secondary Archive - Mathematics and Science in SD#38 (Richmond)

Archive for the ‘secondary’ Category

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.

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

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

link to Graduation Numeracy Assessment information

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

~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.

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.

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”.

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?

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.

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

January thinking together: What is numeracy?

Posted on: January 31st, 2018 by jnovakowski

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

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

For January, let’s consider what is numeracy?

This January, two of our secondary schools – Steveston-London and Burnett – had students take part in the managed implementation of the Graduation Numeracy Assessment. Other secondary schools in our district are considering both pedagogical and logistical details as they approach the first regular sitting of the assessment for students in June 2018. The Graduation Numeracy Assessment is a new graduation requirement for BC students along with a Graduation Literacy Assessment. Students currently in grades 10 and 11 will begin writing the assessment and have three opportunities to write the assessment to improve their proficiency mark if they choose to. The assessment is not linked directly to a mathematics course or grade and it is thus, the responsibility of all K-12 educators to nurture and develop numerate students. Just as literacy isn’t just about literature, numeracy is not just about numbers – numeracy is being able to apply all areas of mathematics to make sense of the world around you and solve problems relevant to you or others.

For the purposes of the assessment, the Ministry is defining numeracy as:

Numeracy is the ability, willingness, and perseverance to interpret and apply mathematical understanding to solve problems in contextualized situations, and to analyze and communicate these solutions in ways relevant to the given context.

As students engage with numeracy tasks, they work through a sequence of five numeracy processes: interpret, apply, solve, analyze and communicate.

For a more detailed analysis of the concept of numeracy, Dr. Peter Liljedahl and Minnie Liu, share their ideas in an article in Vector, the BCAMT journal: Vector Summer 2013 – Numeracy, pages 34 -39

The following information about the Graduation Numeracy Assessment is available online on the Ministry’s curriculum website:

Graduation Numeracy Assessment Design Specifications 2017

Link to online Graduation Numeracy Assessment sample assessment

Graduation Numeracy Assessment – information for parents

GNA student-choice questions scoring guide and exemplars

Pre-assessment collaborative learning videos

I highly recommend that all BC educators try the sample assessment available online (linked above) to get a sense of the types of questions we can all be using with our students, regardless of grade or course. Last Friday, on a professional development day, the whole Richmond Secondary School staff worked in groups to collaborate on some of the sample assessment questions and to consider how to embed opportunities for numeracy in their courses.

Looking forward to continuing the conversation around numeracy and what it means to be numerate.

~Janice

November thinking together: What is number sense?

Posted on: November 29th, 2017 by jnovakowski

What is number sense?

How are numeracy and number sense the same and how are they different?

What routines nurture the development of number sense?

~Janice

October thinking together: What is balanced numeracy?

Posted on: October 31st, 2017 by jnovakowski

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

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

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

The BC Numeracy Network has created a website full of linked references and resources to support teachers’ professional learning: https://sites.google.com/view/bcnumeracynetwork/home

As you think about balanced numeracy, consider…

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

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

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

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

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

~Janice

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

Math Workshop by Jennifer Lempp

Guided Math in Action by Dr. Nicki Newton

Guided Math by Laney Sammons

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

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

(more…)

September thinking together: What is math?

Posted on: September 19th, 2017 by jnovakowski

For September, I thought we’d start with What is math?

I am fortunate to have opportunities to sit around tables with educators from many contexts – elementary, secondary, post-secondary as well as working with parents and students. What I have found over many years of having the conversation around What is math? is that there is much diversity in definitions and responses. Some views are quite narrow and focus on number, computation and operations while other views are much broader in topics but also involve what it means to be a mathematician.

Mathematicians such as Fields medallists Maryam Mirzakhani and Cédric Villani have said that mathematics is a creative, collaborative endeavour. Other mathematicians emphasize that mathematics is more about justification and proof than getting the “right answer”. One thing that pretty consistently comes up from those who engage in mathematics is that it takes time – sometimes a problem or proof takes days, weeks, years.

