Archive for the ‘secondary’ Category

March thinking together: engage in problem-solving experiences connected with place, story and cultural practices and perspectives

Posted on: March 14th, 2019 by jnovakowski No Comments

This month’s curricular competency focus is engage in problem-solving experiences that are connected to place, story, cultural practices and perspectives relevant to local First Peoples communities, the local community, and other other cultures. This curricular competency is the same across grades K-12 and courses and falls under the organizer of “Understanding and Solving” which suggest the focus of using contextual and meaningful experiences to support mathematical understanding.

Elaborations are suggestions for educators to consider as they plan for developing this curricular competency:

  • in daily activities, local and traditional practices, the environment, popular media and news events cross-curricular integration
  • have students pose and solve problems or ask questions connected to place, stories and cultural practices

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The focus and thinking behind this curricular competency are the ideas of authenticity, meaningfulness, engagement and connectedness. Not all mathematics learning needs be contextualized or connected to “real life” but for many students who may see math as something that they do at school between 9 and 10am and don’t yet see the relevance of the math they are learning, providing tasks and problems that connect to place, community and culture may support their mathematical thinking and learning and broaden their understanding and appreciation for what math is and how it can be experienced. Experiential and holistic learning are foundational to the First Peoples Principles of Learning and these are considerations for all learners. The First Peoples Principles of Learning also remind of us of the importance of connecting learning through place and story, working with others and developing a self of self, family, community and culture. This curricular competency is aligned with the Personal and Social Core Competency – positive personal and cultural identity, personal awareness and responsibility and social responsibility.

Some resources to consider:

Messy Maths by Juliet Robertson (elementary resource for taking math learning outdoors)

Tluuwaay ‘Waadluxan Mathematical Adventures edited by Dr. Cynthia Nicol and Joanne Yovanovich (mathematical adventures from Haida Gwaii developed by community members, elders and educators)

BC Numeracy Network – Connecting Community, Culture and Place

First Peoples Mathematics 8&9 developed by FNESC - this teacher-created resource is being revised to reflect the current BC mathematics curriculum and provide more learning experiences across grades and disciplines.

 

Blog posts from this site with related information:

Place-Based Mathematics

Place-Based Mathematical Inquiry

Primary Study Group 2018-2019 – Outdoors Math

Indigenous Content and Perspectives in Math

 

Some questions to consider as you plan for learning opportunities to develop the competency of engaging in problem-solving experiences connected to place, story and cultural practices and perspectives:

How does place/land/environment inspire mathematical thinking? What potential numeracy or problem-solving tasks emerge when we think about local land-based contexts?

What problems or issues are facing the local community? How might mathematics help us to think about and understand these problems or issues? What information or data might be collected and shared? How can we use different tools to communicate mathematical information to create an opportunity for discussion and engaging in a problem-solving process?

How does Indigenous knowledge connect, intersect and support the curricular competencies and content in our mathematics curriculum? Who is a knowledge holder in your local First Nations community that you could learn from and with? 

What are authentic resources? What stories and cultural practices are public and able to be shared? What doe it mean to use authentic resources, stories, and elements of culture in our mathematics teaching? How are resources specific to a local context? Who can we go to to find out more information and learn about local protocols?

What cultural practices in your community have mathematics embedded in them? How might we use the structure of “notice, name and nurture” to expand awareness of what mathematics is and how it can be experienced?

How can stories help us think about the passage of time, relationships, connections and mathematical structures, actions and models?

~Janice

February thinking together: develop, use and apply multiple strategies to solve problems

Posted on: February 28th, 2019 by jnovakowski No Comments

This month’s curricular competency focus is using multiple strategies to solve problems. There is a development in how strategies are used from K-12 and for what types of problems.

In K-5 the curricular competency language is “develop and use multiple strategies to engage in problem solving” with elaborations including examples of strategies involving visual, oral and symbolic forms and through play and experimentation.

