Archive for the ‘provocations’ Category

thinking about fractions

Posted on: June 21st, 2017 by jnovakowski No Comments

One of the foundational concepts in grades 3-5 is an understanding of fractions – some of the questions we investigate with students are:

What is a fraction? What makes a fraction a fraction?

How can we order and compare fractions?

When do we use fractions in our daily life?

What different ways can we represent fractions?

What are equivalent fractions?

In our BC mathematics curriculum, the big idea for grade 3 that we guide students to understand by the end of the school year is that “fractions are a type of number that can represent quantities” – this is a significant concept. I often have discussions with older students who have the conception that fractions have something to do with shapes/geometry, possibly because of the models used in school to represent fractional numbers (think circles/pies/pizzas or rectangles/chocolate bars). An intentional focus is to provide opportunities for students to see and represent fractional amounts using different models – area/region, set and linear. In grade 4, students learn about the relationship between fractional and decimal numbers and in grade 5, consolidate their understanding of fractions by working with equivalent fractions. During these investigations, students may begin to see relationships and connections to whole number operations when working with fractions and decimals. We want students to be able to think flexibly with fractions and decimals, just as they do with whole numbers and think about composing and decomposing, benchmark numbers, etc as they consider addition, subtraction, multiplication and division.

This term I have been thinking a lot about fractions with students and teachers. I visited two classes at Homma and a class at Wowk and hosted classes at The Studio at Grauer to investigate fractions including a grade 4 class from Woodward, the grades 3&4 class from Grauer and the Richmond School Program students from Blundell.

The following are some images sharing our investigations. As you scroll through the images, consider:

What do you notice? What do you wonder?

What instructional routines and structures have we used to support students in their understanding of fractions?

What different materials have been provided to create opportunities to think about fractions?

What conceptions do students reveal in their representations of fractions? What might you ask students? How does this information guide where we go next?

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~Janice

The Studio at Grauer

Posted on: June 11th, 2017 by jnovakowski 2 Comments

The Studio at Grauer came to be based on a need we felt existed in our district – a space to engage in professional learning experiences for teachers as well as for a learning environment for students that could be left  “set up”. My office partner, Marie Thom, and I have been talking about this for the last couple of years. The notion of a “pop-up” classroom emerged and Andrew Ferguson, the principal at Grauer, was approached to see if we could use one of the school’s unused classrooms.

December 16 2018 – Room 102

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Room 102 was being used as a storage room until we began our transformation of it in January 2017. Blending Marie’s background in learning environments and my understanding of mathematics teaching and learning, we developed a space focused on mathematics, filled with inspiring materials in a learning environment designed for learners K-Adult. Our goal was to create a flexible, responsive and inclusive learning environment.

Room 102 – January 10 2017

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January 13 2017

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The learning environment is set up to create opportunities for choice, collaboration, personalized learning and inquiry. More specifically for mathematics, our hope was to broaden understanding of what mathematics is and what the teaching and learning of mathematics can be. Often school mathematics is perceived as “arithmetic” and mathematics is a much broader discipline that this. We wanted students and teachers to see math all around them and be inspired to think about mathematics in different ways – to see mathematical ideas in the materials, in pinecones, in buildings and structures, in images of our community, in art, in stories.

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As we discussed how we were going to use the space, we decided to call it The Studio, inspired the notion of an atelier, a studio space used in the early childhood schools of Reggio Emilia.

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Classes from Grauer, as well as visiting classes on “math field trips” visit The Studio to engage in mathematical inquiry. Marie and I take on the role of atelierista, working with the classroom teacher to facilitate learning experiences through different materials in the space. We have intentionally curated both mathematically structured materials like pattern blocks and Cuisenaire rods alongside materials often known as loose parts such as ribbons, gems, rocks, pinecones, etc. We also have art materials available to the students such as paint, clay, charcoal, yarn and wool so that students can express themselves and think using different languages. Students also have access to various tools to support their investigations such as measuring tapes, protractors, grids and ten frames.

