Archive for the ‘communication’ Category

December thinking together: visualize to explore mathematical concepts

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

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

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

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

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

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

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

 

Instructional Resources

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

 

 

 

 

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

 

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

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

 

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

visualize and graph linear relationships and functions and relations.

 

 

So what does it mean to be proficient with visualizing?

As we begin to work with the new proficiency scale across BC, we need to consider what it means to be proficient with visualizing to explore mathematical concepts in relation to the grade level curricular content. As more teachers across the provinces the the scale, we will have examples of student proficiency that demonstrates initial, partial, complete and sophisticated understanding of the concepts and competencies involved.

For example, a grade six student at the end of the year would be considered proficient with visualizing geometric transformations if they were able to follow directions to mentally translate, rotate and reflect a 2D shape and show or describe the resulting orientation/position.

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

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

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

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

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

~Janice

 

References

Thinking Through and By Visualizing (NRICH)

The Power of Visualization in Math by Jeremiah Ruesch

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

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

 

September thinking together: mathematics curricular competencies

Posted on: September 28th, 2018 by jnovakowski No Comments

For the 2018-19 school year, the “thinking together” series of blog posts will focus on the curricular competencies in the mathematics curriculum.  The “thinking together” series is meant to support professional learning and provoke discussion and thinking. This month will provide an overview of the curricular competenecies and then each month we will zoom in and focus on one curricular competency and examine connections to K-12 curricular content, possible learning experiences and assessment.

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The curricular competencies are the “do” part of the know-do-understand (KDU) model of learning from BC’s redesigned curriculum.

The curricular competencies are intended to reflect the discipline of mathematics and highlight the practices, processes and competencies of mathematicians such as justifying, estimating, visualizing and explaining

The curricular competencies are connected the the Core Competencies of Communication, Thinking  and Personal & Social. More information about the Core Competencies can be found HERE.

 

Screen Shot 2018-09-28 at 9.45.26 PMThe curricular competencies along with the curricular content comprise the legally mandated part of the curriculum, now called learning standards. This means these competencies are required to be taught, assessed and learning achievement for these competencies is communicated to students and parents.

Something unique about the mathematics curricular competencies is that they are essentially the same from K-12. K-5 competencies are exactly the same with some slight additions in grades 6-9 and then building on what was created in K-9 for the grades 10-12 courses. Because they are the same at each grade level, to be assessed at “grade level” they need to be connected to curricular content. For example, one of the curricular competencies is “estimate reasonably” – for Kindergarten that will mean with quantities to 10, for grade 4 that could mean for quantities to 10 000 or for the measurement of perimeter using standard units and for grade 8 estimating reasonably could be practiced when operating with fractions or considering best buys when learning about financial literacy.

The new classroom assessment framework developed by BC teachers and the Ministry of Education focuses on assessing curricular competencies and can be found HERE.  A document outlining criteria categories, criteria and sample applications specific to K-9 Mathematics can be found HERE. The new four-point proficiency scale provides language to support teachers and students as they engage in classroom assessment.

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As we are begin a new school year and are thinking about year plans and overviews we might consider the following questions:

  • What opportunities do students have to learn about what it means to be a mathematician and what mathematicians do?
  • What opportunities can be created over the school year for students to name, be aware of, practice, develop and reflect on the core and curricular competencies in mathematics?
  • How can we make the core competencies and curricular competencies in mathematics visible in our classrooms and schools?
  • As we are planning for instruction and assessment, how are we being intentional about weaving together both curricular competencies and content? What curricular content areas complement and are linking to specific curricular competencies?

~Janice

April thinking together: How do the core competencies connect with mathematics?

Posted on: June 7th, 2018 by jnovakowski

The Core Competencies are at the centre of BC’s redesigned curriculum and underpin the curricular competencies in each discipline, such as math. An overview video about the Core Competencies can be viewed HERE. Drawing from global education research and through provincial consultation with stakeholder groups, three Core Competencies were identified – Thinking (creative and critical), Communication and Personal & Social (positive personal and cultural identity, personal awareness and responsibility, and social responsibility).

