Anticipating Misconceptions
Preparing for Errors and Guiding to Understanding
Anticipating student misconceptions occurs in the lesson planning stage as a preparatory measure for what could possibly unfold in the classroom and how students will react to the material. Rather than having to always respond in the moment to a student misunderstanding, teachers can try to predict some of the approaches their students might use and some of the misinterpretations they may have (Kasten, 2009). Initially, thinking about what possible errors my students would make was difficult because I personally know what is correct and cannot necessarily remember the mistakes that I made when I was first learning the material. Kasten (2009) refers to this block as the “expert blind spot,” where experienced individuals have difficulty taking on a novice perspective.
Teachers should think about both the incorrect and correct methods that their students could use to solve a problem. Although it is not possible to think of every method that students could use, the preparation helped me to better serve my students. From these possible errors and approaches, I could brainstorm effective ways to respond to them should they arise— utilizing guiding/probing questions, relevant examples, visuals, etc.
Gaining Lesson Planning Experience
When planning how to support my students, I still wanted them to make the mistakes that they would but to be equipped to guide, not lead, my students to accurate understanding. Smith and Stein (2011) describe one teacher’s approach as “Although he wanted students to be able to figure out their errors on their own, he wanted to be ready with some questions that would guide them in the right direction” (p. 34). Throughout the year, I tried to incorporate guiding questions into my lesson plans. As a novice student-teacher who spent a significant amount of time just trying to solidify the structure of the lesson, I often did not get to this point of anticipating how my students would respond. I believe that with more experience in planning I will become better about addressing this aspect of lesson planning.
Comparing these two “Errors/Misconceptions” sections from my lesson plans, I noticed how the one for parallel lines is more thought-out than the two-variable inequalities lesson. It not only lists possible student misconceptions but also has guiding questions that I could ask my students to help them rationalize and reason through their thinking to more accurate understandings. Having these questions prepared beforehand helps to ensure that I am wording them in an appropriate way that gives minimal guidance and does not diminish the cognitive demand for my students. As much as possible, I would like to try to not only brainstorm possible misconceptions but to also concretely think beforehand about how I could respond to them, including what specific questions I could pose.
Example: Promoting Conceptual Understanding
Some of my students were forgetting when to use a dashed or solid line for an inequality graph. A student could just memorize that the inequality signs < and > require a dashed line. However, if they understand that these signs mean less than and greater than, respectively, and that means the points on the line are not included, they can logically reach the conclusion that they should use a dashed line. I wanted my students to have these conceptual understandings, rather than “memorized understanding,” because their learning would be deeper and longer-lasting.
Since my students had struggled with the solid and dashed lines, I predicted that they would also have some trouble with when to use brackets or parentheses when writing out domain and range from a graph. In my lesson planning, I knew that I had to provide meaning to these notations, and so, I created a table for math notations to include and exclude values. This table provides students with a visual medium with which to draw connections and go beyond memorizing what to do for individual cases.
Knowing My Students
As I got to know my students more and become more familiar with the ways that they tended to think, I was better able to anticipate what misconceptions that they would have. I knew that they often struggled with synthesizing and integrating new knowledge that closely resembled previous material. I found myself listing out mostly procedural and technical errors that I thought my students would have. This trend pointed to a possible tendency of my students to try to memorize steps and facts, which could be attributed my own tendency to teach with direct instruction as well as them not having conceptual understandings of why they had to perform certain steps.
Reflecting on these things about my students and my own teaching, I focused my anticipations on the procedural errors that my students would make. To promote conceptual understanding, my preparations needed to focus on helping my students gain the “how’s” and “why’s” behind the material. My students who had good memories were able to just remember the steps and execute them on their own; however, I felt that my other students who were struggling needed the steps to be grounded in logic. In this way, if they “forgot” a step they could fall back on the “why” and reason back to what the step should be.