Moving the Focus

One of the things that I've been reflecting on this summer has to do with student-driven focus on getting the answer.

Recently, I watched Phil Daro's Against "Answer-Getting".  I like the phrase answer-getting because it sums up exactly what my students are trying to do in math class.  I am aware of this and I have used various strategies over the years to move my students farther from just answer-getting, and towards other things mathematical.

Here in Quebec, students are evaluated on their ability to reason mathematically and on their ability to solve problems.  Reasoning is evaluated throughout the year and students sit a final exam.  Lots of answer-getting here.

Students are also evaluated on their ability to solve problems, without a final exam.  Here was my chance to expose my students to forms of evaluation which didn't focus on getting the answer.

This year, I gave my students some evaluation tasks based on Dan Meyer three-act tasks.  I've used these tasks in the past for instruction but never for evaluation.

In the first instance I used Dan Meyer's three-act task called Finals Week.  I showed the students only the first act.  Multiple times.  As many times as they wanted, actually.  Then I gave out the sheet below.  I wanted them to do a number of things: describe the problem, list what they would need to know, list what they would not need to know, describe/list the problem solving process they would follow, and estimate an answer.

The brief rubric at the bottom of the page is from what Quebec students are expected to be able to do under the problem solving competency.

The second  task I used was Dan's Leaky Faucet.

The third task I used this year was Dan's Meatballs.

I do not have student samples (note to self: conserve student samples!), but I did make a number of observations about the student work.

Some students had success because the numbers weren't in the way.  Sometimes students just make up math to arrive at the "answer-getting".  This forced them to think about the process not the product.

Some students were able to show their problem solving process not by way of a series of steps, but in one compact formula.  They created a new formula which incorporated all of the elements required (here I'm thinking about Meatballs).

This is definitely something I will keep doing, and do more of in the future.  I'm proud that I moved my students a little farther away from the focus on answer-getting.

Taking the Time

My students completed the Des-man project through Desmos.

The original, original Des-man project was created by Fawn.  She is so inspirational.

The post by katenerdypoo at in pursuit of nerdiness, was my starting point.  Kate also teaches at an IBMYP school, and so the language and her assignment set-up made sense to me.

I used her assignment to develop my own.  I also evaluated Communication within the IBMYP framework.  I teach secondary 3, grade 9.

I let the students have one 75-minute period to work on their project.  At the end of the period, I realized that they had just barely had enough time to get used to Desmos, figure out what the project was, and begin to work.  At the end of the period I promised them another, even though on the site they suggest that it is a 45-minute lesson.

I have spent the weekend grading these assignments.  As I evaluated them, I looked through what they had produced during the first period.

One pair of students produced the following:

The first effort.

The final product

Two 75-minute periods were devoted to this assignment.  To some this may seem like a lot.  Looking back it was time very well spent.  A number of things struck me as I was grading their assignments. 

The first period allowed them to get used to the graphing calculator and do some trial and error.  The Teacher Dashboard really helped here because I was able to put it up on the SMART board, and the students were able to identify who was doing what.  I encouraged them to visit other groups and ask for equations and ways of making certain lines and parts of the faces. 

The first period also let the students figure out what I was asking them to do.  I asked them to use at least two linear functions.  I asked them to restrict the domain for at least one of the linear functions.  The written part asked them to identify why what they had chosen was a function.  I had not done a lot of direct teaching in these areas, and so during the time that they took, they were actually learning, from their notes, from each other, from Google.

At the end of the first period, once we were back in the classroom, I asked how many knew if they had used a linear equation in their Des-men.  Even though I had seen many in their Desmos faces, not many people raised hands.  I knew I needed to reinforce this.

A second pair of students did the following:

The first effort.

The final product.

During the second period let the students start again.  I let them see their previous attempt and use the equations.  I put up the Teacher Dashboard again.  I let them visit again.  They finished during the second 75-minute period and were able to begin on the written report.

A third pair of students produced this:

The first effort.

The final product.

I was struck by the students' creativity.  I had let them play, and they really did.  In the side-by-side Des-people above, I can see the transformation to the wink and crooked smile, the addition of the hat, and feminine aquiline nose.  

I am happy that I devoted two periods to this learning, and I am glad I took this time.