New School Year Eve

Tomorrow is the first day of school for teachers in my board, and really most of the province.  The students don’t start for 6 more sleeps, but tomorrow morning school libraries across this vast city will be full of educators ready to discuss how we are going to make this year the best one yet.

Or, maybe, full of people hoping we’ll have a few minutes at the end of the day to make sure the classroom is ready.

From home, on rainy days, I have been making plans.  I think I know what I am doing on the first 2 days.  I’ve spent a lot of time thinking about how I am going to start math this year.  Every August I feel like I have never taught before.  I can’t remember anything I did on the first day in previous years. I have vague memories of starting off with art projects and activities related to identifying 2D and 3D shapes, or of asking students to play math games.

The awesome math facilitators in my board have created a “First X Days” of school document for students in junior and intermediate grades, and are working on a primary version.  I attended workshop in June and so have decided to arrange my first 2 weeks recommended in this document.

I am really excited about 2 of the activities! I mean, I’m excited about the whole thing, but REALLY excited about 2 specific things.

First, Amy Krause Rosenthal and Tom Lichtenheld wrote a really great book called “Duck! Rabbit”.  Throughout the book, there is one drawing and unseen people are arguing about whether it is a duck or a rabbit.  (I’m assuming they are people.  It doesn’t really say.)

From Duck! Rabbit!  by Amy Krause Rosenthal and Tom Lichtenheld.  

Each gives his/her/its well supported opinion. I think it really shows an important idea we need children to consider in mathematics:  There isn’t always one right answer. Two people can have different opinions and still be right.  The important thing is being able to justify one’s opinion.  (PS:  I know that’s not just in math.  I’m trying to stay focused here though.)

After, we are going to read this awesome book:


I’m waiting for some permission to photocopy a page for students to write on.  I am going to ask the students which one doesn’t belong, and then let pairs of students talk for 10 minutes about their opinion. Then they will present to the larger group.  My goal with this day’s activity is to have the students really think about justifying their thinking.  I want to introduce that word to them early on.  I’ve read Cathy Fosnot’s book “Conferring with Young Mathematicians” and she talks a lot about asking good questions that get the students to really reason their way through and around an answer so they understand their thinking deeply, rather than just accidentally stumbling upon the right answers and moving on. That should get us through one day of the first week.

The second thing I am excited about is also related to a read-aloud (because that’s how I do things!)  This one is called “Great Estimations” by Bruce Goldstein.  Inside, there are pictures  of every day items.  A small amount is sectioned off and labeled, a larger amount is also sectioned off and labeled, and then there is a large amount of the same item and readers are asked to estimate how many there are.  Here is an example:

From Great Estimations by Bruce Goldstone. I highly recommend this book! I think it is appropriate for use in math lessons for students in grades 1-12. And I think kids will love the pictures and challenges enough to read it on their own time, no matter how old they are.

After we talk about the pictures in the book, which will be too far away from the students to count by ones using their fingers to touch each one therefore “forcing” them to estimate, I am going to send them off to their tables.  On each table I will have 2 jars of everyday items.  One will be full, the other will have 10 of that item.  I am going to ask them to work in pairs and estimate how many are in each jar, record their answers, and then move on to at least 3 more sets of jars.  I am thinking this will take 2 days.  I’d like them to have to work out a strategy, and then use it again after a good night’s sleep to make sure they are really getting it.  I’m also hoping this will reinforce the idea that we must record our thinking clearly!  The estimation jars are not my own original idea.  I know I have read about them in an Effective Guide to Mathematics Instruction, but I can’t remember which one and I am not going down the long and windy road of to try and find it for you.  You’re on your own! Or you could just take my word for it. I’ve used them many different times, sometimes even having a new set of jars every month and revisiting this idea of estimation often.  I like it, the kids like it, and they develop a pretty good sense of magnitude, comparing, and counting if you ask me. Oh, and estimating.  They get pretty good at estimating.

In conclusion, I think this really will be my best start yet.  I am loving this idea of focusing on setting up the class so that our first 9 conversations are all about problem solving as a good thing, mistakes as an important part of learning, and about being able to participate in a productive argument about your math.  I’m glad I had someone else guide me in that direction.


Chapter 3: Type of Problems

This is one of my Summer math PD books. I am blogging as I read to help me consolidate my learning. 

This chapter is about the different types of math problems we (can/should/do?) pose to students. This is actually something I remember learning in university, in a “How to teach math” class.  That, by the way, was the first math class I ever earned an A in!  I remember us having to learn the types of problems, and then create problems of each type.  This still felt like new information to me, rather than a review. Perhaps I have been out of university longer than I realize?  Say it isn’t so!!  I will say that I am in the habit of thinking about the math required to solve the problems I ask, and wondering if they will help move us toward our goal.  I think this information will help me refine that process, ask more specific questions, and move kids along on a mapped out course, instead of that “Let’s see if this road takes us to where we want to go!” way of posing problems that I will admit to sometimes using.  And I also drive that way sometimes.  But that’s a blog post for another day.

One of the things that stood out for me in this chapter is the fact that each type of problem creates different mathematical demands on the learner. As I was reading, I kept thinking of how Cathy Fosnot stresses that children need to be given a chance to answer problems on their own without the teacher telling them how to do it.  The act of puzzling their way through the problem is an important part of them developing an understanding of when it makes sense to add, or when subtraction is required, or how to figure out the unknown without someone showing them what is unknown in the problem.

I also noticed that once again Lawson points out that students will fall back (she says “fold back”) on less efficient strategies that they feel more confident about when they encounter more complex problems.  Again this makes a lot of sense to me. Once they figure out the answer and are confident about being right, then they can consider solving the problem again with a strategy they still feel apprehensive about.  I am reading Cathy Fosnot’s book about conferring, she she says  that when we see students falling back on one of their tried and true strategies, that is the perfect time to push them ahead to a new spot on the landscape by suggesting a strategy they could consider trying.  For example, “I know you solved this by counting all the blocks by ones.  The other day I saw you solve a problem by making groups of 5.  Do you think that could try that here and see what happens?”  That prompt does not tell them how to solve a problem, but rather suggests they use a strategy you have already seen them use in other situations.

I made a little graphic of the information from this chapter about the types of math problems we can pose in class.  I think I am going to print it off, put a copy in my day book,  and use it to help me with my planning. Hopefully after a few months it will become second nature and I can make them up on the fly.