(Don’t worry, this is just a Google Series intermission!)
As I was cleaning the kitchen, a thought occurred to me: “Write me a problem whose answer is 4.”. What an amazing application this type of backwards learning has in math.
Scaffolded: “Write me a polynomial which can be simplified to 4x + 1.”
Scaffolded again: “Write me a polynomial which can be simplified to 4x + 1 in more than 3 steps.”.
Again: “Draw me a line with a slope of ___ and write the equation (f(x))”.
You may have noticed that I’m not a math teacher. But I am. And, if you are a language teacher reading this… chances are, you are too.
I hear from parents (and students) all the time: But, my child is SO good at English! Well, that’s great, I reply, but the problem is, learning a second language has more in common with Calculus and Algebra, than it does with English Class.
Sure! I teach transition phrases and how to write a paragraph or how to write a sentence instead of a fragment (where is your verb?!?!?!?). Sure! We read literature and analyze it and look for cultural connections. Sure! We do all of that. In Spanish.
BUT, you see, we also look at grammar. Sometimes, explicitly, sometimes implicitly. Those explicit moments are sometimes needed, but often, they are the reason kids end up hating their language class as much as they hate their math class. And, they can’t figure out why.
This is why. A new theory is on the rise in the world of linguistics, that, as far as I have researched, I happen to agree with. It is the mathematical analysis and comparison of linguistic structures to the math of the world. You see, math makes the world work. Science is math applied. Math makes it all make sense. Languages have to end up making sense in order to communicate a message, and it turns out, that is a job math can do. Grammatical sentences are complex formulas, and just past that equal sign (=) is the message you communicate. When your formula is bad, your message is too.
All of these revelations and random thoughts of math while I clean my kitchen, bring me to a few points.
- Just as language teachers are moving away from the explicit teaching of Grammar… and seeing amazing results… math teachers are going to have to do the same. Unfortunately, this means that this change will need to be reflected in the standards as well. Just as language standards have become communicative (answer based), math standards will have to do the same. Instead of process based, we’ll need standards like, “Students will engineer a bridge… ect.”; because they can’t meet that standard without implicit math. Math standards will need to be results based.
- Language teachers need to be cognizant of their students who struggle in math and communicate with these students’ parents. This will prevent the poop-storm that ensues when said kid struggles and their parents are blindsided–because they thought Spanish was an English class.
- The example problems I mentioned above are similar to the ones language teachers use in their classroom every day. Compare:
- “Tell me 2 things you like to do.”
- “Write me a paragraph explaining what you would do if “X” happened.”
- “Tell me your favorite memory as a child.”
In each of the above examples, we give the kids a product, and they must fumble with the pieces to come up with an answer. Like in math, we give formulas, functional chunks, that kids use in the gap to achieve the task.
What do you think?