Archive for the ‘math’ Category

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

Posted on: June 28th, 2018 by jnovakowski No Comments

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:

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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.

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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):

BC Ministry of Education curriculum redesign information

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)

 

Screen Shot 2018-06-28 at 11.07.23 AMTable 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

Table Talk Math website link

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.

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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.

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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.

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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.

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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 No Comments

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:

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.

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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.

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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.

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BMI_April_2018_textslides

~Janice

Talk With Our Kids About Money 2018

Posted on: May 12th, 2018 by jnovakowski No Comments

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

~Janice

March thinking together: What is computational fluency?

Posted on: May 12th, 2018 by jnovakowski No Comments

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

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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?

~Janice

elementary math focus afternoon 2018

Posted on: May 11th, 2018 by jnovakowski No Comments

On the afternoon of January 26, staffs from twelve elementary schools gathered at Grauer Elementary for our annual Elementary Math Focus Afternoon.

The overview slides (photographs from classrooms not included to reduce file size) from the opening to the afternoon can be found here:

Math_Focus_Opening_2018_textslidesonly

Many school teams brought displays to share how they have been working with BC’s redesigned mathematics curriculum.

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Educators could choose from a variety of Richmond teacher-led sessions to learn about instructional routines and practices that are aligned with the BC redesigned curriculum.

FINAL_Elementary Math Focus Afternoon Jan 26 2018 program

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Handouts from Fred Harwood’s sessions can be downloaded here:

Elem Focus Day Jan 2018 Rich Investigations

2018 Elem Math Focus Visual patterns

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Thanks to Tracy Weeks of the Canadian Federation for Economic Education (CFEE) for coming and sharing information about financial literacy with Richmond educators.

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As educators gathered back in the gym for an end of afternoon prize draw of math resources, they were left with a reminder to consider the mathematical story that is being told in their classrooms and schools. What story do we want our students to tell about their mathematical experience here in our district?

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~Janice

graduation numeracy assessment – January 2018

Posted on: May 11th, 2018 by jnovakowski No Comments

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 

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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.

~Janice

2017-18 primary teachers study group: session 2

Posted on: May 10th, 2018 by jnovakowski No Comments

On December 7, Anne-Marie Fenn hosted our primary teachers study group at Woodward Elementary. We went outside and Anne-Marie shared the vision and plans for their new outdoor learning space.

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As the sun was going down, we played with the elements of light and shadow and considered ways we could include these ideas into our outdoor (or indoor) storytelling experiences, thinking about how these ideas might enhance or add new problems to students’ stories.

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After coming back in to Anne-Marie’s classroom as it started to get dark, teachers shared different outdoor storytelling experiences they had tried with their students.

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Thanks for hosting us Anne-Marie!

~Janice

February thinking together: How can we rehumanize mathematics?

Posted on: March 1st, 2018 by jnovakowski

For February, let’s consider how can we rehumanize mathematics?

I was able to attend and present at the NCTM Regional Conference in Chicago this past November/December.

Words that came up over and over again throughout the conference were: EQUITY, ACCESS, EMPOWERMENT, POWER, AUTHORITY, PRIVILEGE, IDENTITY and AGENCY.

These may not be the words you may initially think of when you think about major themes at a mathematics education conference but there is a definite shift in how the role of mathematics within a society is viewed, and who is being included and what voices are being heard.

The conference opened with a panel of speakers addressing issues of access, equity and empowerment.

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The link to the archived Facebook live video form the opening session of the NCTM Regional Conference in Chicago on November 29 2017 is HERE

Kassia Omohundro Wedekind shared her thoughts on “hands down, speak out” practices, disrupting the traditional practice of having students putting their hands up to respond to questions, which in classrooms often reflects the inequities in society at large. She encourages teachers to create conversation maps of the mathematical discourse in their classrooms and to encourage all students to see themselves as mathematicians and contributors to the discourse.

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Dr. Tyrone Howard discussed the issues of inequity in classrooms with regards to race. He affirmed the importance of context and that students’ issues of identity need to be addressed.

Annie Perkins shared practices from her own secondary classroom that support all her students in seeing themselves as mathematicians. She developed “The Mathematicians Project” with a focus on introducing students to mathematicians that are “not just white dudes”.

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Dr. Rochelle Gutierrez is a well recognized researcher and author in the area of equity in mathematics. Over the last few years, her papers and presentations have focused on the idea of re-humanizing mathematics. Photos of some of her slides provide a beginning glimpse into her work. What stands out for you? What are curious about learning more about?

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Another presentation from Dr. Rochelle Gutierrez that might be of interest and would be great to share with during a pro-d day to open up discussion around equity, access and culturally responsive pedagogies for all students:

NCTM 2016 ShadowCon: Stand up for Students 

Dina Williams closed the opening panel with stories from her classroom and her version of a powerful song –  A Change is Gonna Come.

Change has been a long time coming.

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So to think about…

Do all of your students see themselves as mathematicians?

What mathematicians do you talk about in your class? Do you provide “mirrors and windows” for your students to see themselves in the curriculum and in others?

What types of mathematics do we privilege?

What is culturally responsive pedagogy in mathematics education?

How is mathematics necessary for engaging with ideas of social justice?

How can we broaden our understanding of math to de-center what is typically viewed as “school mathematics”?

How do we create mathematics experiences in our schools that are inclusive for all learners?

~Janice