Introduction

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Gavin, M.K., Belkin, L.P., Spinelli, A.M., & St. Marie, J. (2001). Navigating throughgeometry in Grades 3–5. Reston, VA: National Council of Teachers of Mathematics.Greenes, C., Cavanagh, M., Dacey, L., Findell, C., & Small, M. (2001). Navigatingthrough algebra in Prekindergarten–Grade 2. Reston, VA: National Council of Teachersof Mathematics.Greenes, C.E., Dacey, L., Cavanagh, M., Findell, C.R., Sheffield, L.J.,& Small, M.(2004). Navigating through problem solving and reasoning in Prekindergarten–Kindergarten. Reston, VA: National Council of Teachers of Mathematics.Kamii, C. (1985). Young children reinvent arithmetic. New York: Teachers College Press,Columbia University.Kamii, C. (1989). Young children continue to reinvent arithmetic: 2nd grade. New York:Teachers College Press, Columbia University.Kamii, C. (1994). Young children continue to reinvent arithmetic: 3rd grade. New York:Teachers College Press, Columbia University.Morrow, L.J., & Kenney, M.J. (Eds.). (1998). The teaching and learning of algorithms inschool mathematics. Reston, VA: National Council of Teachers of Mathematics.Ohanian, S., & Burns, M. (1997). Math by all means: Division, Grades 3–4. Sausalito,CA: Math Solutions Publications.Pugalee, D.K., Frykholm, J., Johnson, A., Slovin, H., Malloy, C., & Preston, R. (2002).Navigating through geometry in Grades 6–8. Reston, VA: National Council of Teachersof Mathematics.Rectanus, C. (1994). Math by all means: Area and perimeter, Grades 5–6. Sausalito, CA:Math Solutions Publications.Rectanus, C. (1994). Math by all means: Geometry, Grades 3–4. Sausalito, CA: MathSolutions Publications.Schifter, D. (1996). What’s happening in math class? Envisioning new practices throughteacher narratives (Series on School Reform, Vol. 1). New York: Teachers CollegePress, Columbia University.Schifter, D., Bastable, V., & Russell, S.J. (1999). Developing mathematical ideas: Numberand operations, part 1 – Building a system of tens. Parsippany, NJ: Dale SeymourPublications.Schifter, D., Bastable, V., & Russell, S.J. (1999). Developing mathematical ideas: Numberand operations, part 2 – Making meaning for operations. Parsippany, NJ: Dale SeymourPublications.80 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One
Sheffield, L.J., Cavanagh, M., Dacey, L., Findell, C.R., Greenes, C., & Small, M.(2002). Navigating through data analysis and probability in Prekindergarten–Grade 2.Reston, VA: National Council of Teachers of Mathematics.Sheffield, S. (2001). Teaching arithmetic: Lessons for first grade. Sausalito, CA: MathSolutions Publications.Skinner, P. (1998). It all adds up. Sausalito, CA: Math Solutions Publications.Small, M., Sheffield, L.J., Cavanagh, M., Dacey, L., Findell, C.R., & Greenes, C.E.(2004). Navigating through problem solving and reasoning in Grade 2. Reston, VA:National Council of Teachers of Mathematics.The Super Source: Base Ten Blocks, Grades K–2. (2000). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Base Ten Blocks, Grades 3–4. (2000). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Base Ten Blocks, Grades 5–6. (2000). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Color Tiles, Grades K–2. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Color Tiles, Grades 3–4. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Color Tiles, Grades 5–6. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Cuisenaire Rods, Grades K–2. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Cuisenaire Rods, Grades 3–4. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Cuisenaire Rods, Grades 5–6. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Geoboards, Grades K–2. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Geoboards, Grades 3–4. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Geoboards, Grades 5–6. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Pattern Blocks, Grades K–2. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Pattern Blocks, Grades 3–4. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Pattern Blocks, Grades 5–6. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Snap Cubes, Grades K–2. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Snap Cubes, Grades 3–4. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Snap Cubes, Grades 5–6. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Tangrams, Grades K–2. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Tangrams, Grades 3–4. (1996). Vernon Hills, IL: ETA/Cuisenaire.The Super Source: Tangrams, Grades 5–6. (1996). Vernon Hills, IL: ETA/Cuisenaire.Professional Resources 81
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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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1.Achievingand SustainingImprovemen
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Educators striving to achieve the c
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In schools that successfully bring
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• Intervention and special assist
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Boards and schools have improvement
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• assisting with team and individ
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• incorporating current knowledge
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• ascertaining the needs of staff
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and reflect on their observations o
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• hosting a family math event, em
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Principles Underlying EffectiveMath
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ideas through problem solving, comm
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• 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
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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
Page 88 and 89: • You must use all the rods to ma
Page 90 and 91: Kilpatrick, J., & Swafford, J. (Eds
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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