Combatting Mental Overload Using Formative Assessment

It is easy to get caught up in a biased definition of a word and let that tunnel vision keep make it difficult to see how easily it can be applied in everyday occurrences. For me, that word is measurement. As a math teacher, I am used to each of my topics having clear and concise definitions. Most of what I do as a math teacher works on the conditional relationships that show themselves in our problems. If there is a missing variable that we are solving for, then it is algebra. If we are dealing with shapes or angles, then it is geometry. However, when trying to think about the word measurement, I wasn’t able to come up with concrete conditions, and it made it very difficult for me to focus in on where exactly to go with a lesson. In terms of measurement, my brain only wanted to process it as “If I am finding the quality or length of an item, then it is measuring.”

My issue, though, is that I was able to stretch this definition that could apply it along with any other topic in math. Do I want to turn that algebra problem into a measurement problem? I need to specify what I'm counting with a label. I can find the area of a triangle in geometry, but if I assign a unit of inches or centimeters to the base and height then it is measuring. I couldn’t think about measuring the same way I could think about other branches of mathematics. It was too broad. This didn’t mean I had to change the way I was thinking about measurement; I just had to embrace the flexibility of measurement. This flexibility allows me to attach measurement to any branch of mathematics I want and essentially teach two things at once.

This whole dilemma got me thinking about my students. If I’m sitting struggling to wrap my mind around this, how do my students feel? Some of them put in so much effort to be successful learning a single concept, but can lose any and all progress on a problem that is presented to them with the added layer of measurement. When we take a problem students know, but situate it in a real-world context with measurement units, students question and doubt everything they have learned up to this point. In my sixth grade classroom, I see this become more of an issue when we begin learning about ratios. My students know that ratios are a way to compare two different things at the same time and can be represented as fractions with all of the same rules of equivalency applying. They can use and manipulate them perfectly fine when they are given on their own, but their proficiency declines dramatically when they are forced to solve a story problem.

To help me combat this, I use different forms of formative assessment, specifically Plickers, which gives me real-time information on student answers to multiple choice questions. I have to be very specific in the questions I ask in order to make the most out of my data. Each question has to be carefully designed using my Knowledge of Content and Students (Hill & Ball, 2009) to contain not only the correct answer, but also other possible answers students can arrive at based on common mistakes. Did they choose B for number two? Well that means they didn’t keep the order of their items consistent and compared blueberries to strawberries instead of strawberries to blueberries like the question asked. Oh, they put A for number five? That means they set their proportion up incorrectly and didn’t simplify. Strategically choosing answer choices gives all possible solutions meaning instead of just being right and wrong. With these additional insights, I gain the ability to group students based on common mistakes, provide them necessary feedback to correct those misconceptions, and become more likely to increase student performance (Humes, 2021).

References:

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

Humes, A. (2021). Formative assessment and technology in the mathematics classroom. [Master's thesis, Northwestern College]. NWCommons.

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