Going into last summer I spent a lot of time reflecting on the failures and successes in my classroom. In particular, I focused on the classroom culture I created. I consider my classroom a high energy (albeit quirky), discussion based classroom. I absolutely LOVE seeing students on the edge of their seats, hands pointed skywards, desperate to volunteer some mathematical tidbit to the discussion. Unfortunately, this is a rare reaction in my room. Sure, every class will have 3-5 “high-achievers” who will raise their hand for anything- often before a question has even been posed. However, I have found that many students lurk in the background, unwilling to become involved. I had to find a way to get these students interested and confident with Algebra I.
This year, the strategy that has been met with the most success (in terms of student engagement, participation, and even math JOY) has been utilizing open ended questions. Open ended questions are questions in which their is no one answer. Sometimes there isn’t even a right or wrong answer. I have found these questions give students breathing room to get creative and helps dismiss their fear over being wrong. When the platform for a question is open all students feel confident that they can bring something to the table. In some classes open ended questions have plunged my room into mathematical chaos (one class applauded a girl who was able to rewrite 2(x + 3) as -2(-x – 3) who’d have thought? All the sudden math confidence and success was associated with being cool).
In this scenario, my question was represent the expression to the right in as many ways as you can- 2(x + 3)
Some answers included– 2x + 6, 2(x) + 2(3), 2(3 + x), (x + 3)(2), x + x + 3 + 3 (that was my particular favorite)
Some incorrect answers included- x(2 + 3), 3(x + 2), 2x + 3, so on and so forth
I’ve found that I can address some very powerful foundational mathematical concepts by having the students explain why the incorrect answers are mathematically unsound. Some classes actually reveled in coming up with creative new ways to represent the expression. Bottom line- my students were engaged, unafraid to provide answers, eagerly discussion, and concretely understanding the distributive property.
Places to Improve- As much as I have loved using these open ended questions there have been areas that I would like to improve. For example, some students use this strategy as an out to pick the most obvious answer and then give up. I am brainstorming ways to continue to push the students to connect with the math on a deeper level. A second issue I have had is classroom management. Generally the students (and myself) are so eager to volunteer that the noise level can be downright deafening. If you have any cool ideas or anecdotes you could share to help me remedy these issues please let me know!