Bridging the Numeracy/Literacy Gaps

Where are you looking for answers?

Changing Curriculum will not change student engagement, student knowledge, student success.

TEACHER Knowing.

 That is what will change results for students.

Teachers who teach students how to think, reason, remember and recall.

Teachers who teach students how to communicate, connect and critically think.

Teachers who “know” mathematics as a way of thinking, reasoning and explaining the world, not as a set of “rules” to memorize or “answers to try to remember.

Teachers who continue to study and evaluate their own practise. Teachers who understand the human brain seeks always to understand.

This Summer… Join the Evolution!!!

University of Lethbridge: K to 3 July, 2017

Hilltop School, Whitecourt: K to 6  July, 2017

WECA, Edmonton: K to 3 only   August, 2017

Grande Prairie, AB: K to 6  August, 2017


They will learn arithmetic faster, more fluently, with confidence, speed and accuracy.


Here’s an article to consider: screen-shot-2016-10-23-at-9-46-26-am



The evolution has begun, WE WILL CHANGE THE WORLD… Join me for SUMMER INSTITUTES 2017…. Multiplication is not repeated ADDITION… It is much, much more and screen-shot-2016-10-11-at-10-39-00-amour KIDS DESERVE TO KNOW “why?” AND “Why DO they have to learn this?” Make the mathematics they learn meaningful in a way that leaves them wanting to LEARN MORE….

LITERACY IS NUMERACY, NUMERACY IS LITERACY and let’s not leave out SCIENCE.  Comprehension, reading and writing skills do not grow in a vacuum. flying frogsWe use the content of math and science in engaging, authentic and challenging explorations and experiments to develop the skills that link them all.

IT IS WELL PAST TIME FOR TEACHING TO EVOLVE OR GO EXTINCT…. THE  world demands it, our kids deserve it… do do bird


JULY 10 to 14:   WHITECOURT, ALBERTA, CANADA      Finding Common Ground: Making the Connections: Literacy, Numeracy, Critical Thinking…. K to 6  Registration is now open



TEACHERS, COACHES, LEADERS who are engaged in change at any grade level… This is the continuing journey. All you need is a mindset not willing to accept the MEDIOCRITY that education contains to MIRE DOWN IN…. and a passion for EXCELLENCE. Every learner deserves to learn…..

Creativity in Mathematics



How do you think about the link between 21st Century Competencies and the learning of mathematics?  The list below sounds suspiciously like the reasons I teach mathematics ergo mathematics is a creative endeavour…. More evidence for why our teaching must EVOLVE or go EXTINCT…. mathematics should make students curious, joyful and excited to discuss, compare and create…..



I would add:

Students composing and decomposing number, space and shape in multiple ways through various mediums.


response to build a number (1)screen-shot-2016-10-01-at-11-12-18-amScreen Shot 2016-09-03 at 7.44.46 PMscreen-shot-2016-10-01-at-11-17-37-am




Parent letters

I do not and will not support DreamBox or any other on line platform for teaching and learning mathematics but this is one of the components that we really really need to learn from…. Christopher writes a great blog, thanks

Overthinking my teaching

Here is an email that a friend of mine—father of a first grader in the Minneapolis Public Schools, and math-teacher-on-parental-leave—received from DreamBox, an “adaptive learning platform” for K—8 math.

Congratulations! [Child] successfully completed a group of DreamBox Learning lessons.

Are you familiar with the concept of compensation? This is a strategy that can be used to make addition problems “friendlier”. To use it, just subtract a “bit” from one number and add that same “bit” to the other to create two new numbers that are easier to add mentally.

[Child] learned this strategy by completing a series of lessons using the special DreamBox tool, Compensation BucketsTM. For example, when shown the problem 29 + 64, [Child] turned it into 30 + 63. Towards the end of this unit, [Child] was adding 3-digit numbers with sums up to 200!

On the Run: Friendly Numbers

Take turns supplying two numbers to add. The other player has…

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Teaching math just as procedures….

This is how too many students respond when we ask them to create their own problems. No understanding, no knowledge and no confidence.Grade 4 student reflection

This is Grade 4… Where will this student be by Grade 6? The research says we never fill the gaps… I say because we still refuse to attend to what we know now to be true: VISUAL, SPATIAL, TEMPORAL REASONING matters….. especially in math. The numbers make sense when you learn to build them, compare them and then image them as related parts and wholes….

If this student had imagery for number and words, she would make sense of the problem, then be able to set up a mental image for what has to happen with the numbers. She still might make a computational error but she would at least understand what the problem is actually asking her to figure out. I cover this in Thinking 101, place value 101…. book a session, workshop or private tutoring session… You will be amazed at how quickly we can turn this student ON, by engaging her in the learning.

I will be all over the province this year, join me for a day of learning…..





So what did you see in math class today?

fixed my spleling (ha,ha)

Thinking 101

Teach kids to think & reason, then teach “math” or “science” or “socials” or..


So here’s my point folks. We present math ideas with a perspective that pushes students’ focus to the wrong place in the picture or in the manipulative. Then we say see that didn’t work and go back to telling them what to think. Instead, I want you to get rid of “fill in the blank math sheets.” Start giving students fully finished equations and have them learn to read, demonstrate and compare them. What can you change and not affect the outcome.

