Section 1

Bibliography for Math 140

Chapter 1 Introduction to Problem Solving

Balka, D.S. "Digit Delight: Problem-solving Activities Using 0 through 9." Arithmetic Teacher36 (November 1988): 42-45.

Ballew, H. "Sherlock Holmes, Master Problem Solver." Mathematics Teacher 87 (November 1994): 596-601.

Bartalo, D.B. "Calculators and Problem-Solving Instruction: They Were Made for Each Other." Arithmetic Teacher 30 (January 1983):18-21.

Burns, M. Problem-Solving Lessons: Grades 1-6. Sausalito, CA: Math Solutions Publications, 1996.

Bush, W.S., and A. Fiala. "Problem Stories: A New Twist on Problem Posing." Arithmetic Teacher 34 (December 1986): 6-9.

Carey, D. A. "The Patchwork Quilt: A Context for Problem Solving."Arithmetic Teacher 40 (December 1992): 199-203.

Charles, R. "Get the Most Out of Word Problems" Arithmetic Teacher 29 (November 1981): 39-40.

Charles, R.I. "The Role of Problem Solving." Arithmetic Teacher 32 (February 1985): 48-50.

Cobb, P., E. Yackel, T. Wood, G. Wheatley, and G. Merkel. "Research into Practice: Creating a Problem-solving Atmosphere." Arithmetic Teacher 36 (September 1988): 46-47.

Farivar, S., and N. M. Webb. "Helping and Getting Help -- Essential Skills for Effective Group Problem Solving." Arithmetic Teacher 41 (May 1994): 521-525.

Finzer, F. and D. Bennett. "From Drawing to Construction with The Geometer's Sketchpad." Mathematics Teacher 88 (May 1995): 428-431.

Frank, M.L. "Problem Solving and Mathematical Beliefs." Arithmetic Teacher 35 (January1988): 32-34.

Herbert, K. and R.H. Brown. "Patterns as Tools for Algebraic Reasoning" Teaching Children Mathematics 3 (February 1997): 340-345.

Jensen, R.J. "Stuck? Don't Give Up! Sub-goal-Generation Strategies in Problem Solving." Mathematics Teacher 80 (November 1987): 614-621, 634.

Mikusa, M.G. "Problem Solving is More than Solving Problems" Mathematics Teaching in the Middle School 4 (September 1998): 20-25.

Polya, G. How To Solve It. Princeton, NJ: Princeton University Press, 1957.

Richbart, C. and L. Richbart. "Promoting Problem-Solving Expertise." Mathematics Teaching inthe Middle School 1 (January-March 1995): 310-316.

Rosenbaum, L., K.J. Behounek, L. Brown, and J.V. Burcalow. "Step into Problem Solving with Cooperative Learning." Arithmetic Teacher 36 (March 1989): 7-11.

Small, M.S. "Using the Telephone Book as a Source of Mathematical Activity" Mathematics Teaching in the Middle School 3 (November-December 1997): 234-238.

Suydam, M.N. "Untangling Clues from Research on Problem Solving." Problem Solving in School Mathematics, 1980 Yearbook. Reston, VA.: National Council of Teachers of Mathematics, 1980.

Thompson, P. W. "Concrete Materials and Teaching for Mathematical Understanding." Arithmetic Teacher 41(May 1994): 556-558.

Wadlington, E., J. Bitner, E. Partridge, and S. Austin. "Have a Problem? Make the Writing-Mathematics Connection!" Arithmetic Teacher 40 (December 1992): 207-209.

Yancey, A.V., C.S. Thompson, and J.S. Yancey. "Children Must Learn to Draw Diagrams." Arithmetic Teacher 36 (March 1989): 15-19.

Boyd, B.V. "Learning about Odd and Even Numbers." Arithmetic Teacher 35 (November 1987): 18-21.

Coburn, T.G., B.J. Bushey, L.C. Holton, D. Latozas, D. Mortimer, and D. Shotwell. Patterns, Curriculum and Evaluation Standards for School Mathematics Addenda Series: Grades K-6. Reston, VA: National Council of Teachers of Mathematics, 1993.

Day, R.P. "A Problem-solving Component for Junior High School Mathematics." Arithmetic Teacher 34 (October 1986): 14-17.

Dougherty, B.J., and T. Crites. "Applying Number Sense to Problem Solving." Arithmetic Teacher 36 (February 1989): 22-25.

Duea, J. and E. Ockenga. "Classroom Problem Solving with Calculators" Arithmetic Teacher 29 (Feb 1982): 50-51

Economopoulos, K. "What Comes Next? The Mathematics of Pattern in Kindergarten" Teaching Children Mathematics 4 (December 1998): 230-233.

Feinberg-McBrian, C. "The Case of Trapezoidal Numbers" Mathematics Teacher 89 (January 1996): 16-24.

Ferrini-Mundy, J., G. Lappan and E. Phillips. "Experiences with Patterning" Teaching Children Mathematics 3 (February 1997): 282-288.

Grassl, R.M., and T.T.Y. Mingus. "Keep Counting Those Boxes — There's More" Mathematics Teacher 91 (February 1998): 122-127.

Kenney, P.A., J.S. Zawojewsky, and E.A. Silver. "The Thinking of Students" Mathematics Teaching in the Middle School 3 (May 1998): 474-477.

Kliman, M., and J. Richards. "Writing, Sharing, and Discussing Mathematics Stories." Arithmetic Teacher 40 (November 1992): 138-141.

Krulik, S., and J. A. Rudnick. "Reflect ... for Better Problem Solving and Reasoning." Arithmetic Teacher 41 (February 1994): 334-338.

Lemon, P. "Pascal's Triangle — Patterns, Paths, and Plinko" Mathematics Teacher 90 (April 1997): 270-273.

Maddon, P. J. "Teacher to Teacher: Making Story Problems Relevant." Arithmetic Teacher 41 (May 1994): 526-527.

Mahoney, D. "'Tri-Square' Numbers." Mathematics Teaching in the Middle School 1 (April-May 1995): 408-409.

Norman, F. A. "Figurate Numbers in the Classroom." Arithmetic Teacher 38 (March 1991): 42-45.

Raphel, A. "Critical Thinking During the December Holidays." Arithmetic Teacher 41 (December 1993): 216-219.

Rulf, B. "A Geometric Puzzle That Leads to Fibonacci Sequences" Mathematics Teacher 91 (January 1998): 21-23.

Shigematsu, K., and L. Sowder. "Drawings for Story Problems: Practices in Japan and the United States."Arithmetic Teacher 41 (May 1994): 544-547.

Shaw, K.L., and L. Aspinwall. "The Recurring Fibonacci Sequence: Using a Pose-and-Probe Rubric" Mathematics Teacher 92 (March 1999): 192-196.

