Teach 180: Discussion to Construct Understanding (Day 63)

Today in PreCalculus class, we were beginning to work with polynomials. I showed students
the following graph in Desmos and asked them what did they notice.  If they had to describe it to someone over the phone for the person at the other end of the line to draw, what would they say?  The conversations I heard at first started with general statements like, "it wiggles in the middle" and "it looks like a parabola that someone dented and bent in the middle".

 "It wiggles in the middle could look like a lot of different graphs," I replied to the one group.  "Can you be more specific?" 

At that point students started talking about x-intercepts and they also noticed that sometimes the graph crossed the x-axis and sometimes it touched the x-axis.  The student who noted the parabola shape on the ends was starting to hint at end behavior.  After a bit more discussion, we decided to play around with the exponents and to see how that impacted the behavior at the x-intercepts.  We also talked about what we could do to change the end behavior of the function.

It is important to note that even before my students put pencil to paper we were discussing concepts and playing around with ideas, dynamically.  At times students were discussing ideas in groups and other times we were putting our ideas together as an entire class.  It takes time and sometimes patience to have students learn this way.  But ultimately, I believe it leads to deeper understanding.  Students come to realize that if they can't recall a concept (like, does it fall on the left and the right for end behavior), they have a way to reconstruct that concept, because they constructed it initially.

Teach 180: The Stalled Start (Day 62)

Today I started my 8 AM class with a Desmos card sort.  Students were to match quadratic and cubic functions with their derivatives.  We did a quick review of what the derivative of a general linear function would be, but this didn't lead to student success with the activity as fast as I thought it would.  An example of a matched derivative and function can be seen below.


Although students worked with pairs, the first 20 minutes of class felt like starting a car up on a cold winter morning after a week of it being idle.  (With no class on Friday due to our rotating schedule, this is probably an accurate analogy.)  We had many mismatched pairs and I had to work with individual groups of students to explain how the graph of the derivative matched with the graph of the function.

So, would I do this activity again?  Most definitely.  However, I think I would create a slide with just 3 matches in the future and have our class work on that together - asking for verbal justification of why students paired certain graphs together.  This would be the equivalent of letting the engine and car heater run for about 5-10 minutes before driving the car.  Perhaps this would have led me to not having a stalled start.

Teach 180: My Voice (Day 61)

To a teacher a voice is a valuable thing.  We can't really do our jobs without it.  This week, I have been losing my voice.  It usually happens around this week, because I have my church Christmas concert and my voice gets quite a workout.  Usually things are fine as long as I don't get a cold.  Unfortunately, my daugher had a slight cold and throat issue before Thanksgiving and she shared it with me. (Thanks, Cassie!) This blog will be a progression of my voice during the day.

8 AM: I don't teach for the first few periods.  I am planning on writing two quizzes and doing lesson plans for next week.  I don't plan on talking much.  My Yeti cup is filled with tea and honey.  I have a chat with a colleague about using our online grade reporting system and visit the Upper School Director for more tea and a chat about Christmas break plans.(Fridays is Dylan's open door day to his office.)

10:15 AM: It's advisory period and we have class meeting first.  Luckily, I don't have to talk during this time.  When class meeting is over, I take my advisees to my classroom and we play banana-grams.  We don't have to talk much to play the game.  Another voice saver.

11:00 AM - 3:15 PM: Lunch and three classes. Unfortunately, I need to do quite a bit of talking in Prob/Stat and PreCalculus.  In Prob/Stat, we are starting a new chapter.  There are basic concepts to be explained related to mean and standard deviation of a random variable.  There is really no way to make this lesson, where students teach each other the concepts.  In PreCalculus, we reviewed two examples involving completing the square to determine the vertex of a parabola and did a Kahoot.  (My random question of the day (RQD) was "What is the name of Mrs. Nataro's blog?")  The day ends with a test in my second section of Prob/Stat and my voice is saved from talking too much.  However, in that class I had multiple students come up and ask me questions during the test.  Based on their questions, I am slightly worried about the grades on the test.  Time will tell.  I'm planning on grading them on Saturday morning.

I am now at home and I am working on finishing my blog.  How's my voice doing?  Not so great.  I am guessing it will be about a week before I am back to 100%.