 3 + 6 = 9Screen Shot 2016-08-04 at 11.13.23 AM is true. No argument.

Now look at my collection of 9 and tell me what else is true?

What happens if you move the collection around? Knowing 9 is the answer is not the same knowledge as “knowing” 9.  Think about it. We have to do the right job in…

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Spatial Reasoners know number…

What is this grade one telling me about his knowledge of number?

More for qd

Flash Math is a term I use for the exercises I do with students to support the development Screen Shot 2016-08-04 at 11.13.23 AMof automatic recall with quantity.

Subitizing, conserving number, developing imagery for commutative property, inverse operations, associative property, making sense of one more, one less, hierarchical inclusion are put a few of the concepts that can be developed with flashmath tasks.  In the early stages I use dot collections and ChunkitZ.




Students look for 3 seconds, then the image is covered and students are asked to recall the image in their mind. Another 3 second look, cover,  recall in their mind. On the last 3 second some students are noting a different way to confirm how many, while others are finally sure they know what they saw. There are 2 goals on flashmath: how many in the set, what parts are related to make the set. So some students say I saw 5 and 3 while others say I saw 8.


dot collection 4The intent is not to match my arrangement,the intent is to know how many you saw and why you are sure of the total without counting. So this boy drew an arrangement he liked better for 8, circled 5 to tell me he saw the five and the three and knew it was 8.




Dot Coll 5

This young man asked me if he could use pictures numbers and words to explain what he saw, then proceeded to show all 3 on each collection.

What collection do you think this boy saw?spatial quickdraw



Did you note his turned down corner?

Here’s another Grade one spatial reasoner… How do  teachers recognize, capture and build on spatial reasoning??

another QD




When he saw what everyone around him was drawing he changed it to this,Screen Shot 2016-08-04 at 10.25.04 AM











What happens with these students if we do not?

Spatial Reasoners?

response to build a number (1)IMG_0369When students use the materials at hand as thinking tools they demonstrate how they are making sense and constructing meaning. Both these students were quite clear how to explain the number they were dealing with and both had no trouble explaining overall how many tens are in their number. 551 has 55 tens, but 50 of them are packed into hundreds. So you can also say 5 hundreds.


This student drew it first, then separated out the pieces in the second part of the drawing to be sure I understood 294 is composed of 2 hundreds, 9 tens ten less than a hundred, so easy to draw) and 4 ones. Again this student had no trouble explaining there are 29 tens in this 3 digit number. 



The struggles I see for students when it comes to place value are all built around a lack of imagery due to lack of experience with the BUILD. We must take time to allow students to build the units, right from the 10 to the 10 000, then backwards to the thousandth.  When we do, the pay-offs are immense. Students understand the positions are based on a proportional growth change. They learn to think before they calculate. They make sense of the “zeroes” and are not forced to “line up” the digits, when they add.

You cannot learn this BUILD on a computer. You have to experience first hand with concrete materials. Every classroom Grade 1, 2 and 3 needs to be equipped with snap cubes ( I like “unifix”). Enough for every student to build to the thousand. Not “base ten” blocks. Snap cubes… Base ten blocks should only come out once students have demonstrated they can be flexible with the units…

When students are challenged to visualize, imagine and then build with snap cubes and paper models they experience how numbers are related and the power of trusting units. The experiences support their understandings of magnitude, density, direction, proportional growth.  Linear, vs area, vs volume. Making one thousand with strips of ten is incredibly different than making the thousand with squares of one hundred. And the thousand cube is impossible with a flat model.

Thousand on wall area

This picture shows the thousand being constructed 3 different ways. Most adults are astounded to see the difference with the linear thousand. The picture only captured to the first 300.





Mystery Bag numbersThis is only one hundred in blocks, can you imagine the length for 1000?

Spatial skills and spatial reasoning engage students in the learning. Flexible thinking, mental fluency, confidence, risk taking, these are the skills that student’s develop. If you want students to build and apply common sense, to develop a foundation of practical math skills engage them spatially. 

Learn to remember? Remember to learn?




Green manI hear adults says kids do not “know” or “remember” or “recall” but I wonder when we actually actively engage in teaching them how to learn, how to know they are learning, and how to remember what they supposedly learned. Do you agree with the statement below?


Dr. Barbara Oakley, A Mind for Numbers, “unless you can prove that the material is moving into your brain by recalling the main ideas without looking at the page: you are not learning.”


Active engagement in your own learning. The teacher’s role is to make sure kids know they are learning … sometimes it is just the exercise of learning itself. So you engage students by having them tell you how they are going to accomplish “learning this”. Make it a challenge, a puzzle to solve… you will be amazed at the difference in attitude and ability….


What is this girl telling me about the task I gave her? About her current knowledge, ability to learn, preferences for tasks, tools and contexts that support learning? About her knowledge of herself as a learner? Maddie 7


And more important what am I going to do as a teacher to prompt more learning and more self awareness for this student? How do I keep her engaged in her own learning?