My First Class Blog

Being so impressed at the personal growth I have experienced through the world of blogs, I made it a professional goal this year to try a class blog in my Grade 12 Advanced Functions course. I used Darren Kuropatwa's suggestions for setting up the blog and an article I found through Will Richardson's blog as my "first blog assignment"(more-less just to get the students on and me trying to figure out how it's going to work).

So far, everything has worked out pretty well. I am a bit disappointed by the spelling issues creeping up in the comments.

The article that I had asked students to comment on was a TIME article titled, "The Way We'll Work". I asked them to comment on how the article connects to how they will approach this course. As I read the comments, I feel some students are trying to write what they think I want to hear rather than really thinking about the greater connection.

I guess (hope) they're just testing me as well.

The String Game to Start

On the first day with my grade 9 applied class I used the "String Game" to begin. It was fantastic to say the least. In this fun game, I was able to do tonnes of assessment for learning. I was able to find out about student interests, how they felt about math, what their previous experiences have been and I also got an early glimpse into their personalities. This was all without any type of prompting. Will definitely do it again...

First Day of School

I am going back to the classroom next fall and I must be quite excited since I find myself sitting here in June anticipating the first day in September.

Anyhow, I am looking for suggestions for first day activities/student surveys/videos, etc. If anyone has anything interesting to pass along, I would love to hear about it!

Math Content vs. Math Pedagogy

Lately, I have been a part of many discussions around the need for rotary math in our system. A colleague of mine, Gina, suggested I take a look at a webcast by Dr. Deborah Ball found on Curriculum Resources Canada (CSC) website, curriculum.org.

Dr. Ball argues that being an affective math educator is not necessarily dependent on knowing higher mathematics, but rather, it is dependent on knowing the level of math that you teach deeply. The webcast is definitely worth checking out. Mathematical Knowledge for Teaching with Dr. Deborah Loewenberg Ball.

Feeling so good about Bansho.

Today, along with 3 other teachers, I co-delivered a lesson we had co-planned around multiplying fractions by whole numbers. The group consisted of two gr.9 teachers and one gr. 7 teacher (whose classroom we were in). We had decided to give bansho a shot as we were interested in seeing the range of responses we would get from the students.

The problem we posed to the students was, "At the end of the party, we noticed that there were 3 pitchers of lemonade on the table and each pitcher had only about 3/5 of its capacity filled with lemonade. If we were to combine all of the leftover lemonade, how much would we have in total?"

We had anticipated 4 degrees of responses and sure enough, the students' responses seemed to be in line with our thinking. We posted student examples of the 4 different responses at the front of the room. The class then got into a discussion around the advantages of each of the methods used. The students were able to clearly identify strengths of each of the examples. The student who submitted what we had considered the "entry" into the problem looked up and smiled as the class talked about how his sample created a great visual to understand the problem more clearly. (I think he would agree it was a good day in math class today.)

An earlier diagnostic test (PRIME) had indicated that a majority of students in this class were still relying on a concrete understanding of fractions. The symbolic understanding was still uncomfortable for most. When students were invited to post their sample in line with the method they thought was most like theirs, we had instantaneous agreement with our PRIME diagnostic results. The teacher's daily goal is to try and bridge this gap. Bansho helped him see who is still struggling with this gap and whether progress is being made.

What made me so impressed with the bansho though was the fact that the student who had only been able to show the most basic concrete solution, then proceeded to work in the next "level" that we had determined along the continuum when it came time for the consolidation practice work. I am still pretty new with using Bansho as an instructional strategy but if that is what helped close this gap for this student... I'm sold.

A school-wide math talk?

Found this problem at The MAA Mathematical Sciences Digital Library.

The site demonstrates solutions to this problem using strategies including data analysis, technology-driven geometric sketches, algebraic analysis and calculus. I think it would be very interesting to present the problem to students in each of your gr.10 - 12 classes and then showcase the different methods they used to explore the problem. I think students would see the value in different representations/methods from peers in higher/lower grades.

How about school-wide math-talk?

Liquid Pythagorean Theorem

Amusing. Link to youtube video.

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.

Check this out!

Maria Andersen has put together this fantastic resource for starting/continuing the journey of using technology within your math class. It's called "Using the internet to spice up your math class". I found it very helpful.

http://www.mindomo.com/view?m=38cc4f6a467acbfde4be796e68399450

top down designing

I have been reading "Understanding by Design" by Wiggins and McTighe(1998). They speak of using "essential" questions to plan your unit. These are 2-5 questions set up ahead of time that students should be able to reflect on daily and build a response to throughout the unit. They suggest posting the overarching questions around the room so that it reminds students of the "big ideas" for the unit/course/discipline. They also suggest building assessment beforehand that address the exploration of these questions. Again, I am reminded of the importance of the design down approach to unit planning. Hello! Of course! So why does it not happen more often? A mathematical example they give in the text is "Why is it true a triangle always has 180 degrees? How can we say that for sure?"

It's Day1

Hi! Today is my first day as a blogger even though I hadn't intended it to be. It is also the first day of spring and what a better day to start off with something new and fresh. I reflect on all the memorable "firsts" I've had with technology growing up:
a) being asked to try the first computer to come to my elementary school...totally impressed
b) being encouraged to communicate with my prof via email in MATH1000 with the chief... didn't think I would really have to go down this road.
c) instant messaging...just cool
d) being a math e-learning teacher...exciting but I worry about effectiveness. Not about "its" effectiveness, about "my" effectiveness

I am not too sure what I want this blog to be about yet. I am going to start with the goal that it will be a place for me to organize a collection of things that inspire me and that challenge me. Maybe every blogger could say the same thing??? I am interested in using a blog in my classroom and in my professional life. I feel as though I need to explore and play before I get all serious though. I'll keep adding to my list : )

Every time I need a push, I am helped with the video Shift Happens.