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How will you support your own learning as the facilitator of mathematical thinking and communication in your class?
Ontario Ministry of Education. (2003a). A guide to effective instruction in mathematics,
Kindergarten to Grade 3 – Number sense and numeration. Toronto: Author.
Ontario Ministry of Education. (2006). A guide to effective instruction in
mathematics, Kindergarten to Grade 6 (Vol. 1. The Big Ideas). Toronto: Author.
Ontario Ministry of Education. (n.d.). A guide to effective instruction in mathematics
Kindergarten to Grade 6 (Vol. 2, Problem Solving and Communication). Toronto: Author.
Ontario Ministry of Education. (2004). Teaching and learning mathematics, The
report of the expert panel on mathematics in Grades 4 to 6 in Ontario. Toronto: Author.
Ontario Ministry of Education. (2005). The Ontario curriculum, Grades 1–8: Mathematics.
Toronto: Author.
Peel District School Board. (2011). Transformational Practices Grades 1-12: Three Part Lesson
Design. Retrieved from https://portal.peelschools.org/SiteDirectory/TransformationalPractices/Resources/3.6%20INSTRUCTIONAL%20PRACTICES%20-%20Three%20Part%20Lesson%20Design.pdf
The Numeracy and Literacy Secretariat (2007). Sketch of a three-part lesson. (Capacity Building
Series). Retrieved from http://professionallyspeaking.oct.ca/march_2010/features/
lesson_study/three-part.aspx
http://www.edugains.ca/newsite/math/guides_effective_instruction.html
According to Ontario Ministry of Education (2004), “Many students may develop procedural fluency, but they often lack the deep conceptual understanding necessary to solve new problems or make connections between mathematical ideas.”
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The current best practices in teaching mathematics involves two foci: mathematical algorithms and understanding of the concepts.
Clearly, if students are expected to apply their mathematical learning outside of school, they need to have a solid understanding of not only how to complete the "equation", but also when to use it and why.
This is why including components such as communicating and brainstorming into math lessons is so important. Without these, there is simply rote learning, with little hope of the learning transferring to other contexts.
According to Ontario Ministry of Education (2004), “Although the standard algorithm is very efficient, when it is taught before students understand the concept of division or have a solid understanding of place value, students are forced to abandon their sense making of the question, and their results may be senseless mathematics.”
Some teacher prompts to gauge student understanding:
How else can you solve this problem? Why would this option not work? What strategy did you use?
Will it be the same if we used different numbers? When do you use this math outside of school?
Key Components of a Daily Lesson Plan
1. Strand
2. Big Idea(s)
3. Curriculum Expectations, with cross-curricular/integrated
links
4. Materials
5. Getting Started Task (include type of student groupings)
6. Working on It Task (include type of student groupings)
7. Reflecting and Connecting Task (include type of student
groupings)
8. Assessment type (i.e., for learning, as learning, or of
learning) and format (e.g., anecdotal, rubric, self
assessment, peer assessment, etc.)
9. Teacher Notes/Reflections
When planning a unit or lesson, it is important to be flexible, keeping in mind the interests of the students, their learning styles and their schema.
The backwards design model for planning ensures that you start with the end in mind (i.e., the learning goal) and then determine what tasks/experiences the students will need to explore in order to achieve that goal.
All plans, be it long range plans for the year, overall unit plans, or daily plans, should be based on the big ideas, and should include cross-curricular and integrated planning as often as possible.
As stated in Ontario Ministry of Education (2005), "In cross-curricular learning, students are provided with opportunities to learn and use related content and/or skills in two or more subjects." Also, "In integrated learning... linking expectations from different subject areas can provide students with multiple opportunities to reinforce and demonstrate their knowledge and skills in a range of settings."
Part 1 Getting Started
10-15 minutes
Purpose: To focus and engage students, activate their prior mathematical knowledge and experiences, to ensure they understand the problem they will be working on.
Examples: KWL chart, read a math story related to the big idea, pose a smaller but similar problem and include brainstorming for possible solutions (e.g., through think-pair-share, placemat)
Part 2 Working on It
30-40 minutes
Purpose: To introduce a new learning or to extend their prior learning by asking them to solve a realistic problem, to give them the opportunity to apply the learning while selecting the appropriate strategies to solve the problem.
Examples: Solve a mathematical task at various learning centres through focus questions, work in groups, in pairs, or independently
Part 3 Reflecting and Connecting
10-15 minutes
Purpose: Students make sense of and reflect on their learning, make connections, share ideas, while their conversations gives the teacher a basis for tailoring subsequent lessons.
Examples: Gallery walk, Bansho, class discussions about strategies/processes used
Operational sense, Relationships, Representation, Proportional reasoning
Properties of 2-dimensional shapes and 3-dimensional figures, Geometric relationships, Location and movement
Attributes, Units and measurement sense, Measurement relationships
Collection and organization of data, Data relationships, Probability
Patterns and relationships, Variables, expressions and equations
There are about 65 specific expectations in the Grade 2 Math curriculum. Teaching all of them in isolated lessons does not relate to how we use math in our everyday lives.
The big ideas in mathematics go beyond the Overall Expectations in the curriculum. Think of them as the umbrella that supports all of the specific expectations within a strand. These umbrellas, or important math concepts, should guide the planning of
your year, your units and your daily lessons in Math.
Planning from big ideas allows you to teach mathematical thinking from a problem solving approach and, as stated in Ontario Ministry of Education (2006, p. 12), "Students are better able to see the connections in mathematics, and thus to learn mathematics, when it is organized in big, coherent “chunks”."
While learning from the big ideas, students should be simultaneously taught to apply the 7 mathematical processes: problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating.
Regardless of how you felt before, during and after your Math class as a student, the recent shift in a dual focus for teaching Math aims at making learning more meaningful and useful for students.
Regardless of how you currently feel about teaching Math, there is a lot of support available to help you get started on the right track or to extend your current practices.