Balanced Mathematics

Area(s) of Focus: math
Division(s): Primary, Junior
Level(s): Grade 1, Grade 2, Grade 3, Grade 4
Abstract:

This project evaluated the balance of our math program by looking at the frequency of our instruction as modelled, shared, guided or independent. We explored ways to achieve this balance and self-reflected on what balance meant for each of us.

In language, the philosophical pendulum has swung from phonics-based programs to whole language and back again. We currently recognize a balanced approach to literacy that sees elements of both whole language and phonics being important. In mathematics, we have experienced a similar pendulum swing from formulas and rote skills to all problem and discovery based. Our project was to create a balanced mathematics program with similar features to a balanced literacy program. Using problem-solving as the foundation of the mathematics program, there were structured opportunities for modelled, guided, shared and independent practice in mathematics. Leaps and Bounds by Marian Small was used as a diagnostic. Problem-solving was incorporated in the three-part math lesson with a Mind’s On, Action, and Consolidation and Independent practice. The diagnostic and independent practice was then used to create the guided mathematics groups. While the class was involved in independent practice and review of all the strands, guided groups were lead through a lesson tailored to their specific misconceptions or missed concepts.

Team Members

  • Jennifer Merrett

    Upper Grand District School Board

  • Susanne Thomson

    Upper Grand District School Board

  • Valorie Giles

    Upper Grand District School Board

  • Gina Betts

    Upper Grand District School Board

Professional Learning Goals

Our professional learning goal is to develop a more effective mathematics program that creates multiple opportunities for student learning by improving skills in knowledge and understanding, thinking, communication, and application. In order for students to improve their learning, we as teachers need to develop a better understanding of how the four categories of Achievement fit into a mathematics program. We want to combine the knowledge we have gained from the various philosophies around mathematics, the best practices in language, as well as our own previous teaching practices, and apply that knowledge to a single balanced mathematics program. This balanced mathematics program will help us make valid judgements about student work that more clearly align with provincial standards.

Activities and Resources

  • create independent activities to be used during guided mathematics time
  • diagnostic and summative evaluations that built grade to grade and incorporate questions that relate to the four categories of Achievement
  • create parallel tasks related to the categories of Achievement across the primary grades

Unexpected Challenges

During our time together, we faced issues related to technology – specifically our school Internet was down and all software is network-/web-based.

We looked at Debbie Diller’s book Math Work Stations: Independent Learning You Can Count On, K-6.  We all agreed that although this might have great application in some environments, there were alternatives for independent time that worked better for us.

Enhancing Student Learning and Development

By using the independent task at the end of the three-part lesson to create our guided math group, we were very familiar with the specific gaps in student learning. Having a guided lesson follow right behind the three-part lesson allowed us to meet in small groups with students who had similar misconceptions or difficulties in their learning. This gave us time to work with individual students on very specific skills and/or misconceptions.

Sharing

We are hoping in the future to continue to work with the program department to present our learning. Gina Betts (one of our team members) works with teachers throughout UGDSB and has been sharing some of our work with the teachers she is working with. We have discussed being part of the Summer Institute and the Learning Fair. We are also interested in submitting a proposal to OAME.

Project Evaluation

Reflecting on our balance in mathematics was insightful. We were able to see how different strands, different groups of  students and different abilities meant balance looks different in each classroom and at different times. Our learning was not that X number of lessons need to be shared, guided, modelled or independent, but that reflecting on that balance was important. Other things we found surprising/insightful was that when we have supply teachers into our room, we typically leave independent work. We challenged this idea towards the end and found ourselves more willing to leave whatever type of lesson the group needed.

After three sessions together, we finally realized that we needed to be using curriculum from the grade before to assess during the diagnostic, which we could then use part of in the summative for that grade later on. This saved us a considerable amount of time. We would have done this from the beginning.

Resources Used

Diller, Debbie. (2011). Math Work Stations: Independent Learning You Can Count On, K-2. U.S.A.: Stenhouse Publishers.

Perrish, Sherry. (2014). Number Talks: Helping Children Build Mental Math and Computation Strategies K-5. California, USA: Scholastic Inc.

Small, Marian. (2011). Leaps and Bounds Toward Math Understanding. Toronto, Canada: Nelson Education Ltd.

Ontario Ministry of Education. (2005). The Ontario Curriculum, Grades 1-8: Mathematics. Ontario, Canada: Queen’s Printer for Ontario.

Ontario Ministry of Education. (2003). Early Math Strategy: The Report of the Expert Panel on Early Math in Ontario. Ontario, Canada: Queen’s Printer for Ontario.

Ontario Ministry of Education. (2004). Teaching and Learning Mathematics: The Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario. Ontario, Canada: Queen’s Printer for Ontario.

Ontario Ministry of Education. (2006). A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 Vol. 1 – 5. Ontario, Canada: Queen’s Printer for Ontario.

Education Quality and Accountability Office. (2015). EQAO.com. Toronto, Canada, Retrieved from http://www.eqao.com/

http://www.eqao.com/

Ontario Ministry of Education. (2004). A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3. Ontario, Canada: Queen’s Printer for Ontario.

Ottawa-Carleton District School Board. (2015). Balanced Mathematics Instruction, K-12. Retrieved from http://www.ocdsb.ca/sta/bmi/Pages/default.aspx.

http://www.ocdsb.ca/sta/bmi/Pages/default.aspx

Complete MathSmart Grade 2. (2010). Richmond Hill, Ontario: Popular Book Company (Canada) Ltd.

Complete MathSmart Grade 3. (2010). Richmond Hill, Ontario: Popular Book Company (Canada) Ltd.

Complete Canadian Curriculum Grade 2. (2010). Richmond Hill, Ontario: Popular Book Company (Canada) Ltd.

Complete Canadian Curriculum Grade 3. (2010). Richmond Hill, Ontario: Popular Book Company (Canada) Ltd.

Mighton, John, C. Sabourin and J. Wyatt. (2007). JUMP Math. Toronto, Canada: Jump Math.

http://jumpmath.org/

My Ontario Math Workbook 1. (1998). Canada: Irwin Publishing.

My Ontario Math Workbook 2. (1998). Canada: Irwin Publishing.

My Ontario Math Workbook 3. (1998). Canada: Irwin Publishing.

Silbey, Robyn. (1996). Skill Builders First Grade Math Review. Torrance, USA: Frank Schaffer Publications.

Small, Marian et al. (2004). Nelson Mathematics 1. Toronto, Canada: Thomas Canada Ltd.

Small, Marian et al. (2004). Nelson Mathematics 2. Toronto, Canada: Thomas Canada Ltd.

Small, Marian et al. (2004). Nelson Mathematics 3. Toronto, Canada: Thomas Canada Ltd.

Small, Marian et al. (2004). Nelson Mathematics 4. Toronto, Canada: Thomas Canada Ltd.

Sparling, Lee. (2005). Balanced Mathematics Grades 2-6. Barrie, Canada: Data Based Directions

Kidzone. Learning About Canadian Money. Retrieved from http://www.kidzone.ws/geography/money/.

http://www.kidzone.ws/geography/money/

Dreambox. Dreambox Learning. Retrieved from http://www.dreambox.com/.

http://www.dreambox.com/

Resources Created

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