Silver, E.A. "Probing the Foundations of Algebra: Grade-4 Pattern Items in NAEP" Teaching Children Mathematics 3 (February 1997): 268-274.

Silverman, F. L., K. Winograd, and D. Strohauer. "Student-Generated Story Problems." Arithmetic Teacher 39 (April 1992): 6-12.

Sinicrope, R. "A Polya Sampler." Mathematics Teacher 88 (March 1995): 196-199.

Stonewater, J. "The 'Mangoes' Problem." Mathematics Teaching in the Middle School 1 (November-December 1994): 204-210.

Talton, C.F. "Let's Solve the Problem Before We Find the Answer." Arithmetic Teacher 36 (September 1988): 40-45.

Van de Walle, J.A., and H. Holbrook. "Patterns, Thinking, and Problem Solving." Arithmetic Teacher 34 (April 1987): 6-12.

Whitin, D.J. "More Patterns with Square Numbers." Arithmetic Teacher 33 (January 1986): 40-42.

Appelbaum, E.B. "Telephones and Algebra" Mathematics Teacher 90 (February 1997): 96-100.

Barb, C. and A.L. Quinn. "Problem Solving Does Not Have to Be a Problem" Mathematics Teacher 90 (October 1997): 536-591.

Battista, M.T. and C. Van Auken Borrow. "Using Spreadsheets to Promote Algebraic Thinking" Teaching Children Mathematics 4 (April 1998): 470-478.

Bennett, A.B., Jr. "Visual Thinking and Number Relationships." Mathematics Teacher 81 (April 1988): 267-272.

Bezuska, S.J. and M.J. Kenney. "Even Perfect Numbers: (Update)²" Mathematics Teacher 90 (November 1997): 628-633.

Blubaugh, W.L. and K. Emmons. "Graphing for All Students" Mathematics Teacher 92 (April 1999): 323-326.

Brunner, A. and S. Sheenan. "The Algebra Launching PAD" Mathematics Teacher 90 (December 1997): 696-701.

Brunner, R.B. "Numbers, Please! The Telephone Directory and Probability" Mathematics

Teacher 90 (December 1997): 704-705.

Cai, J. "Developing Algebraic Reasoning in the Elementary Grades" Teaching Children Mathematics 4 (December 1998): 225-229.

Chia, D.T. "Weather Mathematics: Integrating Science and Mathematics" Teaching Children Mathematics 5 (September 1998): 19-22.

Davidenko, S. "Building the Concept of Function from Students' Everyday Activities" Mathematics Teacher 90 (February 1997): 144-149.

Davis, S., and D.R. Thomson. "To Encourage "Algebra for All", Start an Algebra Network" Mathematics Teacher 91 (April 1998): 282-286.

Dion, G.S. and I.B. Fetta. "Everybody Talks About It! -- Weather Investigations" Mathematics Teacher 89 (February 1996): 160-165.

Fouche, K.K. "Algebra for Everyone: Start Early" Mathematics Teaching in the Middle School 2 (February 1997): 226-229.

Gannon, G. and M. Martelli. "Cutting a Chain — a Problem Made to be Generalized" Mathematics Teacher 89 (April 1996): 292-293.

Greenes, C. and C. Findell. "Developing Students' Algebraic Reasoning Abilities" Developing Mathematical Reasoning in Grades K-12. 1999 Yearbook of the National Council of Teachers of Mathematics, edited by Lee V. Stiff and Frances R. Curcio, pp. 127-137. Reston, VA: National Council of Teachers of Mathematics, 1999.

Hiatt, A.A. "Discovering Mathematics." Mathematics Teacher 80 (September 1987): 476-478.

Jones, G.A., C.A. Thornton, C.W. Langroll and Tarr. "Understanding Students' Probabilistic Reasoning" Developing Mathematical Reasoning in Grades K-12. 1999 Yearbook of the National Council of Teachers of Mathematics, edited by Lee V. Stiff and Frances R. Curcio, pp. 146-155. Reston, VA: National Council of Teachers of Mathematics, 1999.

Johnson, J.M. "Sharing Teaching Ideas" Mathematics Teacher 90 (January 1997): 20-22.

Kennedy, J. and E. McDowell. "Geoboard Quadrilaterals" Mathematics Teacher 91 (April 1998): 288-290.

Kieran, C. "Helping to Make the Transition to Algebra." Arithmetic Teacher 38 (March 1991): 49-51.

Kieren, T.E., and A.T. Olson."Imagination, Intuition, and Computing in School Algebra." Mathematics Teacher 82 (January 1989): 14—17.

Kinzel, M.T. "Understanding Algebraic Notation from the Students' Perspective" Mathematics Teacher 92 (May 1999): 436-442.

Lara-Alecio, R., B.J. Irby and L. Morales-Aldana. "A Mathematics Lesson from the Mayan Civilization" Teaching Children Mathematics 5 (November 1998): 154-158.

Loewen, A. C. "Lima Beans, Paper Cups, and Algebra. Arithmetic Teacher 38 (April 1991): 34-37.

Naylor, M. "Nonperiodic Tilings: The Irrational Numbers of the Tiling World" Mathematics Teacher 92 (January 1999): 34-40.

Nibblelink, W. H. "Teaching Equations." Arithmetic Teacher 38 (November 1990): 48-51.

O'Daffer, P.G. "Write an Equation." Arithmetic Teacher 32 (May 1985): 14-15.

Perlstein, R. "Sharing Teaching Ideas" Mathematics Teacher 89 (January 1996): 28-29.

Philipp, R.A. and B.P. Schappelle. "Algebra as Generalized Arithmetic: Starting with the Known for a Change" Mathematics Teacher 92 (April 1999): 310-315.

Ploger, D., L. Klinger, and M. Rooney. "Spreadsheets, Patterns, and Algebraic Thinking" Teaching Children Mathematics 3 (February 1997): 330-334.

Quinn, A.L. and K.R. Larson. "When Does a Dog Become Older Than Its Owner?" Mathematics Teacher 89 (December 1996): 734-737.

Ruopp, F., A. Cuoco, S.M. Rasala, and M.G. Kelemanik. "Algebraic Thinking: A Theme for Professional Development" Mathematics Teacher 90 (February 1997): 150-154.

Sarama, J. and D.H. Clements. "Using Computers for Algebraic Thinking" Teaching Children Mathematics 5 (November 1998): 186-190.

Scavo, T.R. and B. Petraroja. "Adventures in Statistics" Teaching Children Mathematics 4 (March 1998): 394-400.

Schultz, J. E. "Implementing the Standards: Teaching Informal Algebra." Arithmetic Teacher 38 (May 1991): 34-37.

Schoenfeld, A., and A. Arcavi. "On the Meaning of Variable" Mathematics Teacher 81 (September 1988): 420-427.

