Archive for the ‘secondary’ Category

summer professional reading: Teaching Math with Google Apps

Posted on: July 20th, 2017 by jnovakowski No Comments

IMG_6290Teaching 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.


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.

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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.


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…

SD38 Ignite logo

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.

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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.

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Some of the guests…

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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.

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Twitter was alive with #sd38ignite…we were trending!

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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!



creative thinking core competency project 2016

Posted on: May 8th, 2016 by jnovakowski

For the third year, our district has invited grade 6-9 teachers to participate in a Core Competencies project. This year, Rosalind Poon and myself hosted the project, focusing on the Creative Thinking core competency in the BC curriculum. A blog post about our first session together can be found here.

Our second session was held in January and teachers shared what they had been trying in their classrooms, nurturing students’ creative thinking focusing on the three facets of novelty & value, generating ideas and developing ideas. Leah, a grades 5&6 teacher shared a force and motion invention fair she co-coordinated at her school with students applying creative thinking to their invention design and purpose. Irene shared the creatures her grade 8 Home Ec students created, considering the facets of creative thinking.

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During the session we looked at the book, Weaving Creativity into Every Strand of Your Curriculum by Dr. Cyndi Burnett and Julia Figliotti, that we have been using in this series and in our school teams, used one of the ideas from the book to think about a concept we were studying with our students. Teachers were asked to use materials to create a soundscape to represent an idea or concept. Challenging! One teacher commented on how a student really has to understand the idea/concept and synthesize thinking in order to do this task.


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Our third and final session of the year was held at the end of April. Teachers shared ho they were weaving opportunities for creative thinking throughout their classroom programs. We asked teachers to write-up a lesson idea that was successful for them and their students and we will be compiling these ideas to share with teachers in our district.

During the session, we introduced teachers to the electronic components littleBits which were piloted in the district two years ago for the purposes of nurturing creative thinking through STEAM experiences. Different ways teachers and students have been using littleBits in the district were shared and then the teachers in the project were asked to create something that does something – being mindful of the three facets of the creative thinking core competency: novelty & value, generating ideas and developing ideas.

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As teachers engaged with the materials, they could see the possibilities for using the littleBits beyond  the electricity component of the science curriculum in grades 7 and 9. More information about littleBits can be found on the website here.

We also asked teachers to record a short professional narrative about their involvement in this project. The following is one teacher’s response:

  • I strongly believe that the focus on the creative thinking competency in my classroom this year had the most impact on my teaching and the students’ learning.  They are called the “core competencies” for a reason! Personal responsibility, communication, and critical thinking developed side by side with creative thinking.  The willingness to take risks and persevere with difficult or ambiguous learning tasks has increased tremendously.  I am also constantly amazed by the depth of thinking the students show in many circumstances. We had 2 students reflect on how learning happens in our classroom. See their thoughts below.

“Creative Thinking is the process of having original ideas of value. The Creative Thinking Challenges we do each Wednesday encourages us to think creatively when faced with a problem. Itís very important to have unique and innovative ideas, and to have different ways of overcoming challenges, especially with our rapidly changing society. We also do something called Monday Morning Provocations. Every Monday, we use a variety of materials to reflect on a question. We have more ways to show what we know, and explain our thinking visually. Not just with pencil and paper.We do a lot of activities helping us learn in different ways, not just reading a textbook, copying facts, and memorizing it. We do discussion circles where everyone shares an opinion and we discuss it. We use iPads and take pictures of our work to communicate and show our learning to parents and teachers. We use an app called FreshGrade. After every activity, we have a self-assessment/feedback frame to let us reflect on our work. Instead of the teacher giving us marks, we actually think about what we did well on, what we need to improve on etc. Overall, we think the new BC curriculum develops a creative and positive mind, which will help us in the near future.” ~ L&L

How valuable to have students reflect and comment on their learning experiences!