The first class to visit The Studio – the grades 3&4 students from Grauer on January 18 2017

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The learning environment is intentionally flexible with choices in seating and tables available for both students and adults. Interestingly, although we have some chairs available, none of the students using The Studio have used them, preferring instead to stand or sit and lie on the carpet or use pillows. We have observed the flow of movement in the space and intentionally have large open spaces for students to move through. Shelves filled with baskets of materials are open and accessible to students. Students can choose the materials they want to use and take them to where they would like to engage.  We took doors off of some cupboards to create more open shelving. All of the furniture, except for four small Ikea open shelves, was found in school storage rooms and thrift shops.

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Provocations are set up on tables for students (and educators) to inspire mathematical thinking and inquiry. Inspired by one of the students’ interests in optical illusions, the grades 3&4 students from Grauer investigated the mathematics embedded in optical illusions. I gathered materials and tools that I hoped would provoke their thinking about optical illusions and the students also accessed and were inspired by other materials in The Studio.

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As we have more classes through The Studio, we have developed documentation to share in the space. Panels, photographs and photobooks are available for students and educators to engage with, to reflect upon and to inspire new experiences.

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One area of pedagogical intention in The Studio has been on noticing, naming and nurturing the Core Competencies and the Mathematics Curricular Competencies from our BC curriculum framework. A focus has been on both communication and creative thinking in mathematics. We intentionally create opportunities for students to engage in different types of communication and to reflect on how they are doing.

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We have had many groups of educators also visit The Studio. Our District Support Team, educators attending our Playful Inquiry professional learning series and teams from schools in our district. Many BC educators involved with our BCAMT Reggio-Inspired Mathematics project have visited the space as well. We have also had visitors from Manitoba and Sweden! We often focus the visits with the questions – what do you notice? what do you wonder?

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We also have a dedicated professional learning library with the teacher resources we recommend around teaching and learning mathematics, the use of loose parts and the importance of the learning environment.

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We had hoped The Studio would inspire similar learning environments in our district but recognize that many schools do not have access to a dedicated room for a studio space – we hope that teachers will be inspired by elements of The Studio for their own classroom learning environments. What has been exciting for Marie and I is that this little project has had a huge ripple effect at Grauer, in our district, and beyond!

~Janice

 

 

creating spaces for playful inquiry: April 2017

Posted on: May 28th, 2017 by jnovakowski No Comments

For our third session of our Creating Spaces for Playful Inquiry dinner series, Richmond educators came together at Grauer Elementary to share and learn together. This year at our sessions we have focused on broad themes or big ideas that cut across curriculum areas and grade levels, beginning with community, then identity and for our third time together this year, we chose to focus on place. Those that attended our Lower Mainland study tour to  the Opal School in Portland created panels reflecting on their experience. Many of our playful inquiry mentors set up either pedagogical provocations or shared provocations they developed to engage their students.

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Four teachers shared their experiences visiting Opal for the first or second time – what had an impact on them and how it is affecting their practice. Thank you to April, Louesa, Laurie and Karen for your thoughtful and passionate presentations!

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Based on feedback from the mentor groups during our January session, Michelle Hikida and I did a short professional learning presentation on playful mathematical inquiry and how we plan around a big idea, use provocations and projects based on students’ interests and curiosities and how we extend and sustain a math inquiry.

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After dinner together, we spent time in our mentor groups, zooming in on an area of interest and sharing and learning from each other.

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We are looking forward to continuing working together next year to support professional learning and building a playful inquiry community across our district.

~Janice

Vision, Mission and Values Project at Blair Elementary

Posted on: March 20th, 2017 by jnovakowski

The two kindergarten classes at Blair Elementary took part in our district’s Vision, Mission and Values project in February. As our district develops new Vision, Mission and Values statements, student comments and contributions are being collected to inform the process.

