Wed, Dec 19 #6

Here is a teacher generated Tree Map about graphing rational functions. I used it to summarize three days of activities, discussions and examples about the complexities of rational functions. The students were asking lots of questions about particular procedures and parts of the examples, but I didn't think they had a strong grasp of the whole picture. Using the Tree Map was very helpful because it made obvious the differences between local and global behavior. It also helped to categorize all of the procedures and definitions and examples we had discussed.

Wed, Dec 19 #5

Here is a student generated Flow Map for graphing a rational function. We had just spent 3 days learning about essential and removeable discontinuities, vertical, horizontal and oblique asymptotes, local and global behavior, etc. The student came for extra help so I did one more example, and then I asked her to create a Flow Map in preparation for the exam. It seemed to work well for her. I know it was on her mind during the exam because when I asked a "stretch" question she let me know that it wasn't on her Flow Map!

Wed, Dec 19 #4

Here is a Double Bubble for comparing and contrasting procedures used to solve rational equations and simplify rational expressions. Students often confuse the two, so I used the Double Bubble to help show the similarities and differences.

Wed, Dec 19 #3

Here is a Dancing Definition for the purpose of the quadratic formula. I put it together quickly during one of the NUA workshop days. I haven't used it with students yet becuase I am not teaching it this year. However, I have proposed to my trig students that they create and play songs for all of the core trig identities. Extra credit is involved if they record their tune and post it on YouTube. I will mention that my 5 year old was having difficulty memorizing our phone number until my wife and I set it to Lullaby. With the tune, he learned it immediately. I will keep the blog posted about the YouTube Trig Identity project. We'll see how it goes.

Wed, Dec 19, # 2

After working with volumes of revolution for 3 days in my calculus class, I asked the students to create a Flow Map for the process used for these particular kinds of problems. The students took between 5 and 10 minutes to create their Flow Map. For me, it was a good way to quickly assess their understanding without having to look at the details of the calculus and algebra of how they set up and solved the problem. In other words, I got better and quicker information about their conceptual understanding from this Flow Map assessment than I do from looking at their alebra and calculus work from a solved problem. In particular, I learned that for most students, the first decision they tried to make was whether to use a disk, washer or shell despite the fact that I had emphasized repeatedly in class that the first decision should be whether or not to use a vertical or horizontal slice. That observation of mine generated some good discussion.

It was obvious the students were using higher order thinking skills, and it obviously pushed them a bit more than the standard requirement of just solving the problem. I didn't tell them to use any specific language or to use any specific number of boxes. I did require that they follow the left to right Flow Map procedure.

Wed, Dec 19 #1

The Multi-Flow map at the left for the Intermediate Value Theorem is a useful way to present any theorem because it emphasizes the hypotheses of the theorem as well as the conclusion. The students tend to focus on the conclusion. The Multi-Flow presentation helps emphasize both parts. This map was teacher generated not student generated.

Tuesday, Dec 11

In calculus class today I used the basic NUA strategy of movement because it was 15 minutes before the end of the school day and the 6th hour students were falling asleep. We were working on volumes of revolution. I asked the students to stand up and put their left hands in the air to represent the revolution axis. I really didn't know what to do next, so I asked them to use their right hand to create a slice perpendicular to the revolution axis. They automatically put their right arms out perpendicular to their bodies and rotatated around creating nice examples of the washer/disk method. Next, they put their right arms up and spun around to make examples of the shell method. After the example they quieted down quickly and the last 10 minutes were, I think, more productive then they would have been without the stretch.