Mak­ing Math Matter

By Ryan Branoff

As an edu­ca­tor it has been my goal to cap­ti­vate my stu­dents and engage them in their work.

How­ever, engage­ment is not easy to come by when many stu­dents are unin­ter­ested in the sub­ject mat­ter that I am try­ing to teach. When I first began teach­ing I rec­og­nized a major issue for my stu­dents (and for me!): they didn’t like math.

Could I blame them? When I was a stu­dent, my atti­tude toward math was no dif­fer­ent. It was the sub­ject I liked least because it was repet­i­tive and we were expected to learn by rote. I found math irrel­e­vant and unim­por­tant. This expe­ri­ence is what moti­vated me as an edu­ca­tor. I asked myself how I was going to engage and chal­lenge my stu­dents crit­i­cally about math when I hadn’t much liked it myself.

I had to con­sider twenty-first-century learn­ers and their demands for engage­ment. I knew that giv­ing my stu­dents own­er­ship and mak­ing math rel­e­vant were my best options.

Enter the three-part lesson

The Three-Part Les­son in Math­e­mat­ics: Co-planning, Co-teaching and Sup­port­ing Stu­dent Learn­ing (http://resources.curriculum.org/secretariat/coplanning/) is a won­der­ful instruc­tional tool pro­vided by the min­istry of edu­ca­tion. This resource gave me an oppor­tu­nity to refor­mat how I taught math. It allowed my stu­dents to take own­er­ship of their learn­ing and allowed me to have a class­room full of crit­i­cal thinkers and prob­lem solvers who were inter­ested in math.

The essence of the three-part les­son is to give stu­dents open-ended prob­lems with mul­ti­ple entry points. Stu­dents work with part­ners at their level to problem-solve and develop a result. They are encour­aged to jus­tify their think­ing by any means nec­es­sary and use the meth­ods that best suit their needs. My role as the teacher is to facil­i­tate and guide their think­ing with­out push­ing them toward one com­monly prac­tised method.

After stu­dents have had the oppor­tu­nity to work through the prob­lem, we dis­cuss as a class the dif­fer­ent meth­ods they used, what worked and what didn’t. This is a fan­tas­tic way to get the dia­logue going in a math­e­mat­ics class­room! I encour­age my stu­dents to jus­tify their think­ing. The dis­cus­sion also pro­vides them with the chance to ask ques­tions, and develop an under­stand­ing of con­cepts that they didn’t quite get. Stu­dents who have devel­oped an inter­est­ing way of solv­ing the prob­lem take a lot of pride in their work and are will­ing to act as peer teach­ers for the rest of the class. The stu­dents who have dif­fi­culty com­ing to an end result are now learn­ing as a result of the inter­ac­tion with their learn­ing part­ners and from the class dis­cus­sion. Stu­dents are not wor­ried about tak­ing a risk or get­ting a “wrong” answer because they know that they will be able to gain an under­stand­ing of the con­cept dur­ing the dis­cus­sion por­tion of the lesson.

One activ­ity my stu­dents did was find­ing per­sua­sive bias in a vari­ety of mag­a­zines, rang­ing from Nin­tendo Power to National Geo­graphic. I asked my grade 7 and 8 stu­dents to com­pare the num­ber of ads and the num­ber of arti­cles in the pub­li­ca­tion and to rep­re­sent their col­lected data in an inter­est­ing way. I also asked them to make a gen­er­al­iza­tion or con­clu­sion about their data.

Dur­ing our dis­cus­sion, stu­dents pre­sented a vari­ety of dif­fer­ent graphs from pie charts to bar graphs, whichever method worked best for them. Some also made gen­er­al­iza­tions about what their data meant. One con­clu­sion they reached was that Nin­tendo Power was a biased pub­li­ca­tion because even its arti­cles adver­tised Nin­tendo prod­ucts. The dis­cus­sion showed many stu­dents new data man­age­ment procedures.

