Friday, September 7, 2012

Student-Driven Inquiry in Math Analysis

I have a lot to blog about later this weekend about the progress in Algebra 1, but I just had to share what happened in my Math Analysis class this afternoon.

Last night, they watched a video on "Finding Zeroes of Polynomials Using Factoring".  They were introduced to the concept of multiplicity but told nothing about it.  One of their WSQ questions asked them: "Explain what multiplicity is, from what you know.  Then, explain what you think it might mean graphically." Most of the kids had no idea and really couldn't conceptualize anything about what it might mean.

Then there was one group. Group B, period 6 :) (great way to end a Friday).  I chatted with them during their WSQ chat. I asked them some follow-up questions.  Then I left and went to another group.

They started sharing ideas, trying to figure out what multiplicity would mean on a graph.  They were so intrigued, and almost frustrated that they couldn't figure it out.  So, they decided (self-directed) to look at the equations they had factored and found zeroes for the night before, and they plugged a few of them into their graphing calculator and looked at what was happening.  Some lightbulbs came on as they noticed some weird things on the graph.

I think they'll be excited when they watch the next video and see what multiplicity really means and that they actually discovered it on their own :)

I'm coming to find that my WSQ chats are actually a great place for students to ask those questions, to probe deeper, to make connections, and even ask them about things that are coming up (not letting them know we will learn them later) just to find out what they think about them right now.

It was a good day :)

In fact, it's been a pretty good week!  We covered Unit E Concepts 2-6 this week Tues-Fri and I am actually very surprised by a few things:

1. Students are on task and working; I don't feel the need to monitor the seating chart - and it's only week 3 of school!
2. Students take charge of leading their groups through the discussions (with their 3 roles of ask questions, keep group focused, keep everyone participating).  That has been working really well!
3. I don't find the need to time the WSQ chats because of the "Today's WSQ chat" screen that you can see below.  It keeps the groups focused and on task, with a goal.

Students have already started taking quizzes, and some are choosing to "waive" out of the PQ assignments by passing the quizzes.  I did talk with them today about the value of practicing math, and gave the example of a student from last year who was "too cocky" and didn't do much practice and then got C's on the tests instead of A's - because even though he passed the quizzes, he didn't have enough practice to truly master the material.

Most students are completing the WSQs nightly; it is about 2-3 a class.  If they don't tell me ahead of time, we call home.  If they text (Google Voice is amazing!) or Edmodo me, taking responsibility for themselves, I let them watch it in class no problem.

I did a small group pull-out today for students who needed to review concept 1, and I love being able to actual help students that want help.  We are starting to get into a routine every day, which I think is good.

5 minutes - announcements and reminders
5 minutes - focus for the day
10-15 minutes - Guided WSQ chat
25-30 minutes - work on PQs, Quizzes, Student Problems, WPP's, Student Videos, etc

All of my Math Analysis classes start "on the hour" (noon, 1pm, 2pm), so I think I will make the "half-hour" my small group time each day and say "at 12:30 I'll be doing a small group on ________" and either have me pick (based on what I've seen in the quizzes) or have them tell me what they need.  I think that will be great for me to kind of "schedule" it in so I don't forget.  If they don't need the extra help, they can be working independently.
 I've started to give my students more structured items for the WSQ chats and have found I actually don't have to time them.  I hold them accountable by asking for certain things to be actually written on the whiteboards while they are chatting about it so I can walk around and see what is going on and ask more questions.

 Math Analysis students engaged in WSQ chats!

 A student explaining to another student different ways to factor the polynomials

 A group discussing the difference between a zero and a factor (and actually writing it on a whiteboard so I can read it!!)

I asked 3 students how they were feeling about our class so far.  Two of them said they loved it and the other one said she liked it but she felt like she didn't do much in class.  After probing further, she said that the math just is really easy right now so maybe she would have a different perspective once we get to a tougher unit.  She said, "All I do is come in and discuss the math for 15 minutes and then do some practice".  After talking with her, I thought of a few things.
#1. Our students don't realize the importance of discussions, even when they understand the material.  When you can verbalize your learning and explain it to someone else, it takes the learning a step further.
#2. Our students are so used to coming to math class and furiously taking notes the entire period... they leave class feeling like they were busy the whole time. Spending a good 10-15 minutes of class in discussion is not something they are used to and it is a different type of learning.

I'm excited to see how this year continues with Math Analysis since I'm already so happy with how the classes are going.  I love being able to probe and challenge... and I will say that some of my kids are already coming up with awesome questions (argh - reminder! I need to do more with the questions!!!) and great comments to further discussion beyond the questions I ask.  I love it!!!!

2 comments:

1. Crystal-

I actually ran into the same thing in my intro unit that you mentioned at the end of this post here - a student feeling like they weren't learning anything because they weren't doing in my classroom what they were used to doing to 'learn' in a history classroom. Fascinating how some students have come to associate lower order thinking skills with 'learning.' I'm looking forward to seeing how this student perception evolves over the course of the year.

I hope things keep going well for you and your students!

-Karl

2. Cool, Crystal. Yesterday I was working with my Algebra 2 students on complex numbers and why square root of -1 is i. Today I had them doing sentence writing to explain how to solve complex numbers. The students self selected pairs and it was interesting to see the development of writing from one group to another. The "write it out on the little white boards" works so well for me too as I see kids teaching each other new items. I need to catch some photos of students doing that in my classroom. I only caught aftermath of the classroom yesterday with the desks all oddly arranged.