Introduction

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• the seven mathematical processes outlined on pages 11–17 of The Ontario Curriculum,Grades 1–8: Mathematics, 2005: problem solving, reasoning and proving,reflecting, selecting tools and computational strategies, connecting, representing,communicating.In this chapter, three planning formats are considered:• the long-term plan – the record of a year-long plan for teaching the mathematicscurriculum. In a long-term plan, concepts are organized in a meaningful and logicalorder, so that mathematical growth is fostered and the needs of the particularclassroom are met;• the unit plan – a series of lessons that build towards a conceptual understanding ofthe big idea(s) and key concepts in a single strand or several strands of mathematics;• the daily lesson plan – a specific lesson that is part of the larger unit plan and thatbuilds towards understanding a key concept.All three formats are connected; they enhance one another and serve different roles.Taken altogether, they provide teachers with a sound and cohesive course of actionin the classroom. Such a course of action, however, should not be adhered to rigidly.Teachers need to be flexible in using their plans and should be prepared to revise andrefine them in light of students’ ongoing needs.Long-Term PlanningIn making a long-range plan for a balanced mathematics program, teachers need toconsider the following questions:• Where do I start?First, teachers should be familiar with the knowledge and skills that students areexpected to acquire at their current grade level, and the knowledge and skills thatthey were expected to aquire in the previous grade. Next, teachers need to beginto plan with their teaching partner(s) (i.e., other teachers in the school who areteaching at the same grade level). Often consultation with teachers of other gradesin the division is also helpful, particularly with the teacher from the previous grade,who can provide an overview of the prior learning and experiences of students.Then, teachers need to review the primary resource to be used in the classroom(e.g., a textbook and/or teacher’s manual), in order to become familiar with its flowand organization. Often the teacher’s manual will include a suggested calendar.Teachers need to be aware that the entire curriculum may not be addressed inthe primary resource or that the resource may include extraneous activities thatare not related to the Ontario curriculum. The primary resource should be designedto assist students in achieving the expectations outlined in the curriculum policy48 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One
document for mathematics and should support an effective mathematics programas described in the report of the Expert Panel on Early Math in Ontario (2003) andthe report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario (2004).• How do I make decisions about when to address the strands?In order to map out the year, teachers should consult the primary resource forhelp in making decisions about the order of the strands and the order of theconnected key concepts that will be addressed each term. Teachers should alsobe familiar with ministry reporting requirements and board guidelines. Teachersshould ensure that the strands addressed in each term make sense in the contextof the whole program and in relation to learning in other subjects. For example,teachers might plan to have their students build structures to meet the expectationsof the Structures and Mechanisms strand of the science and technology curriculumat the same time that they are learning linear measurement in the Measurementstrand of the mathematics curriculum.Teachers should consider the implications of teaching one concept before another.For example, some concepts from the Measurement strand might be clearer tostudents after they have worked with and understood some of the concepts fromthe Number Sense and Numeration strand.• How do I record my long-range plans?Organizers can be helpful in providing an overview of the year-long plan formathematics. Included in this chapter are two sample templates suitable for usein long-term planning (see Appendices 3-1 and 3-2). Note that long-range plansneed not be as detailed as unit plans or daily lesson plans.The generic templates provided in this chapter may be helpful to some teachers intheir planning, but they are not the only templates that promote effective planning.Many school boards have developed their own templates for planning. The Ministryof Education’s Ontario Curriculum Unit Planner (available at www.ocup.org) is alsohelpful for developing long-range and unit plans.Unit or Short-Term PlanningUnit planning is key to effective mathematics instruction. Teachers need to havean overall plan for the series of daily lessons (subtasks) that they will use to helpstudents achieve the curriculum expectations outlined for a particular strand or partof a strand of mathematics during the school term.“Backwards design” (also called “design down”) templates are constructed with theend in mind. Teachers determine ahead of time the conceptual understanding andprocedural knowledge (the key concepts) that they want their students to havePlanning the Mathematics Program 49
Page 9 and 10: Belief 4: The teacher is the key to
Page 11 and 12: Chapter 10 is devoted to the subjec
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Page 16 and 17: Educators striving to achieve the c
Page 18 and 19: In schools that successfully bring
Page 20 and 21: • Intervention and special assist
Page 22 and 23: Boards and schools have improvement
Page 24 and 25: • assisting with team and individ
Page 26 and 27: • incorporating current knowledge
Page 28 and 29: • ascertaining the needs of staff
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Page 35 and 36: Principles Underlying EffectiveMath
Page 37 and 38: ideas through problem solving, comm
Page 39 and 40: • working with concrete materials
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Page 80 and 81: • asking questions that help stud
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Page 86 and 87: Say: “Put 4 red counters in the f
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Page 92 and 93: Gavin, M.K., Belkin, L.P., Spinelli
Page 94 and 95: Tank, B., & Zolli, L. (2001). Teach
Page 96 and 97: Leadership ResourcesBurns, M. (Ed.)
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Page 103 and 104: cooperative learning structure. A p
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Page 109 and 110: number sense. The ability to interp
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Research indicates that procedural
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subtrahend. In a subtraction questi
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ReferencesAdams, L., Waters, J., Ch
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Ginsberg, H.P., Inoue, N., & Seo, K
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Payne, J.N. (Ed.). (1990). Mathemat
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Introduction

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