Archive for the ‘mathematics’ Category

April thinking together: How do the core competencies connect with mathematics?

Posted on: June 7th, 2018 by jnovakowski

The Core Competencies are at the centre of BC’s redesigned curriculum and underpin the curricular competencies in each discipline, such as math. An overview video about the Core Competencies can be viewed HERE. Drawing from global education research and through provincial consultation with stakeholder groups, three Core Competencies were identified – Thinking (creative and critical), Communication and Personal & Social (positive personal and cultural identity, personal awareness and responsibility, and social responsibility).

As we develop awareness about the Core Competencies during the school year, we consider the ideas of “notice, name and nurture” – looking for evidence of core competency development or application in our classrooms and schools.

In our district, we have created Core Competency posters in both English and French, overviewing all the core competencies as well as posters specific to one core competency (all available through the district portal). These posters are up in classrooms and schools to create awareness and develop common language around the core competencies.

In The Studio at Grauer, much of the work we do in mathematics has elements of the core competencies involved. In the mathematics curriculum, each of the curricular competencies is linked to one or more of the core competencies. The COMMUNICATION chart in the photograph below is an example of how I make this focus clear to myself, teachers and the students when we work together in The Studio. I often identify a specific curricular competency in our initial gathering meeting, that we are going to focus on together as we work with a mathematical idea. For example, I might say to the students,
“Today as you are thinking about comparing and ordering fractions with materials, practice explaining and justifying your decisions to a partner – that will be our focus when we come back as a whole group at the end of our time together today.” 

Other times, I will ask the students to reflect on their last experience in The Studio and consider what they need to work on around communication, either personally or as a class.

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The following are documents that show the links between the Core Competencies and the Curricular Competencies in Mathematics:

SD38 K-5 Math Connections between Core and Curricular Competencies

SD38 6-9 Math Connections between Core and Curricular Competencies

SD38 K-5 Math Communication

We have woven self-assessment and reflection about the core competencies into our projects and learning together throughout the year. During the last school year, there was a requirement for students to do a “formal” self-assessment to be included in the June report card. For students to authentically self-assess and reflect, they need to be familiar with the language of the core competencies and be able to connect to learning experiences they have had throughout the school year. During the third term last year, the grades 3&4 class from Grauer visiting The Studio weekly to engage in a mathematics project around the work of Coast Salish artist Susan Point. At the end of each session together, we had the students share their learning – what did you learn? how did it go/what did you do? what’s next for your learning/what are you wondering about? Sometimes students turned and talked to someone near them, other times, students shared their learning and thinking to the whole class.

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Every few weeks, we had the students do a written/drawn self-assessment and reflection. We have found that using question prompts to support reflection and considering evidence of learning has been the most authentic and personalized way to have students think about and connect to the core competencies. We developed some recording formats to capture students’ thinking, with the clear intent that students are not expected to “answer” all the questions – that they are they to prompt and provoke reflection and self-assessment. A team of Grauer educators were working together on an Innovation Grant project around creative thinking and growth mindset and we wove these ideas in to some of the self-assessments.

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Here is one example of a recording form:


As we are coming to the end of another school year and are thinking about the student self-assessment of the core competencies component for year-end communication of student learning, we might consider the following questions:

  • What opportunities have students had to experience and develop the core competencies in their mathematics learning?
  • What opportunities over the school year have students had to name and reflect on the core and curricular competencies in mathematics?
  • How have we made the core competencies and curricular competencies in mathematics visible in our classrooms and schools?
  • How have the core and curricular competencies language and ideas been embedded in the mathematical community and discourse in our classrooms and schools?
  • What different ways have students been able to share, reflect on and self-assess their mathematical thinking and learning?


2017-18 big mathematical ideas for grades 3-5

Posted on: May 13th, 2018 by jnovakowski 2 Comments

In its fourth year, a group of grades 3-5 teachers came together three times after school to think about the big mathematical ideas for this grade range, considering the pedagogical content knowledge needed to teach and assess student learning. Our first session of the year on October 18 focused on the number concepts big ideas in our curriculum which at gates 3-5 focus on a deep understanding of fractions.

We began with an image from – a website curated by Canadian math educator Nat Banting. We considered what students needed to understand about fractions to engage with this task and anticipated how are students might respond to the challenge of figuring out what fractional part of the large square is the shaded blue triangle.


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We considered how different materials provided different affordances for thinking about fractions, particularly thinking about different ways to represent fractions – set, area and linear. Some of the text slides from the session and a handout follow.



