Archive for the ‘assessment’ Category

2017-18 big mathematical ideas for grades 3-5

Posted on: May 13th, 2018 by jnovakowski 2 Comments

In its fourth year, a group of grades 3-5 teachers came together three times after school to think about the big mathematical ideas for this grade range, considering the pedagogical content knowledge needed to teach and assess student learning. Our first session of the year on October 18 focused on the number concepts big ideas in our curriculum which at gates 3-5 focus on a deep understanding of fractions.

We began with an image from fractiontalks.com – a website curated by Canadian math educator Nat Banting. We considered what students needed to understand about fractions to engage with this task and anticipated how are students might respond to the challenge of figuring out what fractional part of the large square is the shaded blue triangle.

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We considered how different materials provided different affordances for thinking about fractions, particularly thinking about different ways to represent fractions – set, area and linear. Some of the text slides from the session and a handout follow.

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Unfortunately, I had to cancel our January session due to illness.

We came together again on April 11 and based on feedback from the group, discussed computational fluency and the role of inquiry in learning mathematics. We revisited instructional routines such as Which One Doesn’t Belong? (wodb.ca) and considered how these routines incorporate questioning, wondering and nurture the curricular competencies in mathematics.

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~Janice

elementary math focus afternoon 2018

Posted on: May 11th, 2018 by jnovakowski No Comments

On the afternoon of January 26, staffs from twelve elementary schools gathered at Grauer Elementary for our annual Elementary Math Focus Afternoon.

The overview slides (photographs from classrooms not included to reduce file size) from the opening to the afternoon can be found here:

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Many school teams brought displays to share how they have been working with BC’s redesigned mathematics curriculum.

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Educators could choose from a variety of Richmond teacher-led sessions to learn about instructional routines and practices that are aligned with the BC redesigned curriculum.

FINAL_Elementary Math Focus Afternoon Jan 26 2018 program

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Handouts from Fred Harwood’s sessions can be downloaded here:

Elem Focus Day Jan 2018 Rich Investigations

2018 Elem Math Focus Visual patterns

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Thanks to Tracy Weeks of the Canadian Federation for Economic Education (CFEE) for coming and sharing information about financial literacy with Richmond educators.

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As educators gathered back in the gym for an end of afternoon prize draw of math resources, they were left with a reminder to consider the mathematical story that is being told in their classrooms and schools. What story do we want our students to tell about their mathematical experience here in our district?

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~Janice

graduation numeracy assessment – January 2018

Posted on: May 11th, 2018 by jnovakowski No Comments

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

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

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

link to Graduation Numeracy Assessment information 

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

~Janice

creating spaces for playful inquiry: thinking about reflection – January 2018

Posted on: May 11th, 2018 by jnovakowski No Comments

On January 25, Richmond educators gathered at Grauer for our second dinner session of our Creating Spaces for Playful Inquiry professional learning series. This month our focus was on reflection and time. Educators shared their experiences engaging in playful inquiry with their students and considering the role of reflection in documentation and making both students’ and our professional learning visible.

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After dinner together, teachers participated in interest groups facilitated by our playful inquiry mentors.

A handout with curricular connections to the idea of reflection can be found here: Reflections_Provocations_Jan25_2018

~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.

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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.

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

~Janice

 

summer professional reading: THINQ Kindergarten (and Grades 4-6)

Posted on: July 28th, 2017 by jnovakowski 2 Comments

IMG_6380THINQ Kindergarten: Inquiry-based learning in the kindergarten classroom

by Joan Reimer and Deb Watters

THINQ series authors: Jennifer Watt and Jill Colyer

published by WAVE Learning Solutions, Canada, 2017

accompanying website: www.wavelearningsolutions.com

This is a relatively new series of books, written by Canadian (Ontario) authors. The Kindergarten book just came out this spring. One of the many things I like about this book is that it acknowledges that there are many interpretations of inquiry and not “one way” to engage in inquiry. There is a focus on remembering that being inquiry-minded is part of being human and that we are born with curiosity. I also like the recognition of the importance of the learning environment and the emphasis on developing inquiry dispositions. The “Inquiry in Action” sections share learning stories or case studies from classrooms. As I read the book, I added lots of post-it notes to pages to go back to, particularly connections I was making to our BC competencies – both core and curricular.

