Abominable Algebra: Beware the Beast

My students and I have differing views on our algebra unit. I, for one, love it because we’re getting into the math that got me interested in the subject and I’ve seen many of my students start to find their groove at this time. The majority of students in my class, however, have no interest in doing this because “math is hard enough, why are we adding letters to it?” I wouldn’t have it any other way. Their apprehension tends to make them more attentive because they know they will be doing this for the rest of their school career, if not longer. My students think algebra is some giant monster to face and conquer. They build up the complexity in their head without knowing how algebra - or at least the areas of it that we cover - spirals and reviews many of the basic math concepts that we covered throughout the year. Eventually, they are able to see the beast for what it really is and get the greatest “ah-ha” moment of the year.

Being aware of my Knowledge of Content and Students (Hill & Ball, 2009), I try to introduce the ideas of variables throughout the course of the school year. This is always the biggest hurdle for my 6th graders, and they can get stuck on this very easily. Whenever I have a missing number for a problem, I’ll always replace it with some kind of symbol. Early on, it’s just a question mark, but will slowly morph into words, and eventually into letters. I let them know the purpose of these labels, like “We’re trying to find out how many beads are on this necklace, so since I’m looking for a number of beads, I can just write that in this spot so I can remember this is what I’m looking for. I might even just use the letter ‘b’ for beads so I don’t have to write so much.” It gets even better once we get to ratios and start counting multiple items at once. Now, if they’re trying to find the amount of bananas and strawberries, they have to use a variable for each to differentiate between items. If I see a ‘b’, then it must be talking about the bananas. If it’s an ‘s’, then that must be strawberries. It becomes a lot easier to understand why there are letters in math when they have context and purpose.

There are a myriad of great online resources that can help bridge the gap to this more abstract way of thinking, but a hands-on approach has always had the best results for me. I like to treat combining like-terms as a zoo, where each term has its own exhibit based on its variable (or lack of one). I give each student a term and have them move randomly throughout the room. After about 10-15 seconds, I randomly pull 4 or 5 students and write an expression on the board using their terms. As a class, we have to determine which exhibit they should go in and if there are any terms that I captured that should go to the same place. This type of interaction is something that wouldn’t be as effective digitally and helps establish a sense of solidarity in the room while creating room for authentic discussion to emerge.

If my students had a better understanding of algebra prior to our module, I don’t feel that they would get as much out of it. All of the build-up and horror stories they've heard have them expecting the worst. By the time everything starts to click for them, they believe that they overcame an impossible obstacle and receive a huge boost in their mathematical confidence. The perceived rigor helps the information stick. Were it not there, it may be shrugged off as unimportant or fall under the category of “Well, if this is that easy, then I can just learn it later if I really need it.” Instead, they walk away with a mark in the win category and perhaps a newfound interest in mathematics.

Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71

Wix. Fresh strawberries [Photograph]. Wix. https://static.wixstatic.com/media/11062b_32fe993f69f749ff81e015f62b468811~mv2.jpg/v1/fill/w_525,h_351,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/11062b_32fe993f69f749ff81e015f62b468811~mv2.jpg

Wix. Hairy monster [Photograph]. Wix. https://static.wixstatic.com/media/c9b600dc474946cc904ee7392a223524.jpg/v1/fill/w_525,h_525,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/c9b600dc474946cc904ee7392a223524.jpg

Wix. Math class [Photograph]. Wix. https://static.wixstatic.com/media/11062b_5c8ecf60fc9b4c2285153ca14e4fb543~mv2_d_5120_3413_s_4_2.jpg/v1/fill/w_525,h_350,al_c,q_80,usm_0.66_1.00_0.01,enc_auto/11062b_5c8ecf60fc9b4c2285153ca14e4fb543~mv2_d_5120_3413_s_4_2.jpg