## Wednesday, February 22, 2012

### Today my flipped class was... amazing

Wow!  If every day were like today... all I can say is wow!

My Algebra 1 classes were great, and I'll talk about that in my weekly reflection on Friday or Saturday.  What makes me so excited was what I did for the first time in my Math Analysis class.

I've talked about "My Perfect Summary" before, but this is the first time I introduced it to my Math Analysis class.  Here is the premise.

1. Students pick one notebook/WSQ to use as their starting piece.
2. Students read it together and cross things off that don't make sense, add phrases or even complete sentences to the summary to make it "perfect".
3. Students make sure that they have at least 3 math vocabulary words used correctly in context and highlight those in the summary.
4. Students go around and answer each others' HOT questions from their individual notebooks and write down those answers as well.

Then comes the fun part...

I get to spend about 4-5 minutes with each group (I have 9 groups total in my class, 54 minute periods) basically grilling them about the content.  I use their summary as a guide, but mainly focus on their math vocabulary words.  I ask them everything about them and have them go deep into the content.  I ask follow-up questions and continue to probe deeper.  The funny thing is, students think they can just carelessly highlight random math vocabulary words, but with this, they actually have to KNOW them, and know them WELL.  It was AMAZING to see the students brains working and to see the material clicking and connecting together in ways that I don't think it had before!  I saw them go from not being able to explain a word or concept to being able to clearly and concisely explain and make connections within a matter of 5 minutes!

Example 1:  I saw the word "quadrant" in their summary.  Here is the list of questions that came from this (with student answers between every question that led to the next one)

How are the four quadrants labeled?
How do the quadrants relate to trig functions?
Which trig functions are positive or negative in the third quadrant?
Why would tangent be positive in the third quadrant if both parts of the ordered pair are negative?
What about the fourth quadrant? Why would cosine be able to be positive?

Example 2: "trig function"

What is a trig function?
What trig functions relate to each other and how?
What are the ratios for the six trig functions?
How do the ratios correspond for the quadrants in which each trig function is positive or negative?
What trig functions can have values greater than 1?
What trig functions could possible have values of exactly 1? -1? 0? undefined?

Example 3: "reference angle"

Students' original definition included them showing me with their arms and pointing.  "That thing" and "closer to there" and "that gap here" is what they used.  Together, they were able to identify the parts (terminal side, closest x-axis) and the qualities (must be positive, must be acute) to define a reference angle concisely as:
"A positive, acute angle located between the terminal side of the angle and the closest x-axis.  This angle corresponds to three other angles around the unit circle by having the same ordered pair values (but different signs)"

...the list of follow-up questions could go on and on, but I limit myself to 5 minutes of questioning with each group...

While I am having these sessions with each group, the other students are working on practice, taking quizzes, and finishing their own discussions to prepare for my arrival.  I have a feeling next time we do this in class they will be more prepared.  Today I think they were a little shocked and how I kept asking them questions, but they liked it.

These are all questions I would have loved to do in a whole class discussion, and I may have done in the past.  But, as well all know, a whole class discussion like that engages maybe 10% of the learners and not everyone participates.  Doing this with a "My Perfect Summary" means I get to do that same questioning with 3-4 students and everyone is engaged, involved, thinking, and participating!

Now that is an amazing flipped class!

*Read a few student's thoughts on this activity in the Math Analysis section of my Week 4 reflection!

Here is what the WSQ's looked like today... sorry they are sideways!  Click on them to read them closer!