Rich Tasks

We haven't been required to post to our journal in a while and to be honest I have been consumed with re-watching all of The Gilmore Girls on Netflix and thus have fallen a bit behind in my math course.  Bad!

I am getting caught up now and this week's focus in on creating rich tasks in a math classroom.  It has been really interesting.  I wish that my teachers had this information when I was a math student.  I would have actually looked forward to math class.

My task for today is to post a list of characteristics of a rich math task.  This has been gleaned from several readings.

Rich math tasks:

• focus on key concepts
• stimulation communication
• captures student interest/engages
• promotes understanding of the concept
• connects to one or more big ideas in the currciulum
• will require that students reason their way to a solution
• allow more than one strategy for arriving at a solution
• require students to explain and justify their thinking about their solution
• don't inlcude information being fed to students in order to do a computation
• encourage student intuition
• has a short question
• lets students ask the questions
• are challenging for most students
• uses contest or situations that are familiar for the students

Theory of Learning

Today I am supposed to write about my theory of learning.  My theory of learning is firmly based in a holistic approach to learning, that people need to learn with all of their whole self - mind and body as well as spirit.  While we obviously use our minds to learn, we learn best when we use our bodies to do so - through touch, movement, sight, taste, smell, sound; we learn best by doing with our whole selves. And I believe our spirit comes in when we connect with others to support our learning and give support to others.  Our spirit comes in again, I believe, when we reflect on our learning experiences.

This applies to math so very deeply.  In my experiences with Leo the Rabbit, I needed to "do" the math, through drawing, thinking, talking about the problem.  And then I had to battle with myself to get to understand the solution.  That is persistence of spirit right there.  And struggling with my internal self.  Good math problems should require this on a regular basis.

Leo the Rabbit

Our next challenges was to try to solve one of two rich task problems.  I chose the somewhat well-known Leo the Rabbit problem.  On first look I knew it had to do with patterns and sequences and that I could probably use a table to solve it.  I drew a few pictures.  My anxiety rose as I realized how many different ways Leo could get up the stairs and I didn't feel I was getting my head around the right approach.  I wished I had someone here to talk to about it.  I had Google so off I went after working on the problem alone for 10 minutes and my anxiety about my skills in math getting the better of me.  As a teacher, I find my anxiety about my math abilities is worse because I feel pressure from myself and other teachers to be able to find the answers skillfully and quickly.  I hate that feeling.  Anyway, Google gave me the helping hand I needed.  Here is one teacher's solution.  The question we were asked for our course is "How would you convince a skeptic that you are right?" To be honest, I would have to sit with the solution a while longer to be able to convince anyone else that it is right.  I totally get the solutions up to step four but when you add a fifth step and rely on Fibonacci's sequence (adding the two previous to get the next) and why that works with the steps, I would need to rattle it around a bit to be able to explain it to someone else.  I know it work and I know the answer 89 is right but I needed someone else to tell me that.  I also get that adding the previous steps options makes sense each time because each three and two step sequence will only have a certain number of options.  But coming up with that on my own? Uh-unh.

Doing Math

We were told to reflect on what it means to me to "do math." If you asked me that questions when I was in high school I would have answered with something like "solve equations" or "add things up" or "find the area of a circle" or "solve for x" or something like the meme above.

Now, my answer would be something like "work through a problem that involves patterns or numbers or symbols and do so in a mathematical way, perhaps collaboratively.  It could be really messy.  You might not get the right answer but you work at it and try different approaches and talk to different people.  You show someone your thinking along the way to show what you did and why."

Overcoming Math Anxiety

We were asked to watch the following video: Getting Kids Motivated: Overcoming Math Anxiety and record our questions on math instruction and learning.

I guess my questions would start with how teachers plan their year in the best way to scaffold learning and therefore diminish math anxiety.  I have overheard a few conversations by seasoned teachers where they debate the best order in which to plan the year regarding math units and they rarely follow an order in a textbook and are not always in agreement with each other in regards to the best way to approach it.  So, what is the answer so that learning is scaffolded in a way that consistently builds but also reinforces so that you are constantly practicing each skill in math.  My issue with math teaching has often been that teachers teach units in math and when the unit is done, it isn't revisited until the following grade.  This does not help reduce math anxiety or reinforce skills or concepts.

In the primary grades, I don't see math anxiety.  I see a lack of confidence and, even more frequently, frustration, when they don't "get it" as easily as others.  I think the anxiety comes in the Junior and Intermediate grades when that frustration has been allowed to fester for too long.

so the challenge is to go from ^ to:

Math AQ

It's been a looooooong time since I have posted anything here.  The last year has gone by in a blur.  A short recap:

September 2015: on OT list for OCDSB (yes!) but OCDSB is under work-to-rule due to labour action by teachers so no work (no!) but then I get a call to come into beloved Hawthorne on September 23 to teach Intermediate Science and Grade 7 math (yes!) and it turns into a two-month LTO (yes!) and then another 2 month LTO after Christmas (yes!).  I learned so so much.  See big holes in math understanding in some Grade 7 students.  Reflect on how to contribute to solving this.

November 2015-February 2016: did my Primary ABQ online through Queens.  Tough grind while doing an LTO and having 3 kids but I mad it and it was so worthwhile to get that on my OCT record.

March 2016: back to daily OT grind.  Lots of work, lots of fatigue.

Summer 2016: destress, plans to prepare for LTO list interview.  Hahahahahah.  Good one.

September 2016: back to daily supply grind.  Very little work until, again, end of September,and then got four weeks at Charles Hulse teaching kindergarten and then Grade 2.  Awesome experience again. Missed my intermediates though.  New way for call-outs through Easy Connect means I had no calls for my the schools I was commonly at last year.  Sad face.

October 2016: LTO list interviews.  Took a week to prepare.  Very stressful but I think I did well.  Will find out November 11.

November 2016: Calls still slow.  Not good.  New system really needs to go back to old system.  I hope the union is getting this message to the Board.  Sign up for primary/junior Math Part 1 AQ through Queens to go November-February.  Realize that holes in Grade 7 math started in primary/junior so this is my starting place.  Turn my blog into a learning journal for the math AQ for a while.  And that's where we are now.