I worked with teachers Lauren MacLean and April Pikkarainen to develop questions to be a part of their regular routine of morning provocations for when the students arrive at school. 

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As the students chose what materials and question to engage with, we had the opportunity to capture some of their thoughts about what schools could be.

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The students had clear ideas about what schools should have and how they should be designed. They talked about natural spaces and spaces to work together. There was a lot of conversation about how schools are for all children and that happiness is a feeling we should have at school.

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The classroom teachers then facilitated a sharing circle during which students shared their ideas about school. We unpacked the questions around Vision, Mission and Values with the students. The students “turned and talked” to a partner about one of these questions.

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Building on and connecting to the ideas they heard from their classmates, the students were given time to go back and revisit their creations and ideas.

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I was able to “interview” some of the students and capture their thinking about what schools could be. This tweet kind of sums up the wisdom from these amazing kindergarten students:

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I am looking forward to a district gathering in April when artifacts from classrooms across the district will be available for us to think about and am glad that the voices of these kindergarten students will contribute to the important discussions our district is having.

~Janice

investigating numbers with the Kindergarten class at Garden City

Posted on: March 20th, 2017 by jnovakowski

I visited the kindergarten class at Garden City twice over January and February, introducing different routines to develop number sense and to investigate numbers. Teacher Lori Williams had initially asked me to come to her class to introduce counting collections to her students and after that lesson, I suggested some other routines or practices she might try with her students.

To introduce counting collections to the class, the students and I sat in a circle together. The class’ “special helper” and I counted a collection in different ways, taking suggestions from the suggestions. I intentionally modelled working together as a “team” – taking turns, taking on different roles (one of us moving the items, the other counting, etc) and having each of us support each other when we were unsure or “stuck”. We counted a collection by 1s in different ways – each of us placing an item in a container taking turns while counting, putting the items in a line and counting them together, moving the items from one pile to another taking turns counting as we moved the items one by one. I asked the students if they could think of any other ways they might count their collections and they had some new ideas as well as some suggesting that they count by 2s or 10s. Pairs of students then went off to choose a collection to count, with the expectation that they count it in at least two or three different ways.

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The students and I came together after about 30 minutes of counting and I invited some pairs of students to share what they counted and how they counted their collections. I encouraged the students to listen and make connections in their mind as to how they had counted their collections.

For my next visit, I introduced the clothesline and explained that it was another way to investigate counting, particularly ordering numbers.

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The students took turns placing different representations of numbers on the clothesline – they were asked to explain their placement decisions. We followed this routine with an invitation to investigate ordering and sequencing numbers using a variety of materials.

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The students were creative in their use of materials and the inspiration of the materials often nudged them beyond their familiar counting range and what the curricular expectation are for kindergarten in BC (number concepts, including counting from 0-10).

For the classroom teacher, this was a time to notice her students engaging in new routines with different materials and to think about how she might incorporate them into her classroom. It is always a conundrum for kindergarten teachers – there are always more materials to add to the classroom but we also have to let things go and put things away, even if temporarily, to create open access to the materials students will use regularly and purposefully.

~Janice

creating spaces for playful inquiry: January 2017

Posted on: March 9th, 2017 by jnovakowski

Richmond’s Playful Inquiry Mentors hosted their second dinner event of Creating Spaces for Playful Inquiry series. For this session, we focused on the theme of identity and its connection to the core competencies as well as curricular competencies and content in BC’s curriculum. As sixty Richmond educators joined us in the Grauer multipurpose room, the playful inquiry mentors had set out provocations to engage in.

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A handout of the provocation questions and curricular connections can be downloaded HERE.

Three Richmond teachers (Kelly, Anna and Christy) who visited the Opal School in Portland last June shared how their visit to Opal has inspired their learning environments and their teaching practice.

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Kelly’s presentation on the impact her visit to Opal on her own teaching was summed up in two words – her presentation can be seen HERE.

