Focus on Math

Helping children become mathematicians!

SD#71 Workshop August 27, 2019

Filed under: General Math — Focus on Math @ 3:34 pm

I am excited for the opportunity tomorrow to present a primary math workshop here in the Comox Valley. This is the perfect time for professional development for teachers as the new school year is about to begin. We will be looking at four important number relationships that we should help young children develop.

One of those relationships is Whole-Part-Part. I know that others refer to this as Part-Part-Whole, but I rearrange those terms quite deliberately. The emphasis is on the WHOLE being pulled into the parts rather than the parts joining together to make the whole. Is is an important difference. For instance, if children take 8 counters they can pull them apart in a number of ways: 4 and 4, 3 and 5, 5 and 3 (which for them is different!), 1 and 7, 6 and 2, etc. Later on when those students begin to add numbers, it will not be surprising to them that those combinations add to 8 — they will have become familiar with them as they decomposed numbers.

No matter what grade your students are in, decomposing numbers is a great way to build up their number sense!

Mathematically yours,



Lost in Translation September 6, 2017

Filed under: General Math — Focus on Math @ 3:17 pm

Screen Shot 2017-09-06 at 12.11.47 PM.png

What is a student really saying when he or she says, “I hate math!”?

To hear someone make the statement, “I hate math!” is, unfortunately, not uncommon. In fact, it is not restricted just to students, but parents, neighbours, and, yes, even educational colleagues say this, too. But what are people really saying with that declaration? For all my experience I believe that what they really are saying is “I don’t get math.” And of course, when folks do not “get math”, then they are generally not good at it, only increasing and solidifying their dislike.

That means the onus is on those of us who teach math to do so in such a manner that allows learners to truly make sense of numbers. Math is supposed to make sense for everyone! Never allow the words to come out of your mouth, “You don’t have to understand this — just do it like this,”  while showing an algorithm that is meaningless to students. That is how the “not getting math” is perpetrated and we need to stop that now. If you want to stop the “I hate math” mentality, then you must teach math for understanding. Don’t settle for anything less.


Calgary City Teachers’ Convention 2017 Power Up your Problem Solving February 16, 2017

Filed under: General Math,Ideas from Carollee's Workshops — Focus on Math @ 7:59 pm

screen-shot-2017-02-16-at-7-42-50-pmOne of the best ways to begin improving problem solving in your math class is simply this: Just do it! Of course. you can learn some techniques for making that problem solving time more of a success than it would otherwise be. You can teach students some strategies for thinking, and help them to use mathematical tools (which I think of as anything concrete or pictorial that helps students build conceptual understanding), but ultimately problem solving is a skill that students master by engaging in it regularly.

Linda Gojak, past president of the NCTM, talks about using “rich tasks” in math lessons, and she defines a rich task in this way:

— A situation in which an appropriate path to a solution is not readily apparent
— Can be adapted to maintain high cognitive demand while meeting individual needs
— Requires students to do more than remember a fact or reproduce a skill
— Encourages investigations and deep thinking
— Has multiple entry points, solution paths and at times multiple solutions

I encourage you to look at the tasks you are asking students to do in your lessons and see how they stack up against such a criteria list.

For those attending the session tomorrow, I am not able right now to create a link for downloading the handout, but if you email me ( in the next 10 days I will see that you get a copy of it.

Mathematically yours,



Calgary City Teachers’ Convention 2017 Big Ideas for Little People…

Filed under: General Math — Focus on Math @ 7:39 pm

screen-shot-2017-02-16-at-7-16-25-pmWe will be talking about number relationships at this session of the convention tomorrow. Once early learners know their numbers in order, have one-to-one correspondence for counting, and understand that the last number in the counting sequence names the set they are ready to develop some number relationships that will serve as a basis for understanding number relationships in other kinds of number.


Since Dropbox has changed its policies on sharing, I am not able to add a link to download the handout. However, if you email me ( in the next 10 days I will send you the handout.

Mathematically yours,



Beginnings… September 10, 2016

Filed under: General Math — Focus on Math @ 10:45 am

screen-shot-2016-09-10-at-10-26-29-amSchool has just begun for a new year here in British Columbia, and the question for all teachers is this: Do you know where your students are? (I confess this particular way of wording the question comes from a public service commercial from many years ago. It went, “It is eleven o’clock. Do you know where your children are?” Does anyone else remember those announcements?)

My version of the question does not refer to their physical whereabouts, of course, but where they are in their learning. This definitely applies to all subject areas, but, as usual, I am most concerned with teachers knowing the learning levels of their students in math. It is easy to just jump into the textbook or materials for the grade group and not take time to do some initial assessment, but it is far better to take the time for those assessments and learn just which students are behind in particular strands/topics of mathematics. Don’t assume all of your students are on the same level. If a student is behind at the start of the year, it is very hard, even nigh unto impossible, to ever catch up without some intervention.

Find some assessments in your school or make some simple ones of your own, but your year will go better if you take the time to know where your students are.

Mathematically  yours,



“Why am I doing this?” August 25, 2016

Filed under: General Math — Focus on Math @ 6:51 pm
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Screen Shot 2016-08-25 at 6.36.45 PMIt is nearly the beginning of the school year here in BC, Canada. New beginnings are always special with untold opportunities and challenges before us. As a teacher, educational assistant, or parent who is home schooling a child, it is important to keep one question at the forefront and ask it of yourself daily: “Why am I doing this?”

I am particularly interested in this question in reference to math lessons because I think the intent behind a lesson matters greatly. For most of us, in our past experiences in school, the main point of doing anything in math was to get the answer, and usually with the added hope of getting it quickly and efficiently. Full stop. The answer was what was important. Indeed, it was the only thing that was important.

But is producing an answer quickly really enough? Consider some other intentions you might have for a lesson:

  • I want my students to be able to explain how they arrived at the answer.
  • I want my students to be able to explain why the answer they got makes sense.
  • I want my students to see how this particular aspect of mathematics fits into the bigger mathematical picture.
  • I want my students to understand this math concept and be able to explain the concept with concrete materials and/or visual representations.
  • I want my students to understand how this mathematical concept relates to the real world.
  • I want to make sure that all of my students have an opportunity to link this new knowledge with previous math knowledge.

I hope your answer to the question is not, “This is the next lesson in the book,” or “The curriculum mandates that I teach this.” Both of those things may be true, but I urge you to rethink your lesson and focus on an intention that will make a difference for the learning of your students.

Mathematically yours,



BCTF New Teachers’ Conf: Seeing Dots February 27, 2016

100 dot array picI am delighted to be here in Richmond, BC, today presenting at the BCTF’s New Teachers’ Conference. I am doing a similar workshop to what I did at the Calgary City Teachers’ Convention two weeks ago, but it is well worth the repeat in this city!

I cannot say enough how important it is for students to be able to visualize and represent numbers in many forms. This tool, the 100-dot array, offers one tool for students to be able to use regularly and thus internalize the number relationships that can be seen when using it.

As before, I am making the handouts available here for downloading:

I will upload the extra large dot sheet (a quarter portion of the regular sized one) which can be made into a poster-sized array once I am home with access to my scanner. Watch for that in the next few days!

Let me know how things go with your students!

Mathematically yours,