Pumpkins, graphing, coloring, computers- what more could you ask for right? Well the answer to that has been difficult to find for the group of students I have this year. Unlike most other schools, I have no idea who my students have had as a teacher before they come to me, what classes they have had, or what their experiences in math has been to this point. I can’t casually call on old teachers to ask about what methods they used for instruction, what worked for the student, or (heaven forbid) what catch-phrase they used to get students to remember an solution path.

It has been a struggle with the pumpkins suddenly. I have a few students who have connected with the generation of lines, but more and more students are falling behind getting mired in their inability to conceptualize or model the situation. What? They can’t model the situation? Don’t they already have a concrete drawing with which to determine the values? Why yes they do, but they are becoming limited by their inability to use that and think beyond what they see visually.

Students have slope nailed down (for the most part, there are some who still mix up the sign), but when it comes to the intercept students start to falter. Many use rulers to get an idea of where their lines go, but they are unable to approximate where that intersection lies when it goes outside the bounds of their graph or paper. I allow students to use DESMOS while they are creating their lines, it is a great visual of what happens when they change the slope or intercept, but this group of students do not want to “guess” their intercept. Many are unable (mentally) to get past the fact that they might not have the exact right intercept. I have students who are even modifying their graphs so they can get more exact.

My classroom is comprised of students with special needs (90% have IEPs), and there is a huge disconnect with the idea to “plug and play” when it comes to intercept and drawing the line in DESMOS. The project is bogging down, but students are not quitting, they are just taking extra time to implement strategies and find more exact intercepts for their equations.

While that may seem the worst, actually having bounding intervals to create line segments has been an even bigger curve-ball. Students were dismayed that there was this big line drawn across the screen, that they weren’t even constructing something that was remotely like the picture they drew. We brainstormed ways we could put constraints on what DESMOS drew. The solution was not apparent to students. They did indicate where it should start and end, and even talked about intervals (“draw it for 2 units”), but the mathematical representation of that evaded us. I hung on to that interval language and asked how to state that for a horizontal line. “Draw it from 3 to 5.” What do you mean by that? “Start where x is 3 and go until x is 5.” Oh, I see. DESMOS understands that by using the following: {3<x<5}. Students experimented with this, and like anything new it took a while to fully understand. Overall it is going well, students are picking up on it fairly well- here are a few projects in the making.