I am excited about our first day! I know students will need more time going over procedures, but I'm glad we jumped right into our curriculum.
We spent a few minutes noticing and wondering today. It felt a bit awkward and students were slow to respond ... but I know that as we practice, we will be able to build their curiosity!
Here are my students noticing and wondering today:
I notice …
- 4 variables in each equation
- They all have f(x)
- Each equation seems to get more complex
- There is x-h in every one
- The last equation does not have “plus k”
- The last one is the only one with a v
- They all have the same layout
I
wonder …
- Why does the last one have a v and none of the others do?
- Does the form help us find the maximum or minimum of the functions?
- How would the last equation look when it is graphed?
- What does “log” mean?
- What do the letters (a, h, k) mean?
- Where are these equations used?
I am posting these questions in our classroom so we can refer to them during our unit of study!
Beth
PS ... follow along with our daily snapshots!
PSS ... here are photos of some of today's noticings and wonderings!
PSS ... here are photos of some of today's noticings and wonderings!
I got to do this activity with my Day B students. Their noticings and wonderings were interesting. In one class, one student said, "I notice that since they are all equal to f(x), they must all be equal to each other." I chuckled! He identified a flaw in my chart ... and made an excellent observation! I add two photos to the post above from today's observations.
ReplyDeleteThanks for posting your noticing and wondering. I love that you'll keep the noticings and wonderings posted all unit so you can see if you're learning stuff that you wondered about (and, I bet, generating lots of new wonderings in the process!)
ReplyDeleteAnd how fun that a student noticed and wondered about all the functions being f(x) and you were able to listen to him and figure out what was going on, instead of having it linger as a misconception and you not know where his thoughts were coming from!
I noticed that no students wondered about the "b" in log-base-b(x-h) + k or in ab^(x-h) + k. I wonder if they're familiar with exponential functions and that's why? I wonder if the b helps give a hint as to the connection between logs and exponents and could be part of figuring out what log means.
Max, thanks for responding to my post! Students are not familiar with exponential and logrithmic functions. It will be interesting next semester when we get to those to think back to this poster with its noticing/wondering.
DeleteWe finished the unit on Friday. I wish I had included a reflective question on the test that took students back to their noticing and wondering ... maybe on the next test!