Roz and I look forward to continuing our work with the core competencies project next year!


inclusive learning communities: grade 8 math at Boyd, year two

Posted on: March 16th, 2016 by jnovakowski

Several schools in our district are participating in Inclusive Learning Communities projects, with a school team working alongside Learning Services staff to consider inclusive principles and practices. Hugh Boyd Secondary is continuing with a its second year in the project, investigating the question: How can we meet the diverse needs of our students in our grade 8 math classes?

A summary of last year’s project can be found HERE.

This year, the school team met with Shelley Moore and myself to look at class profiles, develop performance tasks for the beginning of a unit of study, consider and plan for inclusive practices within lessons and discuss ways of assessing students. This year, the teachers chose to focus on algebra (solving equations) and linear relations (graphing). We looked at the prescribed learning outcomes, considering what students needed to know to be successful at the grade 8 level – language, concepts, processes, skills. I introduced the team to the number balance as a way to think about balancing equations and emphasizing the concept of equivalence.

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New this year was a collaboration with SetBC – the school was provided with a half-class set of iPad tablets loaded with apps suitable for communicating learning in mathematics. SetBC facilitators provided support to the Boyd teachers in learning how to use screencasting apps such as doceri.

One of the lessons we developed together was having the students use the number balances to represent algebraic equations and then use the app ShadowPuppet to capture their process and understanding.

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A short video of this lesson can be viewed HERE. The teachers noticed the high engagement of the students and how some students were able to demonstrate their understanding of the mathematics in ways that played to their strengths.

The teachers followed up with lessons, continuing with the students creating screencasts using iPad technology.  The students were provided with choices of algebraic equations to create a table of values for and then graph using the doceri app (it has various graph paper backgrounds to choose from).

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During our debrief session before spring break, the teachers identified the new practices that helped to meet the needs of their students and that they felt would endure for them: using a performance task before the unit of study to assess where students are in their understanding, using manipulatives/models, using open-ended learning experiences, presenting three or more different entry points for students (different complexity of questions or problems) and using iPad technology.


creative thinking core competency project

Posted on: November 18th, 2015 by jnovakowski

For the third year in our district, Rosalind Poon and I are facilitating a Core Competencies Project. This series takes place over the school year, with release time provided to grades 6-9 teachers. This year, we have narrowed our focus to closely examine the Creative Thinking Competency and ways we can provide opportunities for students to develop this competency across disciplines.

For our first session together, we asked teachers to engage in a “chalk talk” about what creativity is- a strategy to record your thoughts about something and make connections between others’ ideas and yours.

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We watched a short video with Sir Ken Robinson discussing what creativity is and how we can assess it. Watch the video HERE.

We unpacked what Core Competencies are and then specifically looked at the Creative Thinking Competency.


The Creative Thinking Competency has three facets – novelty & value, generating ideas and developing ideas. Each teacher or school team of teachers was asked to choose one facet to play around with in their classrooms between our first and second sessions. Roz Poon documented our first session using Pages:

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We are using the Spirals of Inquiry cycle to engage in professional learning together. Teachers each received a copy of a teacher resource book that is full of ideas for the “taking action” part of the cycle.

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In order for teachers to connect to the Creative Thinking profiles and illustrations, we facilitated a series of mini-challenges from Destination Imagination and had teachers consider the facets of the Creative Thinking competency – novelty & value, generating ideas and developing ideas – and consider how they might describe their own competencies in these areas.

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Information about BC’s Core Competencies can be found in this short video HERE.

The information about the Creative Thinking Competency can be found HERE.

We are meeting together in January and I look forward to seeing how the creative thinking competency is coming alive in Richmond classrooms!



my first ignite

Posted on: October 29th, 2015 by jnovakowski

As part of the Northwest Math Conference, I was invited to present an Ignite session- defined in the program as “math educators present on topics that ignite their individual passions. Each talk is 5 minutes long and consists of 20 slides that auto-advance every 15 seconds, whether the speaker is ready or not!”

Five minutes is fast – as is 15 seconds per slide! I had to really think about one big idea and how I would tell the story I wanted to tell.