Smith, L. "Mathematics on the Balance Beam" School Science and Mathematics 85 (October 1985): 494-497.

Stacey, K. and M. MacGregor. "Ideas about Symbolism That Students Bring to Algebra" Mathematics Teacher 90 (February 1997): 110-113.

Taylor, L.M. and J.L. King. "A Popcorn Project for All Students" Mathematics Teacher 90 (March 1997): 184-196.

Usiskin, Z. "Why Elementary Algebra Can, Should, and Must Be an Eighth-Grade Course for Average Students." Mathematics Teacher 80 (September 1987): 428—438.

Van Dyke, F. and T.V. Craine. "Equivalent Representations in the Learning of Algebra" Mathematics Teacher 90 (November 1997): 616-619.

van Reeuwijk, M. and M. Wijers. "Students' Construction of Formulas in Context" Mathematics Teaching in the Middle School 2 (February 1997): 230-236.

Williams, D.E. "Activities for Algebra." Arithmetic Teacher 33 (February 1986): 42—47.

Chapter 2 Sets, Functions, and Logic

Spence, L. "How Many Elements Are in a Union of Sets?" Mathematics Teacher 80 (November 1987): 666-670, 681.

Van de Walle, J., and C. Thompson. "Promoting Mathematical Thinking" Arithmetic Teacher 32 (February 1985): 7-13.

Welchman-Tischler, R. "Making Mathematical Connections." Arithmetic Teacher 39 (May 1992): 12-18.

Axelson, S. L. "Supermarket Challenge." Arithmetic Teacher 40 (October 1992): 84-88.

Blubaugh, W.L. and K. Emmons. "Graphing for All Students" Mathematics Teacher 92(April 1999): 323-326.

Crouse, R. and A. Alison. "Tips for Beginners: The Human Coordinate System" Mathematics Teacher 84 (February 1991): 108-109.

Davidenko, S. "Building the Concept of Function from Students' Everyday Activities" Mathematics Teacher 90 (February 1997): 144-149.

Day, R.P. "Helping Students Create Magic Arrays." Arithmetic Teacher 36 (November 1988): 46—47.

Dion, G.S. and I.B. Fetta. "Everybody Talks About It! -- Weather Investigations" Mathematics Teacher 89 (February 1996): 160-165.

Dixon, J.K. and C.J. Falba. "Graphing in the Information Age: Using Data from the World Wide Web" Mathematics Teaching in the Middle School 2 (March-April 1997): 298-304.

Foshay, J.D. and W.L. Wells. "Sharing Teaching Ideas" Mathematics Teacher 90 (December 1997): 712-714.

Geer, C. P. "Exploring Patterns, Relations, and Functions." Arithmetic Teacher 39 (May1992): 19-21.

Glicksberg, Joy. "Taste that Graph!" Arithmetic Teacher 38 (December 1990): 53.

Graham, K.G. and J. Ferrini-Mundy. "Functions and Their Representations." Mathematics Teacher 83 (March 1990): 209-216.

Gustafson, D.A.T. "Skiing the Slopes." Mathematics Teacher 80 (December 1987): 733—739.

Hopkins, M. H., and D. M. Gard. "Ideas." Arithmetic Teacher 40 (October 1992): 93-105.

Howden, H. "Implementing the Standards: Patterns, Relationships, and Functions." Arithmetic Teacher 37 (November 1989):18-24.

Johnston, A. "Introducing Function and Its Notation." Mathematics Teacher 80 (October 1987): 558—564.

Karp, K. "Telling Tales: Creating Graphs Using Multicultural Literature." Teaching Children Mathematics 1 (October 1994): 87-91.

Kennedy, J.B. "Sharing Teaching Ideas" Mathematics Teacher 90 (April 1997): 284.

McCoy, L.P. "Algebra: Real-Life Investigation in a Lab Setting" Mathematics Teaching in the Middle School 2 (February 1997): 220-224.

Mercer, J. "Teaching Graphing Concepts with Graphing Calculators" Mathematics Teacher 88 (April 1995): 268-273.

Metz, J.R. "Slope as Speed." Mathematics Teacher 81 (April 1988): 285—289.

Phillips, E., T. Gardella, C. Kelly, and J. Stewart. Patterns and Functions. Curriculum and Evaluation Standards for School Mathematics Addenda Series: Grades 5-8. Reston, VA: National Council of Teachers of Mathematics, 1991.

Quinn, A.L. and K.R. Larson. "When Does a Dog Become Older Than Its Owner?" Mathematics Teacher 89 (December 1996): 734-737.

Quinn, R.J. "Developing Conceptual Understanding of Relations and Functions with Attribute Blocks" Mathematics Teaching in the Middle School 3 (November-December 1997): 186-190.

Sand, M. "A Function Is a Mail Carrier" Mathematics Teacher 89 (September 1996): 468-469.

Schloemer, C. G. "Tips for Teaching Cartesian Graphing: Linking Concepts and Procedures." Teaching Children Mathematics 1 (September 1994): 20-23.

Shealy, B. "Becoming Flexible with Functions: Investigating United States Population Growth." Mathematics Teacher 89 (May 1996): 414-418.

Smith, R.F. "Let's Do It: Coordinate Geometry for Third Graders." Arithmetic Teacher 33 (April 1986): 6—11.

Sulzer, J.S. "The Function Box and Fourth Graders: Squares, Cubes, and Circles" Teaching Children Mathematics 4 (April 1998): 442-447.

Van Dyke, F. "Visualizing Cost, Revenue, and Profit" Mathematics Teacher 91 (September 1998): 488-493, 500-503.

Vissa, J.M. "Coordinate Graphing: Shaping a Sticky Situation." Arithmetic Teacher 35 (November 1987): 6—10.

Westegaard, S.K. "Stitching Quilts Into Coordinate Geometry" Mathematics Teacher 91 (October 1998): 587-592, 598-600.

Willoughby, S.S. "Functions from Kindergarten through Sixth Grade" Teaching Children Mathematics 3 (February 1997): 314-318.

Arnold, B., P. Turner, and T.J. Conney. "Analyzing Teaching and Learning: The Art of Listening" Mathematics Teacher 89 (April 1996): 326-329.

Bright, G.W. "Teaching Mathematics with Technology: Logical Reasoning." Arithmetic Teacher 36 (October 1988): 54-55.

Epp, S.S. "A Unified Framework for Proof and Disproof" Mathematics Teacher 91 (November 1998): 708-713.

Galbraith, P. "Mathematics as Reasoning." Mathematics Teacher 88 (May 1995): 412-417.

Garofalo, J. and D.K. Mtetwa,"Implementing The Standards: Mathematics As Reasoning". Arithmetic Teacher 37 (January 1990): 16-18

Gill, A. J. "Multiple Strategies: Product of Reasoning and Communication." Arithmetic Teacher 40 (March 1993): 380-387.

