ED5850

Teaching Elementary Mathematics

Dr. J. Dale Burnett

Introduction

Rationale

Description

Pre-requisites

Goals

Format

Instructor

Textbook

Assignments

References

None specifically identified. The students will be expected to locate relevant articles in the library, within the ERIC microfiche system, and on the web.

Individuals taking this course will be encouraged to share their own resources with their classmates.

• Conway, J. H. & Guy, R. K. (1996). The book of numbers. New York: Copernicus.
  
  
• Davis, P. J. & Hersh. (1981). The mathematical experience. Boston: Houghton Mifflin.
  
  
• Enzensberger, H. N. (1997). The number devil: A mathematical adventure. New York: Metropolitan Books.
  
  
• Flegg, G. (1983). Numbers: Their history and meaning. Harmondsworth, England: Penguin.
  
  
• Gullberg, J. (1997). Mathematics: From the birth of numbers. New York: W. W. Norton.
  
  
• Johnson, D. B. & Mowry, T. A. (2001). Mathematics: A Practical Odyssey. Pacific Grove, CA: Brooks/Cole.
  
  
• King, J. (1992). The art of mathematics. New York: Fawcett.
  
  
• MacNeal, E. (1994). Mathsemantics: Making numbers talk sense. New York: Viking.
  
  
• Mankiewicz, R. (2000). The story of mathematics. London: Cassell.
  
  
• O'Daffer, P., Charles, R., Cooney, T., Dossey, J. & Schielack, J. Mathematics for elementary school teachers. 7th ed. Boston: Addison-Wesley.
  
  
• Polya, G. (1957). How to solve it: A new aspect of mathematical method. 2nd ed. Princeton, New Jersey: Princeton Unviersity Press.
  
  
• Rucker, R. (1987). The five levels of mathematical reality. Boston: Houghton Mifflin.
  

• Brainerd, C. J. (Ed.) (1982). Children's logical and mathematical cognition: Progress in cognitive development research. New York: Springer-Verlag.
  
  
• Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. Beckingham, England: Croom Helm.
  
  
• Devlin, K. (2000). The math gene. New York: Basic Books.
  
  
• Gelman, R. & Gallistel, C. R. (1986). The child's understanding of number. Cambridge, Mass.: Harvard University Press.
  
  
• Ginsburg, H. (1977). Children's arithmetic: the learning process. New York: D. Van Nostrand.
  
  
• Ginsburg, H. P. (Ed.). (1983). The development of mathematical thinking. New York: Academic Press.
  
  
• Hughes, M. (1986). Children and number: Difficulties in learning mathematics. Oxford: Basil Blackwell.
  
  
• Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago: University of Chicago Press.
  
  
• Lakoff, G. & Nunez, R. E. (2000). Where mathematics comes from. New York: Basic Books.
  
  
• Larcombe, T. (1985). Mathematical learning difficulties in the secondary school: Pupil needs and teacher roles. Milton Keynes: Open University Press.
  
  
• Lesh, R. & Landau, M. (Eds.). (1983). Acquisition of mathematics concepts and processes. New York: Academic Press.
  
  
• Lester, F. K., Jr. & Garofalo, J. (Eds.). (1982). Mathematical problem solving: Issues in research. Philadelphia: Franklin Institute Press.
  
  
• Mason, J. (1985). Thinking mathematically. Rev. ed. Reading, Mass.: Addison-Wesley.
  
  
• McLeod, D. B. & Adams, V. M. (Eds.). (1989). Affect and mathematical problem solving. New York: Springer-Verlag.
  
  
• Orton, A. (1987). Learning mathematics: Issues, theory and classroom practice. London: Cassell.
  
  
• Piaget, J., Inhelder, B. & Szeminiska, A. (1960). The child's conception of geometry. New York: W. W. Norton.
  
  
• Skemp, R. R. (1971). The psychology of learning mathematics. London: Penguin.
  

• Baroody, A. J. (1998). Fostering children's mathematical power. Mahwah, New Jersey: Lawrence Erlbaum.
  
  
• Beckmann, S. (2003). Mathematics for elementary teachers. Preliminary edition. Vol. 1: Numbers and operations. Boston: Pearson Education.
  
  
• Beckmann, S. (2003). Mathematics for elementary teachers. Preliminary edition. Vol. 2: Geometry and other topics. Boston: Pearson Education.
  
