Archive for the ‘math’ Category

summer professional reading: Teaching Mathematical Thinking

Posted on: July 25th, 2017 by jnovakowski No Comments

IMG_6362Teaching 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 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,

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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

summer professional reading: Engaging Minds in Science and Math Classrooms

Posted on: July 11th, 2017 by jnovakowski No Comments

Sharing some of my summer reading here on the blog.

First professional read of the summer -

IMG_6149Engaging Minds in Science and Math Classrooms: The Surprising Power of Joy by Eric Brunsell and Michelle A. Fleming. Published in 2014 by the ASCD.

This book is a follow-up to Engaging Minds in the Classroom: The Surprising Power of Joy by Michael F. Opitz and Michael P. Ford. These two original authors edited this volume. They define joyful learning as “acquiring knowledge or skills in ways that cause pleasure or happiness.” They surmise that when students are engaged learners, joy emanates from the learning process. Their joyful learning framework is the foundation for this follow-up book.

This book has four short chapters -

1) Understanding Joyful Learning in Science and Math

Drawing upon current research, the authors outline the joyful learning framework and answer the question Why joyful learning? with:

  • it capitalizes on what we know and how to best motivate students.
  • it enables us to build upon what we currently know about engagement
  • it enables us to focus on the whole child
  • it acknowledges that the learner is influenced by the contexts in which learning takes place

2) Evaluating and Assessing Joyful Learning

This chapter outlines frameworks to evaluate learners, ourselves as teachers, texts and materials, assessments and school-wide configurations. The frameworks for evaluating learners parallels the one for evaluating teachers and both provide some thoughtful questions for consideration.

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3) Implementing Joyful Learning in Science and Math

Strategies, structures and examples of ways to implement joyful learning are provide for several contexts: school community, classroom environment, whole-group instruction, small-group instruction and individual instruction.

4) Using Joyful Learning to Support Education Initiatives

The final chapters makes connections to standards, accountability and assessment, RTI, achievement gaps and professional development, drawing upon research studies to support the importance of engagement and interest in learning to standardized test results.

The book ends with a reminder to teachers to assess their own joyful learning and to look for joy in unexpected places and a quote from author Henri Nouwen:

“Joy does not simply happen to us. We have to choose joy and keep choosing it every day.”

The ideas of identity, student self-efficacy, challenge, choice, creativity and goal orientation resonate throughout the book. This speaks to me about students’ understanding of what it means to be a learner and what their role in that is – not as a passive, compliant recipient, but as a fully engaged, curious learner.

One issue that the authors return through out the book is that for students to be engaged in joyful learning, they need to focus themselves on “mastery” goals (learning that focuses on learning content) versus performance goals (learning for the purpose of getting a grade or being compared to others). After hearing Megan Franke’s keynote presentation at the CGI Conference in Seattle this year, I bristle at the term “mastery” and would rather consider these goals as just learning goals.

Another area of interest that reading this book re-ignited for me was the concept of engagement. I have thought about this a lot over the years and read quite a bit in this area during my doctoral studies. The authors look at the relationship between motivation and engagement but don’t tease apart what they mean by engagement very thoroughly even though they come back to and use this term throughout the book. They describe engagement as “being attentive, committed, persistent, and seeking meaning.” There are many types of engagement – physical, emotional, cognitive etc and sometimes I think compliance can actually be perceived as engagement which is a concern.

As I zipped through this quick read, I made many connections to both of the books Mathematical Mindsets by Jo Boaler and Embracing a Culture of Joy: How Educators Can Bring Joy to Their Classrooms Each Day by Dean Shareski. I highly recommend both of these books!

~Janice

reflections and highlights from 2016-2017

Posted on: June 29th, 2017 by jnovakowski No Comments

To say this has been an interesting year in our district is an understatement. We began the year with a new email system, a new “portal”, a new eportfolio platform, a huge changeover in our district curriculum department all while under the umbrella of the full launch of BC’s K-9 curriculum framework across all subject areas. New layers were added as information about communicating student learning and core competencies self-assessment were added to the mix. We began the year with uncertainty about school closures and ended it with concerns about whether we would have our jobs and where money would come from to fund teaching jobs in our district.

In all of these twists and turns, there were some downs but also many ups.

There were many opportunities for educators in our district to come together and figure everything out (an ongoing process for sure). Professional development days, our Curriculum Implementation Day, professional learning events and series and the power of twitter to share ideas and collaborate.

In thinking back on this year, I will remember all the times I was surrounded by inspiring colleagues and in classrooms thinking alongside students about big ideas – this is what fills me up and sustains me.