This prob­lem allowed us to talk about dif­fer­ent kinds of dis­crete data graphs, the dif­fer­ence between dis­crete and con­tin­u­ous data, how to use data col­lec­tion to iden­tify bias, and how to use data col­lec­tion to per­suade an audi­ence. These tasks also high­lighted how math­e­mat­ics con­nects to tex­tual and media literacy.

Dif­fer­en­ti­ated learning

Using the three-part les­son allows me to address the var­i­ous learn­ing styles, needs, excep­tion­al­i­ties, and mul­ti­ple intel­li­gences of my stu­dents. Because the prob­lems are open-ended, the tasks and lessons are auto­mat­i­cally dif­fer­en­ti­ated for any learner, giv­ing stu­dents work­ing at dif­fer­ent lev­els an oppor­tu­nity to be suc­cess­ful and to bring their own back­ground knowl­edge into the solu­tion. Elim­i­nat­ing the stress of fol­low­ing a spe­cific for­mula or method takes the lim­its off of what they are capa­ble of doing.

Being allowed to approach math in a way that is rel­e­vant and mean­ing­ful cre­ates a risk-free envi­ron­ment that allows math­e­mat­ics dis­cus­sions to become richer and deeper. My stu­dents have formed a com­mu­nity of thinkers where everyone’s opin­ion, strat­egy, and solu­tion is val­ued. Even solu­tions that don’t quite work are val­ued, because every thought con­tributes to the col­lec­tive under­stand­ing of the con­cept under investigation.

Engag­ing the reluc­tant learner

My stu­dents’ atti­tudes toward math have com­pletely changed as a result of this three-part struc­ture. When I allow my stu­dents to work through and inves­ti­gate what I am try­ing to teach them, they feel as though they are an essen­tial part of the learn­ing process. Stu­dents who have pre­vi­ously shown frus­tra­tion and dif­fi­culty with math are now enjoy­ing it and becom­ing engaged in what they are learning.

Last year, I had a stu­dent who showed min­i­mal inter­est in learn­ing math. He would often say that he found math bor­ing and repet­i­tive. Through­out the year, I saw this stu­dent blos­som and find an inter­est in the sub­ject. He thrived because his class­mates and I val­ued and used his opin­ions and thoughts. Dur­ing a les­son on deter­min­ing the vol­ume of a rec­tan­gu­lar prism, this reluc­tant math­e­mati­cian devel­oped a cre­ative and unique approach to solv­ing the prob­lem. He equated it to “stack­ing pan­cakes”: he solved the area (a con­cept pre­vi­ously taught) and lay­ered the area repeat­edly to rep­re­sent the height of the prism. The rest of the class was fas­ci­nated by his think­ing and he took great pride in being able to “teach” his peers.

My math pro­gram has also had a great impact on those who pre­fer to think cre­atively, and on higher-level stu­dents. When not lim­ited to the con­fines of “one right answer,” those who are already at a higher level are encour­aged to go beyond what is expected. They are able to extend their under­stand­ing of math con­cepts to other areas of the cur­ricu­lum, such as using data man­age­ment as a per­sua­sive strat­egy. This method has par­tic­u­larly ben­e­fited those who pre­fer cre­ative learn­ing as opposed to learn­ing con­crete con­cepts. When math was made rel­e­vant and was con­nected in a cross-curricular way, these cre­ative thinkers devel­oped a greater under­stand­ing of why math is important.

When it comes to engag­ing stu­dents in math, the lim­i­ta­tions do not lie with the sub­ject mat­ter, but rather with the way it is taught. By mov­ing away from reg­i­mented and tra­di­tional approaches, teach­ers can engage stu­dents and make math pur­pose­ful for them.

Math can be excit­ing! And I’ve learned that if I am excited and pas­sion­ate about what I’m teach­ing, my stu­dents will be as well.

Ryan Bra­noff is a mem­ber of the York Region Teacher Local.