## November thinking together: develop mental math strategies

Posted on: December 2nd, 2018 by jnovakowski

Develop, demonstrate and apply mental math strategies

is the focus of one of the Reasoning and Analyzing curricular competencies from grades K-9. For K-5 the focus is on developing mental math strategies as a means to developing fluent and flexible thinking with numbers. In grades 6-9 the focus is on demonstrating and applying these whole number strategies to new number contexts.

As is the case with all the mathematics curricular competencies, the learning standard is the same for K-5 and then continues for grades 6-9. Grades K-5 focus on the development of mental math strategies while grades 6-9 focus on the application of mental math strategies. The grade level-ness is enacted when the curricular content and curricular competency are connected.

So for example, in grades 6-9, the competency using mental math strategies with whole numbers is applied to decimals in grade 6, integers in grade 7, fractions in grade 8 and rational numbers in grade 9 and it is this intersection of curricular content and competency that is assessed.

The suggested mental math strategies are listed in the elaborations for the curricular content for each grade. Elaborations are suggestions and support for instructional decision-making and are not meant to be used as a requirement or an assessment checklist. Mental math strategies are strategies that are intended for students to be able to do mentally. Computational fluency involves  flexible strategy use – both mentally and recorded with paper/pencil, whiteboards, etc. The strategies are transferable to working with larger numbers or to different types of numbers such as fractions and integers. Students may be introduced to the strategies by their peers during a number talk or during an instructional task. When strategies are introduced, specific mathematical language and visual scaffolds such as ten frames or number lines are often used. Some strategies may need to be practiced in different ways before students are able to use them mentally in flexible ways, and choose strategies that make sense for the numbers they are working with. As an example, the following are the computational strategies suggested in the content elaborations for grade 2:

In our 2007  curriculum (WNCP) there was a clear definition of what Mental Math is (in the 2007 iteration of our curriculum, it was named as a mathematical process). “Mental mathematics is a combination of cognitive strategies that enhance flexible thinking and number sense. Mental mathematics enables students to determine answers without paper and pencil. It improves computational fluency by developing efficiency, accuracy, and flexibility.”

Goals of developing fluency with mental mathematics include:

• developing confidence in doing mathematics
• being liberated from calculator dependence
• becoming more flexible thinkers
• be more able to use multiple approaches when problem solving

(Rubenstein, 2001)

Strategies develop over time and complement each other. Examples of mental math strategies drawn from the elaborations in our BC curriculum framework include:

• counting on
• making ten
• decomposing (to make tens/hundreds, by place value)
• double and related doubles (doubles plus one, etc)
• bridging over tens (transferable to hundreds, thousands etc)
• compensating
• adding to find the difference
• commutative, associative and distributive principles
• annexing zeroes
• halving and doubling

Different visual tools can be used to support students’ development of mental math strategies such as ten frames, hundred grids (numbered and blank) and open number lines.

Teachers in Richmond have been developing their own understanding of mental math strategies through Number Talks over the last several years and I believe it is the most used instructional routine in our K-7 classrooms.

The following is a record of some of the number talk experience in Richmond classrooms.

SD38 Number Talks panel 2016

Carrie Bourne and I have started creating a math video series for Richmond educators that our available on our district portal. The series is called Doing the Math Together and the videos are intended support teachers with their understanding of mental math strategies and how they might record students’ strategies during number talks. For example, there are videos in both English and French on the importance of the “making ten” strategy.

They are located in the district portal on the Mathematics page, under the blue tile titled Doing the Math Together Video Series.

Professional resources to support the development of mental math strategies through the development of number talks include:

So what does it mean to be proficient with mental mathematics?

As we begin to work with the new proficiency scale across BC, we need to consider what it means to be proficient with developing, demonstrating or applying mental mathematics in relation to the grade level curricular content. As more teachers across the provinces the the scale, we will have examples of student proficiency that demonstrates initial, partial, complete and sophisticated understanding of the concepts and competencies involved. For example, a grade 2 student at the end of the year would be considered proficient in adding two-digit numbers mentally if they were able to be efficient, accurate and flexible when using two or more different mental math strategies such as decomposing or compensating.

Some questions to consider as you plan for learning opportunities to develop the competency of using mental math strategies:

What strategies or knowledge do students already have about mental mathematics? What opportunities do students have to show and share what they know?