  
• Bennett, A. B., Jr. & Nelson, L. T. (2001). Mathematics for elementary teachers: An activity approach. 5th ed. Boston: McGraw-Hill.
  
  
• Bennett, A. B., Jr. & Nelson, L. T. (2001). Mathematics for elementary teachers: A conceptual approach. 5th ed. Boston: McGraw-Hill.
  
  
• Billstein, R., Libeskind, S. & Lott, J. W. (2001). A problem solving approach to mathematics for elementary school teachers. Boston: Addison-Wesley.
  
  
• Brumbaugh, D. K., Rock, D., Brumbaugh, L. S. & Rock, M. (2003). Teaching k-6 mathematics. Mahwah, New Jersey: Lawrence Erlbaum.
  
  
• Dossey, J. A., McCrone, S., Giordano, F. R. & Weir, M. D. (2002). Mathematics Methods and Modeling for Today's Mathematics Classroom. Pacific Grove, CA: Brooks/Cole.
  
  
• Easterday, K. E., Henry, L. L. & Simpson, F. M. (1981). Activities for junior high school and middle school mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
  
  
• Hoyles, C. & Sutherland, R. (1989). Logo mathematics in the classroom. London: Routledge.

  
  
• Inspiration Software Incorporated. (1998). Classroom ideas using Inspiration: For teachers by teachers. (1998).
  
  
• Krulik, S. & Reys, R. E. (1980). Problem solving in school mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
  
  
• Lamon, S. J. (1999). Teaching fractions and ratios for understanding. Mahwah, New Jersey: Lawrence Erlbaum.
  
  
• Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, New Jersey: Lawrence Erlbaum.
  
  
• Meyer, C. & Sallee, T. (1983). Make it simpler: A practical guide to problem solving in mathematics. Menlo Park, Calif.: Addison-Wesley.
  
  
• New South Wales Department of Education and Training. (2001). Count Me In Too Professional Development Package.
  
  
• New Zealand Ministry of Education. (2001). An evaluation of the Count Me In Too pilot project.
  http://www.tki.org.nz/e/r/literacy_numeracy/clarifying/schools_1-8/executive.php
  
  
• New Zealand Ministry of Education. (2002). Year 4 – 6 Numeracy Exploratory Study.
  http://www.tki.org.nz/e/r/literacy_numeracy/clarifying/schools_1-8/executive_nesa.php#exec
  
  
• Paulos, J. A. (1988). Innumeracy: Mathematical illiteracy and its consequences. New York: Vintage.
  
  
• Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving. New York: John Wiley.
  
  
• Resnick, L. B. & Ford, W. W. (1981). The psychology of mathematics for instruction. Hillsdale, N.J.: Lawrence Erlbaum.
  
  
• Reys, R. E., Suydam, M. N. & Lindquist, M. M. (1989). Helping children learn mathematics. 2nd ed. Englewood Cliffs, New Jersey: Prentice Hall.
  
  
• Schoenfeld, A. H. (Ed.) (1987). Cognitive science and mathematics education. Hillsdale, New Jersey: Lawrence Erlbaum.
  
  
• Silver, E. A. (Ed.). (1985). Teaching and learning mathematical problem solving: Multiple research perspectives. Hillsdale, New Jersey: Lawrence Erlbaum.
  
  
• Sterrett, A. (Ed.). (1990). Using writing to teach mathematics. New York: The Mathematical Association of America.
  
  
• Wright, R. J., Martland, J., & Stafford, A. (2000). Early numeracy: Assessment for teaching and intervention. London: Paul Chapman Publications /Sage.
  
  
• Wright, R. J., Martland, J., & Stafford, A. (2002). Teaching number: Advancing children's skills and strategies. London: Paul Chapman Publications /Sage.

II. ERIC REFERENCES

The following articles are all available from Dale Burnett. In the case of ED documents (identified in red), they are available as pdf files from the ERIC Document Site.

(a) Mathematics

ED456036. Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop (March 19-21, 1999). 2001.

(b) Learning Mathematics

ED453166. Anghileri, Julia; Beishuizen, Meindert. From Informal Strategies to Structured Procedures: Mind the Gap! 2001.

