's had pattern maybe 2 x 7, 3 x 7, 5 x 7, 7 x 7 and probably 10 x 7. As well as starting with an easy one, I found ending easy made students feel good , and successful, so ready to try again tomorrow. I always tried to include the square as well.
Interesting! I did them as a kid in the 90s and I've seen them at a few different schools. Grouping facts together helps, and it's the obsession with timing that I find unhelpful.
English teacher here. I like the idea of kids knowing Math facts. Multiplication tables never killed us. It's so weird when kids can't do basic calculations in their heads. Even watching them with calculators, they struggle when they don't understand what a number is. But I could ramble here.
Now if only they could read analog clocks...
"Student knowledge of math facts predicts lots of other outcomes later on in math class."
I don't doubt that this is true. But I also suspect that many people draw the wrong conclusion from this observation -- that student knowledge of math fact **causes** later outcomes. On the face of it, that seems plausible; for instance, students cannot perform basic single-digit arithmetic will struggle when they encounter fractions. And I'm sure that many math teachers will have experienced this phenomenon in their own practice. But this is a classic example of confusing correlation with causation, and we should also consider the possibility that the causal connection isn't quite so strong.
Instead, I think a more plausible explanation is that there is an innate ability to do math, and that varies from person to person. Thus, an inability to grasp basic math facts is simply an early indicator that that person does not have a strong innate ability, and then later on this manifests as struggling with more advanced concepts. In this view, lack of skill with basic math facts doesn't **cause** difficulties in math later on; instead, students do not have strong innate abilities at math, and this then causes struggles with math at the early stages, which are observable when trying to learn basic math facts.
Both concepts can be simultaneously true! It can be the case that not learning basic math facts leads to problems later on, and it can also be the case that struggling with basic math facts is indicative of low innate ability. So they aren't mutually exclusive possibilities. But we should think carefully about the possibility that the causal connection isn't quite as strong as we might assume at first.
I draw a different conclusion here. One study on this topic is this one: https://www.sciencedirect.com/science/article/abs/pii/S0885201415000106
It looks at a bunch of different predictors of fraction knowledge. Multiplication fact fluency is a predictor even when lots of other stuff is controlled for. I do think there is a causal relationship here. There are some people who overstate the size of the effect, but I see evidence that one causes the other.
Another factor the study looked at is working memory capacity. Working memory is one component of what we might call "innate ability." There isn't much we can do to influence working memory, and working memory impacts math learning and performance. But that actually leads me to a different conclusion than yours. We shouldn't be trying to increase students' working memory capacity, or problem solving skills, or grit -- despite a lot of research we haven't found reliable ways to influence those things. Instead, we should focus on things like fact fluency. Fact fluency is just making knowledge secure in long-term memory, and I haven't seen any convincing evidence that a significant number of students can't learn their math facts with the right instruction.
Are there some things we could refer to as "innate ability" that we can't do much to influence, and that have a causal impact on math performance? Yes. But fact fluency is not one of them, which is why I think it's worth doing right.
I had never even heard of mad minutes, after 35 years of teaching secondary maths. I may have done something similar as a quick five for starters, but they would have been from related tables e.g.2,4 and 8 or 3,6 and 9, never a random mix. even 7's had pattern maybe 2 x 7, 3 x 7, 5 x 7, 7 x 7 and probably 10 x 7. As well as starting with an easy one, I found ending easy made students feel good , and successful, so ready to try again tomorrow. I always tried to include the square as well.
Interesting! I did them as a kid in the 90s and I've seen them at a few different schools. Grouping facts together helps, and it's the obsession with timing that I find unhelpful.