How can we encourage students to be metacognitive when using mental mathematics rather than just applying procedures? How can we develop the concept of efficiency and support students in choosing strategies that are a good fit for the numbers provided?

How can we help students understand the purpose and usefulness of developing mental math strategies?

What opportunities are we creating for students to use mental mathematics across other disciplines such as science or ADST?

~Janice

References

Mental Mathematics beyond the Middle School (2001) by Rheta N. Rubenstein

Five Keys for Teaching Mental Math (2015) by James R. Olsen

## October thinking together: estimating reasonably

Posted on: October 31st, 2018 by jnovakowski

Estimate reasonably” is one of the mathematical curricular competencies under Reasoning and Analyzing, the first strand of curricular competencies. The curricular competency of being able to estimate reasonably is a learning standard at every grade level from K-12. Because the curricular competencies in mathematics are not grade specific, they need to be connected to curricular content to be assessed and evaluated at grade level. For example, estimating reasonably:

• at Kindergarten could be estimating within quantities to 10,
• at grade 4 it could be computational estimation when adding and subtracting numbers to 10 000 or estimating the order of fractions along a number line using benchmarks
• at grade 8 it could be estimating answers when calculating with fractions, estimating the surface area and volume of regular solids or estimating best buys when using coupons (financial literacy)

Curricular competencies to connect to many areas of curricular content but not all. When planning mathematical learning experiences, it is important to consider what competencies complement the content. For example, there are connections to estimating working with number concepts such as quantities, fractions and percentages as well as computational estimation, financial literacy and measurement.

Another consideration is that because this curricular competencies is the same essentially from K-12, it can be used as an access point for all students when planning for multi-age or cross-grade classes, developing IEPs and looking at class profiles.

What does it mean to be able to estimate reasonably?

As students begin their development of competency in estimation, they are comparing quantities as being more than or less than a known quantity. This further develops in using a referent for estimating such as if you know a handful of cubes is 10 cubes, you can use this information for estimating the total quantity of cubes in a jar. Likewise, a personal referent of knowing the size of your step that is about one metre long can help you to estimate distances. As students develop a strong sense of number, they are able to estimate within a reasonable range, knowing which numbers are too high and too low. As students become more competent with estimation and knowledgeable about quantity and other math concepts they are able to apply more abstract estimation strategies such as approximation and rounding.

How can we assess a student’s competence in estimating reasonably?

The Lower Mainland Mathematics Contacts network began to develop assessment tools to use with students to assess the curricular competencies. A draft of the estimating tool is here and teachers might find it a helpful starting place in thinking about how estimation develops along a continuum and the types of  “I can” statements that can be used with students for self-assessment:

Estimating Ideas – LMMC DRAFT 2016

This assessment tool is still in draft form as we put this project on hold while the Ministry was developing a classroom assessment framework. General information about the classroom assessment framework, developed in collaboration with teachers, can be found HERE and the information specific to mathematics can be found HERE. The mathematics classroom assessment framework includes criteria categories and descriptors as well as examples from across grade levels. The Ministry is now using a four-point proficiency scale to provide descriptive feedback to where students are in their development.

Some resources to support competency development in estimation:

Andrew Stadel curates a website called Estimation 180 that is full of estimation tasks with a photograph as a starting point. Students are asked to consider what number would be too low and then which would be too high to develop their reasoning around what a reasonable range would be.

Many “three-act tasks” involve an element of element. Both Graham Fletcher and Dan Meyer have archived videos and examples of three-act tasks.

For our BCAMT Reggio-Inspired Mathematics project, we have create a pedagogical content knowledge four-pager about estimating. You can download it here:

estimating-final

Two favourite picture books that focus on estimation, with a focus on using visual referents are Great Estimations and Greater Estimations by Bruce Goldstone.

Other picture books to connect to estimation:

How Many Seeds in a Pumpkin? by Margaret McNamara

Counting on Frank by Rod Clement

Betcha! by Stuart J. Murphy

Some questions to consider as you plan for learning opportunities to develop the competency of estimating reasonably:

Do students understand what it means to estimate, that there is reasoning involved?

How can we connect the curricular competencies of estimating and visualizing? Are students scanning quantities and using visual referents? How can we encourage students to explain their strategies and make what they are doing in their mind visible?

What opportunities can we create for students to make adjustments to their original estimates based on new information? Are they making meaning of the situation?

