*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.*

A common form of formative assessment is the Do Now activity. Students come into the classroom, and once they’ve taken their seats, they are expected to solve the problems on the board. The problems usually cover material that students have already learned and are expected to know. During my last observation, there were three Do Now problems on the board for the precalculus class:

- cos x = 3/5
- cos x = -2
- 5x
^{2}+ 7x = 6

Some of the students were struggling to arrive at the right answers, so Mr. Brown posed some guiding questions to help them along. For instance, for problem 1, he asked students to look at the unit circle and use their intuition to decide how many answers they thought there were. When a student offered a solution, Mr. Brown asked the class if they agreed, disagreed, or were unsure. This strategy of asking students to reflect upon their own thinking is valuable because it trains them to be metacognitive. There was an article I read about teaching math (I forgot the title of the article) that brought up a really good point: If students truly understand the math they are doing, they should be able to argue the correctness of their answers rather than rely on an answer key to tell them that they are right. Having students defend their answers is also a good way to promote “math talk” between students. Becoming more fluent with the math terminology is beneficial for students and helps them view math problems in a different light.

After the students arrived at the correct answers for the three Do Now problems, Mr. Brown revealed a fourth problem: 5 cos^{2} θ + 7 cos θ = 6. By solving the Do Now problems, the students had actually completed almost all the steps necessary to solve the fourth problem. I thought this was a clever way of building off the students’ prior knowledge and using scaffolding to introduce a new type of math problem.

That same day, the precalculus class also started a new project. This weather project would serve as their summative assessment on sinusoidal functions. The goal of the project was to generate a model to predict average monthly temperatures for different cities. Each student chose a city, looked up the monthly average temperatures for a given year, and was asked to derive a sinusoidal function that best represented the data. The final product comprised a chart on a poster and a write-up describing how closely the model lined up with the actual data. The project successfully focused on a simplified version of a problem that people face in real life: weather prediction. Students would learn how sinusoidal functions are useful for modeling and predicting real life phenomena, and the write-up portion of the project would help students understand the limitations of using mathematical models.