How do these ideas about mathematics resonate with you? with your mathematical story?

As a classroom teacher and when working with pre-service teachers at UBC, I began the year with an individual brainstorm or web around “What is math?” – and these responses were added to a collective chart or web. For the pre-service teachers I worked with, I also asked them to tell me a little a bit about their background and experience with mathematics. These short narratives and webs usually gave me quite a bit of insight and where we needed to begin as a class.

What assumptions, conceptions and understandings about mathematics do students carry with them into our classroom communities? What feelings and beliefs do they hold?

This week a grades 2 and 3 class visited The Studio at Grauer and we began by talking about what is math? I then invited them to explore the materials, images and books in the studio space and to investigate something that piqued their interest.

As we gathered back together, the students added to our original list. Interestingly, there additions were much more focused on mathematical experiences, different from naming mathematical content.

What do our classroom environments say about what mathematics is? Do the images, books and materials we offer inspire our students and nurture connections? Do all students see openings to engage in mathematics?

Ideas to nudge students’ thinking about what mathematics is:

What is math?

Create a class chart or math graffiti wall that can be added to as the school year progresses. Students can add images, diagrams, words, phrases, etc. Students can also use materials to create representations of what math is. The following is “math sun” created by a kindergarten student at Grauer last year – when I asked her what made it a math sun, her reply was that it was “full of math”.

Where do we see math? What math lives here?

Encourage students to think about math beyond the classroom and school. Where do they experience and see math outdoors? in the community? at home? Create an area in the classroom to add photographs and materials found in the local environment that might inspire mathematical thinking and connections.

A grade 4&5 class I worked with in The Studio at Grauer shared some of the math they experienced over the summer and then the grade 2&3 class added to their list this week:

Many elementary classrooms have “wonder windows” to encourage students to observe and wonder the local environment. This year, we have added a math window to The Studio.

I facilitated a K-7 place-based mathematics project at Byng a few years ago and one of the tasks classes engaged in was math walks around the school and in the community. Sometimes a specific focus was selected such as What shapes can we see? but we mostly looked for math to world connections. One class created a photo book while others created math problem posters (sharing problems the students posed inspired by their photographs) or concept panels.

For the last three summers I have participated in a Twitter challenge with mathy types from around the world. Each week a math concept is posted and the challenge it to take photographs of the world around us that connect to that concept. Concepts such as estimation, tessellation and scale were explored this year. You can find this year’s posts on Twitter by searching #mathphoto17 – and here is a photo book I created of my photos and tweets from this year’s challenge:

I will be launching a district-based K-12 math photo challenge on Twitter soon – hashtag #mathphoto38 (the 38 for school district 38) with plans to document and share the photos over the school year. We will begin with photos that respond to the question: What is math?

Make mathematics visible in your classroom and school

I also try and make different ideas about what math is visible to students, to parents and to colleagues. The following panel was created with images of the representations created by Kindergarten students as they responded to the question, What is math?

A middle school teacher created an interactive bulletin board based on the instructional routine Which One Doesn’t Belong? to engage the whole school population in mathematical reasoning and communication – important mathematical work and this idea builds mathematical community in a school.

source: Twitter

source: Twitter

And for high schools – I think this is inspiring and helps to expand students’ notions of what math is. High school math teacher, Sara VanDerWerf, from Minnesota, has created a play table space in her classroom to engage students in thinking and playing with mathematics in different ways. She shares photos on twitter HERE and shared a blog post about play tables in high school classrooms HERE. Is there a secondary math classroom in Richmond that would like to set up a play table? I’d be happy to help.

Think about how mathematics is experienced across cultures, across the world and across time.