What opportunities are we creating for students to think about estimation across math content areas – number, quantity, measurement, financial literacy and other areas in context?

~Janice

## September thinking together: mathematics curricular competencies

Posted on: September 28th, 2018 by jnovakowski

For the 2018-19 school year, the “thinking together” series of blog posts will focus on the curricular competencies in the mathematics curriculum.  The “thinking together” series is meant to support professional learning and provoke discussion and thinking. This month will provide an overview of the curricular competenecies and then each month we will zoom in and focus on one curricular competency and examine connections to K-12 curricular content, possible learning experiences and assessment.

The curricular competencies are the “do” part of the know-do-understand (KDU) model of learning from BC’s redesigned curriculum.

The curricular competencies are intended to reflect the discipline of mathematics and highlight the practices, processes and competencies of mathematicians such as justifying, estimating, visualizing and explaining

The curricular competencies are connected the the Core Competencies of Communication, Thinking  and Personal & Social. More information about the Core Competencies can be found HERE.

The curricular competencies along with the curricular content comprise the legally mandated part of the curriculum, now called learning standards. This means these competencies are required to be taught, assessed and learning achievement for these competencies is communicated to students and parents.

Something unique about the mathematics curricular competencies is that they are essentially the same from K-12. K-5 competencies are exactly the same with some slight additions in grades 6-9 and then building on what was created in K-9 for the grades 10-12 courses. Because they are the same at each grade level, to be assessed at “grade level” they need to be connected to curricular content. For example, one of the curricular competencies is “estimate reasonably” – for Kindergarten that will mean with quantities to 10, for grade 4 that could mean for quantities to 10 000 or for the measurement of perimeter using standard units and for grade 8 estimating reasonably could be practiced when operating with fractions or considering best buys when learning about financial literacy.

The new classroom assessment framework developed by BC teachers and the Ministry of Education focuses on assessing curricular competencies and can be found HERE.  A document outlining criteria categories, criteria and sample applications specific to K-9 Mathematics can be found HERE. The new four-point proficiency scale provides language to support teachers and students as they engage in classroom assessment.

As we are begin a new school year and are thinking about year plans and overviews we might consider the following questions:

• What opportunities do students have to learn about what it means to be a mathematician and what mathematicians do?
• What opportunities can be created over the school year for students to name, be aware of, practice, develop and reflect on the core and curricular competencies in mathematics?
• How can we make the core competencies and curricular competencies in mathematics visible in our classrooms and schools?
• As we are planning for instruction and assessment, how are we being intentional about weaving together both curricular competencies and content? What curricular content areas complement and are linking to specific curricular competencies?

~Janice

## number glass gems

Posted on: September 18th, 2018 by jnovakowski

One of the elements of The Studio at Grauer that teachers often notice is the collection of numerals we have in baskets and trays on our shelves. I have collected these over the years and find them in craft and scrapbooking stores, thrift stores, Habitat for Humanity ReStore, and Urban Source on Main Street in Vancouver. I am always on the lookout for numerals. Students use them in their play and investigations, ordering them, using them to label/represent their collections or sets of materials or to use as purposeful numbers in their creations (addresses, phone numbers, parts of a story, etc).

Just to clarify some terms…

Digit – A digit is a single symbol used to make numerals. 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the ten digits we use in our number system to make numerals.

Numeral – A numeral is a symbol that stands for a number.

Number – A number is a count or measurement that represents an idea in our mind about a quantity.    Numerals are often used to represent a number.

It is how these materials are used that leads to them becoming called numbers – they are used to connect meaning to the symbols by matching the symbol to a set or quantity or are put in order/sequence which gives meaning to the symbols. They can also be used to represent the number in an expression or equation.

I chose to make my most recent set of glass gems using the digits 0-9. This way students can put them together to create different numerals/numbers to label their representations/sets/quantities.

Materials needed: large glass gems (found at Michael’s and some dollar stores), foam paintbrush, Mod Podge and number stickers or cutouts

Instructions: Using the flat side of the glass gem, apply a light coat of Mod Podge and lay a numeral upside down, centred on the back of the gem. Press down and smooth surface so that the numeral adheres and there are not air bubbles between the surfaces. Let dry for a couple of minutes and then apply a coat of Mod Lodge to the entire surface of the flat side of the glass gem. Let dry for 20-30 minutes and then apply a second coat. Let dry and then they are ready to be used.