Gregg, J. "The Perils of Conditional Statements and the Notion of Logical Equivalence" Mathematics Teacher 90 (October 1997): 544-548.

McGinty, R. and J. Van Beynen. "Deductive and Analytical Thinking" Mathematics Teacher 78 (March 1985): 188-194.

O'Daffer, P. "Inductive and Deductive Reasoning" Mathematics Teacher 83 (May 1990): 378-384.

O'Regan, P. "Intuition and Logic" Mathematics Teacher 81 (November 1988): 664-668.

Redmond, C., M.P. Federici and D.M. Platte. "Proof by Contradiction and the Electoral College" Mathematics Teacher 91 (November 1998): 655-659, 713.

Rothbart, A. "Learning to Reason from Lewis Carroll" Mathematics Teacher 91 (January 1998): 6-10, 96.

Sanders, W. and R. Antes. "Teaching Logic with Logic Boxes" Mathematics Teacher 81 (November 1988): 643-647.

Silver, J.A. "Can Computers Be Used to Teach Proofs?" Mathematics Teacher 91 (November 1998): 660-663.

Szombathelyi, A. and T. Szarvas. "Ideas for Developing Students' Reasoning: A Hungarian Perspective" Mathematics Teacher 91 (November 1998): 677-681.

Schwartz, J. E. " 'Silent Teacher' and Mathematics as Reasoning." Arithmetic Teacher 40 (October 1992): 122-124.

Thompson, A.G. "Developing Student's Mathematical Thinking." Arithmetic Teacher 33 (September 1985): 20-23.

Van Dyke, F. "A Visual Approach to Deductive Reasoning." Mathematics Teacher 88 (September 1995): 481-486, 492-494.

Chapter 3 Numeration

Bohan, H.J., and P. B. Shawaker. "Using Manipulatives Effectively: A Drive Down Rounding Road." Arithmetic Teacher 41 (January 1994): 246-248.

Bove, S.P. "Place Value: A Vertical Perspective." Teaching Children Mathematics 1 (May 1995): 542-546.

Gluck, D. "Helping Students Understand Place Value" Arithmetic Teacher 38 (March 1991): 10-13.

Harrison, M., and B. Harrison." Developing Numeration Concepts and Skills." Arithmetic Teacher 33 (February 1986): 18-21, 60.

Hooven, B. "Place Value Wheels" Arithmetic Teacher 39 (May 1992): 50.

Joslyn, R.E. "Using Concrete Models to Teach Large-Number Concepts." Arithmetic Teacher 38 (November 1990): 6-9.

Kamii, C., and L. Joseph. "Teaching Place Value and Double-Column Addition." Arithmetic Teacher 35 (February 1988): 48-52.

Kouba, V.L., C.A. Brown, T.P. Carpenter, M.M. Lindquist, E.A. Silver, and J.O. Swafford. "Results of the Fourth NAEP Assessment of Mathematics: Number, Operations, and Word Problems." Arithmetic Teacher 35 (April 1988): 14-19.

Lara-Alecio, R., B.J. Irby and L. Morales-Aldana. "A Mathematics Lesson from the Mayan Civilization" Teaching Children Mathematics 5 (November 1998): 154-158.

Payne, J.N. "Research into Practice: Place Value for Tens and Ones." Arithmetic Teacher 35 (February 1988): 64-66.

Rathmell, E.C., and L. P. Leutzinger. "Implementing the Standards: Number Representations and Relationships." Arithmetic Teacher 38 (March 1991): 20-23.

Reys, B.J., R. Barger, M. Bruckheimer, B. Dougherty, J. Hope, L. Lembke, Z. Markovics, A Parnas, S. Reehm, R. Sturdevant, and M. Weber. Developing Number Sense. Curriculum and Evaluation Standards for School Mathematics Addenda Series: Grades 5-8. Reston, VA: National Council of Teachers of Mathematics, 1991.

Ross, R., and R. Kurtz. "Making Manipulatives Work: A Strategy for Success." Arithmetic Teacher 40 (January 1993): 254-257.

Ross, S.H. "Parts, Wholes, and Place Value: A Developmental View." Arithmetic Teacher 36 (February 1989): 47-51.

Sowder, J., and B. Schappelle. "Number Sense-Making." Arithmetic Teacher 41 (February 1994): 342-345.

Trowell, J. "Let Your Fingers Do the Counting." Arithmetic Teacher 36 (October 1988): 50-53.

Zepp, R.A. "Numbers and Codes in Ancient Peru: The Quipu." Arithmetic Teacher 39 (May 1992): 42-44.

Beattie, I.D. "Modeling Operations and Algorithms." Arithmetic Teacher 33 (February 1986): 23-28.

Bobis, J. F. "Using a Calculator to Develop Number Sense." Arithmetic Teacher 38 (January 1991): 42-45.

Burton, G. M., A. Mills, C. Lennon, and C. Parkers. Number Sense and Operations. Curriculum and Evaluation Standards for School Mathematics Addenda Series: Grades K-6. Reston, VA: National Council of Teachers of Mathematics, 1993.

Carroll, W.M. and D. Porter. "Alternative Algorithms for Whole-Number Operations." The Teaching and Learning of Algorithms in School Mathematics. 1998 Yearbook of the National Council of Teachers of Mathematics, edited by L.J. Morrow and M.J. Kenney, pp. 106-114. Reston, VA; National Council of Teachers of Mathematics, 1998.

Englert, G. R., and R. Sinicrope. "Making Connections with Two-Digit Multiplication." Arithmetic Teacher 41 (April 1994):446-448.

Kamii, C., B.A. Lewis, and S.J. Livingston. "Primary Arithmetic: Children Inventing Their Own Procedures." Arithmetic Teacher 41 (December 1993): 200-203.

Kamii, C., and L. Joseph. "Teaching Place Value and Double-Column Addition." Arithmetic Teacher 35 (February 1988): 48-52.

McClain, K., P. Cobb, and J. Bowers. "A Contextual Investigation of Three-Digit Addition and Subtraction." The Teaching and Learning of Algorithms in School Mathematics. 1998 Yearbook of the National Council of Teachers of Mathematics, edited by L.J. Morrow and M.J. Kenney, pp. 141-150. Reston, VA; National Council of Teachers of Mathematics, 1998.

Nagel, N.G., and C.C. Swingen. "Students' Explanations of Place Value in Addition and Subtraction" Teaching Children Mathematics 5 (November 1998): 164-170.

Page, A. "Helping Students Understand Subtraction." Teaching Children Mathematics 1 (November 1994): 140-143.

Pearson, E.S. "Summing It All Up: Pre-1900 Algorithms." Arithmetic Teacher 33 (March 1986): 38-41.

Reys, B.J. "Mental Computation."Arithmetic Teacher 32 (February 1985): 43-46.