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In K-5, we support students in developing a repertoire of strategies to draw upon and we encourage the practice of choosing and using these strategies in different problem solving experiences ranging  from structured word/story problems, open problems or questions or problem-based or numeracy tasks. During the development of strategies, students will notice similar strategies being shared by their classmates and these strategies might be named such as “looking for a pattern” or “acting it out” or “represent with materials”. Naming strategies such as these helps to enhance mathematical communication, discourse and community in the classroom when discussing mathematical problems.

As with many of the curricular competencies in math, there are slight variations between grade bands, showing the developing application and demonstration of these competencies.

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In grades 6-9 the curricular competency language is “apply multiple strategies to solve problems in both abstract and contextualized situations” with elaborations including examples of strategies focusing on those that are familiar, personal or from other cultures. Students in this grade range are refining and reflecting on their own use of problem solving strategies and we encourage students to listen and learn from their peers in order to consider new ways to think about a mathematics problem.

 

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In grade 10 the curricular competency language is “apply flexible and strategic approaches to solve problems” with elaborations such as deciding what tools to use to solve a problem as choosing from a list of known strategies such as guess and check, solve a simpler problem, model, use a chart, role-play or use diagrams. The numeracy processes for engaging in numeracy tasks are related to this competency at the secondary level - interpret, apply, solve, analyze and communicate.

 

Although specific strategies such as “guess and check” or “solve a simpler problem” are not named specifically in the elaborations from K-9, it is these more formally named strategies that are developed with understanding, meaning and purpose over time. Alternative or personally derived or preferred strategies may also be developed by students and shared with their solutions, supported with their reasoning and explanations to demonstrate their understanding of the problem and the mathematics involved.

Many math educators and researchers have found over decades of research and classroom experiences that students who have multiple strategies or approaches to problems are more fluent and flexible in their thinking. An important aspect of using multiple strategies is knowing when a particularly strategy is helpful or efficient. Not all strategies are suitable for all problems and this an important part of the progression of developing this competency in mathematics  One particularly effective instructional strategy is engaging students in comparing the strategies they used to solve a problem. Researchers have recently examined the cognitive process of comparison and how it supports learning in mathematics. The sharing and comparison of multiple student strategies for a problem was found to be particularly effective for developing procedural flexibility across students and to support conceptual and procedural knowledge for students with some background knowledge around one of the strategies compared. (Durkin et al, 2017 – referenced below). Based on their findings, the researchers share some significant instructional moves that will support student learning:

1) regular and frequent comparison of  alternative strategies

2) judicious selection of strategies and problems to compare

3) carefully designed visual presentation of the multiple strategies

4) small group and whole class discussions around comparison of strategies with a focus on similarities, differences, affordances and constraints

 

Examples of what the use of multiple strategies might look like in the classroom include:

Primary: The teacher reads the story The Frog in the Bog and asks the grade 1 students to figure out how many critters are in the frog’s tummy. The teacher invites the students to think about how they might solve this problem and what they will need. The students work on their own or with a partner to solve the problem through building with materials, acting it out, drawing or recording with tally marks and numbers. Some students accompany their solutions with an equation and one student records his ideas orally using iPad technology. As the students are working, the teacher pauses the students and asks them to walk around the room and see what their classmates are doing and see if they can find a new idea for their own work. After solving the problem, the students prepare to share their solutions and strategies with the class and the teacher gathers the students on the carpet and chooses some students who used different strategies to share. The teacher records the strategies on the chart and then asks the students if they have a new idea for a strategy for the next time they do a problem like this.

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Intermediate: In a grades 6&7 class, the teacher projects the first three figures of a visual pattern on the class whiteboard (examples on visual patterns.org). The teacher asks the students what they notice about the figures and records some of the students’ responses and then asks them to consider what comes next. Students are asked to consider what strategies or approaches might help them think about this. After some thinking time, the teacher asks the students to turn and talk with one or two other students and compare each others’ strategies and consider new ways of thinking about the problem. The teacher then invites the students to apply more than one strategy to solve what figure 43 will look like. The students share their solutions and strategies with the teacher recording the different strategies through different representations such as a drawing, a narrative, an expression, a table or a graph. The teacher then facilitates a discussion comparing the representations and how they are connected and support the understanding of the problem.

