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• What are the concepts and procedures that I want students in my classto learn at this time?Teachers refer to the unit plan that has been developed, select one of the conceptsoutlined in that plan, become familiar with the concept and how students bestlearn it, and use this knowledge to create lessons that are engaging and developmentallyappropriate. In some cases, a lesson may be found in an existingresource. Such a lesson should be reviewed with a critical eye and adjusted ormodified, if necessary, to ensure that its focus is on problem solving and communicationand that it supports students in achieving the curriculum expectations.(See the subsection “Providing Appropriate and Challenging Problems” inChapter 5: Problem Solving, in Volume Two, for information on reviewing andrevising problems from existing resources.)For grade-specificexamples of dailylessons in mathematics,see thelearning activitiesprovided in thecompanion documentsto this guidethat focus on theindividual strands.• How will I structure the learning experience to help students learn theseconcepts and procedures?When developing lessons, teachers should:– begin with a thought-provoking question or problem that will encourage studentsto reason mathematically;– plan learning experiences that allow students to connect new mathematical ideaswith concepts that they already understand;– structure the lesson to include “Getting Started”, “Working on It”, and “Reflectingand Connecting” segments;– consider which instructional groupings best suit the purpose of the lessonand meet the needs of all students, including English language learners andstudents with special needs;– use a balance of shared, guided, and independent mathematics (see Chapter 4:Instructional Approaches);– consider how students will use tools (e.g., manipulatives, calculators, computers)to investigate mathematical ideas and to solve problems;– determine ways in which students will represent mathematical ideas (e.g.,using concrete materials, pictures, diagrams, graphs, tables, numbers, words,symbols);– design probing questions that will help students focus on important mathematicalconcepts;– plan ways in which students will communicate their mathematical thinking,strategies, and solutions;– include time at the end of the lesson for a class discussion in which studentsreflect on and discuss mathematical ideas they have learned.52 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One
• How will I know when students have learned the concepts and procedures?Teachers can refer to Chapter 8: Assessment and Evaluation, in Volume Four,for assistance in learning how to assess students’ work and especially learninghow to “assess on their feet”, in order to address misconceptions and determineappropriate next steps in instruction.• How do I record my daily lesson plan?Included in this chapter is a generic template that will help teachers in theirplanning for instruction in the key concepts or big ideas (see Appendix 3-4).The template lends itself to a problem-solving focus; emphasizes the instructionalapproaches of guided mathematics, shared mathematics, and For examples of the three-part lessonindependent mathematics; and provides for a three-part lessonstructure, see “Problem-SolvingVignette – Grade 1” and “Problemstructureof “Getting Started”, “Working on It”, and “ReflectingSolving Vignette – Grade 4” in Chapter 5:and Connecting”.Problem Solving, and “CommunicationVignette – Grade 4” in Chapter 6:The template provided in Appendix 3-4 for daily lesson planningCommunication, all in Volume Two.is one way of organizing a daily plan; it may help the teacher For various other examples, see thenavigate the sections of this guide as they apply to daily planning.This is not, however, the only way of doing daily lessonlearning activities provided in thecompanion documents to this guidethat focus on the individual strands.plans. Other ways of planning may be more appropriate to theFor further information about theteacher’s grade, students, or school community.three main parts of a lesson, see thesubsection “Supporting and ExtendingIt is valuable to use a pre-arranged structure for a daily plan toLearning” in Chapter 5: Problemhelp ensure that all the components of an effective lesson are Solving, in Volume Two, and theincluded. Using a structure becomes automatic over time and subsection “The Three-Part Lessonhelps teachers stay on track while at the same time allowingFormat: Grades 1–6” in Chapter 7:Classroom Resources and Management,more freedom for the “teachable moment”.in Volume Three.Planning the Mathematics Program 53
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Belief 4: The teacher is the key to
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Chapter 10 is devoted to the subjec
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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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