January 19, 2016
Realizing our impact...
Rita Pierson's Every Kid Needs a Champion is my personal favorite.
Which one is yours?
All under 10 minutes- and all pretty inspiring!
Monday, January 19
Tuesday, January 20
mClass Testing (Bartochowski, Kempf, Mains, Miller)
Wednesday, January 21
Weekly PD @ 8:05 am (Location TBD)
mClass Testing (Bartochowski, Kempf, Mains, MIller)
Thursday, January 22
mClass Testing (King, Morey, Olenik, Taylor)
Jillian OOB 8:45-12:15 (INALI Meeting)
REPORT CARDS HOME
Friday, January 23
mClass Testing (King, Morey, Vickrey, Taylor)
Jan 25-mClass Testing (Lachowicz, Olenik, Open, Open)
Jan 26-mClass Testing (Lachowicz, Vickrey, Open, Open)
Jan 28- SOTM Breakfast
Feb 5- Winterfest
Notes and Other News...
- I have had some recent reports of uncleanliness in classrooms. If you have a concern, please share with me.
- Items needing to be printed in color can be emailed to Anita.
- Complete Grades by Wednesday at 9 am. Jennifer will print them during the day on Wednesday. You will send home on Wednesday.
- Remember to NOT complete the Academic Behavior scale. I am working on something to send home explaining this new tool.
- Continue mClass Testing with fidelity.
- Decide as a team how you will share the mClass results with parents.
- Continue recording Parent Contacts on Google Form. Many have not been updated since early this fall.
- Submit your weekly newsletter via email (preferred).
- Learning Goals and Tracking Student Progress are embedded in your daily work. New teachers: speak with your mentors about this.
A Five-Step Model for Leading Classroom Math Discussions
In this article in Mathematics Teaching in the Middle School, Margaret Smith, Elizabeth Hughes, and Mary Kay Stein (University of Pittsburgh) and Randi Engle (University of California/Berkeley) suggest a way to conduct classroom math discussions that builds on and honors student thinking while ensuring that the key ideas being taught remain central. The authors use the Bags of Marbles problem as an example:
Bag X contains 75 red and 25 blue marbles.
Bag Y contains 40 red and 20 blue marbles.
Bag Z contains 100 red and 25 blue marbles.
Each bag is shaken and a student, eyes closed, takes out one marble from each bag.
With which bag would the student have the best chance of picking a blue marble?
The challenge with problems like this is how to orchestrate student exploration and an all-class discussion so the different ways of solving it are explored, students can draw on their varying levels of expertise, and students get enough – but not too much – help from the teacher.
Smith, Hughes, Engle, and Stein suggest a particular sequence for conducting a rigorous math discussion. “These practices give teachers control over what is likely to happen in a discussion,” they say, “as well as more time to make instructional decisions. This is possible because much of the decision making has been shifted to the planning phase of the lesson.”
• Step 1: Anticipating student responses – The ideal scenario is for a group of teachers to meet and come up with as many solutions as they can, perhaps also looking at student work from previous years. This will help think through different student strategies and prepare teachers to deal with likely errors and misconceptions. For example, one common but invalid way to solve the Bags of Marbles problem is to look at the number of extra red marbles in each bag (50 in Bag X, 20 in Bag Y, and 75 in Bag Z). Teachers should be ready to ask the right questions of students who are using this strategy.
• Step 2: Monitoring students’ work and engagement – As students work on the problem (probably in groups), the teacher circulates and pays close attention to their mathematical thinking and solution strategies. It’s helpful to have a list of all the possible solutions (fraction, percent, ratio unit rate, ratio scaling up, additive, and others not anticipated) and jot down which strategies different groups are using. “During this time, the teacher should also ask questions that will make students’ thinking visible and help students clarify their thinking,” say the authors. “The teacher should also ensure that all members of the group are engaged in the activity and press students to consider aspects of the task to which they need to attend.”
• Step 3: Selecting students to present – While circulating, the teacher thinks about which students to call on in the all-class discussion. The goal is to get all possible solution strategies on the table (including strategies that students don’t come up with) and teach the key concepts, namely: (a) to compare bags of marbles, you need a common basis of comparison, and (b) there are different types of comparisons: part-to-part, part-to-whole, and percents).
• Step 4: Sequencing student responses for display – The teacher might start the all-class discussion with the strategy used by most students in the class, which would validate their work and engage as many students as possible. Alternatively, the teacher might begin with a strategy that is the most concrete, using drawings and hands-on models, and move into the more-abstract solutions. Or the teacher might start with incorrect strategies to clear up misconceptions early on. Whatever approach is used, the sequence should allow students to see the differences between different solutions and appreciate the diversity of solutions to a seemingly simple problem.
• Step 5: Connecting different student responses and linking them to key math ideas – The closure of this lesson should pull the threads together and help students evaluate the accuracy and efficiency of different solutions and see the mathematical patterns and principles involved.
“Orchestrating Discussions” by Margaret Smith, Elizabeth Hughes, Randi Engle, and Mary Kay Stein in Mathematics Teaching in the Middle School, May 2009 (Vol. 14, #9, p. 548-556), available for purchase at http://bit.ly/1Qj8xue