(with thanks to Fawn Nguyen and Marc Garneau for the inspiration)

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Secondary: Students in a grade 10 class are assigned to be in random groups of three and work on a numeracy task on a whiteboard or window around the classroom. The class has been learning about prime factorization and the teacher shares the following problem orally:

Prime numbers have exactly two factors – 1 and itself. Which numbers have exactly 3 factors? Exactly 4 factors? And so on. Given any positive integer, n, how can you tell exactly how many factors it has?

Each group of students begins talking and sharing their ideas. Students begin to record their thinking, using diagrams, charts, numbers, etc. and build on and challenge each others’ thinking about the problem and approaches to solving it. Students move around the room and watch or engage with other groups. The teacher facilitates students’ sharing of solutions and approaches to the problem and then provides a set of related problems for students to continue practicing with, either in their groups or independently.

Numeracy tasks such as this one can be found HERE and HERE and HERE.

(with thanks to Mike Pruner and Dr. Peter Liljedahl for the thinking classroom inspiration)

 

Some questions to consider as you plan for learning opportunities to develop the competency of using multiple strategies and approaches to solve problems:

What strategies and approaches do you notice your students using? Are some students “stuck” using the same strategy? How could you nudge students to try different strategies and approaches?

What different types and structures of math problems are being provided to your students? Are students flexible with their strategy choice or approach, making decisions based on the problem they are working on?

How might you and your students record their strategies and approaches to make this thinking visible?

What opportunities are we creating for students to watch and listen to others think through, choose and apply strategies and solve problems? How might this support their learning?

What tools, materials and resources do students have access to to support choice and application of different strategies and approaches when solving math problems?

~Janice

References

Elementary and Middle School Mathematics: Teaching Developmentally by John van de Walle et al

Teaching Mathematics through Problem-Solving (NCTM) edited by Frank Lester and Randall Charles

Why Is Teaching With Problem Solving Important to Student Learning (NCTM Research Brief)

Durkin, K., Star, Jon. R. & Rittle-Johnson, B. (2017) Using Comparison of Multiple Strategies in the Mathematics Classroom: Lessons Learned and Next Steps, ZDM: The International Journal on Matheamtics Education 49(4), 585-597.

 

January thinking together: use technology to explore mathematics

Posted on: January 31st, 2019 by jnovakowski

This month’s focus is on the curricular competency: use technology to explore mathematics.

This is the language that is used from K-5 with the accompanying elaborations:

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This is the language of the learning standard for grades 6-9:

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And this is the language of the learning standard in grades 10-12, with elaborations that are more course-specific:

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There are many questions that arise for educators and parents around the use of technology. In some contexts the use of personal devices becomes a management and liability concern for schools and in other contexts there are access and equity concerns around technology. In terms of pedagogy and appropriate use, there is always a professional judgement made as to the suitable use of technology and whether it is enhancing the learning experience in some way. Technology is not to be used just for the sake of using technology but instead, choices are made around technology use based on intention, context and purpose. In mathematics, there are many applications that allow for students to visualize and experience mathematics in ways they would not otherwise be able to (one example is the use of Desmos). Another aspect of using technology in mathematics teaching is as a tool to represent and share students’ learning. There are many accessibility features available on devices for students who may need different tools to support their communication or recording of ideas. Technology can be a powerful tool to support inclusive practices, choice and differentiation.