We have also created materials similar to this by adhering stickers to tree cookies/slices or to smooth stones. It’s just handy to have a collection of these and students find all sorts of ways to use them.

~Janice

## making truchet tiles

Posted on: September 18th, 2018 by jnovakowski

What are truchet tiles?

Truchet tiles are square tiles cut across the diagonal into two triangles of contrasting colours.

In 1704, Sebastien Truchet considered all possible patterns formed by tilings of right triangles oriented at the four corners of a square. The tiles create patterns in grids of tiles. Since the original version was investigated, other variations have been created.

Once again, I have been inspired by Christopher Danielson and his lovely math materials. His version of truchet tiles can be found HERE.

I have made a simple version for an upcoming make and take afternoon with teachers in The Studio. You need square tiles, paint and a brush. I painted the tops and edges of the tiles in colour first. You could leave them naturally coloured. Once the paint was dry, I used a piece of tape to “mask” off one side, lining up the tape from corner to corner along the diagonal. Press firmly along the edge of the tape so you don’t get any paint seepage under the tape. Paint the exposed side of the tile black or other high contrasting colour. Depending on your paint, you might need a second coat. I left the tape on as it was handy to hold onto as I turned the tile over to paint the back (once the first side is dry). I chose to paint the second side all black but you could also leave it natural, or paint it a colour or paint it the same way you painted the first side. Let completely dry and then carefully peel off the tape.

Note: I used a “value” paint for this project and I didn’t like the feel of the tiles in my hands so I added a coat of Mod Podge and they are much smoother to the touch now.

Each tile has four orientations:

Combining two tiles together and then using these in different orientations allows for many different patterns and designs. How many permutations of two tile combinations are there? ( a great spatial reasoning investigation)

These tiles are great for thinking about spatial reasoning, orientation and transformation as well as composing and decomposing shapes.

Finding lots of square tiles in bulk isn’t easy. I ended up ordering 400 from a craftsperson on etsy. I used 1-inch tiles but you could make them in any size. I think you need at least 25 (5×5 grid) to create patterns using the different shape compositions you can create. They could also easily be made with construction paper or cardstock but the wood is more durable and I am not a fan of laminating (reasoning – make the materials more slippery and hard to tessellate and takes hundreds of years to decompose).

I am looking forward to seeing how students across the grades in Richmond investigate and create with these tiles.

~Janice

## the new playground at Grauer: where’s the math?

Posted on: September 18th, 2018 by jnovakowski 1 Comment

Last year the families, staff and community fundraised for a new playground for Grauer Elementary. Grauer is a small school with only five, six or seven divisions (depending on the year) and it is hard work for a small school to raise \$60 000! It was very exciting when the school reached their goal and is such a good example of an authentic numeracy experience for students to think about. In the BC curriculum, numeracy is defined as an application of mathematics to solve or interpret an issue or problem in context.

Last Saturday, I joined staff, parents and community members coming together to install the playground (self-installation with staff support from the playground company saves thousands of dollars). As Ms Partidge and I helped to read the specifications for the installation of one of the fire poles, we commented to a couple of parents around us how much mathematics was involved in the process.

I shared some of the photos from the installation day with the two grades 1 & 2 classes. All of these students had been to The Studio last year with me and had spent some times exploring the idea of “what is math?” so I framed this investigation as “where is the math?” I knew for some students this would create some dissonance as even young children can sometimes already have a very narrow view of what mathematics is and think that it is about counting, numbers and “plussing”. Part of this investigation was to disrupt this thinking. Of course counting, numbers and arithmetic operations are important content areas of mathematics, but they are not the only content. This investigation was one avenue to create meaning for learning mathematics, having students make connections to math beyond the walls of the classroom. The students came up with some initial ideas and we will continue to add to our thinking over the next couple of weeks.

The students were invited to design and create playgrounds and to consider where, when and how mathematics would be applied/used. One group of students followed the kit diagrams to create a Playmobil playground set – there was lots of math talk during that collaboration! Some students chose to draw and paint a playground from their imagination and some built playgrounds with blocks and loose parts, including a playground for animals.

After our first time together, I noticed the students were very interested in the photographs of adults using the levels and measuring tapes so I ordered some (not toy) tools to add to the construction area of The Studio. It was great to watch the students use these tools in authentic ways.

