2. I made a Critical Mistake: Warm-Ups and Weeklys

I made a critical mistake: Warm-ups and "Weeklys"

This we believe (NMSA, 2010).

* Students and teachers are engaged in active, purposeful learning. Active Learning

This we believe (NMSA, 2010) identifies sixteen characteristics that exist in exemplary middle schools. This blog addresses the second characteristic, and is part of the section that addresses curriculum, instruction, and assessment.

When I was teaching in another state, tests were based on students’ abilities to use algorithms. In my classroom, I gave a warm-up every day that included a variety of mathematical skills. Today, tests include basic computation, but also assess students’ abilities to interpret and analyze problems. And while students can benefit from algorithms, warm-ups, and worksheets to practice such activities, I believe learning to think critically must include direct instruction as well as opportunities for students to think independently and in groups, based on problem solving and communication. But this is not new.

In the late twentieth century, when the National Council of Teachers of Mathematics (1989) presented their Standards, discourse and problem solving were part of the original design. So I started the year drilling my students on algorithms and vocabulary. In keeping with traditions of other math teachers, and many elementary teachers, I gave out a “weekly,” which included questions that called for students to be able to think critically, and to solve problems on their own.  For an entire semester, my students have been slogging through "weeklys," not overly impressed, nor interested in the beauty of thinking “outside the box.”

What I found was students trying to do problems, but regularly having few ideas to begin to solve the problems. Those students with older siblings had help, and had answers. Those who had little support, either would not complete the problems or had random answers. The “weekly” format didn’t work for me; but I love the idea of the weekly. I have been concerned that giving challenging problems, like those on the 'weekly,' without communication may reinforce misconceptions, and serve to frustrate my students, rather than engage them in deeper thinking and the joy of playing with mathematics. By the time students turned them in, their interest in going over the 'weekly' also wained.

So starting this week, I have shifted the focus to critical thinking during our warm-up time as opposed to drilling basic facts. I now start my class with two to three questions from the ‘weekly’ that ask students to read, draw pictures, and analyze the question, prior to punching numbers into a calculator. Every day our warm-up consists of problems that allow students the opportunity to work independently, or in pairs, to analyze, draw, try, and communicate their thinking. Because there are only a few problems, students are becoming more comfortable, going back to the original problem, looking at their work, and seeing if the answer makes sense and when possible, checking their work against the original data.

This week, at least five students shared, “I am so glad we are doing these in class.” Students are showing their work and we are spending the first part of our day having a conversation about the problems. I use four steps: Draw something; decide what the question is; make a plan; see if the plan makes sense and check it if you can. This format is based on Polya’s 1965 problem solving strategy. Student success is providing a more positive climate. We are taking the problems and using the TI-84s to check the work, or illustrate the data. There is more joy in the class.

I now believe, that had I started the year with this approach, by now, my students would be able to work on 'weeklys' independently. As teachers, we need to be sure our students have the tools to think before we challenge them to think on their own.

Advice

1) I am finding that my students are willing to think, but different levels of students need different levels of scaffolding. In some classes, I challenge them to work together and think independent of my “hints.” Many of my advanced students beg to think on their own; I let them. In other classes, I give hints, and in some cases I am giving direct instruction. In all classes, I would have to say there is direct instruction. I ask them to share their thinking and model how they examine problems; I talk about how I think about the problems, so that we engage in a conversation about mathematics, problem solving, and ultimately tools they can use when they are assessed.

2) At the beginning of the year, each week, I created my own 'weekly,' or asked to use another eighth grade teacher's sheets. We created them from www.problemattic.com.   This website gives problems in a multiple-choice format and problems are identified by concepts so the weekly reinforces common topics each week. I believe, having students conduct similar problems over time is the best way to help them process algorithms and problem solving.

3) Do not be afraid to change your approach if it is not working. Many teachers use 'weeklys' with their students. They distribute the handout out on a Friday and the assignment is due the following Friday. Right now my "weeklys" are taking about a week and a half. I love listening to my students as they think. To me their ideas are a fresh mathematical bouquet of problems. (:  (I know, kind of geeky.)