As we develop awareness about the Core Competencies during the school year, we consider the ideas of “notice, name and nurture” – looking for evidence of core competency development or application in our classrooms and schools.

In our district, we have created Core Competency posters in both English and French, overviewing all the core competencies as well as posters specific to one core competency (all available through the district portal). These posters are up in classrooms and schools to create awareness and develop common language around the core competencies.

In The Studio at Grauer, much of the work we do in mathematics has elements of the core competencies involved. In the mathematics curriculum, each of the curricular competencies is linked to one or more of the core competencies. The COMMUNICATION chart in the photograph below is an example of how I make this focus clear to myself, teachers and the students when we work together in The Studio. I often identify a specific curricular competency in our initial gathering meeting, that we are going to focus on together as we work with a mathematical idea. For example, I might say to the students,
“Today as you are thinking about comparing and ordering fractions with materials, practice explaining and justifying your decisions to a partner – that will be our focus when we come back as a whole group at the end of our time together today.” 

Other times, I will ask the students to reflect on their last experience in The Studio and consider what they need to work on around communication, either personally or as a class.

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The following are documents that show the links between the Core Competencies and the Curricular Competencies in Mathematics:

SD38 K-5 Math Connections between Core and Curricular Competencies

SD38 6-9 Math Connections between Core and Curricular Competencies

SD38 K-5 Math Communication

We have woven self-assessment and reflection about the core competencies into our projects and learning together throughout the year. During the last school year, there was a requirement for students to do a “formal” self-assessment to be included in the June report card. For students to authentically self-assess and reflect, they need to be familiar with the language of the core competencies and be able to connect to learning experiences they have had throughout the school year. During the third term last year, the grades 3&4 class from Grauer visiting The Studio weekly to engage in a mathematics project around the work of Coast Salish artist Susan Point. At the end of each session together, we had the students share their learning – what did you learn? how did it go/what did you do? what’s next for your learning/what are you wondering about? Sometimes students turned and talked to someone near them, other times, students shared their learning and thinking to the whole class.

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Every few weeks, we had the students do a written/drawn self-assessment and reflection. We have found that using question prompts to support reflection and considering evidence of learning has been the most authentic and personalized way to have students think about and connect to the core competencies. We developed some recording formats to capture students’ thinking, with the clear intent that students are not expected to “answer” all the questions – that they are they to prompt and provoke reflection and self-assessment. A team of Grauer educators were working together on an Innovation Grant project around creative thinking and growth mindset and we wove these ideas in to some of the self-assessments.

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Here is one example of a recording form:

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As we are coming to the end of another school year and are thinking about the student self-assessment of the core competencies component for year-end communication of student learning, we might consider the following questions:

  • What opportunities have students had to experience and develop the core competencies in their mathematics learning?
  • What opportunities over the school year have students had to name and reflect on the core and curricular competencies in mathematics?
  • How have we made the core competencies and curricular competencies in mathematics visible in our classrooms and schools?
  • How have the core and curricular competencies language and ideas been embedded in the mathematical community and discourse in our classrooms and schools?
  • What different ways have students been able to share, reflect on and self-assess their mathematical thinking and learning?

~Janice

Story Workshop series – 2018

Posted on: May 24th, 2018 by jnovakowski

A group of district teacher consultants and school-based teachers came together this spring to facilitate a three-part Story Workshop after school series. This was in response to many requests and questions  from teachers in our district about Story Workshop. The facilitators of the series were: Sharon Baatz, Louesa Byrne, Michelle Hikida, Carrie Bourne, Lisa Schwartz, Marie Thom and myself.

A goal of this series was to honour the work of Opal School educators who developed the structures and practices of Story Workshop as a way to connect the arts and literacy. Opal School educators draw upon social-constructivist learning theory and have been informed by the early childhood educators in Reggio Emilia, Italy as well as American educators such as those working with Harvard’s Project Zero initiatives. Opal School has a deep commitment to equity and access for all students and to develop student agency.

