Thanks to a post by Maria Anderson, I was inspired by the TED video shown in my last post by Neil Turok. His background slides (which had huge visual impact) were created using worldmapper.org. I navigated to the site to explore some more. What a great way to incorporate some social justice ideas into your math course. The files come with MSExcel ready data and posters that can be printed.



The first image is a plain old map of the world. The second map has been created such that territory size is proportional to the world distribution of the excess male over female enrolment in primary education.

Neil Turok & Africa

Great day in the classroom!

Today I got the chance to work in a grade 7 classroom where we were working on an introductory lesson for probability. As we planned the lesson, the classroom teacher and I anticipated some of the misconceptions students generally have when dealing with proability, e.g. being probable does not imply being certain.

As I often do, I used Marian Small's book, Making Math Meaningful to Canadian Students, K-8, as a source of inspiration. We chose to try out an activity in the book for the"mind's on" portion of our lesson. We began the conversation with trying to place 3 scenarios along the continuum and label them accordingly. The scenarios we had decided upon were hoping to bring out the terms: "impossible", "certain" and "equally likely" as well as the percentages, decimals & fractions related to each of those concepts. Trying to come up with a name for the middle of the continuum got to some great conversation around the misconceptions. We then distributed sets of cards to each group where students selected an everyday example of probability (e.g. from a newspaper)and then had them try and estimate where along the continuum they felt their example fit. In addition to being a useful tool to help students describe and compare the likelihood of real events, we were able to work on the students' flexibility around decimals/fractions/percentages. Students were negotiating with each other where they should place their card and for students who were struggling, we got a chance to probe them with further questions to help them deduce where their card belonged. What a rich way to start a unit that assumes great flexibility in number sense around fractions/decimals/percentages. Thanks Marian!

Formative Assessment

I think that on the whole, teachers believe in the value of formative assessment. I also believe that there is still some uncertainty about what formative assessment can look like. And of course, some very real concerns about the time it takes to assess it so that it becomes an effective piece in the student's portfolio.

I was reading an article by Linda Dacey and Karen Gartland in the online newsletter Math Solutions titled, "Lessons from the Classroom: Post-Assessment Tasks". (A sample student response is pictured here.)

This particular assessment focusses on similar triangles at a gr.6-8 level. How would the responses be different from your gr.10 applied students? The task is open and the responses offer some real insight into the students' understanding and into where the gaps (possibly) lie. (At least it allows the teacher to further probe as to whether it is in fact still a gap or simply an ommission.)

Challenge: Select the "big idea(s)" from the unit as a starting point. Create an open assessment task that will allow you into their inner thoughts about the big idea.

The Real Challenge: Use the information gathered to guide your instruction for the remainder of the unit. Allow the insight to start the conversation within your department. Is this the same stumbling block every year? Are we spending the appropriate amount of time planning and delivering this topic? Reflect, reflect, reflect. Revisit again.

With standardized tests, like it or not, the reality is that we are very concerned with ensuring that our students not only maintain previous year's performance results but also improve upon their collective performance every year. No band-aid solution here; formative assessment anyone?

Toronto Island Math Beauty

As I like to do every sunny chance I get, I headed over to Toronto Island this past weekend to play some disc golf. Every time I bike over to the first tee, I ride past this play structure and it makes the math person in me smile.

Calling Quadratics???

This year, I am lucky enough to be a part of the math coaching initiative funded by the Ministry of Ontario. This role allows me to sit with 1 (or a couple of) teacher(s) and work collaboratively on lessons with the goal of increased student learning. We try to go as deep as we can both in our thinking of the mathematical content and also in the instructional strategies we can use with our students. I was working with one group last week where the expectations were focussed on a quadratics lesson. Immediately, a recent post by Dan Myer titled, What can you do with this: Projectile Motion, came to mind.

The group I was working with was pumped to incorporate his idea into their lesson. As we continued with the lesson, we got hung up on the idea of coming up with real-world models that were in fact, quadratic. The conversation was good.

Today I was catching up on some new posts and read Kate Nowak's post: f(t): Real World Once Again Inconvenient. She had also taken Dan's idea and morphed it into her own lesson.

Surely, I have to share this with my group. The power that blogging can bring to collaboration and refining an idea is unlimited. This is a great way for teachers to connect, collaborate and create.