Monthly Archives: September 2014

We held our first bowl team session in MTPS today: an friendly, informal competition dividing the class into two groups of roughly equal 'ability.' The bowl competition we attend at the University of Nebraska-Lincoln in November consists of games of 15 questions with 30 seconds to answer each question.

Here is a question we spent some time on in class today.

Original_Cube_Bowl_Question

 

Here is a screenshot from my Promethean board of the work we did as a group with students:

Find_Side_of_Cube_Given_Sum_of_All_Possible_Edges

And here is a screenshot from the Geogebra sheet students constructed in front of the class at my computer terminal to demonstrate what is going on in this problem. If you would prefer to download the Geogebra sheet for your own tinkering, you can find it here.

Cube_Bowl_Question

No one got this question right in the allotted 30 seconds, so we spent some time developing the various parts of the expression. We color coded the edges on the cube (segments AB, AD, and AG) orange. We color coded the diagonals on faces of the cube (segments AC, AH, and AJ) green. We color coded the segment inside the cube (segment AI) black.

The kids had a lot of fun with building the Geogebra sheet and then trying to reconcile between sqrt(2) and the crudely rounded segment length 1.41. Or the sqrt(3) and 1.732.

The pink stuff at the top of Promethean board screen shot is our efforts to generalize this question. I tell the kids we are trying to "hack all possible problems." We use the term invariant and that we are looking to write a question that covers all possible question types. For example, what would happen to the question if s = 2? Or if s=3? Or if s=n? Is it possible to answer the question before the moderator finishes reading it? If so, at what point can we be confident we can buzz in and answer correctly?

My elective math class has all grade levels represented within it. While not ideal, this is a feature of our scheduling system. So I have freshmen in Algebra I all the way up to seniors that have already completed Calculus AB. This poses a huge classroom differentiation challenge each Monday, Wednesday and Friday we hold class. Here is an instructional strategy I use that gets students writing about the mathematics they do in class.

Students worked on one of four things in the computer lab last Friday.

1. Construct 2013 Probe I Problem 7 diagram (2D)

2013_Probe_I_Problem_7

2. Construct 2013 Probe I Problem 23 diagram (2D)

2013_Probe_I_Problem_23

3. Construct 2013 Probe I Problem 11 diagram (3D)

2013_Probe_I_Problem_11

 

4. Work on Alcumus problems independently

After we spent approximately 55 minutes in the lab, we returned to my classroom for a writing activity.

Here is the writing prompt I put on the board:
(Writing exercise on a separate sheet of paper to turn in to me)
Think about what you learned about the diagram or diagram(s) you built in Geogebra. Write a letter to the you of October 12. How did building diagrams in Geogebra help you understand the problem better?

I put eight minutes on the clock and informed students they would need to continuously write for the eight minute timeframe. Here are some samples of student writing from the activity. For convenience, I have inserted another copy of the problem. Immediately below each problem appears student writing associated with the problem.

2013_Probe_I_Problem_7

 

Problem_7_Writing_Example

Problem_7_Writing_Sample_2

 

2013_Probe_I_Problem_23

 

Problem_23_Sample_1

 

2013_Probe_I_Problem_11

 

 

Problem_11_Sample_1

 

The Students revealed their thinking about these math problems throughout their writing. While some students chose to concentrate on the construction process in Geogebra, others also revealed some of the mathematical structure they encountered while making the diagrams.

Writing samples from students that worked on Alcumus:

Alcumus_Writing_Sample_1

 

Alcumus_Writing_Sample_2

 

 

 

 

 

 

 

 

 

These writing samples revealed to me the depth of student thinking going on in the classroom. If I could have a superpower, I would be a mind reader. Then I wouldn't have to guess at what my students are thinking. Having the students write for an extended period of time gives me insight into how they are seeing the mathematics and gives me ideas on how I can help further their understanding and guide them as they struggle.

I collected these writings immediately after students completed them. I ran the pages through my ScanSnap scanner and converted them to a PDF for me to review later. I told students we would get these writings back out in a month's time, emphasizing the need for specificity on what they were working on and what they learned that day.

Going forward, these writings help me be more efficient with respect to differentiating classroom instruction. We don't need to be working on the exact same thing at the exact same time at the exact same pace for the students to engage in meaningful problem solving.