Who:  24 eighth grade students

What: Mathematics (Discrete versus Continuous Functions)

Where: Messmer Preparatory Catholic School (Urban, Voucher, Religious)

Characteristics of Students: 100% minority - 22 African-American, 1 Hispanic, 1 Asian

Students typically have a short attention span, are difficult to redirect, and are below grade-level academically on average.  A few students are either at grade-level or above.

  • This lesson satisfied Standard Nine: Teachers are able to Evaluate Themselves. Teachers continuously, and daily reflect on their lessons and how they can improve. Teachers can do this by asking for additional observations, coaches, and even student feedback on the lessons. In my review, I immediately knew that I should have stopped the lesson and issued students assigned seats due to excessive talking. As far as the content was concerned, I also knew that I would have included more graphic visuals to demonstrate what it looks like to see a discrete graph or a continuous graph. I also could have had pictures cut out or displayed on the projector and students could have stated whether the image shown was discrete or continuous. I also welcomed feedback from my observer as she had many positive comments to make about the lesson and agreed with my reflection of where I could have modified my lesson.
  • I demonstrated Diagnosis in my classroom by asking follow-up questions to student responses. Once a student classified an example as continuous or discrete, I would ask them how they knew, or why they believed, the graph was continuous or discrete. I also asked students to go further by calculating our output if we changed the input to the function, and if we could really have “half a bus.” I also am aware of how I need to model and break down the steps for my students since I am aware of their diverse ability levels. Due to their diverse abilities, I broke the problems down to the students’ level by giving discrete examples they could relate to, such as cookies, busses, textbooks, and the height of people. We also talked about how continuous functions could relate to time, speed, and filling a tub with water. I also was able to relate the material to the students by changing a problem to represent the height of basketball players instead of just a sports player. We joked about the heights being a little short for a basketball player, but the kids were able to understand the concept once I also asked about each of their heights individually, and if it would be considered discrete or continuous.
  • I definitely felt that I made the connection with Conceptualization for the educational framework. I encouraged students to think about their own examples of discrete and continuous functions, which helped make the connection to the content. A few of the students were able to get to the higher level thinking by modifying a problem to change it from discrete to continuous. I also knew to give problems such as buying a book, and that it didn’t make sense to buy half a book, and that there were no such things as half-busses. I used examples that I knew the students could relate to instead of picking examples that were outside of there culture.