Focus on Math

Helping children become mathematicians!

Calgary City Teachers’ Convention: PS February 10, 2016

It is my pleasure to present this session “Power Up Your Problem Solving” to the participants of this session.

Regular problem solving is a powerful way to help students develop conceptual understanding in the various strands of mathematics. Since there is a tradition in North America of “teaching by telling” (the “here’s-how-to-do-it-go-practice-50-of-these” method), it may take many weeks to develop a culture of deeper thinking in a classroom. Students need a variety of thinking tools and strategies to work with, as well as skills and practice in talking about math problems, but the time it takes to help students gain these needed things is time well spent. The payoff is huge!

I hope many of you will be encouraged to begin building a regular problem solving program with your students. It works at every grade level!

All the here are the downloads for the problem solving session:

I would love to hear from you how it goes in your classrooms!

Mathematically yours,



GAD Workshop, Surrey, BC October 23, 2015

learning to speak math picThanks to the teaching staff of GAD Elementary in Surrey, BC, for their warm welcome and heartfelt participation as we delved into problem solving, math tools and strategies, and math processes (especially communication). Changing our teaching practice is not an easy feat, but if we commit to some small changes, practice them regularly, add more changes, practice those regularly, and keep on going in that manner, we can end up making a significant and lasting change that will benefit students greatly.

Remember, “math talk” does not just happen. We have to plan ways to incorporate it into each math lesson. It is a good idea to create math partners so students are responsible to talk to someone about their math thinking. Modeling (letting students hear YOU talk through a demonstration problem) is always a good idea. Responding to students with proper math language/vocabulary (when they have not used such) is helpful. Posting “sentence stems” is a great way to give them an easier start in speaking math. Additionally, try creating a “math words” chart with the students that they can use as an on-going reference in both their speaking and writing (click here to see an example of a “math words” chart.)

As promised, I am adding links from this post to the handouts from today’s session (see bottom of the post) and some that we just talked about.

I would LOVE to hear from any of the GAD staff of how things go in your math lessons in the next weeks. You all listed something that you could begin to do right away in your classrooms, and I hope you will share what you are doing and the effect it is having on the students.

Remember, understanding “lives” in the processes! Reflect on your teaching regularly to see if you are embedding those processes into math classes. It will make a big difference in students’ understanding if they are immersed in the processes!

Mathematically yours,



Download materials here:

100 dot array (teacher size)

100 dot arrays 4 per page

100 dot arrays 6 per page

100 dot arrays 12 per page

break apart number sheet – 2’s

break apart number sheet – 3’s

problem solving assessment rubric

10 frames (teacher size)

10 frames (student size)

10 frames blank mini’s


Ten Things about Teaching Math I Wish I Had Known as a New Teacher September 22, 2015

Filed under: General Math — Focus on Math @ 6:09 pm
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Screen Shot 2015-09-22 at 6.10.24 PM Every teacher has a first year of teaching, one  which often seems overwhelming. Even the next few years can be taxing as one tries to deal with all the planning, the lessons, the assessment, the special needs, the routines, the supplies, the parents, the responsibilities, etc. Whoever says teaching is a piece of cake needs to step into the classroom for a while.

Besides spending years as a classroom teacher, I have been a math coach, a teacher of university math education courses, and a full time district math coach. My math journey has been exciting, but looking back I wish I had known in those early years of teaching some of what I know now.

Here are some thoughts along that line:

  1. My attitude toward mathematics matters. If I don’t like it, the students won’t either. If I love it, they will, too.
  1. Every child can learn math
  1. Concepts need to be developed beginning with concrete materials (manipulatives).
  1. It is important to use many kinds of visual/pictorial representations regularly.
  1. My students need my help to learn how to “talk math” and need time in my lessons to do it.
  1. There really are many ways to solve a problem, not just one “right way” (that was demonstrated by me, the teacher).
  1. It is better to do one problem five ways than five problems one way (Polya).
  1. Students need to develop strategies for solving problems, strategies that they understand and can explain.
  1. Adults use mathematical estimation daily. Kids need to practice it often.
  1. Doing algorithms requires no mathematical understanding, just a knowledge of how to follow rules.

What do you think? Let me know.

Mathematically yours,



10 New Year’s Resolutions for the Math Classroom December 31, 2014

Screen Shot 2014-12-31 at 2.59.05 PM

1. praise effort, not correct answers
2. make sure my students know their intelligence is not fixed: hard work pays off
3. make my classroom a safe place for students to take risks
4. encourage students to take risks
5. give my students rich problems that require they engage in problem solving
6. build a class repertoire of strategies
7. have “thinking tools” handy
8. give regular attention to basic facts (for students who do not know them)
9. give students lots of opportunity to talk to each other when solving problems
10. support math vocabulary learning with a word wall chart

Mathematically yours,



Seeing Dots: NCTM 2014 New Orleans Presentation April 11, 2014

Screen shot 100 dot arrayI am excited to be here in New Orleans at the 2014 NCTM conference. Yesterday was a great day of sessions for me, and I am delighted to be presenting a session in just a couple of hours! “Seeing Dots: Using Arrays to Add, Subtract, Multiply and Divide” will focus on all the different ways the 100 dot array can be used to help students visualize and represent numbers — something which leads to a deeper understanding of numbers.

I am posting the handout from the workshop as well as links to 100 dot arrays is the different sizes.

I hope you try using the 100 dot array in your elementary classroom!

Download the conference handout here.

Download a 100 dot large array here.

Download 4 arrays on a page here.

Download 6 arrays on a page here.

Download 12 arrays on a page here.

Mathematically yours,



A Thought for Today April 2, 2014

Screen shot 2014-04-02 at 8.43.24 AM“A typical classroom narrows our thinking strategies and answer options. The teacher insisting on a ‘right answer’ is NOT healthy for growing a smart, adaptive brain. Good quality education education encourages the exploration of alternative thinking, multiple answers, and creative insights.”Eric Jensen

What kind of classroom do you have?

Mathematically yours,



Student Participation: Using Technology to Choose the Next Speaker January 30, 2014

Screen shot 2014-01-30 at 9.57.22 AMI do an extensive amount of problem solving with students, and part of each such lesson is devoted to sharing strategies for solving the problem. As teachers, many of us have looked for ways to give “equal opportunity” for all during sharing (which also ensures that no students are “coasting” and never choosing to share an answer, a strategy, or an opinion).

There are some “low-tech” ways to accomplish that, such as to write the name of each student on the end of a popsiscle stick, place all the sticks in a jar or can, and then pull the sticks out of the container one at a time. When a name is called the student is asked to share something.

I have recently learned of an app for iOS devices that can replace the popsiscle stick jar (or any other low-tech method you may be using).

iLeap Pick A Student is a simple app designed specifically to help teachers pick students to help or participate in class. It supports multiple different classes and various options to choose students. Choosing a student randomly will pick any student from the class, and using turn based selection every student will be picked before any student is picked again. It requires the teacher to input the class list (or multiple class lists), and the rest is easy.

Pick a Student is available to download for free on the  iPhone App store.  It can be used on iPhones, iPads, iPods, and other such iOS devices. You can find out more about the app here:

Happy Problem Solving!

Mathematically yours,