A common theme in many chapters of Powerful Problem Solving is Gallery Walks. Several techniques are offered throughout the book, but the common goal is to allow students to view their classmates’ approaches to problems.
One of my faults with online book chats is lack of follow-through. I can sometimes use an extra nudge of accountability. There are often so many great ideas and strategies in the books we are chatting that I get overwhelmed and not sure where to begin. Advice: pick 1 thing. Try it. Reflect. Revise. Try it again.
So here is my attempt at a gallery walk. I simply cut apart a pre-assessment for a Formative Assessment Lesson and each pair of students taped it to a large sticky note, discussed and responded. I was confident in many of the questions, but my goal was to identify the few some students were still struggling to understand completely, mostly questions involving transformations.
1. The large majority are fine with creating a possible equation, given the x-intercepts.
2. Initially these students tried -6, -4 and 2 as their intercepts. I asked them to graph their equation then reread the instructions. Oh. They had read write an equation, looked at the graph for possible intercepts and failed to read the y-intercept of (0, -6). One quickly stated the connection between y-intercept and factored terms and was able to adjust their response with ease. I believe it happens often to see a graph skim question and think we know what we’re supposed to do, only to realize skimming sometimes results in miseed information.
3. Within the lesson, many students quickly realized when a factor was squared it resulted in a “double root” and the graph would not actually pass through the x-axis at that point.
The 4 transformations seemed to causes the most disagreements. These were the ones we discussed folowing our gallery walk. However, it was during the gallery walk most students were able to adjust their thinking.
4.i. Listening to students as they were at the poster helped me realize there was not a solid understanding of the reflection across x-axis and maybe we needed to revisit. Possibly, they are confusing with across y-axis?
ii. A few students disagreed initially, but the convo I overheard was addressing that changing the x-intercepts was not sufficient, they looked at the graphs, then said, the functions needs to be decreasing at the begiining, that’s why you have negative coefficient.
iii. Horizontal translations always seem to trick students up. One disagreement actually stated ‘they subtracted and did not add.” Of course, we definitely followed up with this one.
iv. This pair of students argued over which one was right. The expaned version or factored form. Simple, graph the new equations and compare to see which one translates the original up 3 units.
A1 & A2 I believe they’ve got this one.
B1 & B2 some confusion here due to the extra vertical line in the graphic. This student was also interchanging graph & equation in their statement.
I thought the gallery walk was a good task to overview some common misconceotions. It was not intimidating, students were able to communicate their ideas, compare their own thinking to others. I truly tried to stand back and listen. They were on task, checking each other’s work. Each station allowed them to focus on one idea at a time. They were talking math. Most misconceptions were addressed through their discussions or written comments.
Having a moment to debrief the following day highlighted the big ideas students had addressed the previously and reinforced the corrections they had made. This was so much more valuable than me standing in front of the room telling them which mistakes to watch for. Their quick reflection writes revealed majority have a better ability to transform the functions, which was my initial goal for the gallery walk. A few still have minor misgivings that can be handled on an individual basis.