Unfortunately, I had to cancel our January session due to illness.

We came together again on April 11 and based on feedback from the group, discussed computational fluency and the role of inquiry in learning mathematics. We revisited instructional routines such as Which One Doesn’t Belong? ( and considered how these routines incorporate questioning, wondering and nurture the curricular competencies in mathematics.

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Talk With Our Kids About Money 2018

Posted on: May 12th, 2018 by jnovakowski

As part of a national financial literacy month every April, the Richmond School District participates in Talk With Our Kids About Money Day (TWOKAM) the third Wednesday in April. Financial literacy is a new part of BC’s redesigned mathematics curriculum with a content learning standard at each grade level from K-grade 9.

To raise awareness of the resources available to teacher, local CFEE (Canadian Federation for Economic Education) representative Tracy Weeks shared materials and information at our Elementary Math Focus Afternoon in January.

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In April, an assembly was held at Burnett Secondary with CFEE president Gary Rabbior talking to students about financial literacy.  Tracy Weeks (CFEE) facilitated an information session for parents at Hamilton Elementary on April 9.

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On April 18 – national TWOKAM day – a finale event was held for parents and students at Brighouse Elementary. Student projects from Burnett Secondary were on display and guest speaker Paul Lermitte shared ideas with parents for developing financial literacy with their children at home. Thank you to Brighouse for hosting this well-attended event!

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We hope to continue to grow the idea of “Money Fairs” (think financial literacy fairs like science fairs) in our district as we continue to teach and learn about financial literacy in our classrooms.

TWOKAM video

TWOKAM – CFEE website link


March thinking together: What is computational fluency?

Posted on: May 12th, 2018 by jnovakowski

Computational fluency is defined as having efficient, flexible and accurate methods for computing.

-NCTM, 2000

Computational fluency develops from a strong sense of number.

(BC Math Curriculum, Big Idea, K-9, 2015)


In BC’s redesigned curriculum, computational fluency has been given a heightened emphasis. In mathematics, there are typically four strands of topics/content and in this iteration of our curriculum, a fifth strand – computational fluency –  has been added and this is reflected in the big ideas and curricular competencies and content.

The meta big idea around computational fluency in our BC K-9 Mathematics curriculum is:

Computational fluency develops from a strong sense of number.

There is a big idea for computational fluency at each grade level:

K: One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers.
Grade 1: Addition and subtraction with numbers to 10 can be modelled concretely, pictorially, and symbolically to develop computational fluency.
Grade 2: Development of computational fluency in addition and subtraction with numbers to 100 requires an understanding of place value.
Grade 3: Development of computational fluency in addition, subtraction, multiplication and division of whole numbers requires flexible decomposing and composing.
Grade 4: Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.
Grade 5: Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.
Grade 6: Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals.
Grade 7: Computational fluency and flexibility with numbers extend to operations with integers and decimals.
Grade 8: Computational fluency and flexibility extend to operations with fractions.
Grade 9: Computational fluency and flexibility with numbers extend to operations with rational numbers.

As computational fluency with whole numbers is focused on in the earlier grades, it is expected that students will apply number sense and computational fluency and flexibility to their work with decimal numbers, greater numbers, integers and fractions.

For addition and subtraction and then multiplication and division, students develop computational fluency over three years – beginning with emerging fluency, then developing through proficiency and then moving on to extending fluency with increased flexibility and ability to apply strategies across contexts and content.

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For example, with addition and subtraction:

In Grade 3, the curricular content learning standard is “addition and subtraction facts to 20 (emerging computational fluency)“.

In Grade 4, it is “addition and subtraction facts to 20 (developing computational fluency)”.

And in Grade 5, it is “addition and subtraction facts to 20 (extending computational fluency)”.

It is also important to be aware of what comes before and after these three stages of development. In grades 1 and 2, students are introduced to the concepts of addition and subtraction as well as the related symbolic notation. They begin to practice mental math computational strategies building on their understanding of five and ten and decomposing numbers to work flexibly with addition and subtraction questions. In grades 6&7, students apply computational strategies that they have developed for addition and subtraction facts with greater whole numbers, decimal numbers and integers.

There is a similar progression for multiplication and division facts.

A note about memorizing…memorizing is one form of learning but is not necessarily related to students having computational fluency. Many teachers in our district report that their students have memorized their addition or multiplication facts but need support with thinking flexibly and fluently with numbers. In our BC mathematics curriculum, the expectation is that by the end of Grade 3 for addition and the end of Grade 5 for multiplication,  that most students will be able to recall their facts. In a previous curriculum, recall was defined as being able to compute within three seconds. For some students, there may be instant memory retrieval and for other students they may bring the sum or product to mind through an efficient mental computational strategy or associative retrieval process.