ED408160. Bolte, Linda A. Assessing Mathematical Knowledge with Concept Maps and Interpretive Essays. 1997.

EJ515490. Butler, Deborah L.; Winne, Philip H.. Feedback and Self-Regulated Learning: A Theoretical Synthesis. Review of Educational Research; v65 n3 p245-81 Fall 1995.

ED452204. Capraro, Mary Margaret. Defining Constructivism: Its Influence on the Problem Solving Skills of Students. 2001.

EJ558832. Carpenter, Thomas P.; Franke, Megan L.; Jacobs, Victoria R.; Fennema, Elizabeth; Empson, Susan B.. A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction. Journal for Research in Mathematics Education; v29 n1 p3-20 Jan 1998.

EJ599882. Fuchs, Lynn S.; Fuchs, Douglas; Kazdan, Sarah A.; Karns, Kathy; Calhoon, Mary Beth; Hamlett, Carol L.; Hewlitt, Sally E.. Effects of Workgroup Structure and Size on Student Productivity during Collaborative Work on Complex Tasks. 2000.

EJ543529. Fuson, Karen C.; And Others. Children's Conceptual Structures for Multidigit Numbers and Methods of Multidigit Addition and Subtraction. Journal for Research in Mathematics Education; v28 n2 p130-62 Mar 1997.

ED461505. McClain, Kay; Cobb, Paul; Gravemeijer, Koeno; Estes, Beth. Developing Mathematical Reasoning within the Context of Measurement. 1999.

ED461504. McClain, Kay; Cobb, Paul; Gravemeijer, Koeno. Supporting Students' Ways of Reasoning about Data. . 2000.

EJ641915. McClain, Kay; Cobb, Paul. Supporting Students' Ability To Reason about Data. Educational Studies in Mathematics; v45 n1-3 p103-29 2001.

EJ645974. Moyer, Patricia S.. Are We Having Fun Yet? How Teachers Use Manipulatives To Teach Mathematics. Educational Studies in Mathematics; v47 n2 p175-197 2001.

EJ604022. Noss, Richard; Pozzi, Stefano; Hoyles, Celia. Touching Epistemologies: Meanings of Average and Variation in Nursing Practice. Educational Studies in Mathematics; v40 n1 p25-51 Oct 1999.

EJ630173. Pugalee, David K.. Writing, Mathematics, and Metacognition: Looking for Connections through Students' Work in Mathematical Problem Solving. School Science and Mathematics; v101 n5 p236-45 May 2001.

EJ565755. Rye, James A.; Rubba, Peter A. An Exploration of the Concept Map as an Interview Tool To Facilitate the Externalization of Students' Understandings about Global Atmospheric Change. 1998.

EJ645973. Selter, Christoph. Addition and Subtraction of Three-digit Numbers: German Elementary Children's Success, Methods and Strategies. Educational Studies in Mathematics; v47 n2 p145-173 2001.

ED367691. Shavelson, Richard J.; And Others. On Concept Maps as Potential "Authentic" Assessments in Science. Indirect Approaches to Knowledge Representation of High School Science. 1993.

EJ638114. Steele, Diana F. Using Sociocultural Theory To Teach Mathematics: A Vygotskian Perspective. School Science and Mathematics; v101 n8 p404-16 Dec 2001.

EJ491852. Thompson, Ian. Young Children's Idiosyncratic Written Algorithms for Addition. Educational Studies in Mathematics; v26 n4 p323-45 Jun 1994.

ED456045. Weinberg, Suzanne Levin. Is There a Connection between Fractions and Division? Students' Inconsistent Responses. 2001.

(c) Teaching Mathematics

EJ490270. Acton, William H.; And Others. Structural Knowledge Assessment: Comparison of Referent Structures. Journal of Educational Psychology; v86 n2 p303-11 Jun 1994.

EJ622090. Bishop, Alan J. What Values Do You Teach When You Teach Mathematics? Teaching Children Mathematics; v7 n6 p346-49 Feb 2001.

EJ606934. Borko, Hilda; Davinroy, Kathryn H.; Bliem, Carribeth L.; Cumbo, Kathryn B.. Exploring and Supporting Teacher Change: Two Third-Grade Teachers' Experiences in a Mathematics and Literacy Staff Development Project. 2000.

