Course: Precalculus

Period: 1

Each morning, students are expected to enter the class and start on the entry task (ET) which is posted on the display in the front of class and is also posted on the class website (each student is provided with an internet capable laptop). For this lesson, the ET stated, “Explain how similarity of triangles is related to trigonometry.” Students write their response to the task in their homework notebook and should be writing for about five minutes. During this time, the teacher took attendance and spent a few seconds preparing the lesson. After the writing period, the teacher interrupted the class to debrief. He asked students, “ What do you suppose todays activity is about?” the conversation lead to a short discussion of “similarity.” he probed students, “Why do we care about similar? and What else?” Students volunteer responses to these questions. After the debrief finished, the day’s activity was introduced and students began working.

The objective was never explicitly stated, although the introductions to start the class was a brief indication of the objective for the class period. During the lesson, I asked students what the objective for the day was and several were able to produce a sufficient explanation as to the goal of completing the activity, but it was not completely accurate. Today was the end of a unit lesson and I would say that the ET prompted students to reflect on previous classes and learning about the relationships of triangles to completely answer the question. Since this lesson was a summary of many lessons, the opener was more theoretical than it has been in the past, so the authenticity and engagement were slightly lower than more application style lessons, however, the ET made a strong segue into the objective of the day’s lesson. I would have liked to see more explicit indication of the day’s goals. If I were to teach this lesson, I would have written something down on the whiteboard. I really liked that the teacher had the students articulate the purpose and the objective of the lesson. This indicated that students were aware of the lesson and the purpose for the day’s activities.

About ten minutes before the class was completed, the teacher held a debrief of the activity, he asked questions such as, “What was *The Sim’s* activity about?” and encouraged a response which aligned with the objective for the lesson which was similar triangles and trigonometry. He then extended the question with “Anyone want to add anything?” which I liked because it gave students another opportunity to share their learning and responses.

Another regular routine for this class is Journal Reflection (JR) in a special notebook kept within the class. Students are aware that they are graded on the effort and thoughtfulness of these daily entries. The goal of a JR is to help students articulate their learning and misunderstandings from the days lesson. The JR is posted on the screen at the end of class. Students know they are expected to be writing on the topic for the last five minutes. The JR for this lesson was “Explain how to use similarity of triangles to solve for unknown parts of a triangle.” This particular closer helped students reinforce the practicality of similarity as a form of trigonometry. In fact, this JR helped summarize most of the unit and goals which followed the Understanding by Design model. During the students JR time, the teacher talked with single students which I think was a little bit distracting to the whole class and made the JR time less valuable. I did not like this because it took away from the reflection time for students who are easily distracted. After the class, the teacher mentioned to me that he wished the students had a more fundamental understanding of what trigonometry was and that even through this lesson, some students are struggling. This lesson was aimed to meet analysis and synthesis in Bloom’s Taxonomy. Students were tasked with recognizing patterns in the activity and the opener and closer helped them see more patterns and create more sophisticated conclusions based on their engagement with the activity.

I really liked that students reflect on their thinking and that they are engaged with prior knowledge to start and end every class. I particularly liked the debrief period because it engaged students and had them articulate their learning and the connections they were making rather than being provided the correct objective. Overall this class was well executed and the opener and closer helped motivate the days activities and facilitated strong learning on many levels of engagement.

Hey Riley,

Great conversation about the opener and closer in PreCalc. I like the idea of having some sort of routine or question that students can turn on their brains to start the period. I would like to know how well the students do in this class as it is a first period class. Was this at Aviation? If I remember right, precalc is usually a junior level class (?) and would have some fairly motivated students in the class. This would change dramatically if it was a geometry class, attendance might be an issue.

You do an excellent job of painting a picture and I can see what is going on in the class. Although I am doing more science, I feel that often times math and science classes have a similar structure. I really like the idea of asking probing questions and something that my mentor teacher has drilled into me is that we must be patient and wait for responses (5-7 seconds) before restating the question or moving onto a different question. I also really like follow up questions. I agree with your statement about how they allow students to show their understanding.

I would also like to comment on the fact that this math class is writing!! Awesome. I felt like most of my math classes missed that opportunity and I didn’t always understand why I was using a formula/equation/theory until much later in life. I think reflection has a powerful place in the classroom and developing understandings.

Thanks, and great job on your website!

Jon,

The students are very responsive during first period, they are probably the most engaged class of the day. Our school starts at 9:00am so students have generally been awake for a while. For the most part, the later classes after lunch are the most challenging because they just ate! The practice of writing is challenging, I had the opportunity to see what students wrote at the end of the year from the left over journals left in the room.

The writing becomes a lot better over time, we just graded the second round of journals and found that students were more thoughtful when they were graded. We followed the method of grading proposed in the literacy class this summer, I really stressed to emphasize the importance of writing for 5 full minutes, the second round resulted in much deeper responses simply because they wrote for longer.

The writing and reflecting in class is cool, I wish there was a little bit more followup with these reflections. Having a class debrief was an oddity and the JR’s aren’t checked as frequently as I would hope.

Riley, I liked the way that you are starting to sort out the way that you might do thinks a bit differently than your mentor. You have a wonderful mentor but you will develop your own style as the year goes on.

Pat