Reys, R.E. "Estimation." Arithmetic Teacher 32 (February 1985): 37-41.

Schielack, J. F. "Reaching Young Pupils with Technology." Arithmetic Teacher 38 (February 1991): 51-55.

Sherrill, J.M. "Magic Squares and Magic Triangles." Arithmetic Teacher 35 (October 1987): 44-47.

Shifter, D. "Reasoning about Operations: Early Algebraic Thinking in Grades K-6." Developing Mathematical Reasoning in Grades K-12. 1999 Yearbook of the National Council of Teachers of Mathematics, edited by Lee V. Stiff and Frances R. Curcio, pp. 62-81. Reston, VA: National Council of Teachers of Mathematics, 1999.

Slovin, H. "Number of the Day." Arithmetic Teacher 39 (March 1992): 29-31.

Stanic, G.M.A., and W.D. McKillip. "Developmental Algorithms Have a Place in Elementary School Mathematics Instruction." Arithmetic Teacher 36 (January 1989): 14-16.

Sutton, J. T., and T. D. Urbatsch. "Transition Boards: A Good Idea Made Better." Arithmetic Teacher 38 (January 1991): 4-8.

Thompson, F. "Two-Digit Addition and Subtraction: What Works?" Arithmetic Teacher 38 (January 1991): 10-13.

Thompson, C.S., and A.D. Hendrickson. "Verbal Addition and Subtraction Problems: Some Difficulties and Some Solutions." Arithmetic Teacher 33 (March 1986): 21-25.

Thornton, C.A., and P.J. Smith. "Action Research: Strategies for Learning Subtraction Facts." Arithmetic Teacher 35 (April 1988): 8-12.

Trafton, P. R., and J. S. Zawojewski. "Implementing the Standards: Meanings of Operations." Arithmetic Teacher 38 (November 1990): 18-22.

Armstrong, B. E. "Teaching Patterns, Relationships, and Multiplication as Worthwhile Mathematical Tasks." Teaching Children Mathematics 1 (March 1995): 446-450.

Baek, J-M. "Children's Invented Algorithms for Multidigit Multiplication Problems" The Teaching and Learning of Algorithms in School Mathematics. 1998 Yearbook of the National Council of Teachers of Mathematics, edited by L.J. Morrow and M.J. Kenney, pp. 151-160. Reston, VA; National Council of Teachers of Mathematics, 1998.

Broadbent, F.W. "Lattice Multiplication and Division." Arithmetic Teacher 34 (January 1987): 28-31.

English, L. "Problem Solving with Combinations." Arithmetic Teacher 40 (October 1992): 72-77.

Graeber, A. O. "Misconceptions About Multiplication and Division." Arithmetic Teacher 40 (March 1993): 408-411.

Hendrickson, A.D. "Verbal Multiplication and Division Problems: Some Difficulties and Some Solutions." Arithmetic Teacher 33 (April 1986): 26-33.

Hope, J. "Promoting Number Sense in School." Arithmetic Teacher 36 (February 1989): 12-16.

Howden, H. "Teaching Number Sense." Arithmetic Teacher 36 (February 1989): 6-11.

Katterns, B., and K. Carr. "Talking with Young Children about Multiplication." Arithmetic Teacher 33 (April 1986): 18-21.

Quintero, A.H. "Children's Conceptual Understanding of Situations Involving Multiplication." Arithmetic Teacher 33 (January 1986): 34-37.

Reys, B.J. "Mental Computation." Arithmetic Teacher 32 (February 1985): 43-46.

Reys, R.E. "Estimation." Arithmetic Teacher 32 (February1985): 37-41.

Sowder, J.T. "Mental Computation and Number Sense." Arithmetic Teacher 37 (March 1990): 18-20.

Whitin, D.J. "Number Sense and the Importance of Asking 'Why?" Arithmetic Teacher 36 (February 1989): 26-29.

Abel, J., G.D. Allinger, and L. Andersen. "Popsicle Sticks, Computers, and Calculators: Important Considerations." Arithmetic Teacher 34 (May 1987): 8-12.

Baker, D., R. Edwards, and C. Marshall. "Teaching Mathematics with Technology: Teaching About Exponents with Calculators." Arithmetic Teacher 38 (September 1990): 38-40.

Bates, T., and L. Rousseau. "Will the Real Division Algorithm Please Stand Up?" Arithmetic Teacher 33 (March 1986): 42-46.

Beattie, I.D. "Modeling Operations and Algorithms." Arithmetic Teacher 33 (February 1986): 23-28.

Burns, M. "Introducing Division Through Problem-Solving Experiences." Arithmetic Teacher 38 (April 1991): 14-18.

English, L. "Problem Solving with Combinations" Arithmetic Teacher 40 (October 1992): 72-77.

Graeber, A. O. "Research Into Practice: Misconceptions About Multiplication and Division." Arithmetic Teacher 40 (March 1993): 408-411.

Graeber, A. O., and K. M. Baker. "Little Into Big Is the Way It Always Is." Arithmetic Teacher 39 (April 1992): 18-21.

Harel, G., and M. Behr. "Ed's Strategy for Solving Division Problems." Arithmetic Teacher 39 (November 1991): 38-40.

Hendrickson, A.D. "Verbal Multiplication and Division Problems: Some Difficulties and Some Solutions." Arithmetic Teacher 33 (April 1986): 26-33.

Kouba, V. and K. Franklin. "Multiplication and Division: Sense Making and Meaning." Teaching Children Mathematics 1 (May 1995): 574-577.

Lappan, G., E. Phillips, and M.J. Winter. "Powers and Patterns: Problem Solving with Calculators." Arithmetic Teacher 30 (October 1982): 42-44.

Reys, R.E. "Estimation." Arithmetic Teacher 32 (February 1985): 37-41.

Usnick, V. E., and P. M. Lamphere. "Teaching Mathematics with Technology: Calculators and Division." Arithmetic Teacher 38 (December 1990): 40-43.

Van Erp, J.W.M. "The Power of Five: An Alternative Model." Arithmetic Teacher 38 (April 1991): 48-53.

Wheatley, G. H. "Research Into Practice: Calculators and Constructivism." Arithmetic Teacher 38 (October 1990): 22-23.

Whitin, D. J. "Becca's Investigation." Arithmetic Teacher 41 (October 1993): 78-81.

Chapter 4 Integers and Number Theory

Avital, S. "The Plight and Might of Number Seven." Arithmetic Teacher 25 (February 1978): 22—24.

Beattie, I. D. "Building Understanding with Blocks." Arithmetic Teacher 34 (October 1986): 5—11.

Bezuska, S.J. and M.J. Kenney. "Even Perfect Numbers: (Update)²" Mathematics Teacher 90 (November 1997): 628-633.

Bezuszka, S. "A Test for Divisibility by Primes." Arithmetic Teacher 33 (October 1985): 36—38.

