Professional Learning Goals

• Deepened their understanding of the Renewed Math Strategies, including the effective use of a Three-Part Lesson Plan and of teaching through problem-solving
• Developed greater confidence and consistency with delivering high-quality mathematics instruction using the board- and ministry-preferred pedagogical approach
• Extended their awareness of resources to support student learning as they continued their shift from the old, top-down model of mathematics instruction to the new, student-work focussed mathematical framework
• Developed a much greater understanding of the progression of the various curricular expectations from K-4 and of the organization of the strands into major concepts, key points and key concepts

Activities and Resources

Teachers involved in this project:

• collaborated to sort through the Ontario Mathematics Curriculum, The Kindergarten Program and the various Guides to Effective Instruction in Mathematics to organize the ideas into a continuum for grades K-4, under the umbrella of  ‘Big Ideas’ which address multiple curriculum areas (quoting the “Big Ideas” as stated by Marian Small, which parallel the Major Concepts in the Guides to Effective Instruction)
• Shared experiences of both success and difficulty with the implementation of the Renewed Mathematics Strategies, for the purpose of developing better teaching strategies for guiding students through known challenges

The majority of our time was spent pooling over, consolidating, and organizing material from the following Ontario Ministry of Education documents:

• The Kindergarten Program, 2016
• The Ontario Curriculum, Mathematics, K-8, 2005
• A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, Number Sense and Numeration, 2003
• A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, Data Management and Probability, 2007
• A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, Patterning and Algebra, 2007
• A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, Measurement, 2007
• A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3, Geometry and Spatial Sense, 2005

(While we also looked at and through the Guides to Effective Instruction for grades 4-6, we focused on the K-3 resources.)

We used several resources to inform our thinking (and from which our resources and activities (which are NOT included herewithin) were planned to derive):

• Good Questions: Great Ways to Differentiate Mathematics Instruction
  by Marian Small
• Making Math Meaningful to Canadian Students K-8
  by Marian Small
• Eyes on Math: A Visual Approach to Teaching Math Concepts
  by Marian Small
• Big Ideas from Dr. Small Grade K-3: Creating a Comfort Zone for Teaching Mathematics
  by Marian Small
• Making Math Meaningful
  by Marian Small
• Number Talks Common Core Edition, Grades K-5: Helping Children Build Mental Math and Computation Strategies
  by Sherry Parrish
• Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching
  by Jo Boaler
• 5 Practices for Orchestrating Productive Mathematics Discussions
  by Margaret Schwan Smith and Mary Kay Stein
• Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction (Volumes I and II),
  by John A. Van de Walle, Karen S. Karp, LouAnn H. Lovin and Jennifer M. Bay-Williams

Unexpected Challenges

The biggest challenge faced by this team was the scope of the project. Our original intent was to take the Big Ideas and simply link activities and resources for teachers to directly access from kindergarten all the way up to Grade 4. Once we began digging more deeply into the documentation, however, it became a real challenge to organize the vast quantity of data and to put it into an understandable, accessible hierarchy. We were not able to get to the level of linking tasks to the grade-by-grade curriculum overviews we created due to time constraints, though we also wondered about whether any direct link to such resources would constitute a violation of copyright. We decided to reduce the focus to a better understanding of the overview of the K-4 progression. (It would be a great starting point for another TLC to continue where we left off.)

Enhancing Student Learning and Development

The teachers in this project (as well as those influenced by it) will have a greater understanding of the cross-grade progression of expectation and mathematical thinking/terminology. It is believed that students being taught by teachers with this more global view of mathematics instruction will have a more consistent grade-by-grade approach being presented to them, and, consequentially, will more consistently:

• describe their mathematical thinking (using terms that are specific and consistent across grades);
• select effective strategies for addressing problems; and,
• demonstrate a more positive attitude about mathematics, having been taught about – and having practised the habits consistent with – a growth mindset.

It is believed this enhanced mathematical metacognition (which comes from cross-divisional consistency and activation of schema) in conjunction with the students’ more adaptive and confident mindset will lead to greater performance across various strands as assessed by classroom teachers. 

Sharing

With the large amount of data that was gathered and compiled, and with the intricate ways in which the multiple layers of information intersect, the format of presentation has become a challenge. In its current format, with different information levels presented in different documents, it is somewhat onerous and challenging to navigate. A different, more interactive and “clickable” program would be more useful, but no such program was identified (despite searching). The best we came up with was to link the multiple Google Documents together via a Google Slides document.

The opportunity to further revise the final submission format (making it more accessible and user-friendly/intuitive) would be appreciated.

(N.B. The project, even in its unfinished form, has been used in several situations and shared via Google Drive with peers during professional development opportunities and team collaborations. The main resources that we’ve created/compiled have been used by the lead author of this project quite extensively and it is hoped that other teachers will do so as well. (Especially if we find a way to share if that uses more user-friendly navigation.))

Project Evaluation

We have mixed emotions and thoughts on this.

We have developed a far greater understanding of the broad scope of mathematics expectations and have a much deeper understanding of the grade-by-grade progression from K-4. We have been able to clarify our thinking about the “Big Ideas” concept (presented by authors such as Marian Small and John A. Van de Walle) and how it relates to the Ministry’s focii within each strand of mathematics (sometimes called “Big Ideas” and sometimes called “Major Concepts”), more thoroughly described in the Guides to Effective Instruction. Through our investigation, we discovered inconsistencies in the Ministry Documents (e.g., Grade 3 Geo&S.S. lists the construction of 3D figures as part of the major concept of “Geometric Properties,” whereas Grade 4 lists is under “Geometric Relationships”). These inconsistencies required us to make organizational decisions throughout the process we did not anticipate (as we thought these things would be consistent in their source documents).

Once we began down this rabbit hole, it became clear that the scope of work to compile and organize this vast amount of interrelated information was going to take much longer than originally anticipated. As a result, we did not get to complete the whole project (as originally envisioned) and we did not get to the level of having specific, grade-by-grade tasks prepared and ready for each major concept of each strand for all grades K-4. It was simply too much all at once.

While we felt our work was/is informative and that the project was worthwhile, we acknowledge that more time would be required before this project could achieve its full potential. (Perhaps this could be the beginning of another TLC in a future year?)

*It should be noted that while the links to activities and resources have not been added to our submitted work, those of us involved have started to collaborate more meaningfully with our school-based colleagues, developing similar tasks to address common big ideas and seeing how students in various grades solve them.