Archive for January, 2015

Learning and the Brain 2015: Supporting Your Child’s Mathematical Thinking

Posted on: January 26th, 2015 by jnovakowski

On Saturday, January 24th I presented a session to about seventy parents at our district’s annual Learning and the Brain conference. I shared information about our BC mathematics curriculum which is publicly accessible to all and is legally mandated for teachers to teach and assess. Many of the parents didn’t realize that the curriculum was actually required and consistent across BC.

Current K-7 Mathematics Curriculum (2007)

Redesigned K-9 Mathematics Framework (draft)

I shared how the curriculum may be enacted in classrooms, with examples from our Richmond classrooms, emphasizing the autonomy teachers have to implement the curriculum in their classrooms. We discussed, and the parents had lots of good questions about the curriculum’s focus on problem-solving, computational fluency and communication of mathematical thinking. We clarified what problem-solving is (not necessarily “traditional word problems”) in that problems might be open-ended and have multiple possible answers (ie. How many ways can you make 72?)  or have multiple ways of coming to a solution. Computational fluency was compared to reading fluency – reading is not just being able to read a list of words, it is creating meaning and understanding the text that is being read. And in mathematics, being computationally fluent does not mean you can answer questions accurately and quickly but that you can work flexibly and fluently with numbers and understand what you are doing. We discussed that we know that students who are able to solve a question such as 48 + 37 in many ways (using number-based strategies) have a greater depth in understanding of both number and operations than a student who relies on one memorized algorithm. The parents who attended this session were very curious about the strategies their students are learning at school, as these were not “thinking” strategies that they had learned during their schooling.

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I also provided some suggestions for ways parents could support their students’ mathematical thinking at home.

Ways to think and talk about math at home:

  • ž Talk about math being useful and enjoyable
  • ž Explain how you use math in your daily life
  • ž Emphasize that computation is just one small part of what mathematics is
  • ž Play math-focused games as a family – Chess, Checkers, Backgammon, Scrabble, Monopoly, Cribbage, card games
  • Highlight how math is used to communicate and make information meaningful – weather, graphs in the newspaper, sports statistics

If your child has math homework…

  • ž Have a basket of tools your child might need, appropriate for the age level (counters, ruler, eraser, calculator, graph paper)
  • ž If you and your child are unsure about the math or the homework, please make sure to ask your child’s teacher
  • ž Interactive Math Glossary

ž Questions and prompts to support your child…

  • —  What do you need to do to get started?
  • —  Have you done a question/problem like this before?
  • —  How is the question/problem like something you have done before? What could you use from that to help you with this?
  • —  Is there another way you could do this?
  • —  What could help you with this? Is there information you need? Where could we find it? Is there a tool you need?
  • Does this make sense to you? Could you explain it to someone else?

As a parent myself, I know that all parents want their children to be successful at school and want to support their children the best they can. This session reminded me of how important the teacher-parent relationship is, as we work together to support student learning.


primary teachers study group: session two

Posted on: January 26th, 2015 by jnovakowski

Our second session began with some sharing. Gillian Partridge shared a project she did with her grades 2&3 students, inspired by the Mix It Up book. The painting on the left is an abstract representation of salad and the one on the right used mixing of colours (focusing on prairie colours as the class is studying Canada) and creating circles and understanding fractions.


Margaret Choinski shared how she used the book What Do You Do With An Idea? to inspire students to create building plans during their study of structures. She has a parent visit the class who is an architect and he explained that the architect is the “idea person” being buildings which was a great connection to the book and the process of creating.

magnificent thingOur new picture book was introduced – The Most Magnificent Thing by local author Ashley Spires. I shared how I used this book with two primary classes at Lee.

We talked about the great messages around habits of mind and dispositions that are highlighted in this story – perseverance, determination, trying something another way, seeing things from different perspectives.

As a science focus for our district this year is Creativity and Innovation, we are very happy that Destination Imagination has donated two copies of this year’s project guide to each of our schools. Even if schools don’t choose to enter into DI’s competitions, the manuals have a wealth of great ideas, including instant challenges, to develop creative thinking in the classroom. We tried out a series of mini-challenges from the book. Each challenge had a specific set of materials to go with it.

#1: Create a device that will move the egg across the table without any team members directly touching the egg.

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#2: Build a bridge between two chairs that will support the weight of the egg.

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#3: Build a tower that will raise the egg above the table as high as possible.

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#4: Tell the life story of the egg non-verbally using gestures, words or drawings.



Each challenge had the constraint of time – 4 minutes. We talked about how that has its pros and cons but creates an urgency that some students need. We also discussed how some students would love the challenge and problem-solving of the building challenges while others would flourish in the final storytelling challenge. We always need to be thinking of creating opportunities for all of our students to shine and be successful.

We also looked at the draft information for the Critical Thinking Competency. Richmond has a long history with critical thinking so for the teachers in our group, the description of critical thinking was not really new information but the idea of the profiles of students will be a new way to assess students’ competency in this area.

IMG_0660We shared some of the resources from the Critical Thinking Consortium (TC2) which has been creating resources for teachers for years.


Thank you to the Blair team for hosting us!


primary inquiry lessons at Lee

Posted on: January 24th, 2015 by jnovakowski

The K-2 primary teachers at Lee Elementary are engaging in a professional collaborative inquiry into inquiry-based teaching and learning practices in their classrooms, with a particular focus on science.

