引言数学教育改革迫在眉睫
[1]Programme for International Student Assessment（PISA），（2003）. Learning from Tomorrow/'s World：First Results from PISA 2003.Italy：Organisation for Economic Co-operation and Development（OECD）.
[2]Glenn, J.（2000）. Before It/'s Too Late.A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21st Century.Education Publications Center：Jessup, MD.http：//www.ed.gov/americacounts/glenn/.
[3]Quoted in Ball, S.（1990）. Politics and Policy Making in Education.London：Routledge, p.103.
[4]Moses, R.，＆Cobb, J. C.（2001）.Radical Equations：Math, Literacy, and Civil Rights.Boston：Beacon Press.
[5]Steen, L. A.（ed.）（1997）.Why Numbers Count：Quantitative Literacy for Tomorrow/'s America.New York：College Entrance Examination Board.
[6]Lave, J.，Murtaugh, M.＆de la Rocha, O.（1984）. The Dialectical Construction of Arithmetic Practice.In B.Rogoff＆J.Lave.eds.，Everyday Cognition：Its Development in Social Context.Cambridge, Mass.：Harvard University Press.
[7]Lave, J.（1988）. Cognition in Practice.Cambridge, England：Cambridge University Press.
[8]Masingila, J.（1993）. Learning from Mathematics Practice in Out-of-School Situations.For the Learning of Mathematics，13（2），pp.18-22.
[9]Nunes, T.，Schliemann, A. D.，＆Carraher, D.W.（1993）.Street Mathematics and School Mathematics.New York：Cambridge University Press.
[10]Lave, J.（1988）. Cognition in Practice.
[11]Boaler, J.（2002）. Experiencing School Mathematics：Traditional and Reform Approaches to Teaching and Their Impact on Student Learning, revised and expanded ed.Mahwah, N.J.：Lawrence Erlbaum.
[12]书中所有学校、老师及学生均为化名。教学研究中涉及的学样均匿名。
01 什么是数学？ 为什么我们都离不开数学？
[1]Brown, D.（2003）. The Da Vinci Code.New York：Doubleday.
[2]Wertheim, M.（1997）. Pythagoras/'Trousers：God, Physics and the Gender Wars.New York：W.W.Norton, pp.3-4.
[3]Devlin, K.（2000）. The Math Gene：How Mathematical Thinking Evolved and Why Numbers Are Like Gossip.New York：Basic Books, p.7.
[4]Kenschaft, P. C.（2005）.Math Power：How to Help Your Child Love Math, Even If You Don/'t, revised ed.Upper Saddle River, N.J.：Pi Press.
[5]Sawyer, W. W.（1955）.Prelude to Mathematics.New York：Dover, p.12.
[6]Fiori, N.（2007）. The Practices of Mathematicians.Manuscript in preparation.
[7]Singh, S.（1997）. Fermat/'s Enigma：The Epic Quest to Solve the World/'s Greatest Mathematical Problem.New York：Anchor Books.
[8]Ibid.
[9]Ibid.，p. xiii.
[10]Quoted in ibid.，p. 6.
[11]Article in The New York Times by Fran Schumer called In Princeton, Taking On Harvard/'s Fuss About Women. The New＆nbsp；York Times, June 19，2005.In it she quotes Diane Maclagan.
[12]Lakatos, I.（1976）. Proofs and Refutations.Cambridge, England：Cambridge University Press.
[13]Cockcroft, W. H.（1982）.Mathematics Counts：Report of Inquiry into the Teaching of Mathematics in Schools.London：Her Majesty/'s Stationery Office.
[14]Wilson, R. in Albers, D.J.，Alexanderson, G.L.，＆Reid, C.（1990）.More Mathematical People：Contemporary Conversations.Boston：Harcourt Brace Jovanovich, p.30.
[15]Devlin, K.（2000）. The Math Gene, p.76.
[16]Pólya, G.（1971）.How to Solve It.New York：Doubleday Anchor, p.v.
[17]Burton, L.（1999）. The Practices of Mathematicians：What Do They Tell Us about Coming to Know Mathematics?Educational Studies in Mathematics，37，p.36.