 

 

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Christy’s presentation on Fine Arts Provocations with her grades 5&6 students can be viewed HERE

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For our professional learning area of focus for the evening, Marie and Hieu shared their thinking about using loose parts as an inclusive practice that particularly supports English Language Learners in our classrooms.

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After dinner together, we broke out into mentor groups to discuss specific areas of interest and to collaborate and plan together.

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Some of the playful inquiry mentors along with some of the participants in this series will be attending a Lower Mainland Study Tour to the Opal School in Portland over spring break and will bring back new sources of inspiration for playful inquiry to share with teachers in Richmond.

~Janice

elementary math focus afternoon 2017

Posted on: January 17th, 2017 by jnovakowski

We hosted this year’s Elementary Math Focus Afternoon on January 16 at Byng Elementary. Over 250 educators attended, from 14 schools.

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There were a range of sessions to choose from and a huge thank you goes out to all the teacher facilitators who shared with their colleagues. A special thank you to our colleagues from Surrey and Delta who shared with us.

Elementary Math Focus Afternoon Jan 16 2017 program FINAL updated Jan 13

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Rebeca Rubio shared some of the many math resources and kits from the District Resource Centre.

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Tracy, from the Canadian Federation for Economic Education, shared resources to support the financial literacy component of the math curriculum, particularly around the Talk With Our Kids About Money initiative.

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The schools attending each contributed a display of materials, documentation or resources sharing an area of professional inquiry amongst their staffs.

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QR code Math Tags were available with links to IGNITE videos, websites and blogs.

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Math Tags 2017

 

General Handouts:

BC K-5 Mathematics Big Ideas (one pager per grade)

BC 6&7 Mathematics Big Ideas

K-5 Math Connections between Core and Curricular Competencies

6-9 Math Connections between Core and Curricular Competencies

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Session Handouts:

Fred Harwood Grid Algebra 1

Fred Harwood Grid Algebra 2

Barker & Schwartz Picture Books Math & Literacy

Bebluk & Blaschuk Formative Assessment

High-Yield Routines September 2015

Linear Measurement final  from Marie Thom’s K-2 Measurement session

Primary Math Routines (Carrusca, Wozney, Ververgaert)

DST Formative Assessment for All

Jacob Martens Numeracy Competencies Presentation

Sentence Frames for Math ELL

ELL Tier 2 words poster

Carrie Bourne Mental Math Poster – Faire 10

Carrie Bourne mental math poster – valeur de position

(contact Carrie for more Mental Math Strategy posters en francais)

MIchelle Hikida Grades 1-4 Mathematical Inquiry

Michelle Hikida Symmetry

Sandra Ball’s Power of Ten Frames presentation and handout

 

A big thank you to the Byng staff for hosting and to all the facilitators for sharing their experiences and inspiring their colleagues in their sessions.

~Janice

uncovering thinking about addition and subtraction in grades 1&2 at McNeely

Posted on: November 3rd, 2016 by jnovakowski

I am doing a series of visits to the early primary classrooms at McNeely Elementary to work with the teachers around inclusive practices that support students’ mathematical thinking and understanding. Meeting the first class of grades 1 & 2, I began with a number talk to see what strategies the students were able to use and to see how the students engaged in mathematical discourse. We named strategies and introduced terms like justify and reason into the students’s math talk.

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To follow this, I had designed several provocations for students to engage with around the concepts of addition and subtraction. I connected some of the provocations to the K-2 big ideas about computational fluency – relationships between addition and subtraction and building on an understanding of five and ten. After the number talk, I adjusted some of the provocations I had planned, being responsive to what the students had demonstrated during the number talk.

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I provided a brief overview of each provocation set out on a table, reading the question and showing the materials. I explained to the students that they would choose what ideas they wanted to investigate or questions they wanted to engage with and they could stay with one provocation the whole time or move to different tables. This was the first time the students has worked in this way during their mathematics time but for the most part, the students made good choices and stayed engaged with the ideas we were thinking about.