I decided to title my presentation “Where’s the wonder in math?” and discuss the importance of students posing their own problems and asking authentic questions that they are interested in finding answers for. I referred to Alfie Kohn’s recent publication in this area, which can be found here. I also shared references from a Google Ad that can be found on youtube here – it’s called “A Question Waiting to be Answered”.  I wanted to provoke educators’ thinking with the question: What openings are we creating for wonder in our math classes? And then I shared my story of what I have seen when the classroom is turned over to students and they are asked to notice and wonder and investigate questions and problems that are important to them. I shared several examples from Richmond classrooms and discussed ways to nurture a stance of inquiry in our classrooms. Lots packed into five minutes!

I have done a lot of presenting over the years to different sizes of crowds but for the first time, I really got the jitters. The room was set for 400 people or so and people kept streaming in, till there were educators standing all around the edges of the room. The fast-paced timing of the whole thing was out of my control and I know this is what made me anxious – usually not my style of presenting at all! The other presenters around me (three others also first-timers) were also displaying different stress behaviours – rustling notes, bouncing knees up and down, talking about how nervous they were. Thankfully, Marian Small was sitting next to me and reminded me that the slides will just keep moving and it will be what it is – not to fret.

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We did it!  All of the other talks were so inspiring and I look forward to watching them when the BCAMT posts them on their website (although I’m not sure I want to see mine – will likely skip over it).

After my heart stopped racing and I had some time to reflect…someone asked me if I would do it again. I am not sure about how I feel about doing it in this large of an arena again but I have been thinking what a great structure Ignites might be for staff meetings, professional learning etc. I am envisioning beginning a professional learning day off with a panel of Ignite sessions and then breaking out into EdCamp sessions based on on topics raised by the Ignites. And of course, what a great way for students to share what they know about a big idea. Lots of possibilities!



updated curriculum frameworks – August 2015

Posted on: August 16th, 2015 by jnovakowski

New revisions to the BC mathematics and science curriculum frameworks for K-9 were posted online mid-August.

You can find them HERE. Significant revisions to note:

1) For mathematics, the curricular competencies are the same K-5 and then a slightly different version for 6-9.

2) For mathematics, the BIG IDEAS for K-5 are now in two parts. The first part is the same across the grades and the second part (after the colon) is specific to the grade level.

3) For mathematics, the content part of the learning standards has been given a bit more detail but the elaborations are still to come (they will appear when you hover over the content).

4) For science, there are some revisions to content and the elaborations (hover over) have been extended.

5) For science, the big ideas include inquiry questions to lead to investigation of the big ideas. Hover over the big ideas to see these.

6) For science, the curricular competencies have a detailed explanation of the concept of place – hover over the word place at the bottom of this section for this to pop up. At some of the grade levels, there are other terms in the curricular competencies that are similarly explained.

There are other revised and new documents posted on the site as well.

Also, pdf versions can be found BC math learning_standards August 2015 and BC Science_learning_standards August 2015.


inclusive learning communities: grade 8 math at Boyd

Posted on: June 14th, 2015 by jnovakowski

Our district is providing release time for teachers to investigate how to better create inclusive learning communities in their classrooms and schools. Schools needed to submit proposals and the projects are being facilitated by members of our district support team. Shelley Moore is working with the grade 8 math teachers at Boyd to consider ways to differentiate instruction in their classes. Because math was the content area, I was asked to be involved. This is the first of the ILC projects with the rest of them beginning in schools in the fall.

We met to look at the curriculum outcomes that we might look at together. We discussed the value of performance-based assessment and beginning with performance tasks to see what the students already know about the concepts involved. We decided to look at the outcomes arounds surface area and volume of prisms and cylinders.