They are many other ways we might engage our students in storytelling experiences – oral, digital, writers workshop etc but the focus of this series was to create awareness and understanding of Story Workshop as developed by Opal educators. The Opal educators have developed five structures or stages of Story Workshop. Some stages are more for the educator to consider and some take more time than other stages. Some of the structures such as negotiation or congress might involve small groups of students and an educator instead of the whole class. Over the series, we hope to develop a deeper understanding of the process of Story Workshop and what it offers the students in our classrooms and what it offers us as educators.

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In our first session on April 9, we focused on the stages of Preparation and Provocation. We watched and discussed the Opal videos and Michelle, Louesa and Sharon shared examples of these stages of Story Workshop from their Richmond classrooms.

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We watched and discussed the first two videos of the series and used the following questions to frame our small group discussions:

What do you notice about the materials the teachers are using?
When you look around your own setting, what unexpected materials might you use in new ways?
What do I want the children to learn?  How can I support this learning?

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Story Preparation begins with our image of children. Preparation is about preparing the environment; setting up the space, creating an environment that supports children to tell their stories. Opal educators strive for environments that are playful, engaging, naturally motivating, with multiple opportunities for all children to enter into the work.

At Opal, educators convert social-constructivist theory and inquiry into practice by offering provocations. A Story Provocation is a question that is introduced to children to engage and support their interests and curiosity.

The Opal videos can be found here:

Story Workshop – Story Preparation

Story Workshop  - Story Provocation 

IMG_6207Educators attending the series were each provided with the book Equity and Access Through Story Workshop.

The videos and supporting text are available at no cost to Opal School Online Sustaining Members and at a small cost to non-members: You’ll find both here.

Educators were asked to make a commitment to something they would try, inspired by the first session, and to be prepared to share a reflection, documentation or an artifact at our next session.

 

IMG_7269At the second session on April 30, we began by having teachers share what they had tried around Story Workshop with their students. Lisa shared how Story Workshop can be part of a balanced literacy program. Marie talked about different ways to approach Story Workshop with different ages of students and that the process needs time and patience, not rushing towards recording/writing the stories.

We also shared copies of this blog post from Opal for educators to read and reflect upon their own practice and how Story Workshop might be enacted in their classrooms and schools.

We focused on the next two stages of Story Workshop – invitation & negotiation and story creation.

At Opal, the invitation and negotiation time focuses on students being metacognitive about their plans for each day. It is often just a few minutes with opportunities for educators to have a one-on-one check in with students.

At Opal, educators invite children to explore the classroom and materials in search of their stories and this time can last about 45 minutes. Story Creation is a time of looking for and finding stories from the child’s real or imaginary life. Children play with materials, talk to each other, and tell and write their stories.

Sharon and Louesa shared examples from their classrooms:

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The Opal videos can be found here:

Story Workshop – Story Negotiation

Story Workshop – Story Creation

Again, teachers were asked to try something around story negotiation or creation and to consider an area of Story Workshop that they would like to go deeper with.

At our final session on May 14, we invited teachers into The Nest and to think about how different materials might inspire different types of stories.

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Each educator was given the book I Am A Story by Dan Yaccarino (it comes in both English and French) as a provocation for adults and children to think about different ways that stories can be shared.

We focused on the importance of Story Congress as a way for educators and peers to give feedback on students’ stories. Sharon, Louesa and Michelle shared some of the structures they use in their classrooms for this stage of Story Workshop.

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The Opal video can be found here:

Story Workshop – Story Congress

Opal School has online courses available to extend and deepen understanding of playful literacy and Story Workshop. More information can be found HERE.

This was a very well attended series with a waiting list and we hope to be able to offer it again next year. Many teachers asked if we could provide opportunities to visit Richmond classrooms to see Story Workshop in action and we will put something in place for this for next year.

Some of the feedback from series participants include:

“I appreciate how professional the mentor presented so many awesome ideas, so well laid out. This series has profoundly affected my thinking and practice.”

“This series helped me think about Story Workshop, storytelling, oral storytelling, loose parts and how they are different yet integrated.”

“It has helped me breathe. Hearing how others navigate and problem-solve the same challenges I have encountered  has given me comfort and loads of inspiration.”