One of the classes had gone outside to look closely at the playground twice, creating detailed labelled diagrams or maps of the playground.

We extended this experience in The Studio by asking the students to create “math maps” indicating “where’s the math?” on recordings of their playground creations.

And what are are we assessing in terms of mathematics? These types of investigations and explorations lend themselves to informal formative assessment and gives us a sense of mathematical language the students have and where students are along a learning trajectory around different concepts and skills such as spatial reasoning, comparison of size and quantities and measuring. This type of assessment, that focuses on observing and listening to the students’ play and math talk is so important at this time of year and informs our instructional plans and focus for the fall.

When students engage in this type of learning through materials we make their learning visible through a sharing session at the end of our time together and capturing photographs, videos and students’ thinking so that we can revisit and reflect on the experiences, make connections to new learning experiences and consider questions for further investigation. The following are examples of documentation panels that we create to post in The Studio to help make our learning visible.

Grauer_playground1_Sept2018 copy

Grauer_playground2_Sept2018

I’m looking forward to seeing where the students take us next on this investigation.

~Janice

## June thinking together: How can we work together with families to support our students’ mathematical development?

Posted on: June 28th, 2018 by jnovakowski

Last June I attended the Cognitively Guided Instruction conference in Seattle and one of the things that really resonated with me was the number of projects around mathematics that schools were working on that had a focus on involving families and connecting to the community. We were asked to commit to “one thing” to connect our learning at the conference to our work in our contexts for the following school year and my one thing was:

Before the CGI conference, I might have used the term parent involvement instead of family engagement but the conference nudged my thinking – there are many people taking care of our students – parents, grandparents, siblings, legal guardians and caregivers. The term “family” is more inclusive and the term engagement rather than involvement is more representative of what our hopes and goals are.

Over the past few years, I have done several event for school and district PACs as well as our annual Learning and the Brain conference for parents. This year I did two outreach interactive sessions about mathematics for parents through the Richmond Public Library, coordinated by our Settlement Workers in Schools program.

Increasing parent engagement and making mathematics education visible in our community area areas and goals that I am going to continue to focus on. Suggestions welcome!

Many parents, guardians and caregivers of our students have questions about the “new” mathematics curriculum and my short response is usually: the content has not changed significantly and new content has been added in the area of financial literacy and more learning standards and big ideas around computational fluency have been added. Those changes were part of the feedback cycle in the curriculum redesign. Parents had many opportunities to provide feedback through stakeholder meetings across the province (and within our district) as well as being able to provide online feedback. Beyond the core content (knowledge) at each grade level, other elements that are part of the curriculum redesign, and not just in mathematics, is the focus on core competencies, curricular competencies, weaving in Indigenous knowledge and perspectives and considering a range of instructional approaches to be inclusive of the diverse learners in our classrooms.

The BC Ministry of Education has provided information for parents on the curriculum redesign on their website and this information is available in four languages (tabs at top of website):

Beginning this year (not including 2018 grade 12 students) students will need to pass a Graduation Numeracy Assessment as part of their graduation requirements. We need to help communicate to our parent community that this is not a “mathematics” exam and is not connected to a specific mathematics grade or course.  The Ministry has provided information for parents on the Graduation Numeracy assessment that you can share with them:

Graduation Numeracy Assessment information for parents

We had one pages of the Ministry document translated into Chinese for our parent community for those schools that were part of the gradual implementation of the assessment in January:

SD38_GNA Information for Parents (Chinese page 1)

Table Talk Math is a website and book created by John Stevens. In it he shares ways parents can engage in talking about mathematics with their children at home. He has a weekly newsletter  that parents and teachers can subscribe to on his website. John’s five-minute Ignite talk is shared on his site. At the end of his talk (with teachers as the intended audience), he suggests four calls to action for educators to work in partnership with their students’ parents:

• celebrate parent involvement
• show your students’ parents that you care
• show parents how they can help
• help parents help their kids be amazing

And here is a collection of suggestions for parents that I have shared at various district and public events:

SD38_Supporting_Mathematics_for_Parents_2018

I am in the process of drafting a parent information bulletin for our school district, which will be translated into multiple languages once it is finalized. Look for it this September!