Mathematics is a human construct and is often narrowly define through a Western or European lens. There is much evidence that mathematics as it is typically defined, existed in Asia long before it was “discovered” by Europeans. There is a long history of cultural practices across cultures from all over the world that we would now label as mathematics. Alan Bishop has done considerable research in this area and describes six mathematical practices or activities that exist in all known cultures – counting, locating, measuring, designing, playing and explaining. I have found students find it interesting to learn about different number systems or how measurement is often contextual to a culture and environment. Some examples of these cultural practices are included in the elaborations for the learning standards in our BC math curriculum.

Seeing and experiencing mathematics as a creative endeavour

For the past three years, Dr. Jo Boaler and her “youcubians” have launched a week of inspirational math to begin the school year. There are a variety of videos and open mathematical tasks available for grade bands from K-12. The focus is developing a mathematic mindset with messages such as: we can all learn math and we learn from mistakes. Resources can be found HERE.

There are many videos available that show mathematics as creative and inspiring but a particularly interesting youtube channel is created by self-defined mathemusician Vi Hart, daughter of acclaimed mathematical sculptor George Hart. I think her videos are particularly great for students in grades 5-12. Her channel is HERE.

There are lots of ways to nurture the creative thinking core competency (BC curriculum) while engaged in mathematics.

The three facets of the competency are: novelty and value, generating ideas and developing ideas. I see these facets enacted when children engage in number talks and consider different strategies for solving mental math questions, when children engage in a rich open task or problem or when they apply mathematics to create or design something.

What is math?

How will you investigate this idea yourself and how will you investigate and extend your students’ thinking about this over this school year?

~Janice

References

A Mathematician’s Lament by Paul Lockhart (with new books Measurement and Arithmetic)

Mathematician Keith Devlin’s blog: Devlin’s Angle

Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms by Tracy Zager

The Crest of the Peacock: Non-European Roots of Mathematics by George Gheverghese Joseph

Bishop’s six universal cultural activities

Mathematical Mindsets by Jo Boaler

summer professional reading: Teaching Mathematical Thinking

Posted on: July 25th, 2017 by jnovakowski

Teaching Mathematical Thinking: Tasks & Questions to Strengthen Practices and Processes

by Marian Small

foreward by Linda Dacey

published by Teachers College Press, 2017

In this recently published book, well known math educator and author Marian Small highlights an important aspect of the discipline of mathematics – the thinking practices and processes that are “the doing of mathematics” when engaging in mathematical problems and learning content.

For those wanting clear examples of practices such as mathematical modeling, structure and argument are – the author clearly defines these with examples from across grade bands (K-2, 3-5 and 6-8).

For each practice/process, the author includes:

1) a definition with examples

2) where that practice/process is seen in K-8 mathematics

3) examples of problems, across grade bands, that might bring out that practice/process, often with examples of student responses

4) assessment questions for the educator to use to help notice and reflect on the students’ use of the practice/process

5) a short summary

I can’t think of another book that makes such careful nods to the Canadian mathematics education landscape. Although the focus is on the eight American Common Core standards for mathematical practice, the author connects these to our mathematical processes/competencies in Canada (with slight differences in different provinces/regions). Because our Canadian emphasis on visualization and mental math and estimation is not explicit in the American practices, the author has added a final chapter dedicated to these processes.

The problems are chosen to connect to each practice/process but should not be considered practice-specific. There are different types of problems – if you are familiar with Marian Small’s other books, you will understand the type of open-ness, differentiation and complexity built into the problems provided. For each practice/process she provides at least one problem for each grade band and then discusses how students take up the problems, with student examples.

I highly recommend this book. So so many wonderful problems for K-8 students and great information for teachers to help us think about the discipline of mathematics.

~Janice

summer professional reading: Teaching Math with Google Apps

Posted on: July 20th, 2017 by jnovakowski

Teaching Math with Google Apps: 50 G Suite Activities by Alice Keeler and Diana Herrington

Foreward by Jo Boaler

Published by Dave Burgess Consulting, Inc. 2017

This book opens with a foreward by Jo Boaler, with a call for educators to transform math classes. She references the Forbes list of skills needed for employment such as teamwork, problem solving, communication – all of which she argues can be enhanced through collaboration with technology. She also addresses the issue of “speed” and mathematics and how some students believe they are not “math people” because they are not fast. Boaler explains how the simple submissions of thinking and solutions on a Google form can take away the focus on speed in mathematics.

