I’ve underestimated the importance of vocabulary

"Words" by Shelly on Flickr

I thought for a long time that I could get by teaching math while deemphasizing vocabulary. Obviously we would discuss the meaning of words, especially the ones that come up frequently. But I thought that if I was able to help students get a feel for the math, and show kids how to do math, without getting too caught up in what the new vocabulary meant, that would be success.

Part of this was time. Or rather to save time. Spending time helping students really understand vocabulary takes more time, especially if it’s something that is more easily shown/practiced. For example, I feel like one of my struggles with helping students understand domain and range is that I don’t do a good job at really helping them understand the words. In algebra II, if I present a new type of function to them and ask them to find the domain and range, they often struggle until they see a few examples. It’s as if they’re simply replicating the process for each type of function.

At risk of this turning into a domain and range post, let me explain a bit further. When we study quadratic functions I tell students the domain is always “all real numbers”. The student thinks, “Sweet. Whenever I see a question over domain on the quiz, I’ll just write ‘all real numbers’.” When we learn a new family of functions they have no understanding of how to find the domain, beyond “that’s something with the x values, right?”.

It’s not just that topic. In fact, the concept that propelled me to write on this topic was grading a quiz over factoring polynomials and finding zeros in polynomials. Way too many of my students don’t know the difference between factors and zeros and constantly get them confused. My most significant observation was that I find students are trying to get by with the least amount of vocabulary understanding, and I don’t think I’m helping things by demphasizing it.

Since I’m having this realization at this point in the school year, I think the fix going forward will be trying to find and develop small activities to help reinforce vocabulary. Simply emphasizing it more is a start. I’ve also done some activities, like concept maps and “functions back-to-back” which help with vocabulary understanding. Next school year I’d like to take a more systematic approach and deliberately build in vocabulary activities into each unit.


Drop your favorite vocabulary activities in the comments below or send them my way on Twitter. Thanks!

Image Credit: “Words” by Shelly on Flickr

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“Opening up” Math Class

In an effort to write more I’m going to be posting shorter posts on things that are on mind regarding education and mathematics. Writing helps me process and refine my ideas and I believe it will make me a better educator.

I often think about “opening up” my math class. By “opening up” I mean developing my class in such a way that students have time to explore ideas (preferably ideas that are of interest to them, but also concepts that are in the standards).  In this setting students would be encouraged to do a number of things on a regular basis.

First, they’d be encouraged to explore wrong answers. If a student got an answer wrong they would take time to figure out why, and represent the correct solution in multiple ways (graphing, algebraically, numerically, verbally, etc.). We so often don’t have time for this and don’t value this type of exploration. I think that should change.

Second, they’d be encouraged to take ideas further on their own, in class. A good example is synthetic division vs. long division of polynomials. We always tell students that synthetic division only works in certain situations, but what about that student that wants to know why? How do we support that student? Because if that student is allowed to explore that idea he/she will likely come away with an understanding of polynomials that is far deeper than if I just told him/her the reason. (God forbid the student came up with a reason I hadn’t thought of!)

Third, students would be encouraged to work on meaningful tasks involving mathematics in small groups. These might be “real world” projects or, equally valuable, deep explorations in mathematics. The objective for the group would be not only to solve the problem(s) but to be able to communicate the solution in a meaningful (dare I say visually meaningful and appealing) way.

I do some of this on a small scale in my various classes, but I am quite often up against two major adversaries: the curriculum and time. Although I am up against this, I think that if I “opened up” my class my students would become better thinkers, communicators, and self-motivated learners. In general I think they’d become more mathematically minded and I think it is incredibly valuable to have a society of mathematically minded individuals (more on this in a future post!). I think this is why educators have to be creative, take risks, and embrace technology. That combination, for me, has been powerful in helping me to take what steps I have toward the “open” math class.

If I think of more ways in which math class could be opened up I will be sure to update. Please give me your feedback and ways in which you “open up” your class (math or otherwise)!

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