Quadrilateral Hierarchies - Productive Struggle

An overarching goal for the semester is to help my pre-service teachers grow more comfortable with "productive struggle" and with persevering on challenging tasks. We worked at it for a long time earlier this semester on problems like the Chessboard Problem, the Cheesecake Task, and many others.

Last week, we moved into Geometry. After spending some time exploring the Van Hiele levels of geometric thought and the kinds of activities that help children progress to higher levels, it was time to put their own geometry knowledge to the test.

In this two-stage lesson, I first divided the class into five teams (of four) and assigned each team a shape class: rectangles, kites, rhombuses, parallelograms, trapezoids (inclusive definition). They were directed to produce a poster with a 2x2 grid with space for examples and properties of general and special members of their shape class.

Here's an example:

Guest Post: The Value of Social Media for Teachers

The following is a reflection written by one of my preservice elementary mathematics teachers (@hollikathryn14) in W14, wherein she summarizes what she learned from an hour of professional development time spent with #MSMathChat on Twitter.

For some background on the assignment, see my post: Professional Growth for (New) (Math) Teachers.

When I read her reflection, I was inspired. I thought she nicely captured the power of looking to social media for professional development, and I hoped that her experience and perspective (pre-service teacher, and Twitter newbie), might inspire others to give it a try.

She graciously granted her permission for me to share this with you. And so, here's Holli's reflection on her first #MSMathChat experience:

Coaching Session - Who's Engaged?

I recently completed a couple of classroom observations with student teachers who had identified student engagement as one of their personal learning goals on the action plan for the observed lesson. We agreed I would collect data on student engagement at five-minute intervals using an annotated seating chart.

Here's the diagram from one of the classes. Letters "A" through "H" mark students who I judged were not on task at at least some point during the five minute time index of the survey.

What do you notice? What questions do you have?

Here's the diagram from another class at a different school. The seating arrangement shifted mid-lesson when students began to work in pairs; these pairings are indicated as bolded connections on the diagram. 

Again, letters "A" through "H" mark students who were not on task at that time index of the survey. You can see a chronicle of this lesson below the chart.