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The SumBlox blocks were presented on a table for students to explore. This was the first time these students had seen these blocks so I wanted to give them to time to explore and investigate the blocks without a specific question to guide their play.

While students were engaged with the materials and ideas, the classroom teacher, the learning resource teacher and I were able to spend time alongside students, listening and noticing. There were opportunities to prompt and provoke and to invite students to explain what they were thinking about or practicing.

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We brought the students to a meeting at the end of our time together, after they had put away all the materials we had been using. The students are beginning to learn how to talk about their mathematical thinking and shared what they did, what they liked and some students were able to share what they learned. With time, the intention is that students will share their findings and questions and make connections with each other during this closing discourse or “congress” time.

At lunchtime, the teachers and I were able to meet and discuss what they had noticed, what questions they had and what assessment information was able to be collected during the practices of a number talk and provocations. A starting point for professional discussion was sharing some of the video I had captured of students explaining their thinking. Based on what we noticed, the classroom teacher and learning resource teacher set some goals as to what they were going to work on with the students before my next visit – developing strategies focused on making ten and developing the language of “decomposing by place value” when explaining their mental math strategies.

These big concepts of addition and subtraction will be explored and investigated in many different ways all year – they are foundational concepts at these grade levels.

~Janice

creating spaces for playful inquiry: October 6 2016

Posted on: October 16th, 2016 by jnovakowski

In the Richmond School District, we have a history of groups of educators visiting the Opal School in Portland, Oregon as it is a school that enacts many of the goals of BC’s redesigned curriculum and the teachers have been researching their practices together for years and share openly through their blog, twitter and visitation days and symposiums. In response to a visit there in January 2015, we have developed a professional learning series in our district to further nurture our thinking around playful inquiry in our school district. Educators who have visited Opal become our district’s “playful inquiry mentors” and open their classrooms to visitors and contribute to professional learning events. This year, our main series is a three part dinner series open to 60 Richmond educators. In September, our playful inquiry mentors met together to think about their role and what their own professional goals are. We thought of a powerful word that captured each of our goals and then wove these words together on a loom.

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We thought about ways to enact and nurture playful inquiry in our classrooms, schools and within the district.

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And finally, we planned our first session of the three-part series. For each session we focus on a big idea or “theme” and after much debate, we settled on the big idea of community for our first session. After hosting this series for two rounds, we have a bit of a structure that works – open with provocations, sharing by educators, a professional learning segment, dinner together, breaking out into interest-based mentor groups and then a closing.

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And so on October 6th at 4:00pm, 60 K-7 Richmond educators descended on IDC and engaged with provocations about community created by the playful inquiry mentors.

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An overview from our BC curriculum was provided as to ways the big idea of community is woven throughout curricular areas and competencies:

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Erin Cammell (grades 4&5 EFI at Dixon) and Kevin Vines (grades 6&7 Quilchena) shared how they began their school years focusing on community, identity and using circle pedagogy. The importance of building relationships was a theme throughout their presentation.

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Sarah Yick (grades 1&2 EFI Dixon) and Carrie Bourne (K-12 French Teacher Consultant) shared how they were both inspired by the responsive learning environments at Opal and are transforming their classrooms (a process…) to better meet their students’ needs and to create access to materials for students to use for thinking and representing their learning.

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Brooke Douglas (VP at Anderson Elementary) led us through the focused professional learning segment of the evening – connecting provocations to the core competencies and using I can statements for self-assessment. Her slides are now available on our site on the portal.

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After a lovely dinner together, educators chose an area of interest and met in small groups to share, ask questions, discuss and set goals. Each group was facilitated by playful inquiry mentors.