Some professional highlights for me include:

  • the Creating Spaces for Playful Inquiry dinner series – this large group of K-7 teachers continues to come together to engage in provocations and think about playful inquiry across the curriculum, this year looking at broad themes of community, identity and place
  • visiting the Susan Point exhibit at the Vancouver Art Gallery twice with colleagues and how that inspired connections in our classrooms – place, ecosystems, environmental sustainability, stories and math
  • having the opportunities to share our thinking from #sd38learn in other places –  Coquitlam, Kamloops, Sooke, Niagara Falls, Seattle, Burnaby, Vernon, Vancouver, Victoria and Cranbrook
  • being part of the BC Numeracy Network – this team of enthusiastic educators from across BC have collaborated to create a website that will support K-12 educators as they think about balanced numeracy through the lens of BC’s curriculum
  • being on the program committee for the National Council of Teachers of Mathematics (an international organization) for their annual conference in San Antonio in April
  • hosting teams of educators as they visit our district (from across BC, Manitoba and Sweden) – it is always interesting to hear about what they are noticing and what is resonating for them
  • working in collaboration with the Musqueam Language and Culture department to develop our first project together
  • being a part of the BCAMT Reggio-Inspired Mathematics collaborative professional inquiry project – this project continues to grow and we are working on publishing a book this summer with contributions from ten districts

But when I think about the biggest highlight of the year for me and what I believe has affected both students and educators on many levels, I think about the creation of The Studio at Grauer. My heart is so full when I think how Marie Thom and I transformed an old classroom being used for storage into a studio space to investigate mathematics through a variety of materials.

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And my summer reading “stack” – yes, there will be novels, travel books and magazines as well!

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I hope to share some of my thoughts on these books on the blog over the summer.

Wishing you a summer full of adventure and time to refresh!

~Janice

thinking about fractions

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

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

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

How can we order and compare fractions?

When do we use fractions in our daily life?

What different ways can we represent fractions?

What are equivalent fractions?

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

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

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

What do you notice? What do you wonder?

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

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

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

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~Janice

The Studio at Grauer

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

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

December 16 2018 – Room 102

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

Room 102 – January 10 2017

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January 13 2017

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

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

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

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

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

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

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

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

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

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

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

~Janice

 

 

TWOKAM Day 2017

Posted on: May 30th, 2017 by jnovakowski No Comments

This year, the Richmond School District held several events to promote Talk With Our Kids About Money Day on April 19. TWOKAM is an initiative coordinated by the Canadian Federation for Economic Education and is endorsed by the Richmond School District’s Board of Trustees.

More information about TWOKAM can be found on the CFEE website HERE

On March 28 we hosted an evening event for parents from across Richmond Schools at Cook Elementary. This event was facilitated by Tracy Weeks, the BC regional coordinator for CFEE and Jonathan Ho, a Richmond School Board Trustee. The event was well-attended and parents received some resources to support them in talking to their children about financial literacy. They engaged in some financial literacy tasks themselves!

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On March 30, we hosted an after school session for intermediate and secondary teachers. I shared the BC Mathematical K-9 curricular components regarding financial literacy. Rebeca Rubio shared some of the new financial literacy resources available through the DRC and then Tracy Weeks shared the CFEE TWOKAM resources with teachers.

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On April 1st, Tracy Weeks continued to share information about financial literacy with parents at our district’s Learning and The Brain conference.

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On TWOKAM day, we hosted an evening event for students and their parents at Hugh Boyd Secondary. Speakers Tung Chan and Paul Lermitte inspired important conversations about financial literacy and the role parents play in supporting their children’s understanding of this important concept.

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We are looking forward to continuing to increase awareness of TWOKAM day in our district and create opportunities for our students to engage in developing financial literacy in our schools.

~Janice

creating spaces for playful inquiry: April 2017

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

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

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

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

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

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

~Janice

Big Mathematical Ideas for Grades 3-5: year four

Posted on: May 25th, 2017 by jnovakowski No Comments

This after school series is in its fourth year, focused specifically on the foundational mathematical concepts in grades 3-5 such as operations, place value and fractions. This year, we met once a term after school in Jennifer Plummer’s French Immersion grades 3&4 classroom at Homma Elementary (thank you for hosting Jennifer!).

For our first session in the fall, we focused on number sense and operations and the curricular competencies of reasoning and communication. I had recently been to the NCTM Regional Conference in Phoenix and shared a great game that I was reminded of in one of the sessions there.

The Product Gameboard

The Product Gameboard instructions

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At our second session, in January, we focused on financial literacy and mathematical inquiry. I shared the new Pizza Co. game for the iPad from Osmo as well as some other resources and children’s books to support the financial literacy content in the BC Mathematics Curriculum.