[18]Peter Hilton, popular quote.
[19]Hersh, R.（1997）. What Is Mathematics, Really?New York：Oxford University Press, p.18.
[20]Devlin, K.（2000）. The Math Gene, p.9.
[21]Fiori, N.（2007）. The Practices of Mathematicians.
[22]Boaler, J.（2002）. Experiencing School Mathematics.
[23]Reid, D. A.（2002）.Conjectures and Refutations in Grade 5 Mathematics.Journal for Research in Mathematics Education，33（1），pp.5-29.
[24]Keil, G. E.（1965）.Writing and Solving Original Problems as a Means of Improving Verbal Arithmetic Problem Solving Ability.Unpublished doctoral dissertation.Indiana University.
02 数学课堂教学的问题 新旧教学模式之争
[1]Schoenfeld, A. H.（2004）.The Math Wars.Educational Policy，18（1），pp.253-286.
[2]Sanders, W. L.，＆Rivers, J.C.（1996）.Cumulative and Residual Effects of Teachers on Future Student Academic Achievement.Knoxville：University of Tennessee, Value-Added Research and Assessment Center.
[3]Wright, S. P.，Horn, S.P.，＆Sanders, W.L.（1997）.Teacher and Classroom Context Effects on Student Achievement：Implications for Teacher Evaluation.Journal of Personnel Evaluation in Education, pp.57-67.
[4]Jordan, H. R.，Mendro, R.L.，＆Weersinghe, D.（1997）.Teacher Effects on Longitudinal Student Achievement：A Preliminary Report on Research on Teacher Effectiveness.Paper presented at the National Evaluation Institute, Indianapolis, Ind.Kalamazoo, Mich.：Western Michigan University.
[5]Darling-Hammond, L.（2000）Teacher Quality and Student Achievement. Educational Policy Analysis Archives 8（1）January 2000.
[6]PISA（2003）. Learning from Tomorrow/'s World：First Results from PISA 2003.Italy：OECD.
[7]Johnson, E. G.，＆Allen, N.L.（1992）.The NAEP 1990 Technical Report（No.21-TR-20）.Washington, D.C.：National Center for Educational Statistics.
[8]Boaler, J.（1997）. Experiencing School Mathematics：Teaching Styles, Sex and Setting.Buckingham, England：Open University Press.
[9]Carpenter, T. P.，Franke, M.L.，＆Levi, L.（2003）.Thinking Mathematically：Integrating Arithmetic and Algebra in the Elementary School.Portsmouth, N.H.：Heinemann.
[10]Flannery, S.（2002）. In Code：A Mathematical Journey.Chapel Hill, N.C.：Algonquin Books, p.38.
[11]Hersh, R.（1997）. What Is Mathematics, Really?New York：Oxford University Press, p.27.
[12]Boaler, J.，＆Greeno, J.（2000）. Identity, Agency and Knowing in Mathematics Worlds.In J.Boaler（Ed.），Multiple Perspectives on Mathematics Teaching and Learning.Westport, CT：Ablex, pp.171-200.
[13]Murata, A（2006）. Personal communication.
[14]Schoenfeld, A. H.（1987）.Confessions of an Accidental Theorist.For the Learning of Mathematics，7（1），p.37.
[15]Rose, H.，（1998）. Reflections on PUS, PUM and the Weakening of Panglossian Cultural Tendencies.The Production of a Public Understanding of Mathematics.Birmingham, England：University of Birmingham, p.4.
[16]Ibid.，p. 5.
03 美好的愿景 提高课堂教学的方法
[1]Siskin, L. S.（1994）.Realms of Knowledge：Academic Departments in Secondary Schools.London：Falmer Press.
[2]Wenger, E.（1998）. Communities of Practice：Learning, Meaning and Identity.Cambridge, England：Cambridge University Press.
[3]Lave, J.（1988）. Cognition in Practice.Cambridge, England：Cambridge University Press.
04 征服“数学考试”这头怪兽 能够激励数学学习的新模式
[1]Kohn, A.（2000）. The Case against Standardized Testing.Portsmouth, N.H.：Heinemann, p.1.