When we look at BC’s redesigned curriculum for information on the role of technology within a learning environment, the following is shared:

ICT-enabled learning environments

Students need opportunities to develop the competencies required to use current and emerging technologies effectively in all aspects of their learning and life. Technology can facilitate collaboration between students, educators, parents, and classrooms while also providing schools with rich online resources. Today’s technology enables classrooms, communities, and experts around the world to share digitally in a learning experience, wherever they may be.

source: https://curriculum.gov.bc.ca/curriculum/overview

E-Portfolios

Communication with families (and others) is an important part of our education system and in our district we are embracing e-portfolios and the use of technology to share and communicate student learning and progress with families. Students are able to take photographs or videos and upload them to their portfolios and annotate their posts with information or self-assessment about their learning. The teacher is also able to add descriptive feedback that is shared between teacher, student and family.

Screencasting

As a classroom and resource teacher and teacher-librarian, one of my favourite uses of technology was the use of screen casting apps. These apps allow students to take a photograph of the math they have been building, creating, diagramming or recording and then use annotation tools such as text labelling and arrows to explain their thinking as well as using audio tools to narrate their thinking. I found that many students were more confident and detailed in sharing their learning through these apps that what I might have found out about their understanding in other ways. There is also an honouring of students’ uniqueness in how they might see or think through the mathematics that can be shown through these types of apps. Some examples of screen casting apps we use in our district our: ShowMe, Educreations, Explain Everything, 30Hands and Doceri.

Math Apps

There are many apps that can support mathematics learning – some are mathematics specific and others are used to represent and share learning. A caution is the type of math apps that are essentially a worksheet and don’t include any sort of feedback to students, visual supports, problem-solving or mathematical thinking. Some locally produced apps include the TouchCounts from SFU that uses the research around gesturing to create an interactive app that focuses on counting and decomposition and composition of quantities. Another series of BC apps are the MathTappers apps developed through the University of Victoria. Each app has visual supports for students developing their understanding of a concept as well as symbolic or abstract notation. There are also choices as the number range that students can work with, allowing for differentiation. These apps are all on our district configured iPad devices. Some specific apps from this series include Find Sums, Multiples, and Equivalents.

Screen Shot 2019-01-31 at 11.10.00 AMThe apps from the Math Learning Centre are also on our district configured iPad devices and allow for content creation and capturing students’ process and thinking. These apps are in web-based and iOS and Android formats. More information can be found HERE.

 

 

There are also so many apps that allow for students to share their thinking such as ShowMe, Educreations, Book Creator, PicCollage, 30Hands and Doceri.

Tracy Zager shares her ideas on evaluating math content apps HERE. Her non-negotiable criteria are:

1) no time pressure

2) conceptual basis for operations

3) mistakes are handled productively

Read through her blog post for explanation and examples.

The following is a link to some recommended apps and blog posts about students using them from #summertech15 and HERE is a blog post about using iPad technology and specific apps to support all students in mathematics.

 

Calculators

Although BC does not yet have a specific statement on calculator use, there is no intent that students will use calculators to complete calculations instead of learning the concepts and practice involved with operations (addition, subtraction, multiplication, division). In some cases, students that have specific learning needs and plans may use calculators as an adaptation. In some cases, teachers may choose to provide the choice of calculators when the focus of the lesson or assessment is not on calculation but on another area of the math curriculum such as problem-solving and calculators can be used for the necessary calculations so that students can focus on the other aspects of the task. Calculators can also be used to investigate patterns and relationships, support student reasoning or justification.

The NCTM has a research brief on calculator use in the classroom which can be found HERE as well as a position paper on calculator use in elementary grades which can be found HERE.

Virtual Manipulatives

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The Math Learning Centre offers a variety of virtual manipulatives in web, iOS and Android formats. They can be accessed HERE.

 

 

 

desmos

Desmos is a free, online graphing calculator application that is used by teachers and students all over the world. There are both web-based and app platforms. Students are “able” to play with parameters in an equation and visually see how the graph changes as the parameters change.  The desmos staff and teachers across the world have developed lessons and tasks that are open source and shared through the desmos teacher website at no cost HERE. There is also an activity builder so that teachers can create their own tasks.