As we think about ways to engage families in mathematics, here are some questions to consider…

• What do your students and their families think about mathematics? What are their feelings and beliefs?
• How are we sharing information about the mathematics curriculum with families?
• Do your students and their families see themselves represented in mathematical learning experiences at school?
• How do you make use of your families’ cultural assets in our mathematics learning experiences in schools?
• How are we sharing and communicating our students’ mathematical thinking and learning to families?
• How do we create reciprocal learning opportunities in mathematics between families and the school context?
• What opportunities do we create to connect mathematical learning to our local community?
• How are families engaged with mathematics learning in our classrooms and schools?

~Janice

## school-based collaborative professional inquiry projects

Posted on: June 14th, 2018 by jnovakowski 1 Comment

One of the professional learning structures used in our district is collaborative professional inquiry based in schools. I collaborate with school teams that come together with a focused area of professional inquiry in the area of mathematical teaching and learning. I support the school teams through developing curricular and pedagogical content knowledge through mini-sessions and providing resources as well as planning together and engaging in adapted lesson study including time each visit to debrief and plan next steps. This year, all school teams involved included at least one teacher in the district’s mentoring program as we focus on supporting teachers new to our district and to the profession.

General Currie (term 1)

The three kindergarten teachers at Currie (two new to teaching K) chose to focus on core concepts and inclusive instructional routines related to these concepts. Inclusive routines are those that provide access points for all students in the class and are used regularly over time to develop mathematical thinking and ideas. The routines focus on developing the mathematical curricular competencies and content in our curriculum. Over several sessions in the kindergarten classrooms we engaged in routines such as counting collections, clothesline, decomposing and number provocations. The three teachers and their classes followed up this project with a field trip to The Studio at Grauer.

Garden City (terms 1 & 2)

Three small groups of kindergarten through Grade 5 teachers came together with a combined focus of “connecting the dots” of the redesigned curriculum – weaving together key elements such as inquiry, teaching and learning through big ideas, new content areas like financial literacy and a focus on First Peoples Principles of Learning and connecting math to place. I spent several sessions in classrooms co-teaching with teachers and having lunch hour meetings.

Tomsett (term 2)

A large group of kindergarten through grade 6 teachers chose to focus on supporting student learning of number concepts through a guided math approach. This approach to teaching math was new to all of the teachers involved. A guided math session (often done once or twice a week) has a focus of a core math concept as the focus. A whole group mini-lesson or routine begins the session followed by opportunities for students to practice in small groups or independently. This practice may involve working with materials, math games, an open task or problem or using an app with visual tools that support mathematical understanding. The teachers works with small groups of 2-5 students round this core math concept for about 5-8 minutes, designing and structuring a mini-lesson for them at their “just right” math level of understanding. The is an opportunity for the teacher to collect assessment evidence of students’ understanding. The end of the session involves connecting the dots between the practice opportunities and consolidating students’ thinking through sharing and discourse.

I spent several in-class sessions with student and teachers as well as lunch hour debriefs, sharing and planning with the teachers.  In between my visits, the teachers collaborated and shared resources and ideas amongst themselves. At the end of the term the grades 5&6 teacher reflected on how the project had transformed her teaching and commented that she will never go back to teaching math the way she used to. All of the teachers commented on how much better they knew each of the students’ mathematical understanding through this approach.

Steves (terms 2 &3)

A team of four grades 2-5 teachers chose to focus on structures that support differentiation in mathematics teaching and learning. In-class co-teaching sessions and lunch hour meetings focused on inclusive instructional routines, rich open tasks and providing choice with a lens to addressing the range of learners in each classroom. In the grades 2&3 class routines such as number talks and Which One Doesn’t Belong? and games were introduced and extended through work with materials. In the grades 3&4 and 4&5 classes, some of the structures we focused on were choice – choice of materials and choice of ways to represent thinking. We also used open questions and contextual problems that focused on big ideas and core concepts and considered how these tasks provided access points for all learners.

I always enjoy being immersed in classrooms and schools, learning together with teachers and students!

~Janice

## 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.

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.

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.

Here is one example of a recording form:

Grauer_Competency_Math_Reflection_May2017

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?

~Janice

## 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 fractiontalks.com – 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.

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.

BMI_October_2017_textslides

BMI_Fractions_2017

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? (wodb.ca) and considered how these routines incorporate questioning, wondering and nurture the curricular competencies in mathematics.

BMI_April_2018_textslides

~Janice