[2]Rosser, P.（1992）. The SAT Gender Gap：ETS Responds.Washington, D.C.：Center for Women Policy Studies.
[3]Pope, D.（1999）. Doing School：“Successful”Students/'Experiences of the High School Curriculum.Stanford, Calif.：Stanford University.
[4]Kohn, A.（2000）. The Case against Standardized Testing.p.30.
[5]Amrein, A. L.，＆Berliner, D.（2002）.High-Stakes Testing, Uncertainty, and Student Learning.Education Policy Analysis Archives 10（18），pp.1-63.
[6]Gunzenhauser, M. G.（2003）.High-Stakes Testing and the Default Philosophy of Education.
[7]Deevers, M.（2006）. Linking Classroom Assessment Practices with Student Motivation in Mathematics.Paper presented at annual meeting of the American Educational Research Association held in San Francisco, Calif.
[8]White, B. Y.，＆Frederiksen, J.R.（1998）.Inquiry, Modeling, and Metacognition：Making Science Accessible to All Students.Cognition and Instruction，16（1），pp.3-118.
[9]Black, P.，Harrison, C.，Lee, C.，Marshall, B.，＆Wiliam, D. Working inside the Black Box：Assessment for Learning in the Classroom.Department of Education and Professional Studies, King/'s College.London.
[10]Elawar, M. C.，＆Corno, L.（1985）.A Factorial Experiment in Teachers/'Written Feedback on Student Homework：Changing Teacher Behavior a Little Rather Than a Lot.Journal of Educational Psychology，77（2），pp.162-173.
[11]Wiliam, D.（2007）. Keeping Learning on Track：Classroom Assessment and the Regulation of Learning.In F.K.Lester Jr.（ed.），Second Handbook of Mathematics Teaching and Learning（pp.1053-1098）.Greenwich, Conn.：Information Age Publishing, p.1085.
[12]Sadler, R.（1989）. Formative Assessment and the Design of Instructional Systems.Instructional Science，18，pp.119-144.
05 把教育驶入“慢行道” 美国分层式教学为何效率如此低下
[1]Stigler, J.，＆Hiebert, J.（1999）. The Teaching Gap：Best Ideas from the World/'s Teachers for Improving Education in the Classroom.New York：Free Press.
[2]Beaton, A. E.，＆O/'Dwyer, L.M.（2002）.Separating School, Classroom, and Student Variances and their Relationship to Socio-economic Status.In D.F.Robitaille＆A.E.Beaton（eds.），Secondary Analysis of the TIMSS Data.Dordrecht：Kluwer Academic Publishers.
[3]Bracey, G.（2003）. Tracking, by Accident and by Design.Phi Delta Kappan, December 2003，pp.332-333.
[4]Yiu, L.（2001）. Teaching Goals of Eighth Grade Mathematics Teachers：Case Study of Two Japanese Public Schools.Stanford, Calif.：Stanford University, School of Education.
[5]Porter, A. C.，and associates.（1994）.Reform of High School Mathematics and Science and Opportunity to Learn.New Brunswick, N.J.：Consortium for Policy Research in Education.
[6]Rosenthal, R.，＆Jacobson, L.（1968）. Pygmalion in the Classroom.New York：Holt, Rinehart＆Winston.
[7]Boaler, J.，Wiliam, D.，＆Brown, M.（2000）. Students/'Experiences of Ability Grouping—Disaffection, Polarisation and the Construction of Failure.British Educational Research Journal，26（5），pp.631-648.
[8]PISA（2003）. Learning from Tomorrow/'s World：First Results from PISA 2003.Italy：OECD.
[9]Oakes, J.（2005）. Keeping Track.How Schools Structure Inequality.New Haven, Conn.：Yale University Press, p.217.
[10]Olson, S.（2005）. Countdown：The Race for Beautiful Solutions at the International Mathematical Olympiad.New York：Houghton Mifflin, pp.48-49.