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After a few closing words from Marie Thom, reminding us “that we are all researchers of life,” teachers left the event with a large black felt mat and a collection of beads, wire and wire cutters so they could use these materials with their students, mirroring one of the provocations teachers had engaged with earlier in the evening.

We have an open group on our Richmond School District portal so that we can continue our conversations and share between our sessions. And of course, there’s twitter ;)

~Janice

questions to inspire mathematical inquiry

Posted on: July 28th, 2016 by jnovakowski 6 Comments

I have had several emails/messages this summer from colleagues wondering and thinking about the teaching and learning of mathematics through inquiry. Our redesigned curriculum here in BC highlights big ideas at each grade level, in each curricular area. One pedagogical approach to develop students’ understanding (the U in the KDU framework) of the concepts embedded in a mathematical big idea is to provide questions to inspire student inquiry. These questions may be provided as a provocation to individual students, to small groups or to the whole class. Students may work on different questions over time, all connected to a big idea. There are many different ways these open-ended questions may be used in the classroom and are an inclusive practice as they provide entry points for all students to engage in mathematics. These questions invite students to engage with materials and mathematical ideas…some examples:

How many different ways can you decompose 10?

What is the relationship between multiplication and division?

What makes a fraction a fraction?

Through students’  investigations, mini-lessons, scaffolding and prompting from the teacher, students are guided to uncover mathematical content and knowledge (the K in KDU) through experiences that also focus on developing curricular competencies or the doing of mathematics (the D in KDU) such as reasoning, problem-solving, making connections and communicating thinking.

A group of us worked together to create questions that correspond to the new math curricular content and competencies. These questions were inspired by the elaborations for the science curriculum, that had been well received by teachers in BC. The questions are meant as starting points for mathematical  inquiry and investigations and may be used to frame a series of varied but related learning experiences. They are written to potentially inspire cross-curicular inquiry as well as integrating the First Peoples Principles of Learning. These elaborations are currently being hosted on the BCAMT website until they are uploaded to the Ministry’s curriculum website. The K-9 document can be found HERE. The following is an example from Kindergarten:

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It is essential that students’ background, interest, experiences and understanding inform the questions that are provided to them. Many teachers like to have questions to begin with, that they can then adjust and adapt for their students. There are many sources for these types of questions, as a starting point.

Resources I recommend:

Screen Shot 2016-07-28 at 12.26.37 AMGood Questions for Math Teaching: Why Ask Them and What to Ask

by Pater Sullivan and Pat Lilburn (elementary version)

 

 

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Good Questions for Math Teaching: Why Ask Them and What to Ask

by Lainie Schuster and Nancy Anderson (middle school version)

 

 

 

Screen Shot 2016-07-28 at 12.27.02 AMGood Questions: Great Ways to Differentiate Mathematics Instruction by Dr. Marian Small (Elementary)

 

 

 

Screen Shot 2016-07-28 at 12.27.12 AMMore Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction by Dr. Marian Small (Secondary)

 

 

 

These four books are all available in many catalogues and online sources.

A new series of books from Canadian Dr. Marian Small – Open Questions for Rich Math Lessons, They can be ordered through Rubicon Publishing HERE.

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For those of you who have been following along with our Reggio-Inspired Mathematics project, there is a blog post with various question frames that we use as we co-construct provocations for our students. It can be found HERE. We have developed provocation postcards for K-2 and are working on postcards for 3-5 and 6-9. They have a photograph and one question on the front and a collection of related questions on the back – all connected to one mathematical big idea.

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The questions we pose as teachers are important – they need to be responsive and intentional. But, I also think there needs to be space for students to pose their own questions. Something that I have noticed as I work with teachers and students who have been using these types of questions over the last few years is that the students begin to ask these questions of themselves and each other. It is very empowering for the students to be the ones asking the questions that frame the learning experiences in the classroom. I believe its essential to find opportunities and openings for the students’ own questions in classrooms. But that is another blog post…or maybe a dissertation ;)

~Janice