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The contents of the companion documents are organized by grade, and material relatedto a specific grade can be pulled out and used on its own. The companion documentshelp teachers to put the ideas in this core instructional guide into practice.The present document can be used as a resource for professional development in thefollowing ways:• Teachers can study the guide on their own. The guide can help individual teachersidentify specific goals for program improvement and can provide them with ideason ways to work towards enhancing their classroom practices.• Parts of the document can be used as focus topics in study groups. Discussion aboutmathematics teaching and learning with colleagues helps teachers reflect on theirown practice.• Sections of the document can be used in systemwide and school-based professionaldevelopment activities.Focusing on the core instructional guide before using the companion documents willprovide teachers with an in-depth view of topics that pertain to mathematicalinstruction in general – for example, the formation of a mathematical community inthe classroom, the three-part lesson structure, or the use of literature in teachingmathematics. The next step would be to take up one of the companion documents tosee how the various principles and strategies can be implemented with respect tostrand-specific material in a particular grade. In some cases, however, teachers mightfind it practical to start with information provided in a strand-specific companiondocument for a particular grade and then consult this core instructional guide forinsights into specific topics – for example, how to achieve a balance of instructionalapproaches, how to teach through problem solving, or how to set up the classroom.Teachers who are comfortably knowledgeable about the contents of this core instructionalguide will be well equipped to use and extend the learning activities in thecompanion documents and will be well prepared to plan lessons independently, toinstruct students effectively, to assess their work meaningfully, and to differentiateinstruction to meet the needs of all students.Locating Information Specific to Kindergarten, Primary, and JuniorStudents in This GuideAn important feature of this guide is the inclusion of grade-relatedinformation and examples that help clarify the principles articulated.Such information is identified in the margins of this guide by means oficons referring to the relevant grades – K for Kindergarten, Grades 1–3for primary, Grades 4–6 for junior. Examples and other materials that areappropriate for use at more than one level or are applicable to more thanone level are identified by the appropriate combination of icons.K – Kindergarten1–3 – Primary4–6 – JuniorLook for the following icons inthe margins of this document:xiiA Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One
1.Achievingand SustainingImprovementChapter ContentsA Framework for School Improvement . . . . . . . . . . . . . . . . . . . . . . 3Improvement Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8The Pace of Implementation of Effective MathematicsInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Working Together to Improve Mathematics Instruction . . . . . . . . . 10Classroom Teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Lead Math Teachers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Principals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Centrally Assigned Staff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Superintendents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Professional Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16The Purpose and Benefits of Professional LearningCommunities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Professional Learning Community Activities . . . . . . . . . . . . . . . . . . 16Peer Coaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Study Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Team Teaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Mentoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Reflective Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Home and Community Connections . . . . . . . . . . . . . . . . . . . . . . . . 18Encouraging Parental Involvement . . . . . . . . . . . . . . . . . . . . . . . . . 18Developing Home-School Partnerships . . . . . . . . . . . . . . . . . . . . . . 19
Page 9 and 10: Belief 4: The teacher is the key to
Page 11: Chapter 10 is devoted to the subjec
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
Page 30 and 31: and reflect on their observations o
Page 32 and 33: • hosting a family math event, em
Page 35 and 36: Principles Underlying EffectiveMath
Page 37 and 38: ideas through problem solving, comm
Page 39 and 40: • working with concrete materials
Page 41 and 42: In general, students first need to
Page 43 and 44: Respect How Each Student LearnsTeac
Page 45 and 46: Recognize the Importanceof Metacogn
Page 47 and 48: DIVERSITY, EQUITY, AND STUDENT ACHI
Page 49 and 50: A CHECKLIST FOR INCLUSIVE MATHEMATI
Page 51 and 52: 12. When I teach graphing, I ensure
Page 53 and 54: Appendix 2-1: Accommodations and Mo
Page 55: • Provide access to computers.•
Page 59 and 60: Planning the MathematicsProgramPlan
Page 61 and 62: document for mathematics and should
Page 63 and 64:
• How will I know when students h
Page 65 and 66:
• How will I know when students h
Page 67 and 68:
The following charts provide exampl
Page 69 and 70:
Example: Daily Lesson in Mathematic
Page 71 and 72:
Appendix 3-1: Long-Range Planning T
Page 73 and 74:
Appendix 3-3: Unit Planning Templat
Page 75:
4.InstructionalApproachesChapter Co
Page 78 and 79:
these terms are not the same in rea
Page 80 and 81:
• asking questions that help stud
Page 82 and 83:
• explaining their own mathematic
Page 84 and 85:
The students’ activities during i
Page 86 and 87:
Say: “Put 4 red counters in the f
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• You must use all the rods to ma
Page 90 and 91:
Kilpatrick, J., & Swafford, J. (Eds
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.)
Page 99 and 100:
GlossaryNote: Words and phrases pri
Page 101 and 102:
(a benchmark) and judging that a la
Page 103 and 104:
cooperative learning structure. A p
Page 105 and 106:
Step 2 - Adjust the estimate to ref
Page 107 and 108:
materials. Learning activities that
Page 109 and 110:
number sense. The ability to interp
Page 111 and 112:
Research indicates that procedural
Page 113 and 114:
subtrahend. In a subtraction questi
Page 115 and 116:
ReferencesAdams, L., Waters, J., Ch
Page 117 and 118:
Ginsberg, H.P., Inoue, N., & Seo, K
Page 119 and 120:
Payne, J.N. (Ed.). (1990). Mathemat
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