MATHEMATICS 2, 5, and 8

What Should Students Learn in Mathematics? Multiplying whole numbers Adding columns of decimal numbers Adding fractions Making change Properties of parallel lines and transversals Calculating area Determining dimensions for given surface area and volume Solving equations Factoring Graphing quadratic equations Proving trigonometric identities Conic sections …

Mathematical Perspective Patterns Flexibility in thinking Relationships Representations Strategies

Goals of K-12 Mathematics Logical Thinking Number Sense Spatial Sense Mathematics as a Human Endeavour

Logical Thinking Through their learning of K-12 Mathematics, students should: develop and be able to apply mathematical reasoning processes, skills, and strategies to new situations and problems.

Number Sense Through their learning of K-12 Mathematics, students should: develop an understanding of the meaning of, relationships between, properties of, roles of, and representations (including symbolic) of numbers and apply this understanding to new situations and problems.

Spatial Sense Through their learning of K-12 Mathematics, students should: develop an understanding of 2-D shapes and 3-D objects, and the relationships between geometrical shapes and objects and numbers, and apply this understanding to new situations and problems.

Mathematics as a Human Endeavour Through their learning of K-12 Mathematics, students should: develop an understanding of mathematics as a way of knowing the world that all humans are capable of with respect to their personal experiences and needs.

What Students Should Learn in Mathematics Multiplying whole numbers Adding columns of decimal numbers Adding fractions Making change Properties of parallel lines and transversals Calculating area Determining dimensions for given surface area and volume Solving equations Factoring Graphing quadratic equations Proving trigonometric identities Conic sections Logical Thinking Number Sense Spatial Sense Mathematics as a Human Endeavour THROUGH

An Outcome and Its Goals N8.3 Demonstrate understanding of rates, ratios, and proportional reasoning concretely, pictorially, and symbolically. [C, CN, PS, R, V] Logical Thinking Number Sense Spatial Sense Mathematics as a Human Endeavour

Distinguishing between Practice and Problem Solving Baroody (1980) classified “problems” seen in mathematics classrooms as Practice True problems Enigmas Practice involves procedures, problem solving has strategies. Inquiry and open-ended questions result in problem solving. Problems can include Mathematics as part of the “real world”.

More Distinctions… Practice is only messy if you don’t use a pencil or don’t have an eraser. Problem solving is messy, challenging, frustrating, and exhilarating.

Supporting FN&M Learners Students construct understanding and knowledge within contexts Valuing and honouring of alternatives Seeking supports from within the community and through students Making connections Keep sight of the big picture all

Supporting Students “Who Don’t Get it” Go back to the root of the problem Students represent and connect understandings Action taken when a misunderstanding first occurs Drill doesn’t work

A Note on Resources Texts approved by WNCP match the WNCP framework. Includes same content Not written for deep understanding Format can dissuade students from engaging in inquiry Manipulatives and Technology Professional Resources

Implications for Teaching and Learning Awareness and openness to thinking about mathematics Uncovering (discovering) versus covering Transferring knowledge as an expectation Active and engaged learning Multiple entry points Diverse student –derived strategies Discussion, reflection, self-assessment Multiple representations Making connections

Implications for Teaching and Learning Accessing prior knowledge Continuous assessment and adjustment Holding back on telling “the right answer” Willingness to say “I’m not sure” Starting with and returning to the big picture Practice within context Open and probing questions Inquiry and learning for deep understanding takes time.

Contact Information Gale Russell Mathematics Consultant (K-12) (306)

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