6 grievances about how we teach math
1. Why do we need so many practice problems?
If you’ve haven’t gotten it ten questions later, maybe you should do something else. If you’ve got it after two questions, maybe you should do something else.
Instead, what if you went deep into one question?
The kid that already gets it is solidifying their understanding with a deep, conceptual, visual, kinaesthetic understanding. The more ways you learn i.e. the more sensory connections your brain makes, the better you encode and retain information. That’s why learning styles aren’t real – learning in multiple ways (not one specific way) is better for everyone.
The kid that doesn’t yet get it is learning from a rich, slowed-down example, so they are seeing where different numbers and measurements come from, and how and why we are doing the math that we are doing. They can develop an understanding, not memorize a process.
2. You’ve got it when you know how to cheat
What if we declared proficiency when you are able to google a question, look at the first couple results or pictures, and know how to solve the problem?
Good enough for me.
Here’s how you can tell a kid doesn’t understand: they can’t even google to find the answer. They aren’t even sure what to search. You give them the step-by-step process, or the formula, and they don’t know what to do with it.
If you know how to cheat, you know enough.
More importantly, if it’s that easy to cheat, we aren’t asking the right kinds of questions.
3. Get rid of the elitism
The person who can understand all methods is the one who has truly learned. The person who can only figure things out with numbers is the one who is lost.
If you can’t prove to me how to divide fractions using pictures, you don’t even understand what division is. I don’t care if you can’t divide fractions, but it is important that you understand conceptually what it means to divide.
As Seth Godin says, connecting the dots (making connections between how division of whole numbers relates to division of fractions) is more important and useful than collecting the dots (memorizing a three-step process to divide fractions).
What are outcomes if not dots to collect?
4. Don’t teach kids to be calculators
Did I just spend two months teaching kids to multiply and divide fractions?
Does this matter in the grand scheme?
To be honest, kids, almost everything you learn can be solved using a computer.
We’re training to you be (not very good) calculators.
Sometimes we make you think about questions or answers and you hate that. So we don’t do it very often.
5. Why are we learning this?
Honestly, why are we ever learning anything?
Students, don’t forget, grades are an illusion.
Teachers, don’t forget, your number one job is to ignite a love of learning in your students’ bones and hearts and souls. A desire to figure things out. An appreciation that we can make the world a better place by learning and applying what we know. A preference for answers found by thought, experimentation, reasoning…not opinions or your news feed.
6. How is the
industrial school complex school system doing?
We are doing so bad at teaching science (and math) (and reading) (and everything?), that there are huge anti-science movements (like the Republican and Conservative parties). We’re literally destroying the Earth because science teaching has made us all HATE science and HATE what science stands for.
We don’t know how to tell a good idea from a bad one, or how to develop an informed opinion, or how to change our mind when presented with counter evidence. That’s how much we all hate reading and writing, thanks to school.
And mathematics. Math has been so useless to people that they purposely avoid anything related to math. So we have the most in-debt populations ever, because balancing a budget would require…MATH.
The number one job of teachers can no longer be to teach the curriculum. At all costs, we need to ignite students’ love of learning. Because the alternative is ignorance, and ignorance breeds hate.
These are fractions. Wow, how do they work? See if you can figure it out. Oh, they’re parts (2 out of 3). But they’re also division (2 divided by 3). And they’re also proportions (2 for every 3).
There you go. You can do anything with them now.