Authors Alice and Diana have both been math teachers at the high school and college levels. They emphasize the importance of digital tools in reimagining the math class with a focus on collaboration. They outline seven ways to use Google Apps to teach math:

1) Post Directions

2) Watch Students Work

3) Collaboration

4) Shift Students to Higher DOK Levels

5) Students Research

6) Shift to Facilitator

7) Conversations for Depper Understanding

The majority of the book is dedicated to overviewing 50 activities to teach math with Google Apps such as “Small Group Investigation,” “Discuss Strategies,” “Analyze Data Sets” and “Create Geometry Constructions”. The authors suggest asking yourself, “how does this activity make learning better?” Most of the activities use Google Classroom, Google Docs, Google Sheets or Google Slides and provides the advantages of using each format. Also used are Google Search, Google Forms, Google Drive, Google Chrome, Google Drawing, and Google Flights,

Links to examples and tutorials are provided. Some key reminders are interspersed throughout this section:

Teach like YouTube and Google exist.

The person doing the work is the person doing the learning.

We are a community of learners and we help each other get better.

The back matter shares examples from classrooms and highlights DOK levels (Depth of Knowledge), the 4 Cs (creativity, critical thinking, communicate and collaborate), mathematical practices for the CCSS and the 5E instructional cycle (engage, explore, explain, elaborate and evaluate).

There are lots of great ideas for tech integration and student collaboration throughout this book. Be mindful that some districts have policies or concerns regarding students having gmail accounts and as Alice has clearly said on Twitter – Outlook and Google apps aren’t really compatible. If having gmail accounts for students is frowned upon, like in my district (Richmond), take some of the ideas from this book and figure out how to make them work with the platforms that you are able to use! That will be one of my goals for the coming year as I see so much opportunity in technology enabling our secondary students to engage in in-class, cross-class and cross-school collaboration around mathematics.

~Janice

inclusive practices in mathematics for grades 6-9

Posted on: October 30th, 2016 by jnovakowski

Building on interest from an ILC (Inclusive Learning Community) project Shelley Moore and I facilitated with grade 8 teachers at Boyd Secondary, we held an after school session in October looking at inclusive practices in mathematics for grades 6-9 teachers. These practices are particularly mindful of the personal, social, intellectual and physical needs of students in the middle school age range.

Shelley began the session by sharing Richmond’s history with inclusive education and sharing some frameworks she has developed for thinking about inclusion (bowling pins, Fisher-Price stacker toy, planning pyramid, etc). She refers to inclusions lenses – personal, social and intellectual as well as places – different classrooms and places in the school as well as out of the school.

In using the planning pyramid, Shelley considers goals, tasks and questions for all students, some students and a few students, starting where ALL students can access the unit or lesson. And here’s Shelley doing the tree pose – using the analogy that everyone/all could start this yoga pose by using the wall for support!

Shelley shared the two year project with the grade 8 teachers and students at Boyd, with the first year addressing the Shape and Space curriculum and the second year examining the linear equations part of the curriculum. One example of a planning framework for an initial lesson on geometry looks like this:

We shared photographs and video from the Boyd ILC project to share how the project unfolded with the students. Blog posts about the project and be found HERE and HERE.

I shared some of the practices and structures that we considered during the ILC project at Boyd and that can be used as a guide for planning mathematics lessons and units with inclusion in mind.

