## First Writing Assignment

I had my students do their first writing prompt on Friday. It took me a while to get started because I was having a hard time deciding what to do. I ended up having them describe how to graph sine and cosine equations. We have been doing that a while, and I thought putting it into words would be easy, but also a good way for them to synthesize the material.

I took the journals (which are in the students’ bell-ringer packets) home and read them over the weekend. I was overall pleased with their efforts, but some were obviously stronger than others. Some students were pretty skimpy with some parts of the description and I cannot be sure if that was because they thought it was obvious, or because they were not totally confident how to describe it. They gave me the steps, but not the reasons behind each step. When teaching the graphing, I had tried repeatedly to relate each step to transformations of other graphs, which they study extensively in algebra 2. Very few students used that vocabulary.

I took the journals (which are in the students’ bell-ringer packets) home and read them over the weekend. I was overall pleased with their efforts, but some were obviously stronger than others. Some students were pretty skimpy with some parts of the description and I cannot be sure if that was because they thought it was obvious, or because they were not totally confident how to describe it. They gave me the steps, but not the reasons behind each step. When teaching the graphing, I had tried repeatedly to relate each step to transformations of other graphs, which they study extensively in algebra 2. Very few students used that vocabulary.

**When asking them to describe how to do something, give them an audience other than me. Have them describe it to an absent student, or to someone in a younger grade.***Lesson 1 learned:*## One thing you do and One thing you don't understand

I am still having trouble coming up with good prompts. I think this is my usual hesitation with new things. I also don’t want the questions to be the same every time. This time I asked them to discuss something that they did and something that they did not understand, or something that confused them, about what we are doing now (simplifying trig expressions.) I told them it had to be in sentences and questions. The part that discussed what they did not understand had to be in the form of a question (or questions) with an example, and clear enough that someone could write them an explanatory answer.

What I found with this assignment was that the students told me they "understood" things that they had memorized (tan = sin/cos), and told me they didn't "understand" things that they were having trouble memorizing because they weren't simple expressions. None of them asked "why" or "how" questions.

I think my students are having several difficulties here: (1)they don't really understand what "simplifying" an algebraic expression is, or why they would ever want to do that; (2) they aren't as much interested in why things work, they want to know the easiest way they can "remember" what to do; and (3) they do not have good algebra habits - they aren't consistent about using parentheses when they should - which makes substituting quantities more confusing. So my task is - how can I get them to

What I found with this assignment was that the students told me they "understood" things that they had memorized (tan = sin/cos), and told me they didn't "understand" things that they were having trouble memorizing because they weren't simple expressions. None of them asked "why" or "how" questions.

I think my students are having several difficulties here: (1)they don't really understand what "simplifying" an algebraic expression is, or why they would ever want to do that; (2) they aren't as much interested in why things work, they want to know the easiest way they can "remember" what to do; and (3) they do not have good algebra habits - they aren't consistent about using parentheses when they should - which makes substituting quantities more confusing. So my task is - how can I get them to

**think**about what it means to substitute things for one another.## Memory Dump

This week the topic I gave my students was to write about everything they could think of that they had learned in this chapter. I reminded them of the topics in a general way, and said that they should write whatever they could explain. I told them they could use pictures to help explain (a suggestion from an NCTM magazine article) and some students did that, but some students drew pictures instead of writing. For things that they just had to memorize, that was probably enough, but didn’t really lead to the metacognition I was hoping for!

I think the big problem here was me not being clear in what exactly I wanted from them. I had hoped that they would explain the topic that they understood (so I could see what they understood) and ask some specific questions about what they didn't understand. My goal with this topic is to get them thinking and speaking mathematically, but I have not done a great job communicating that.

I think the big problem here was me not being clear in what exactly I wanted from them. I had hoped that they would explain the topic that they understood (so I could see what they understood) and ask some specific questions about what they didn't understand. My goal with this topic is to get them thinking and speaking mathematically, but I have not done a great job communicating that.

## Describe How To (Again, with a more difficult topic)

We started learning about limits this week, so I had my students describe how to find the limit of a specific graph so that students not in the class could understand. That was successful to different degrees. I feel like they were still explaining it more to me, because they were not giving the level of detail necessary for someone outside the class. But overall, I think that was better. I just can’t do that (how-to questions) all the time.

NOTE: I found out later that the example I picked for this assignment was one that students mostly understood - the limit as x-> infinity. Next time I do this, I need to focus more on what it means for x->some number, because they struggle with finding the limit approaching a vertical asymptote.

NOTE: I found out later that the example I picked for this assignment was one that students mostly understood - the limit as x-> infinity. Next time I do this, I need to focus more on what it means for x->some number, because they struggle with finding the limit approaching a vertical asymptote.

## Bell Ringers and Other Formats For Writing

In addition to having the students write reflective responses at the end of class, I created some bell-ringers with "Explain your thinking" questions. I did these on separate paper (not their usual bell-ringer packet) so that I could collect them and get/give feedback quickly and easily. Using this format definitely limits you to things that the students should know and be able to explain in just a few minutes, but this can be very useful. I also put similar questions on quizzes. I started, since the whole writing thing was new, by making it an extra credit question. Interestingly, I found more students attempted the extra credit when it was a writing assignment than usually do when it is a math "problem."

## Looking back on the semester

I found over the course of the semester that I was having my students do a lot of "How to" writing. While I think that this is useful to students, I realized that I didn't ask them to make connections between topics, and I didn't ask them a lot of higher level thinking questions. I think this happened because I was creating them as I went along, and those kind of questions are easier to create. So as I go into next year, I need to think about reflective questions for each chapter ahead of time. The more I think about that, the more I think that will be as beneficial to me in my teaching as it is to my students, because it will help me focus more on those kinds of questions in the curriculum, rather than just the mechanics.