ED425069. Bright, George W.; Bowman, Anita H.; Vacc, Nancy N.. Teachers' Frameworks for Understanding Children's Mathematical Thinking. 1998.

EJ604026. Carnine, Douglas; Gersten, Russell. The Nature and Roles of Research in Improving Achievement in Mathematics. Journal for Research in Mathematics Education; v31 n2 p138-43 Mar 2000.

ED435591. Chi-chung, Lam; Yun-peng, Ma; Ngai-ying, Wong. Teacher Development, Not Accountability Control, Is the Key to Successful Curriculum Implementation: A Case Study of Two Primary Schools in Northeast China. 1999.

ED389535. Cobb, Paul; Yackel, Erna. Constructivist, Emergent, and Sociocultural Perspectives in the Context of Developmental Research. 1995.

EJ475088. Cochran, Kathryn F.; And Others. Pedagogical Content Knowing: An Integrative Model for Teacher Preparation. Journal of Teacher Education; v44 n4 p263-72 Sep-Oct 1993.

ED457831. Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.. Mathematics. [SITE 2001 Section]. 2001.

ED452054. Coy, Jessica. Teaching Fifth Grade Mathematical Concepts: Effects of Word Problems Used with Traditional Methods. 2001.

ED394823. Daniel, Patricia. Aspects of Interactive Multimedia Environment Supporting Beginning Mathematics and Science Teachers' Construction of Knowledge about Teaching and Learning. 1995.

ED350162. Edgerton, Richard T.. A Description of the Assessment Practices of Teachers Who Have Begun to Implement the Instructional Practices Suggested in the NCTM Standards Documents. 1992.

EJ549381. Ferris, Angeline; And Others. Technology and Preservice Education: Models that Work, Models that Don't. Educational Technology Review; n7 p13-19 Sum 1997.

EJ631443. Fuchs, Lynn S.; Fuchs, Douglas; Karns, Kathy. Enhancing Kindergartners' Mathematical Development: Effects of Peer-Assisted Learning Strategies. Elementary School Journal; v101 n5 p495-510 May 2001.

ED364405. Gross, Sandra, Ed.. Constructing Teaching and Research Practice in Elementary School Mathematics. Elementary Subjects Center Series No. 92. 1993.

ED457000. Gu, Wenyuan. The Lattice Method Used in Teaching Multiplication with Whole Numbers and Decimals to Students with Learning Disabilities. 2001.

EJ580448. Hiebert, James. Relationships between Research and the NCTM Standards. Journal for Research in Mathematics Education; v30 n1 p3-19 Jan 1999.

EJ637787. Kazemi, Elham; Stipek, Deborah. Promoting Conceptual Thinking in Four Upper-Elementary Mathematics Classrooms. Elementary School Journal; v102 n1 p59-80 Sep 2001.

EJ643838. Kilpatrick, Jeremy. Understanding Mathematical Literacy: The Contribution of Research. Educational Studies in Mathematics; v47 n1 p101-16 2001.

EJ576298. Klein, Anton S.; Beishuizen, Meindert; Treffers, Adri. The Empty Number Line in Dutch Second Grades: Realistic versus Gradual Program Design. Journal for Research in Mathematics Education; v29 n4 p443-64 Jul 1998.

ED349184. Kloosterman, Peter; And Others. Preparing Elementary Teachers to Teach Mathematics: A Problem-solving Approach. Final Report. Volume V: Research and Evaluation Component. 1992.

EJ646020. Lewis, Scott P.; Alacaci, Cengiz; O'Brien, George E.; Jiang, Zhonghong. Preservice Elementary Teachers' Use of Mathematics in a Project-Based Science Approach. 2002.

EJ643888. Lowery, Norene Vail. Construction of Teacher Knowledge in Context: Preparing Elementary Teachers To Teach Mathematics and Science. School Science and Mathematics; v102 n2 p68-83 Feb 2002.

EJ480149. Markovits, Zvia; Sowder, Judith. Developing Number Sense: An Intervention Study in Grade 7. Journal for Research in Mathematics Education; v25 n1 p4-29 Jan 1994.

ED462276. McClain, Kay; Cobb, Paul; Bowers, Janet. A Contextual Investigation of Three-Digit Addition and Subtraction. 1998.