I attended a math conference a few years ago where Eli Luberoff, CEO of desmos, shared his passion for the teaching and learning enabled and enhanced by this tool. In particular, I was captivated by the marble slides task he shared and the authentic learning that we witnessed happening for students in the video he shared.

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More information about Desmos and access to many classroom activities can be found HERE.

Coding and Computational Thinking

There are many links between coding and computational thinking. Two new senior math courses – Computer Science 11 and 12 have been added to our BC curriculum framework and these courses focus on coding, programming and computational thinking.  I will be sharing a blog post specific to coding and math in the next few months.

Osmo

Screen Shot 2019-01-29 at 10.56.25 PMOsmo is an interactive accessory for iPad technology that uses the camera to create Reflective Artificial Intelligence. The red camera clip and white base are used with free apps and game materials that can be purchased online or at the Apple Store. Two of its earliest games focused on mathematics – the Tangram game focuses on spatial reasoning and the Numbers games focuses on decomposition and composition of numbers. Osmo is always developing new games including a Pizza game that focuses on financial literacy and a series of coding games.

More information about Osmo can be found in a blog post here and on their website here. The SD38 DRC has five Osmo kits available to borrow. Note that one iPad device is needed for each kit.

Augmented Reality (AR)

Augmented reality (AR) is an interactive experience of a real-world environment where the objects that reside in the real-world are “augmented” by computer-generated perceptual information, sometimes across multiple sensory modalities (from Wikipedia). There is an interplay in AR between digital and real-world environments whereas in Virtual Reality (VR) you engage with a simulated environment. A few years ago we had a Google Expeditions team visit Homma school and share their Google cardboard virtual reality devices with the students. A blog post about that experience can be found HERE. This was a first foray into thinking about ways this kind of technology could support teaching and learning. My first experience with AR was a few years ago when the colAR app created a special event to go along with Dot Day (inspired by the book by Peter Reynolds). The information about this can be found HERE and is a great starting point to use AR with students.

Our new technology integration teacher consultant Ellen Reid has been exploring AR with the iPad app AR Maker . We talked about the mathematical possibilities for using AR and along with the development of spatial reasoning, the following concepts came to mind: surface area, volume, transformational geometry, scale, proportion, ratio, 2D and 3D geometry, and composition and decomposition of shapes. The following are some photos Ellen captured as she created AR WODBs (Which One Doesn’t Belong?):

WODB_AR Image-13.png(movie file)

 

 

 

 

 

 

For Richmond teachers, please also check out the Integrating Technology for Teachers page, curated by Chris Loat, on our district portal linked HERE.

 

Some questions to consider as you plan for learning opportunities to develop the competency of using technology to explore mathematics:

How can technology enhance students’ mathematical experience and see and think about mathematics in different ways?

What specific curricular content and competencies at your grade level could be explored and investigated through technology, including the use of calculators?

How can technology be used to support students’ collaboration and communication in mathematics?

What opportunities are we creating for sharing and communication with families through the use of technology?  How are we communicating with parents how forms of technology are being used in our schools to support learning in mathematics?

~Janice

December thinking together: visualize to explore mathematical concepts

Posted on: December 11th, 2018 by jnovakowski

This month’s focus is on the curricular competency: visualize to explore mathematical concepts.

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In the 2007 WNCP mathematics curriculum, visualization is defined as involving “thinking in pictures and images, and the ability to perceive, transform and recreate different aspects of the visual-spatial world”. Concepts such as number, spatial relationships, linear relationships, measurement, and functions and relations can be explored and developed through visualization.

In the new BC grades 10-12 courses, the elaborations for this curricular competency are:

  • create and use mental images to support understanding
  • visualization can be supported using dynamic materials (e.g., graphical relationships and simulations), concrete materials, drawings, and diagrams

Visualization and spatial reasoning involve the relationship between 2D and 3D shapes as well as dynamic imagery such as different perspectives, movement, rotations and reflections. Visualizing involves an interplay between internal imagery and external representations  (Crapo cited in NRICH article below). Students need experience with concrete and visual representations/pictures/models as well as being able to visualize something in their minds, often referred to as the “mind’s eye”.