Brown, G. "Searching for Patterns of Divisors." Arithmetic Teacher 32 (December 1984): 32—34.

Bunham, W. "Euclid and the Infinitude of Primes" Mathematics Teacher 80 (January 1987): 16-17.

Dearing, D. and B. Holtan. "Factors and Primes with a T Square" Arithmetic Teacher 34 (April 1987): 34.

Dunham, W. "Euclid and the Infinitude of Primes." Mathematics Teacher 80 (January 1987): 16-17.

Fitzgerald, W. M., and J. U. Boyd."A Number Line with Character." Arithmetic Teacher 41 (March 1994): 368-369.

Hohfold, J. "An Inductive Approach to Prime Factors." Arithmetic Teacher 29 (December 1981): 28—29.

Hopkins, M.H. "Number Facts—or Fantasy?" Arithmetic Teacher 34 (March 1987): 38—42.

Juraschek, B. and A.S. Evans. "Ryan's Primes" Teaching Children Mathematics 3 (May 1997): 472-474.

Lappan, G., and M. Winter. "Prime Factorizations." Arithmetic Teacher 27 (March 1980): 24—27.

McGinty, R. and J. Van Beynen. "Deductive and Analytical Thinking" Mathematics Teacher 78 (March 1985): 188-194.

Newman, C.M. and S.B. Turkel. "Integrating Arithmetic and Geometry with Numbered Points on a Circle." Arithmetic Teacher 36 (January 1989): 28—31.

Quesada, A.R. "Recent Improvements to the Sieve of Erathosthenes" Mathematics Teacher 90 (April 1997): 304-307.

Schaefer, M.G. "Motivational Activities in Elementary Mathematics." Arithmetic Teacher 28 (May 1981): 17—18.

Edwards, F. "Geometric Figures Make the LCM Obvious" Arithmetic Teacher 34 (March 1987): 17-18.

Ewbank, W. "LCM — Let's Put It in Its Place" Arithmetic Teacher 35 (November 1987): 45-47.

Lamb, C., and L. Hutcherson. "Greatest Common Factor and Least Common Multiple." Arithmetic Teacher 31 (April 1984): 43-44.

Padberg, F.F. "Using Calculators to Discover Simple Theorems–An Example from Number Theory." Arithmetic Teacher 28 (April 1981): 21-23.

Robold, A. "Patterns in Multiples." Arithmetic Teacher 29 (April 1982): 21-23.

Roy, S. "LCM and GCF in the Hundred Chart." Arithmetic Teacher 26 (December 1978): 53.

Scheuer, D., Jr. "All-Star GCF." Arithmetic Teacher 26 (November1978): 34-35.

Sherzer, L. "A Simplified Presentation for Finding the LCM and the GCF." Arithmetic Teacher 21 (May 1974): 415-416.

Stern, P. "GCF and LCM, Korean Style!" Arithmetic Teacher 32 (December 1984): 3.

Thiessen, D. "David's Algorithm for the L.C.D." Arithmetic Teacher 28 (March 1981): 18.

Zerger, M.J. "How Many Cards? Let's Ask the LCM" Mathematics Teacher 89 (April 1996): 298-299.

Battista, M. "A Complete Model for Operations on Integers" Arithmetic Teacher 30 (May 1983): 26-31.

Bennett, A.B. Jr. and G.L. Musser. "A concrete approach to integer addition and subtraction." The Arithmetic Teacher, 23 (May 1976): 332-336.

Conaway, B. and R. Midkiff. "Connecting Literature, Language, and Fractions" Arithmetic Teacher 41 (April 1994): 430-434.

Crowley, M. and K. Dunn. "On Multiplying Negative Numbers" Mathematics Teacher 78 (April 1985): 252-256.

Kohn, J. "A Physical Model for Operations with Integers" Mathematics Teacher 71 (December 1978): 734-736.

Peterson, J. "Fourteen Different Strategies for Multiplication of Integers, or Why (^-1)(^-1) = 1" Arithmetic Teacher 19 (May 1972): 396-403.

Chapter 5 Introduction to Fractions

Barson, A. and L. Barson. "Ideas" Arithmetic Teacher 35 (January 1988): 19-24.

Bezuk, N. "Fractions in the Early Childhood Mathematics Curriculum" Arithmetic Teacher 35 (February 1988): 56-60.

Caldwell, J. H. "Communicating About Fractions with Pattern Blocks." Teaching Children Mathematics 2 (November 1995):156-161.

Conaway, B., and R.B. Midkiff. "Connecting Literature, Language, and Fractions." Arithmetic Teacher 41 (April 1994): 430-434.

Curcio, F.R., F. Sicklick, and S.B. Turkel. "Divide and Conquer: Unit Strips to the Rescue." Arithmetic Teacher 35 (December 1987): 6-12.

Dorgan, D. "What Textbooks Offer for Instruction in Fraction Concepts." Teaching Children Mathematics 1 (November 1994): 150-155.

Edelman, L. "The Fractions of a Day" Mathematics Teaching in the Middle School 3 (November-December 1997): 192-195.

Edge, D. "Fractions and Panes" Arithmetic Teacher 34 (April 1987): 13-17.

Empson, S. "Using Sharing Situations to Help Children Learn Fractions." Teaching Children Mathematics 2 (October 1995): 110-114.

Ettline, J. "A Uniform Approach to Fractions" Arithmetic Teacher 32 (March 1985): 42-43.

Kamii, C., and M.A. Washington "Teaching Fractions: Fostering Children's Own Reasoning." Developing Mathematical Reasoning in Grades K-12. 1999 Yearbook of the National Council of Teachers of Mathematics, edited by Lee V. Stiff and Frances R. Curcio, pp. 82-92. Reston, VA: National Council of Teachers of Mathematics, 1999.

Kennard, R. "Interpreting Fraction Form" Mathematics Teaching 112 (September 1985): 46-47.

Mack, N. "Making Connections to Understand Fractions" Arithmetic Teacher 40 (February 1993): 362-364.

Maher, C. A., R.B. Davis, and A. Alston. "Implementing the Professional Standards for Teaching Mathematics: Teachers Paying Attention to Students' Thinking." Arithmetic Teacher 39 (May 1992): 34-37.

McBride, J. W., and C. E. Lamb. "Using Commercial Games to Design Teacher-Made Games for the Mathematics Classroom." Arithmetic Teacher 38 (January 1991): 14-22.

Ockenga, E. "Chalk Up Some Calculator Activities for Rational Numbers." Arithmetic Teacher 31 (February 1984): 51—53.

Payne, J.N., and A.E. Towsley. "Implications of NCTM's Standards for Teaching Fractions and Decimals." Arithmetic Teacher 37 (April 1990): 23-26.