EJ590246. McClure, John R.; Sonak, Brian; Suen, Hoi K.. Concept Map Assessment of Classroom Learning: Reliability, Validity, and Logistical Practicality. Journal of Research in Science Teaching; v36 n4 p475-92 Apr 1999.

ED442672. Mewborn, Denise S.. An Analysis of the Research on K-8 Teachers' Mathematical Knowledge. 2000.

EJ582596. Moss, Joan; Case, Robbie. Developing Children's Understanding of the Rational Numbers: A New Model and an Experimental Curriculum. Journal for Research in Mathematics Education; v30 n2 p122-47 Mar 1999.

EJ539897. Prawat, Richard S.; Jennings, Nancy. Students as Context in Mathematics Reform: The Story of Two Upper-Elementary Teachers. Elementary School Journal; v97 n3 p251-70 Jan 1997.

EJ556629. Quinn, Robert J.; Wilson, Mary M.. Writing in the Mathematics Classroom: Teacher Beliefs and Practices. Clearing House; v71 n1 p14-20 Sep-Oct 1997.

EJ500529. Rosenshine, Barak; Meister, Carla. Reciprocal Teaching: A Review of the Research. Review of Educational Research; v64 n4 p479-530 Win 1994.

EJ625558. Ruiz-Primo, Maria Araceli; Schultz, Susan E.; Li, Min; Shavelson, Richard J.. Comparison of the Reliability and Validity of Scores from Two Concept-Mapping Techniques. 2001.

EJ643895. Rye, James A.; Rubba, Peter A.. Scoring Concept Maps: An Expert Map-Based Scheme Weighted for Relationships. School Science and Mathematics; v102 n1 p33-44 Feb 2002.

EJ635959. Stacey, Kaye; Helme, Sue; Steinle, Vicki; Baturo, Annette; Irwin, Kathryn; Bana, Jack. Preservice Teachers' Knowledge of Difficulties in Decimal Numeration. Journal of Mathematics Teacher Education; v4 n3 p205-25 2001.

ED395797. Tittle, Carol Kehr; Pape, Stephen. Selected References for Assessment and Evaluation of Mathematics and Science Teaching Reforms in Classrooms: A Bibliography. 1995.

EJ630132. Watanabe, Tad. Content and Organization of Teacher's Manuals: An Analysis of Japanese Elementary Mathematics Teacher's Manuals. School Science and Mathematics; v101 n4 p194-205 Mar 2001.

EJ622085. Zaslavsky, Claudia. Developing Number Sense: What Can Other Cultures Tell Us? Teaching Children Mathematics; v7 n6 p312-19 Feb 2001.

III. Articles, Chapters in Books (not in ERIC)

Artzt, A. F. & Armour-Thomas, E. (1992). Development of a cognitive-metacognitive framework for protocol analysis of mathematical problem solving in small groups. Cognition and Instruction, 9 (2), 137 - 175.

Beishuizen, M. & Anghileri, J. (1998). Which mental strategies in the early number curriculum? A comparison of British ideas and Dutch views. British Educational Research Journal, 24 (5), 519 - 538.

Burnett, J. D. (1999). Inspired mathematics: Semantic mapping software and the mathematics curriculum. Paper presented at MCATA annual conference, Jasper, Alberta.

Griffin, S. & Case, R. (1997). Re-thinking the primary school math curriculum: An approach based on cognitive science. Issues in Education, 3 (1), 1 - 49.

McIntosh, M. E. & Draper, R. J. (2001). Using learning logs in mathematics: Writing to learn. Mathematics teacher, 94 (7), 554 - 557.

Steffe, L. P. (1994). Children's multiplying schemes. In G. Harel & J. Confrey (Eds.) The development of multiplicative reasoning in the learning of mathematics. Albany: State University of New York Press. 3 - 39.

Thomas, G. & Ward, J. (2001). An evaluation of the Count Me In Too pilot project. Wellington, New Zealand: Ministry of Education.

von Glasersfeld, E. & Kelley, M. F. (1982). On the concepts of period, phase, stage and level. Human Development, 25, 152 - 160.

IV. University of Lethbridge Library

V. Web Sites

http://www.wcer.wisc.edu/NCISLA/?Publications/articles/

This list will be continually modified during the course.

ED5850 Home Page

Notices

Gradebook

Discussion Board

Links