We taught lessons in two grade 8 classes with other teachers and resource teachers being able to come in and observe. Photos and video captured how the students engaged with the mathematics. We asked students to first create rectangles with an area of 12 square centimetres to see what their understanding of area was. Many students found all the possibilities. We then asked them to build a rectangular prism with a volume of 24 cubic centimetres. Many students were able to find more than one prism with this volume. The students were then asked to figure out the corresponding surface area of the prism, recording how they did this using pictures, numbers and words. Students were asked to share what they found out on the whiteboards in the classroom. A final task was to ask the students to share their understanding using a screencasting app on an iPad or to create a net for a rectangular prism with a volume of 24 cubic centimetres. A particular focus of the lessons was on use of mathematical vocabulary and seeing what language students used when communicating their thinking.

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After the introductory lessons in the two math classes, the math teachers, resource teacher and Shelley and I met to review the evidence of students’ understanding of surface area and volume by looking at photos, video, student work and debriefing the lessons. The teachers noticed that most students had a good understanding of area and surface area but had not yet generalized a “formula” for surface area of a prism. The students had a good understanding of volume of a rectangular prism and the teachers wondered if they would be able to generalize this to other prisms and cylinders. They also noted the high engagement of all the students and the value of having tools like grid paper and cubes to support the students’ understanding.

With the information from this performance task, the teachers and Shelley were able to put together class profiles and develop learning goals for all students in the class. Lessons were developed with entry points for all students.

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A framework was developed looking at the concepts for this particular “unit” and what an assessment continuum would look like for “not yet meeting, meeting, fully meeting and exceeding expectations” as well as modified expectations for each outcome. Shelley did another lesson with one of the grade 8 classes and we viewed photos and video as well as some student work to discuss student learning.


The teachers in this project commented that they valued the collaboration time and through the experience came to understand what “differentiation” could look like in their classrooms. One teacher commented that “inclusion is good for everyone” after seeing evidence of this in the classes. The teachers involved felt they could see how this planning framework could be applied to the whole grade 8 course and how well it complemented the middle years IB program at Boyd. They are curious what this might look like with a more abstract content area like algebra and are interested in how technology might support a more inclusive learning community. So although the “ILC” project is formally over for this group of teacher, they are hoping to continue their own professional learning in this area next year and we will be looking for ways to make this happen!


UBC K-12 Aboriginal Math Symposium 2015

Posted on: March 2nd, 2015 by jnovakowski

On Friday, February 27, some of our Richmond School District math mentor teachers joined about 200 other educators from across BC to participate in the annual K-12 Aboriginal Math Symposium at UBC, sponsored by UBC and PIMS. More information can be found HERE.

It was a day full of thinking, connecting and being inspired.

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We began the day with a story from Dr. Jo-ann Archibald about Lady Louse and then a guided drawing experience with Haida artist Billy Yovanovich. As he explained his drawing process, he mathematized his practices for us – lots of thinking about doubling, fractions and ratios.

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Students from two UBC Math 335 courses shared their “math fair” projects, all of which incorporated Aboriginal content or themes.

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As in last year’s symposium, the mathematics of weaving was introduced and many participants wove throughout the day as they listened to various presentations.


Educators from around the province shared projects and initiatives.




And to end our day, we came back to a story and listened to a Haida elder share Raven Steals the Light on a CD produced by CBC Radio. An online audio file can be found HERE. The Raven Steals the Light story can be found starting at the 42:00 minute mark. We were asked to consider what mathematics the story inspired. One of the ideas that consistently came up was exploring the volume/capacity of nesting boxes. We watched three young girls on a video very quickly created some boxes through paper folding and tried to keep up! The creation of one box inspired all sorts of new mathematical thinking and questions such as What is the constant ratio for the size of the paper to have a set of boxes “nest”? What size ball/sun could the box hold? How could different shaped based boxes be created?


As Weily Lin, one of our secondary math mentors teachers observed on our drive home, he sees three aspects of Aboriginal mathematics education – supporting Aboriginal students for success in mathematics, weaving Aboriginal content and culture into our school mathematics program and teaching and learning through an Aboriginal perspective. It is a lot to think about for teachers who are not of Aboriginal descent and for us in a district with such a small population of self-identified Aboriginal students. We have few elders or families to collaborate with in our context so opportunities like the symposium are really important for us to attend.