[11]Boaler, J.（2006）. The“Psychological Prison”from Which They Never Escaped：The Role of Ability Grouping in Reproducing Social Class Inequalities.Forum，47（2＆3），pp.135-144.
[12]Dixon, A.（2002）. Editorial.Forum，44（1），p.1.
06 作为糖与香料的代价 女性为何与数学渐行渐远
[1]Zohar, A.，＆Sela, D.（2003）. Her Physics, His Physics：Gender Issues in Israeli Advanced Placement Physics Classes.International Journal of Science Education，25（2），p.261.
[2]Gilligan, C.（1982）. In a Different Voice：Psychological Theory and Women/'s Development.Cambridge, Mass.：Harvard University Press.
[3]Belenky, M. F.，Clinchy, B.M.，Goldberger, N.R，＆Tarule, J.M.（1986）.Women/'s Ways of Knowing.New York：Basic Books, pp.214-229.
[4]Brizendine, L.（2007）. The Female Brain.New York：Morgan Road Books, p.4.
[5]Ibid.
[6]Sax, L.（2007）. Why Gender Matters, p.101.
[7]标准差仅为+0.15。
[8]Rosser, P.（1992）. The SAT Gender Gap：ETS Responds：Washington, D.C.：Center for Women Policy Studies.
[9]此项考试后来被称为“0”水准考试。
[10]例如2003-2004年评分为A、B和C的学生中，51%是女孩。
[11]Becker, J.（1981）. Differential Treatment of Females and Males in Mathematics Class.Journal for Research in Mathematics Education，12（1），pp.40-53.
[12]Herzig, A.（2004）. Becoming Mathematicians：Women andStudents of Color Choosing and Leaving Doctoral Mathematics.Review of Educational Research，74（2），pp.171-214.
[13]Herzig, A.（2004）. Slaughtering This Beautiful Mathematics：Graduate Women Choosing and Leaving Mathematics.Gender and Education，16（3），pp.379-395.
[14]Cohen, M.（1999）.“A Habit of Healthy Idleness/'：Boys/'Underachievement in Historical Perspective.”In D. Epstein, J.Elwood＆V.Hey（eds.），Failing Boys?Issues in Gender and Achievement.Buckingham, England：Open University Press, p.24.
[15]Bennett, J. cited in ibid.，p.25.
[16]Rogers, P.，＆Kaiser, G.（eds.）（1995）. Equity in Mathematics Education：Infuences of Feminism and Culture.London：Falmer Press.
07 数学应该怎样学 关键策略与辅助教学方法
[1]Gray, E.，＆Tall, D.（1994）. Duality, Ambiguity, and Flexibility：A“Proceptual”View of Simple Arithmetic.Journal for Research in Mathematics Education，25（2），pp.116-140.
[2]Thurston, W. P.（1990）.Mathematical Education.Notices of the American Mathematical Society，37，pp.844-850.
[3]Beck, T. A.（1998）.Are There Any Questions?One Teacher/'s View of Students and Their Questions in a Fourth-Grade Classroom.Teaching and Teacher Education，14（8），pp.871-886.
[4]Good, T. L.，Slavings, R.L.，Harel, K.H.，＆Emerson, H.（1987）.Student Passivity：A Study of Question Asking in K-12 Classrooms.Sociology of Education，60（July），pp.181-199.
[5]Boaler, J.，＆Staples, M.（2008）. Creating Mathematical Futures through an Equitable Teaching Approach：The Case of Railside School.Teachers/'College Record，110（3）.
[6]Greeno, J. G.（1991）.Number Sense as Situated Knowing in a Conceptual Domain.Journal for Research in Mathematics Education，22（3），pp.170-218.
[7]Boaler, J.，＆Humphreys, C.（2005）. Connecting Mathematical Ideas：Middle School Video Cases to Support Teaching and Learning.Portsmouth, N.H.：Heinemann.
[8]Ball, D. L.（1993）.With an Eye on the Mathematical Horizon：Dilemmas of Teaching Elementary Mathematics.The Elementary School Journal，93（4），pp.373-397.
[9]Lampert, M.（2001）. Teaching Problems and the Problems ofTeaching.New Haven：Yale University Press.