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BC K-5 Mathematics Big Ideas

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For our third session in April, teachers in the series requested a focus on assessment, place-based learning and connecting the core and curricular competencies.

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BC K-5 Math Communication

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We explored curricular content and competencies by investigating with power polygons.

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Looking forward to continuing the conversation around big mathematical ideas next year!

~Janice

Provincial Numeracy Project in Richmond – year two

Posted on: April 24th, 2017 by jnovakowski

For the second year, Richmond is one of several districts in the province that are taking part of an adapted version of Changing Results for Young Readers in the form of Changing Results for Young Mathematicians. Provincially, this project is not just focused on young students but for K-12 students and their teachers and has been called the Provincial Numeracy Project.

This year, three school teams of primary teachers and a Learning Resource Teachers are participating – teams from Whiteside, Grauer and McNeely.

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Several routines such as Counting Collections (see tedd.org) and High Yield Routines (book published by NCTM) were shared with teachers as elements that could be introduced as both whole class and small group instruction.The  importance of assessment to inform instruction was discussed and the importance of spending time being present with our students – listening, noticing and talking with them. This is a critical practice in this project – really zooming in on students’ mathematical thinking.

One of the handouts provided to teachers was a collection of Number Sense tasks and background information connected to the Kathy Richardson book we would be using. The handout package can be downloaded here: Didax Number Sense guide

number concepts kathy richardsonUnfortunately, our second session together was cancelled due to a lack of TTOCs. Between sessions, copies of Kathy Richardson’s book How Children Learn Number Concepts was delivered to each teacher in the project. Teachers were asked to zoom in on one section of the book and make connections to what they were noticing as their students engaged in counting or other number routines.

Each Orange Had 8 Slices Teachers were also provided with a copy of the classic math picture book Each Orange Had 8 Slices and were encouraged to share some of the pages with their students and engage in playful and joyful mathematics – counting, problem posing and problem solving.

The one-pager that was created to accompany the book to send home with students to engage in joyful math with their parents can be downloaded here: Each Orange Had 8 Slices.

For our third and final session in March, school teams shared what they had been trying and what they had been noticing in their classrooms.

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A specific focus on the reasoning and analyzing section of the curricular competencies was explored through estimation. Estimation is a good indicator of students’ number sense and is an important competency to develop and use in many contexts – both computational and with measurement. The estimation information and connections to literature that was developed as part of the BCAMT Reggio-Inspired Mathematics project can be downloaded here: Estimating final

We also looked at the curricular competency: “use reasoning to explore and make connections” through routines such as Number Talk Images and Clothesline.

How many ducks are there? How do you know? What different ways can you see the quantity?

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A blog post of how clothesline math has been used in kindergarten classes in Richmond can be found HERE.

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Teachers in the project each received a copy of Which One Doesn’t Belong? by Christopher Danielson and connections to our BC curricular competencies in math were made – communication, reasoning, justifying and explaining.

As part of the project, teachers were asked to pay attention to a child who they were wondering about – a child whose math learning was causing questions for the teacher. Based on the findings from Changing Results for Young Readers, we felt that focusing on the learning of one child, and how that child  responds to new ways of approaching math learning, would influence the class’ learning as a whole. Teachers were asked to reflect on this as well as write a short professional narrative reflecting on their own professional inquiry during the project. A collection of excerpts from the teachers’ reflections are included below:

“We are having to unlearn the ways we learned math in order to think about ways we can help the students build a solid number sense foundation.”

“I noticed increased student ownership over their own learning. They are choosing collection at their just right level and are trying to figure out, on their own, ways to count their collection in multiple different ways. Students are beginning to be able to communicate their thinking about the strategies they use to count their collections.”

“I have a better understanding of number concepts and where to go next to help/challenge a student.”

“High Yield Routines had high engagement levels and encouraged a lot of math talk in our classroom.”

“I noticed that I was taking chances in my teaching during this project, allowing myself to learn alongside my students.”

“I learned that math is about exploring and sense-making.”

“Students were engaged with math talk images of actual objects rather than dots or ten frames.”

“My students are more engaged and more hands on with the math now as a result of the changes I made.”

“Students are now expected to voice and articulate and justify their thinking about why they feel their answer could be right.”

“I learned about recognizing the phases of mathematical development and how foundational skills contribute to deeper meaning and understanding for students in subsequent years.”

“I noticed that I need to step back and invest time to delve into student learning and understanding beyond the correct answer.”

*****

~Janice