As part of my education class, I conducted classroom observations at a precalculus class and a calculus class once a week. The following post is a reflection on one of my classroom observations. Note: The names used are pseudonyms.
Over the course of my schooling, I had the impression that being a substitute teacher was incredibly difficult, mostly because students tended to bully the substitute. However, during my last classroom observation, I saw something that surprised me. Mr. Brown, who normally teaches the math classes, was not at school, so the substitute teacher, Mr. Green, took care of the class. I learned that Mr. Green was actually a “permanent” substitute teacher at the school and substituted for about five teachers every day. His goal was to become a high school psychology teacher in the future, but said he would probably end up teaching English instead because there was higher demand for English teachers than psychology teachers. Because Mr. Green substituted for many different classes, all the students already knew him and were comfortable around him.
At the beginning of the period, Mr. Green told a story. It had absolutely nothing to do with mathematics, but the students were all very attentive when he told the story. The moral of the story was open to interpretation, and overall I thought it was a neat little way of getting the students to focus on being in the classroom again right after the lunch break. Classroom management wasn’t a problem at all even though there was a substitute teacher.
The lesson plan that Mr. Brown had left consisted of separating the students into tutor and tutee pairs. About half the students had missed class the previous day due to some academic event off campus, so the students who were absent were tutees. The students who were present the day before were the tutors. The tutor in each pair was given the responsibility of guiding the tutee in completing Khan Academy exercises on sinusoidal functions. Mr. Green wasn’t all too familiar with the material, so I was responsible for answering the students’ questions.
Because the students only had to answer three consecutive questions correctly, many of them ended up rushing through the exercises and focused solely on memorizing procedures. The first topic was finding the midline of a sinusoidal function, and many of the students who asked me for help phrased their questions like this: “How do I know when to add the numbers they give us and when to subtract them?” I did the best I could to bring their attention to the bigger picture. I asked them what the midline of the function represented and what the numbers they provided represented (e.g. max value, min value, amplitude). Some of them gained a better understanding of what they were doing conceptually, but I’m afraid not all of them fully understood why they had to add sometimes and subtract at other times. Students who have a solid conceptual understanding of what the midline is should have no trouble answering questions correctly on the Khan Academy platform. However, it is also possible for students who don’t have a solid conceptual understanding of the material to score well on the exercises. It’s important to realize this distinction and use other methods of assessment to get a more accurate measurement of student understanding.