Canadian and International research has shown that there are links between strong abilities to visualize and success in mathematics. One widely used psychological assessment for visualization involves “The Paper Folding Test”  in which a paper is folded and a hole is placed through a specific location and the participant is asked to visualize what the paper will look like when it is unfolded, utilizing the ability to generate, maintain and manipulate a mental image, (Lohman, 1996 cited in Moss et al 2016). A recent study also found a link between the ability to visualize and success with solving mathematical word problems, citing the ability to mentally visualize and make sense of the problem contributed to success in diagramming and solving problems (Boonen et al 2013 cited in Moss et al 2016). The Canadian work of (Moss et al 2016 ) and their Math for Young Children research project focuses on spatial reasoning and the importance of developing students’ flexible use of visualization skills and strategies.

 

Instructional Resources

Screen Shot 2018-12-11 at 4.11.50 PMThe book Taking Shape (referenced below) provides several visualization tasks on pages 30-35 but visualization is an important component of most of the spatial reasoning tasks in the book.

 

 

 

 

Quick Images is an instructional routine that supports the visualization of quantities and shapes. Dot patterns and Screen Shot 2018-12-11 at 2.26.05 PMcomposition of shapes are often used as quick images. More information and videos can be found on the TEDD website HERE.

 

A short article from the NCTM explaining the connection between visualization and subitizing can be found here:

NCTM_quickimages_tcm2016-12-320a

 

Screen Shot 2018-12-11 at 2.28.51 PMFawn Nguyen has compiled a collection of visual patterns HERE. Visual patterns provide the first three steps of the pattern and then students are asked to visualize the next steps, which involves both arithmetic, algebraic and geometric thinking.

 

Desmos in an online graphing calculator that allows for students to predict, Screen Shot 2018-12-11 at 2.52.41 PM

visualize and graph linear relationships and functions and relations.

 

 

So what does it mean to be proficient with visualizing?

As we begin to work with the new proficiency scale across BC, we need to consider what it means to be proficient with visualizing to explore mathematical concepts 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 six student at the end of the year would be considered proficient with visualizing geometric transformations if they were able to follow directions to mentally translate, rotate and reflect a 2D shape and show or describe the resulting orientation/position.

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

How is the core competency of communication developed through the process of visualization? What different ways can students show and explain what they are visualizing – using materials, pictures or words?

How do the competencies of estimating and visualizing complement each other to support reasoning and analyzing in mathematics? How can using visual referents support estimating?

How can we help students understand the purpose and usefulness of developing visualization skills and strategies? What examples can we share of scientists and inventors that used visualization to develop theories and ideas?

What opportunities are we creating for students to practice and use visualization skills and strategies across different mathematical content areas such as geometry, measurement, number, algebra and functions?

~Janice

 

References

Thinking Through and By Visualizing (NRICH)

The Power of Visualization in Math by Jeremiah Ruesch

Spatial Reasoning in the Early Years: Principles, Assertions, and Speculations by Brent Davis and the Spatial Reasoning Study Group, 2015

Taking Shape: Activities to Develop Geometric and Spatial Thinking by Joan Moss, Catherine D. Bruce, Tara Flynn and Zachary Hawes, 2016

 

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.

KDU_knowdounderstand

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.

 

Screen Shot 2018-09-28 at 9.45.26 PMThe 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.

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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

May thinking together: How can we weave Indigenous content and perspectives into the teaching and learning of mathematics?