I am spending one day a month at Lee, collaborating with teachers in their classrooms and meeting together over lunch time. In January, we talked about ways to create a tone in the classroom that encourages inquiry. We talked about different ways to think about inquiry-based teaching – structured, guided and open.

The Kindergarten classes are beginning a study of penguins. As we can’t actually have a penguin in the classroom or go outside to observe one, the closest we can get is observing penguins via video. I found the “10 best penguin videos” from Discovery, on site in Antarctica. I turned the audio off intentionally, to focus the students on what they could see  – what the penguins looked like and how they moved. We watched a few short clips and then recorded the students’ observations, interpretations and questions, using the thinking frame of  I see, I think, I wonder.



There were lots of interesting questions that the teachers can continue to take up with their students.

One of the classes enjoyed role-playing the movements of the penguins while the other class did some observational drawings of the penguins. At this age, it is common to get “cartoon” drawings, or copies of drawings the students have seen of penguins. I paused the video on the Smartboard and really tried to draw students attention to the shape of the “real” penguins and what they looked like.


magnificent thing In two grades 1 and 2 classes our focus was on imaginative inquiry and we read the story The Most Magnificent Thing, written by local author Ashley Spires. The story has a great message of perseverance. The main character has a vision and plan to create “the most magnificent thing” but she has some setbacks along the way. In the end, although not perfect, the “thing” she creates is magnificent to her and her friend. We asked the students to think of something everydayish or typical and think about how they could make it magnificent. Some students wanted to draw a plan, like in the story, while others wanted to start creating and making. We didn’t set any materials out but asked students to find things in the classroom. Students chose art materials, lego, blocks and items from the recycling bin. A competency in the redesigned curriculum is creative thinking and this book is ideal for introducing the facets of the competency:

The students were highly engaged and as I walked around talking to them, I came back to the big idea or question of “What makes it magnificent?”



this is a flying flower pot, on a paper airplane


a water bottle holder, created with materials from the recycling bin


an airplane that holds a lot of passengers and has special openings to for parachutists


The grade 2 class is just beginning a science study of magnets. I did a silent demonstration with a magnet and some different materials to spark the students’ interest and focus them on what they were observing, what they thought was happening and what questions they had. We used the I see, I think, I wonder thinking frame again, though this time it was done orally. The classroom teacher recorded the students’ wonder questions. We asked the students to choose a question they were curious about and use magnets and materials (such as tubs of paper clips and materials in the classroom) to investigate their questions. We provided time for students to share their findings and I know the students have lots more questions they want to investigate. They were particularly interested in different shapes of magnets and how the shape affects their magnetism and the students were also curious about which coins and metals are magnetic. I’m curious to see what they have been able to find out!

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Can a magnet attract another magnet?


thinking about mathematical inquiry in grades 2&3

Posted on: January 14th, 2015 by jnovakowski 3 Comments

The Reggio-inspired patterning kit arrived in Michelle Hikida’s grades 2 & 3 class at Diefenbaker Elementary during the first week of January. Michelle is one of our district’s math mentor teachers and she and I were curious about how the materials might be used with the grades 2 & 3 students to enhance and extend their thinking about patterns. We also were wondering what inquiry questions might emerge during students’ investigations with the materials.

We began with a short whole-class discussion around the question, “What is a pattern?” with students sharing some examples and I showed them the materials from the kit. We asked them to continue to investigate the question as they explored the materials.



“1234, 4321, back and forth.”


Asking students to explain their patterns often reveals their mathematical understanding of this concept and gives you information about where to go next with instruction.

“It’s a pattern that gets smaller and smaller and then it goes over again because with a pattern you have to repeat.”


This student creating a decreasing pattern and to solve the problem when she got down to 1 and maybe not being sure what to do at that point, she just started at 5 again. From this discussion, I would want to ask the students to think about: “Do all patterns repeat?” and “What happens to a decreasing pattern when you decrease to 1, 0, etc?”

As Michelle and I expected, questions began to emerge from the students as they worked with the materials and thought about patterns.

“Can you make a pattern with just one colour?”

“Can you make subtracting patterns?”

“I was wondering if I could do a 3D pattern?”

Michelle’s plan is to take each of the students’ questions and begin a lesson with one of them as a way to focus students investigations with the materials and to get to some of the big ideas in patterning through the students’ own inquiry questions. We took photographs of the students’ patterns as they explained them and Michelle thought she might also use these as provocations for the students’ investigations.


“I have 10 different patterns!”



“Most of these are AB patterns.”


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Noticeable differences between the Kindergarten classes that have used these materials and the grades 2&3 students is that the older students are able to synthesize and generalize – seeing the big mathematical ideas in what they are doing as well as that the older students clearly just needed more materials than were in the kit. We had to pull out tubs of math materials from Michelle’s class to satisfy the need for quantity. The students’ patterns were bigger, longer, involved larger quantities of materials and I will be digging into my tubs at home to share some new materials with the students. I don’t see why these materials could also not be used in grades 4&5 classes to explore number and geometric pattern and part of this inquiry process is thinking about how the materials will be used and what the materials can offer for different mathematical concepts and grade levels.