[10]Kent, P.，＆Noss, R.（2000）. The Visibility of Models：Using Technology as a Bridge between Mathematics and Engineering.International Journal of Mathematics Education, Science＆Technology，31（1），pp.61-69.
[11]Noss, R.，＆Hoyles, C.（2002）. Abstraction in Expertise：A Study of Nurses/'Conceptions of Concentration.Journal for Research in Mathematics Education，33（3），pp.204-229.
08 给孩子最好的数学 启蒙兴趣活动和教育建议
[1]Fiori, N.（2007）. In Search of Meaningful Mathematics：The Role of Aesthetic Choice.Doctoral dissertation.Stanford, Calif.：Stanford University.
[2]Casey, M. B.，Nuttall, R.L.，＆Pezaris, E.（1997）.Mediators of Gender Differences in Mathematics College Entrance Test Scores：A Comparison of Spatial Skills with Internalized Beliefs and Anxieties.Developmental Psychology，33，pp.669-680.
[3]Duckworth, E.（1996）.“The Having of Wonderful Ideas”and Other Essays on Teaching and Learning. New York：Teachers College Press.
[4]Ryan, A. M.，＆Patrick, H.（2001）.The Classroom Social Environment and Changes in Adolescents/'Motivation and Engagement during Middle School.American Educational Research Journal，38（2），pp.437-460.
[5]Eccles, J.，Wigfield, A.，Midgley, C.，Reuman, D. A.，MacIver, D.，＆Feldlaufer, H.（1993）.Negative Effects of Traditional Middle Schools on Students/'Motivation.The Elementary School Journal，93（5），pp.553-574.
[6]Stipek, D.，＆Seal, K.（2001）. Motivated Minds：Raising Children to Love Learning.New York：Henry Holt.
[7]Frank, M.（1988）. Problem Solving and Mathematical Beliefs.Arithmetic Teacher，35，pp.32-34.
[8]Garofalo, J.（1989）. Beliefs and Their Influence on Mathematical Performances.Mathematics Teacher，82（7），pp.502-505.
[9]Flannery, S.（2002）. In Code：A Mathematical Journey.Chapel Hill, N.C.：Algonquin Books.
[10]Ibid.，p. 8.
[11]Ibid.
[12]Kenschaft, P. C.（2006）.Math Power：How to Help Your Child Love Math, Even If You Don/'t.New York：Pi Press.p.50.
[13]Boaler, J.，＆Humphreys, C.（2005）. Connecting Mathematical Ideas：Middle School Video Cases to Support Teaching and Learning.Portsmouth, N.H.：Heinemann.
[14]Kenschaft, P. C.（2006）.Math Power, p.51.
[15]Eccles, J.，＆Jacobs, J. E.（1986）.Social Forces Shape Math Attitudes and Performance.Signs：Journal of Women in Culture and Society，11（21），pp.367-380.
[16]Kenschaft, P. C.（2006）.Math Power, p.35.
[17]Beilock, S. L.，Holt, L.E.，Kulp, C.A.，＆Carr, T.H.（2004）.More on the Fragility of Performance：Choking under Pressure in Mathematical Problem Solving.Journal of Experimental Psychology，133（4），pp.584-600.
[18]Pólya, G.（1957）.How to Solve It.New York：Doubleday Anchor.
[19]Lee, K. S.（1982）.Fourth Graders/'Heuristic Problem-Solving Behavior.Journal for Research in Mathematics Education，＆nbsp；13（2），pp.110-123.
[20]RAND Mathematics Study Panel（2002）. Mathematical Proficiency for All Students：Toward a Strategic Research and Development Program in Mathematics Education（DRU-2773-OERI）.Arlington, Va.：RAND Education＆Science and Technology Policy Institute, p.x.
[21]Lee, K. S.（1982）.Fourth Graders/'Heuristic Problem-Solving Behavior.
[22]Gray, E.＆Tall, D.（1994）. Duality, Ambiguity, and Flexibility：A Proceptual View of Simple Arithmetic.Journal for Research in Mathematics Education，25（2），pp.116-140.