Payne, J.N. "Curricular Issues: Teaching Rational Numbers." Arithmetic Teacher 31 (February 1984): 14—17.

Post, T., and K. Cramer. "Children's Strategies in Ordering Rational Numbers" Arithmetic Teacher 35 (October 1987): 33-35.

Post, T. "Fractions and Other Rational Numbers" Arithmetic Teacher 37 (September 1989): 3, 28.

Pothier, Y., and D. Sawada. "Partitioning: An Approach to Fractions." Arithmetic Teacher 38 (December 1990): 12-17.

Prevost, F. "Teaching Rational Numbers — Junior High School" Arithmetic Teacher 31 (February 1984): 43-46.

Rees, J.M. "Two-sided Pies: Help for Improper Fractions and Mixed Numbers. "Arithmetic Teacher 35 (December 1987): 28—32.

Reys, B.J., R. Barger, M. Bruckheimer, B. Dougherty, J. Hope, L. Lembke, Z. Markovics, A. Parnas, S. Reehm, R.Sturdevant, and M. Weber. Developing Number Sense. Curriculum and Evaluation Standards for School Mathematics Addenda Series: Grades 5-8. Reston, VA: National Council of Teachers of Mathematics, 1991.

Sowder, J., and B. Schappelle. "Research Into Practice: Number Sense-Making." Arithmetic Teacher 41 (February 1994): 342-345.

Thompson, C. and V. Walker. "Connecting Decimals and Other Mathematical Content." Teaching Children Mathematics 2 (April 1996): 496-502.

Trafton, P., J. Zawojewki, R. Reys, and B. Reys. "Estimation with 'Nice' Fractions" Mathematics Teacher 79 (November 1986): 629-630.

Witherspoon, M. L. "Fractions: In Search of Meaning." Arithmetic Teacher 40 (April 1993): 482-485.

Alterman, A. E. "The Number 2 Challenge." Arithmetic Teacher 40 (November 1992): 180-183.

Bitner, J., and M. E. Partridge. "`Stocking Up' on Mathematics Skills." Arithmetic Teacher 38 (March 1991): 4-7.

Brinker, L. "Using Recipes and Ratio Tables to Build on Students' Understanding of Fractions" Teaching Children Mathematics 4 (December 1998): 218-224.

Collyer, S. "Adding Fractions" Mathematics Teaching 116 (September 1986): 9.

Cramer, K., and N. Bezuk. "Multiplication of Fractions: Teaching for Understanding." Arithmetic Teacher 39 (November 1991): 34-37.

Dirkes, M.A. "Draw to Understand." Arithmetic Teacher 39 (December 1991): 26-29.

Dorgan, D. "What Textbooks Offer for Instruction in Fraction Concepts." Teaching Children Mathematics 1 (November 1994): 150-155.

Edge, D. "Fractions and Panes." Arithmetic Teacher 34 (April 1987): 13—17.

Hanselman, C.A. "Stop Using Foul Language in the Mathematics Classroom" Mathematics Teaching in the Middle School 3 (October 1997): 160.

Huinker, D. "Letting Fraction Algorithms Emerge Through Problem Solving" The Teaching and Learning of Algorithms in School Mathematics. 1998 Yearbook of the National Council of Teachers of Mathematics, edited by L.J. Morrow and M.J. Kenney, pp. 170-182. Reston, VA; National Council of Teachers of Mathematics, 1998.

Kalman, D. "Up Fractions! Up n/m!" Arithmetic Teacher 32 (April 1985): 42-43.

Kroll, D.L., and T. Yabe. "A Japanese Educator's Perspective on Teaching Mathematics in the Elementary School." Arithmetic Teacher 35 (October 1987): 36—43.

Lester, F. "Teacher Education: Preparing Teachers to Teach Rational Numbers" Arithmetic Teacher 31 (February 1984): 54-56.

Mack, N.K. "Building a Foundation for Understanding the Multiplication of Fractions" Teaching Children Mathematics 5 (September 1998): 34-38.

Malcolm, P.S. "Understanding Rational Numbers" Mathematics Teacher 80 (October 1987): 518-521.

Ott, J. M., D.L. Snook, and D. L. Gibson. "Understanding Partitive Division of Fractions." Arithmetic Teacher 39 (October 1991): 7-11.

Ott, J.M. "A Unified Approach to Multiplying Fractions," Arithmetic Teacher 37 (March 1990): 47-49.

Payne, J.N., and A.E. Towsley. "Implications of NCTM's Standards for Teaching Fractions and Decimals." Arithmetic Teacher 37 (April 1990): 23-26

Payne, J. "Curricular Issues: Teaching Rational Numbers" Arithmetic Teacher 31 (February 1984): 14-17.

Prevost, F. "Teaching Rational Numbers — Junior High School" Arithmetic Teacher 31 (February 1984): 43-46.

Reys, B. "Promoting Number Sense in the Middle Grades" Mathematics Teaching in the Middle School 1 (September-October, 1994): 114-120.

Schultz, J. E. "Area Models -- Spanning the Mathematics of Grades 3-9." Arithmetic Teacher 39 (October 1991): 42-46.

Sharp, J. "A Constructed Algorithm for Division of Fractions" The Teaching and Learning of Algorithms in School Mathematics. 1998 Yearbook of the National Council of Teachers of Mathematics, edited by L.J. Morrow and M.J. Kenney, pp. 198-203. Reston, VA; National Council of Teachers of Mathematics, 1998.

Steiner, E.E. "Division of Fractions: Developing Conceptual Sense with Dollars and Cents." Arithmetic Teacher 34 (May 1987): 36—42.

Sweetland, R. "Understanding Multiplication of Fractions" Arithmetic Teacher 32 (September 1984): 48-52.

Warrington, M.A., and C. Kamii. "Multiplication with Fractions: A Piagetian, Constructivist Approach" Mathematics Teaching in the Middle School 3 (February 1998): 339-343.

Warrington, M.A. "How Children Think About Division with Fractions" Mathematics Teaching in the Middle School 2 (May 1997): 390-394.

Chapter 6 Exponents and Decimals

Carraher, T.N. and A.D. Schliemann. "Using Money to Teach about the Decimal System." Arithmetic Teacher 36 (December 1988): 42—43.

Goldenberg, E. P. "A Mathematical Conversation with Fourth Graders." Arithmetic Teacher 38 (April 1991): 38-43.

Hiebert, J. "Research Report: Decimal Fractions." Arithmetic Teacher 34 (March 1987): 22—23.

Lester, F. "Teacher Education: Preparing Teachers to Teach Rational Numbers" Arithmetic Teacher 31 (February 1984): 54-56.

Malcom, P.S. "Understanding Rational Numbers" Mathematics Teacher 80 (October 1987): 518-521.