Number Talks are an essential instructional routine in developing strategies, mathematical discourse and creating awareness about computational fluency. Key resources include:

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Number Talks



So some questions to think about…

How would you define computational fluency? What does it look like? sound like?

What do your students need move towards more developed computational fluency?

What do you need to understand more about regarding a continuum of learning and specific strategies related to computational fluency?

What are different ways to develop computational fluency? What instructional routines, games or tasks could we use for practice?

How can we communicate the goals of computational fluency to parents?


graduation numeracy assessment – January 2018

Posted on: May 11th, 2018 by jnovakowski

On January 26, I spent part of my morning at Richmond Secondary working with the whole staff to examine the Graduation Numeracy Assessment – how numeracy is defined, the numeracy processes, example questions and ways to embed numeracy tasks in all courses. Educators worked in cross-disciplinary groups to choose one of the sample questions to work through together, being mindful of how their students might engage with these questions.

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The overview slides from the morning can be found here: GNAoverview_Richmond_January_2018

Detailed information about the BC Graduation Numeracy Assessment can be found through the BC curriculum website. There is a design specifications package, pre-assessment tasks that students/classes can do before the assessment to learn about the numeracy processes, a collaborative learning guide, videos, sample questions, scoring guide and student exemplars as well as information on the background and development of the assessment and information for parents.

link to Graduation Numeracy Assessment information 


In Richmond, two of our secondary schools (SLSS and Burnett) participated in the gradual roll-out of the writing of the Graduation Numeracy Assessment. Two or three classes from each school participated in the assessment and will receive their results in April. Both schools collected student feedback and the Vice-Principals shared this feedback along with their logistical recommendations at a secondary vice-principals meeting in April.


October thinking together: What is balanced numeracy?

Posted on: October 31st, 2017 by jnovakowski

This year I am going to share a monthly focus as a way for educators in our district (and beyond, of course!) to think together, collaborate and share ideas around K-12 mathematics education. On the list are number sense, estimation, reasoning, spatial awareness…it is a list in progress so suggestions are welcome.

My intentions are to begin each month with a blog post highlighting the focus area in our BC mathematics curriculum and connecting it to the broader field of mathematics education. I plan to share links to websites and resources, share books that I have found helpful and provide examples of mathematical tasks from Richmond classrooms. During each month, I will also tweet out related links, ideas, blog posts and photographs from classrooms.

For October, let’s consider what is balanced numeracy?

I have been fortunate to be a part of a Ministry initiated project drawing together educators from across BC to form the BC Numeracy Network. Our first project together was to consider balanced numeracy within the redesigned mathematics curriculum.

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The group of educators involved in this network began our professional collaborative inquiry together considering the question, What is balanced numeracy? Although we drew on the practices of balanced literacy, we looked to the current research in mathematics education to inform our thinking. In thinking about a balanced numeracy approach, we looked beyond mathematical content and foundations (which needs to remain in the foreground) to also consider the role of the learning environment, instructional and assessment approaches, the habits, dispositions and competencies of the discipline of mathematics, the importance of connection-making and the role of engagement in learning. We considered balance in terms of the day, week, month, term and year as well as what learning opportunities are provided to our students for individual practice and problem-solving, small group work and whole class routines, discourse and mathematical community building.

The BC Numeracy Network has created a website full of linked references and resources to support teachers’ professional learning:

As you think about balanced numeracy, consider…

What do you consider when planning a balanced literacy program in your classroom? What aspects of this might apply to thinking about balanced numeracy?

How are numeracy experiences different from mathematics experiences and how are they connected?

What opportunities can I provide for my students to engage in small group work in mathematics/numeracy? (The North American classroom landscape suggests that most “math time” is either whole class or individual work).

How am I balancing the two components of the BC learning standards in mathematics – curricular competencies and curricular content?

How might providing balanced numeracy experiences for my students extend or enhance their thinking about mathematics?



There are many resources now available to support aspects of balanced numeracy in the classroom. Consider the following professional resources:

Math Workshop by Jennifer Lempp

Guided Math in Action by Dr. Nicki Newton

Guided Math by Laney Sammons

Dr. Peter Liljedahl of SFU has many numeracy tasks available on his website

This part of our website defines numeracy in the BC context and looks at the parallels between balanced literacy and balanced numeracy.