I lamented the other day that I didn’t capture a question I was sure students would ask about my pH videos.
And today they didn’t ask it.
But they asked other stuff I had not anticipated.
I taught the lesson today. I chose the video in which I measure the pH of water and the pH of pure concentrate. We clarified what we had seen (including the lovely question Did the color of the orange juice concentrate (orange) affect the resulting color of the pH strip (also orange)?)
Then I asked them what there was to ask or wonder about here. Their questions:
- How are logarithms used in the calculations of pH?
- How much water do we need to add to the concentrate to get a pH of exactly 7 (in the video, the water measures pH=7.2)
- What is the concentration of hydrogen ions in the orange juice concentrate?
- How does the mixing of pH work? Does 1 unit of pH 1 mixed with 1 unit of pH 2 give us 2 units of pH 1.5?
Two of these questions were from students who have come to office hours many times, but who have never piped up with a question or answer in a whole class session. They are always engaged and on task, but never vocal.
I hadn’t thought of adding water to concentrate. I had thought of adding concentrate to water. So I had to tweak question 2 into one closer to something my premade answer videos could answer. To wit:
How much concentrate do I need to add to 100 ml of water in order to make the pH exactly 7? (Recall that the water starts at 7.2)
In pairs, students wrote their answers on slips of paper I had provided, then held them up all at once. Their guesses ranged from 3 ml to 300 ml. The median was approximately 7 ml.
We watched the 10 ml answer video and I asked whether anyone wanted to change their guess. They all did.
We watched the 1 ml answer video. And students revised their guesses again.
Then I restated the definition of pH and demonstrated solving for the hydrogen ion concentration in the orange juice concentrate (question 3, recall).
On Friday, we’ll do some pH computations to verify/approximate the experimental results.
On the way out of class, a student left her final guess on my desk.
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I also love reflecting on the student ideas and questions that come up that I didn’t anticipate. In fact, that is part of my ideal routine prep: brainstorm all the ideas, questions, difficulties ahead of time, and then reflect on how my predictions compare to reality. It helps hone skills at getting better at anticipating.
It’s been fun watching your ideas and thinking evolve with this lesson. What kind of class is this again?
It’s college algebra at a community college.
Yes, I have been following your blog. So I’m not the only one who struggles with anticipating questions! And I was expecting you to have a clear cut answer as to how to better anticipate. . Maybe I need to just reframe my thinking and call the “unexpected” part of the fun of teaching. . the element of surprise. I just need to be prepared to handle it, so it’s a good surprise (like a surprise party) and not a bad surprise (like a car accident.) 🙂
A colleague and I have been talking a lot about our very different personality types. She is Type A and is uncomfortable with the idea of teaching a lesson that might not go exactly as planned.
I am not Type A (is B the only other choice, or are there others? I’ll have to look this up sometime.) I am totally comfortable with the idea that no matter how much planning I do, something I didn’t anticipate will come up. For me the planning isn’t about getting it perfect, it’s about exploring the possibilities deeply enough that I’ll be prepared to handle whatever comes up.
It’s through repetitions of lessons that the wrinkles get ironed out in my classroom.
And yes, I do see the unexpected as part of the fun of teaching. Especially in those lessons whose wrinkles I thought I had ironed out long ago.
But I have learned a lot from my Type A colleague (and her like-minded brethren in the field). I have learned how to construct my own classroom so that she would feel welcome as a student. I have learned to raise my standards for quality of initial lesson materials.