McBride, J. W., and C. E. Lamb. "Using Commercial Games to Design Teacher-Made Games for the Mathematics Classroom." Arithmetic Teacher 38 (January 1991): 14-22.

Ockenga, E. "Chalk Up Some Calculator Activities for Rational Numbers." Arithmetic Teacher 31(February 1984): 51—53.

Payne, J. "Curricular Issues: Teaching Rational Numbers" Arithmetic Teacher 31 (February 1984): 14-17.

Payne, J.N., and A.E. Towsley "Implications of NCTM's Standards for Teaching Fractions and Decimals."Arithmetic Teacher 37 (April 1990): 23-26.

Post, T., and K. Cramer. "Children's Strategies in Ordering Rational Numbers." Arithmetic Teacher 35 (October 1987): 33—35.

Post, T. "Fractions and Other Rational Numbers" Arithmetic Teacher 37 (September 1989): 3, 28.

Simms, A.J. "Repeating Decimals into Fractions: A Microwave Recipe." Mathematics Teacher 80 (January 1987): 61—62.

Sowder, J. "Place Value as the Key to Teaching Decimal Operations" Teaching Children Mathematics 3 (April 1997): 448-453.

Sullivan, P., and D. Clarke. "Catering to All Abilities Through `Good' Questions." Arithmetic Teacher 39 (October 1991): 14-18.

Thompson, C.S., and V. Walker. "Connecting Decimals and Other Mathematical Content" Teaching Children Mathematics 2 (April 1996): 496-502.

Wesson, J. B., and C. Lawhorn. "Standards in the Methods Class, an Example." Arithmetic Teacher 40 (September 1992): 38-39.

Zawojewski, J. "Initial Decimal Concepts: Are They Really So Easy?" Arithmetic Teacher 30 (March 1983): 52—56.

Lobato, J. E. "Making Connections with Estimation." Arithmetic Teacher 40 (February 1993): 347-351.

Lyon, B. C. "Creating Magic Squares." Arithmetic Teacher38 (December 1990): 48-53.

Markovits, Z., R. Hershkowitz, and M. Bruckheimer. "Estimation, Qualitative Thinking, and Problem Solving."Mathematics Teacher 80 (September 1987): 461—464.

Moniuszko, L. K. "Reality Math."Arithmetic Teacher 39 (September 1991): 10-16.

Parker, J., and C. C. Widmer. "Teaching Mathematics with Technology: Computation and Estimation." Arithmetic Teacher 40(September 1992): 48-51.

Payne, J. "Curricular Issues: Teaching Rational Numbers" Arithmetic Teacher 31 (February 1984): 14-17.

Payne, J.N., and A.E. Towsley. "Implications of NCTM's Standards for Teaching Fractions and Decimals."Arithmetic Teacher 37 (April 1990): 23-26.

Reys, B.J. and R.E. Reys. "Implementing the Standards: Estimation - Direction from the Standards." Arithmetic Teacher 37 (March 1990): 22-25.

Schultz, J. E. "Area Models -- Spanning the Mathematics of Grades 3-9."Arithmetic Teacher 39 (October 1991): 42-46.

Williams, S.E. and J.V. Copely. "Promoting Classroom Dialogue: Using Calculators to Discover Patterns in Dividing Decimals" Mathematics Teaching in the Middle School 1 (April 1994): 72-75.

Section 6.3 Ratio, Percent, and Scientific Notation

Bennett, Jr., A. B., and L. T. Nelson. "A Conceptual Model for Solving Percent Problems." Mathematics Teaching in the Middle School 1 (April 1994): 20-25.

Bitner, J., and M. E. Partridge. "`Stocking Up' on Mathematics Skills." Arithmetic Teacher 38 (March 1991): 4-7.

Brinker, L. "Using Recipes and Ratio Tables to Build on Students' Understanding of Fractions" Teaching Children Mathematics 4 (December 1998): 218-224.

Carr, M.J. "Get Away from the Table! Make Interest More Interesting." Mathematics Teacher 79 (December 1986): 703—705.

Coburn, T. "Percentage and the Hand Calculator" Mathematics Teacher 79 (May 1986): 361-367.

Comstock, M., and F. Demana. "The Calculator Is a Problem-Solving Concept Developer." Arithmetic Teacher 34 (February 1987): 48—51.

Cramer, K., and T. Post. "Making Connections: A Case for Proportionality." Arithmetic Teacher 40 (February 1993): 342-346.

Curcio, F., and N. Bezuk. "Understanding Rational Numbers and Proportions" Curriculum and Evaluation Standards for School Mathematics Addenda Series Grades 5-8 (National Council of Teachers of Mathematics) 1994.

Haubner, M. A. "Percents: Developing Meaning Through Models." Arithmetic Teacher 40 (December 1992): 232-234.

Middleton, J. and M. Van Den Heuvel-Panhuizen. "The Ratio Table." Mathematics Teaching in the Middle School 1 (January-March 1995): 282-287.

Quintero, A. "Helping Children Understand Ratios" Arithmetic Teacher 34 (April 1987): 17-21.

Rossini, B. "Using Percent Problems to Promote Critical Thinking" Mathematics Teacher 81 (January 1988): 31-34.

Shealy, B.E. "Becoming Flexible with Functions: Investigating United States Population Growth" Mathematics Teacher 89 (May 1996): 414-418.

Strickland, J.F., Jr., and J. Denitto. "The Power of Proportions in Problem Solving." Mathematics Teacher 82 (January 1989): 11—13.

Wiebe, J. "Manipulating Percentages" Mathematics Teacher 79 (January 1986): 21, 23-26.

Bonsangue, M.V. "A Geometrical Representation of Primitive Pythagorean Triples" Mathematics Teacher 90 (May 1997): 350-354.

Chow, P. and T. Lin. "Extracting Square Roots Made Easy" Arithmetic Teacher 29 (November 1981): 48-50.

Housinger, M.M. "Trap a Surprise in an Isosceles Trapezoid" Mathematics Teacher 89 (January 1996): 12-14.

Lufkin, Dan. The Incredible Three-by-Five Card!" Mathematics Teacher 89 (February 1996): 96-98.

Miller, W., and L. Wager. "Pythagorean Dissection Puzzles" Mathematics Teacher 86 (April 1993): 302-308, 313-314.

Morrow, L. J. "Geometry Through the Standards." Arithmetic Teacher 38 (April 1991): 21-25.

Naraine, B. "If Pythagoras Had a Geoboard" Mathematics Teacher 86 (February 1993): 137-140, 145-148.

Naylor, M. "Nonperiodic Tilings: The Irrational Numbers of the Tiling World" Mathematics Teacher 92 (January 1999): 34-40.

Serra, Michael. Patty Paper Geometry. Berkeley, CA: Key Curriculum Press, 1994.

Tirman, A. "Pythagorean Triples" Mathematics Teacher 79 (November 1986): 652-655.