Posted on: June 12th, 2018 by jnovakowski 1 Comment

Screen Shot 2018-06-12 at 11.25.11 PMThe First Peoples Principles of Learning is a foundational document in the redesign of BC’s curriculum frameworks. The Principles were developed by FNESC (First Nations Education Steering Committee) and the poster in English can be found HERE and in French can be found HERE. As Jo Chrona would say, the FPPL are much more than the poster – they are principles that are inclusive of all children in BC while honouring Indigenous ways of being and knowing. FNESC has developed teaching resources such as the In Our Own Words resources for K-3 and the Math First Peoples resource for Grades 8&9 (currently being updated) but much of the information and ideas in the resource can be adapted for all grade levels.

 

On May 17, Leanne McColl, Lynn Wainwright and myself attended the 8th annual K-12 Aboriginal Math Symposium. Educators from across BC attend this symposium. Information about the symposium can be found HERE and there is a tab on the website that links to archived resources.

I have attended this symposium for years and was fortunate to share a project from The Studio at Grauer at this year’s event. Some of the slides from my presentation can be found HERE , under May 2018.

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A focus of my presentation was on three of BC’s mathematics curricular competencies. These competencies are part of the learning standards for the K-9 mathematics curriculum and are aligned with the First Peoples  Principles of Learning and the Core Competencies.

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The BC Numeracy Network has archived different types of resources to support the redesigned curriculum. Under the Connections tab, there is a page dedicated to resources that support the weaving of the First Peoples Principles of Learning into mathematics teaching and learning.

Link to BCNN page here

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In the Richmond school district, two of the four goals of our Aboriginal Education Enhancement Agreement (AEEA) are focused on all learners (not just those with Indigenous ancestry) developing an understanding about the First Peoples Principles of Learning, our local First Nations community and Indigenous worldviews and perspectives as part of engaging in the process of reconciliation through education.

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Teachers often ask me about where to start in this area and are concerned about not doing things properly or that they do not have enough knowledge themselves. I suggest that teachers contact someone in their district about local protocols and then try something in collaboration, maybe inspired by one of the above suggested resources. Look for authentic connections within your community and across disciplines in the curriculum..  Some of the things that I have done to continue to learn more in this area are: read articles and books recommended to me, seek out opportunities to learn from elders and Indigenous community members and colleagues, get involved with district or university-based collaborative projects,  connect with your district’s Aboriginal Education team, attend workshops and tours offered through museums, cultural centres and local Indigenous organizations. There are lots of opportunities to learn and see connections to mathematics…we need to go forward together with an open mind and an open heart.

To consider…

How can the First Peoples Principles of Learning be embedded in our mathematics teaching and learning? How do BC’s mathematics curricular competencies reflect these principles?

One of the principles is that “learning takes patience and time” – how does this principle bump up against some ideas around the teaching and learning of mathematics?

How might we work towards the goals of our Aboriginal Education Enhancement Agreement within our mathematics classrooms? What role could mathematics play in the process of reconciliation?

What does it mean to use authentic resources, stories and elements of culture in our mathematics teaching? How is this affected by the land and the story of the place where we live and teach? Who can help us think about these ideas? Where can I learn more and find resources?

What opportunities do your students of Indigenous ancestry have to see their community, family and culture represented in the mathematics they are learning at school? Within our diverse community, how do all students see themselves reflected in their mathematics experience? What is the relationship between our students’ mathematical identities and their personal and cultural identities?

What interdisciplinary projects might connect mathematics with Indigenous knowledge and worldviews?

~Janice

Talk With Our Kids About Money 2018

Posted on: May 12th, 2018 by jnovakowski

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

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

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

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

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

TWOKAM video

TWOKAM – CFEE website link

~Janice

March thinking together: What is computational fluency?

Posted on: May 12th, 2018 by jnovakowski

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

-NCTM, 2000

Computational fluency develops from a strong sense of number.

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

 

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

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

Computational fluency develops from a strong sense of number.

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

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

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

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

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For example, with addition and subtraction:

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

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

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

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

There is a similar progression for multiplication and division facts.

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

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

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Number Talks

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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

graduation numeracy assessment – January 2018

Posted on: May 11th, 2018 by jnovakowski

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

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

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

link to Graduation Numeracy Assessment information 

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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

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