Some of the choices that students were provided were what types of materials they might use. For example, during our lesson together about the volume of prisms, some students built prisms with cubes, some students used centimetre graph paper to create nets for their prisms and other drew 3D drawings that represented the measurements they were working with. Another choice was the range within the concept being addressed – for example, in the geometry lessons, identification of basic 2D shapes (faces) was an access point for all while some students investigated a range of 3D prisms. In the study of linear equations, choices of equations to investigate and represent with balances and other materials were provided, increasing in complexity or number of operations. Students were also provided with choices in how they processed or representing their thinking, for example, iPad technology was available and students could use the camera to take video or photos and then use a choice of screencasting apps to provide evidence of their understanding of the concept. Non-permanent vertical surfaces (NPVS) aka whiteboards or windows provide another choice for students who may not want to sit and work at a desk or table or use paper and pencil. The research-based practice of using NPVS has been shown to increase engagement and mathematical discourse, particularly at the middle-school age range.

I shared the idea of mathematical routines such as number talks as inclusive practices with starting points for all and a way to build an inclusive mathematical community in the classroom. These routines also focus on the nurturing and development of the curricular competencies which are the same for grades 6-9. One of the routines shared was WODB (Which One Doesn’t Belong?). This routine has become very popular in Richmond classrooms as it provides an opportunity for the clear connection between curricular competencies and content. Four items are presented and they all belong to a set/group of some sort – integers, polygons, etc but each item is unique is some way. The goal of the routine is for the students to analyze and use reasoning to justify or defend which one they think doesn’t belong in the set and why. WODBs for geometry, number, graphs, etc are available at WODB.CA – a site curated by an Ontario secondary math teacher.

Shelley has posted a pdf version of our slides from the session on her blog. They can be found HERE.

Because of interest, we will be facilitating a repeat of this session on December 6 from 3:30-5:00pm at IDC – register on our district’s event page with further follow-up sessions planned in the new year.

~Janice

Richmond’s first IGNITE event – #sd38ignite 2016

Posted on: May 10th, 2016 by jnovakowski

The Richmond School District hosted its first IGNITE event on Monday, May 9th at the Big River Brew Pub. The first IGNITE took place in Seattle in 2006 and is now a movement that is international in scope. An IGNITE talk is a five minute presentation consisting of 20 slides, auto-advancing after 15 seconds whether the speaker is ready or not. The IGNITE tagline is….”Enlighten us, but make it quick!” More information about the IGNITE movement can be found here.

Having presented a few ignite talks and experiencing the inspiration and fun that goes along with these social events, I really wanted to be able to bring this professional learning format to our district and my colleagues Rosalind Poon and Lorraine Minosky were on board and we ran with it. Chris Loat created our logo for us…

And both Chris and Lisa Schwartz agreed to be our technical support for the event. We found a site and had a meeting at the Big River Brew Pub to see where attendees would sit and how the technology and food service would play out.

We invited Richmond educators representative of primary, intermediate and secondary as well as a balance of teachers and administrators to share a story about something they are passionate about. We also invited two out of district colleagues to add to our Richmond stories.

Two weeks before the event, we hosted a rehearsal especially for educators who were new to the ignite format. It gave them a chance to meet other igniters and to practice their presentation in front of an audience. By seeing and discussing what we appreciate about others’ presentations, I think it also gave presenters some ideas for their own ignites. And its always great to have sushi…and pens.

As we were setting up on May 9th, we were all so excited to see everything fall into place. The venue was great and it was a beautiful day so the patio was open, the technology was cooperating and the tables were set with programs and sweet treats from Sinfully the Best for our guests.The burger bar was a hit and the company was great. Unfortunately two of our igniters (Neil Stephenson and Sarah Garr) had to pull out due to personal reasons.

Some of the guests…

And then the talks began! I was live streaming the talks using the Periscope app and people that weren’t able to attend the event could still watch the talks live. Between each “set” there was a 15-minute break for guests to chat about the talks, etc.

Twitter was alive with #sd38ignite…we were trending!

It was such a positive, passionate event and such a great way to build community amongst colleagues. All our igniters shared their own personal narratives within their professional narratives and these stories are what connect us and make us better together.

We will be releasing the IGNITE talks on youtube soon…watch twitter for announcements!

A HUGE thank you to our igniters…you are what made the event the success it was!

~Janice