Math Methods Course

Mathematical Planning Prompts & Interview

In my methods class, I closely analyzed several math problems of varying difficulties. For each of the problems, I identified what mathematical skills the students will develop and practice, what previously studied concepts students will need to understand in order to be successful, and where the mathematics will lead in the short-term and the long-term. I also identified what makes the problems worthwhile and I anticipated likely student responses from students who are making strong progress, from students who are making marginal progress, and from students who are struggling and have misconceptions. For each of the problems I analyzed, I thought of questions I could ask to help struggling students realize why their misconceptions are incorrect, and I wrote extension problems for students who need an additional challenge. Please see my analyzes of the boarder problem, the hours and wage problem, and the car wash problem.

After I analyzed these problems, I interviewed a middle school student as he worked on solving the problems to try and analyze his thought process. Interviewing can be a highly effective, although time-consuming, method of formative assessment as teachers can figure out how a student thinks about mathematics and identify what the student does and does not understand. I interviewed Mathew who is a family friend in the sixth grade. Here is a video of our interview, and here is my written report of the interview containing my assessment of Mathew's mathematical thought process.

Lesson Plans & Unit Plan

My experience closely analyzing math problems prepared me to write detailed lesson plans that include support I would give to students who are struggling with common misconceptions. The following two lesson plans cover the curriculum in section 3.3 and section 3.4 of Carnegie's Algebra 1 textbook.

In collaboration with Niki Matusko, I created this unit plan that covers all of the material in Chapter 3 of Carnegie's Algebra 1 textbook. In addition to budgeting time and identifying the core worthwhile mathematical task students will work on in the unit, our unit plan contains a formative assessment plan for each lesson and hyperlinks to two quizzes, an alternative/authentic assessment, and a unit test.

Practicum Course

Periodically throughout the Spring of 2019, I observed Mr. David Rochemont's classroom. Mr. Rochemont taught five hours of Algebra 2, and one hour of AP Statistics that semester. I kept a detailed journal of my experiences in his classroom and then wrote these midterm and final observation reports. Mr. Rochemont does a very good job of involving students in activities, so that math class is more than just the teacher lecturing and the students solving exercises in a textbook. I also liked how he grouped students with mixed ability levels so that struggling students can get peer support as they work on the activities. Finally, Mr. Rochemont frequently used several types of formative assessments and was knowledgeable of each student's individual strengths and weaknesses. I plan on incorporating these techniques into my own classroom.

On my final day of my practicum experience, I taught this lesson to the students in Mr. Rochemont's Algebra 2 classes. Thankfully, the students had just finished their polynomial unit, and Mr. Rochemont was kind enough to let me teach any topic I wanted to. After consulting with my professor, I decided to teach a lesson that would challenge and develop students' problem solving abilities. In the context of figuring out how many handshakes would take place if every student in the room shook hands with each other, we derived Gauss's formula. I also challenged students to figure out how many rectangles are on and within a 4 x 4 grid. Ultimately, it turned out that I had planned to much content to fit into one class period. The first time I taught the lesson it felt rushed, and with the advice of Mr. Rochemont, I eliminated some parts of it. I taught the lesson five times and it got better each class period. Based on the exit ticket I gave them, the majority of the students were able to recall and apply Gauss's formula, which I considered to be the most important part of the lesson. Here is my full reflection on teaching this lesson.