There are seven chapters:

1) Inquiry-based learning in kindergarten

2) Wondering and questioning

3) Creating an inquiry environment

4) Negotiating the curriculum

5) Documentation

6) Inquiry assessment in kindergarten

7) Final thoughts

IMG_6381The layout for each chapter is very similar. There is lots of “white space” and use of text boxes and colourful visuals to support the content of the chapter. Each section has a big idea and often quotes from well-known educators and authors.

 

 

 

 

IMG_6382At the end of each chapter there is a chapter summary with some questions to provoke reflective thinking. There are also “thumbnails” of the blackline masters/printables that accompany each chapter and can be found at the back of the book.

 

 

 

 

 

 

IMG_6383The printable resources at the back of the book correspond to each chapter and focus on the big ideas from the chapter as well as templates for educators to use for planning and assessment.

 

 

 

 

The Grades 4-6 book was release last year and is very similar in format to the Kindergarten book. Interestingly, in this book, the assessment chapter is up front and then assessment ideas are woven throughout the rest of the book. I wonder if that is because this is a pressing issue for intermediate teachers – how to assess student learning during the process of inquiry? I know this question comes up a lot in my work with teachers. There is also much more of an emphasis on questions of personal significance, inquiry approaches across disciplines and the importance of providing feedback (often through questioning_ during the inquiry process in the Grades 4-6 or Junior book. The printable resources focus more on student self-assessment templates than the Kindergarten book.

The Grades 1-3 book and the Grades 7-9 book are supposed to be released this summer or fall.

~Janice

summer professional reading: Teaching Mathematical Thinking

Posted on: July 25th, 2017 by jnovakowski

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

Big Mathematical Ideas for Grades 3-5: year four

Posted on: May 25th, 2017 by jnovakowski

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

Vision, Mission and Values Project at Thompson Elementary

Posted on: March 20th, 2017 by jnovakowski

The Richmond School District is embarking on a legacy project, developing new Vision, Mission and Values statements for our district. Teachers were invited to engage in discussions with their students and collect artifacts to contribute to the district process of creating new VMV statements. Two intermediate classes and their teachers from Thompson agreed to do some special filming for a district video for this legacy project.

At the beginning of January, I was able to meet with classroom teachers Lyanne McCaskill (grades 5&6) and Kevin Dimmick (grades 6&7) to plan how this project might unfold. The teachers put a lot of thought into the experiences they wanted to provide for their students. I was fortunate to be able to attend three different learning experiences with the students and to capture the students’ thinking and ideas with photographs and videos.

On the first day, as is the usual routine, the students in both classes entered their rooms to the morning provocation: What do you imagine school could be? They were invited to respond to the question using loose parts. Some students focused on the physical environment while others focused on metaphors and ideas. Each class paused to go to each table group and have those students share what they had done. Students could go back to their spots to revisit their work, connecting to new ideas or inspiration. Students were then asked to reflect on their thinking using a familiar response form.

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In the grades 5&6 class…

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In the grades 6&7 class…

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On the second day, the teachers used the Vision, Mission and Values from the Vancouver Aquarium website to initiate discussion about what Vision, Mission and Values are. In one class, the students were asked to use a familiar response format (Notice, Connect, Wonder) as they discussed and thought about the Aquarium’s VMV statements while in the other class, they used the Vision, Mission, and Values framework and questions as a way to respond.

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In one of the classes, the students sorted different statements they had made in their own reflective writing about VMV – there were very interesting discussions that emerged as students distinguished between what was part of a vision, mission or values statement.

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The students worked in small groups to create charts of words and phrases that connected to Vision, Mission or Values and these were displayed in the classroom for students to read and discuss.

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On our third day together, the teachers began their days as they had the first day – with a morning provocation posted for the students to engage with and loose parts available. The original question of What do you imagine school could be? was now linked to Vision, Mission and Values. The students could choose one or all of the three areas to represent and record their ideas about.

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It was fascinating to watch how the students’ ideas evolved over time and how each class had its own particular culture it terms of what came out in the students’ representations – kindness, inclusion, community, diversity and collaboration were the five big ideas that stood out to me as I listened to and read the students’ contributions to the project.

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An short video compilation of the Thompson VMV experience can be viewed HERE.

What has stuck with me, while spending time in these classrooms is the wisdom of our students. Their lived experiences in different types of learning environments, their understanding of each other, the importance of collaboration and the purpose of schools within a society made my heart sing. Our future is in good hands.

~Janice