“This series extended my thinking about Story Workshop by exposing me to more diverse ways to engage with stories – outdoor, leaves/herbs, spindle whorl, clay markings etc.”

~Janice

elementary math focus afternoon 2018

Posted on: May 11th, 2018 by jnovakowski

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:

Math_Focus_Opening_2018_textslidesonly

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

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

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

creating spaces for playful inquiry: thinking about relationships – September 2017

Posted on: October 5th, 2017 by jnovakowski 1 Comment

Inspired by our staff’s visits to the Opal School in Portland, we continue this year with our Creating Spaces for Playful Inquiry Series. Sixty Richmond educators registered for this three-part dinner series, with a growing waiting list of educators wanting to be part of this series. This continued interest in this work speaks to the ripple effect that our playful inquiry community is having in schools and in our district. Many new teachers have heard about playful inquiry and how it aligns with goals and aspects of BC’s redesigned curriculum. A goal for the series is for teachers to consider: How can we create new possibilities for joy, wonder and inspiration?

So what is playful inquiry? Playful inquiry is not a new term and much has been written about it as a pedagogical stance. In Richmond, we have drawn upon our experiences and relationship with the Opal School in Portland and made connections to our BC context and curriculum. At our last study tour to Portland in March, the following explanation of playful inquiry was provided:

Opal_playfulinquiry_quote

In this explanation of playful inquiry words such as community, collaboration, citizen and uncertainty pop out. The term “learning alive” resonates with the spirit of inquiry we are hopeful of nurturing in our classrooms. Why playful inquiry? The above definition suggests an approach that will support students in thinking through the uncertainty in the world around them and nurture student agency in seeing themselves as contributing citizens in their community. So we can work together towards the goals and vision of what playful inquiry can bring to our classrooms and schools.

So how do we enact playful inquiry in our classrooms? For planning purposes, we often use the framework of -

  • playing with materials
  • playing with language
  • playing with ideas

to help us consider different ways to engage our students and ourselves with playful inquiry.

Playful inquiry creates opportunities for deeper engagement with concepts and idea, choice in ways students may pursue uncovering the curriculum, personalization and meaning-making as well as providing openings for connection-making, seeking relationships – both with self, each other and with ideas.

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As teachers arrived at Grauer Elementary, they were provided with provocations created by our playful inquiry mentors. These provocations were either pedagogical – meant to experience through the lens of an educator and to reflect on practice or, were those that students engaged with in Richmond classrooms.

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After a welcome, introductions and an overview of the series, teachers shared and discussed questions such as:

What is a provocation? How is a provocation alike and different from an invitation or a rich open task? 

Some conditions for provocations were shared:

  • žresponsive
  • žprovokes thinking
  • žconnects to a big idea, concept or theme
  • žis ongoing, lingering, extends

We talked about the theme of relationships for this session and how relationships were an inherent part of teaching and learning – social and emotional relationships but also relationships with and between curricular ideas. Some of the provocations shared and how the concept of relationships is embedded throughout our BC curriculum were provided to participants here:

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Other big ideas and themes that we have engaged with as a playful inquiry community were shared:

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Three of our playful inquiry mentors shared stories from their classrooms. Michelle Hikida from Diefenbaker shared how her and grades 2-4 group planning team are focusing on the big idea of stories this year and how they collaborate together to plan provocations based on students’ interests an questions. Laurie David-Harel from Whiteside shared the movie trailer she created for her school’s parent evening to share how the Kindergarten students in her class engage in playful learning. Karen Choo from Blair shared how sharing circles and using clay as a metaphor supports relationship building in her grades 4&5 classroom.

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After dinner together, teachers met in interest groups with conversations and sharing facilitated by our playful inquiry mentors.

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Many of the interest-based inquiry groups will continue their conversations with schools visits, online collaboration or other forms of sharing before our next whole group session together in January.

Participants were asked to consider what “one thing” they will play with, try , take risks with…what might be your one thing?

Blog posts from previous years can be found HERE

More information about the Opal School can be found HERE

~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