The adventures of a fourth grade teacher in East Central Illinois.

Expressing Mathematical Thinking

As much as I would like to wish that the regular course of classroom instruction will adequately prepare my students for the standardised testing administered during the first week of March, the reality of the situation is that my regular teaching methods only prepare them for the content. The format of standardised tests is typically considerably different than what we use in the classroom. The reason for this is simple: I believe in differentiated instruction (teaching that meets the needs of my students where they are at) and that means I also need to utilise differentiated assessment (determining their understanding through various strategies). Standardised tests, on the other hand, assess all students the same way at the same time. Testing in this format is useful for generating massive data across a broad spectrum and gives educators a large-scale view of student understanding at that moment. From a small-scale view, though, there are more useful tools for assessment.

All of this is why I find it worthwhile to take time during the couple of weeks leading up to our annual testing to prepare my students for format of the test. This isn’t such a bad thing, though. I believe it is useful for students to get used to the idea that different circumstances call for different responses. Just as we discuss that the language we use at home may be different from the language we use at school, or the way we dress for a wedding may be different from the way we dress for a day at the pool, we discuss that the way we do an assessment in the classroom for our own use is different than the way we do an assessment for that the state is using.

Of course, that doesn’t mean I am going to just stop what we are doing and do test prep that isn’t related to our learning goals. Instead, I incorporate the prep into our curriculum. In fact, I incorporate elements of this prep throughout the year but as we get closer, the incorporation becomes more explicit. Knowing that multi-step word problems are often a challenge for fourth graders, and knowing that they are a common feature of the state tests, I decided now was a great time to focus on them.

We started today with making T-charts to organise the steps for solving arithmetic problems. There are a lot of ways that T-charts can be used, but I like to use them for extended math responses because they let students keep track of what they are doing on one side of the paper and how or why they did it on the other side. Many of my students have used T-charts in the past, so it was fairly easy to introduce them as a tool for expressing their mathematical thinking. We have also been working on expressing mathematical thinking verbally for several months, but this is the first time we have really focused on writing those thoughts down. I had the class use the T-charts first with arithmetic problems. We will continue with them throughout the week as we work through one-step word problems before getting to the multi-step problems. We will also explore alternative strategies for solving the same problem. All of these are things that will help my students be stronger mathematical thinkers, but they will also help them be better prepared for the standardised tests in just a few weeks.


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