Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement

This study explored whether and how teachers’ mathematical knowledge for teaching contributes to gains in students’ mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders’ mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found that teachers’ mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This result, while consonant with findings from the educational production function literature, was obtained via a measure focusing on the specialized mathematical knowledge and skills used in teaching mathematics. This finding provides support for policy initiatives designed to improve students’ mathematics achievement by improving teachers’ mathematical knowledge.

[1]  Walter Doyle,et al.  4: Paradigms for Research on Teacher Effectiveness , 1977 .

[2]  David T. Burkam,et al.  Inequality at the Starting Gate: Social Background Differences in Achievement as Children Begin School , 2002 .

[3]  Gaea Leinhardt,et al.  Overlap: What's Tested, What's Taught?. , 1981 .

[4]  Mary M. Kennedy.  Teaching Academic Subjects to Diverse Learners. , 1991 .

[5]  E. Begle,et al.  Critical Variables in Mathematics Education: Findings from a Survey of the Empirical Literature , 1979 .

[6]  Deborah Loewenberg Ball,et al.  Knowledge and reasoning in mathematical pedagogy : examining What prospective teachers bring to teacher education. (Volumes I and II) , 1988 .

[7]  Eric A. Hanushek,et al.  Education and race;: An analysis of the educational production process , 1972 .

[8]  S. Raudenbush,et al.  Resources, Instruction, and Research , 2003 .

[9]  D. Bob Gowin,et al.  Science, Curriculum, and Liberal Education: Selected Essays , 1978 .

[10]  Larry V. Hedges,et al.  The Effect of School Resources on Student Achievement , 1996 .

[11]  D. Ball.  The Mathematical Understandings That Prospective Teachers Bring to Teacher Education , 1990, The Elementary School Journal.

[12]  Eric A. Hanushek,et al.  A More Complete Picture of School Resource Policies , 1996 .

[13]  Sam Wineburg,et al.  Peering at History through Different Lenses: The Role of Disciplinary Perspectives in Teaching History , 1988, Teachers College Record: The Voice of Scholarship in Education.

[14]  Brian Rowan,et al.  Using research on employees' performance to study the effects of teachers on students' achievement? , 1997 .

[15]  Peter A. Youngs,et al.  Teacher Characteristics and Student Achievement Gains: A Review , 2003 .

[16]  Greg J. Duncan,et al.  Family background, parenting practices, and the Black–White test score gap. , 1998 .

[17]  Alexander M. Mood,et al.  Equality of Educational Opportunity. , 1967 .

[18]  Susanna Loeb,et al.  Public Policy and Teacher Labor Markets. What We Know and Why It Matters. , 2004 .

[19]  Ralph W. Hanushek Eric A. Harbison,et al.  Educational Performance of the Poor: Lessons from Rural Northeast Brazil , 1992 .

[20]  Gaea Leinhardt,et al.  Analysis of Arithmetic for Mathematics Teaching , 1992 .

[21]  Hyman Bass,et al.  Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. , 2000 .

[22]  Nathaniel Gage,et al.  The Scientific Basis of The Art of Teaching/N.L. Gage , 1979 .

[23]  Anthony E. Boardman,et al.  A Simultaneous Equations Model of the Educational Process: The Coleman Data Revisited with an Emphasis on Achievement. , 1973 .

[24]  Rebecca Barr,et al.  How Schools Work , 1991 .

[25]  David Rogosa,et al.  A growth curve approach to the measurement of change. , 1982 .

[26]  M. Carnoy,et al.  Does External Accountability Affect Student Outcomes? A Cross-State Analysis , 2002 .

[27]  M. Wittrock.  Handbook of research on teaching , 1986 .

[28]  Raven Wallace,et al.  New Tools for Research on Instruction and Instructional Policy: A Web-Based Teacher Log. A CTP Working Paper. , 1999 .

[29]  Patrick W Thompson,et al.  Talking about Rates Conceptually, Part I: A Teacher's Struggle. , 1994 .

[30]  A. M. White.  The Process of Education , 1994 .

[31]  J. Dewey.  The child and the curriculum , 1902 .

[32]  Brian Rowan,et al.  What Large-Scale, Survey Research Tells Us About Teacher What Large-Scale, Survey Research Tells Us About Teacher Effects on Student Achievement: Insights From the Prospectus Effects on Student Achievement: Insights From the Prospectus Study of Elementary Schools Study of Elementary Schools , 2015 .

[33]  Douglas A. Grouws,et al.  Active mathematics teaching , 1983 .

[34]  E. Begle,et al.  Teacher Knowledge and Student Achievement in Algebra, School Mathematics Study Group Reports Number 9. , 1972 .

[35]  C. Jencks,et al.  The Black-White Test Score Gap. , 1998 .

[36]  L. Shulman.  Knowledge and Teaching: Foundations of the New Reform , 1987 .

[37]  Herbert J. Walberg,et al.  Research on teaching : concepts, findings and implications , 1981 .

[38]  Brian Rowan,et al.  Using Instructional Logs to Study Mathematics Curriculum and Teaching in the Early Grades , 2004, The Elementary School Journal.

[39]  J. Calderhead.  Exploring teachers' thinking , 1987 .

[40]  Richard J. Murnane,et al.  The Contribution of Training and Subject Matter Knowledge to Teaching Effectiveness: A Multilevel Analysis of Longitudinal Evidence from Belize , 1996, Comparative Education Review.

[41]  S. Schilling,et al.  Developing Measures of Content Knowledge for Teaching Reading , 2004, The Elementary School Journal.

[42]  J. Brophy.  Teacher behavior and student achievement , 1984 .

[43]  D. Ball.  Bridging Practices , 2000 .

[44]  Bernard Myers,et al.  The Scientific Basis of the Art of Teaching by N. L. Gage (review) , 1982 .

[45]  T. P. Carpenter,et al.  Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study , 1989 .

[46]  William K. Cummings,et al.  Comparing the effectiveness and costs of different approaches for educating primary school teachers in Sri Lanka , 1993 .

[47]  Heather C. Hill,et al.  Teachers' Mathematics Knowledge for Teaching and School Context , 2007 .

[48]  P. Grossman.  The Making of a Teacher: Teacher Knowledge and Teacher Education , 1990 .

[49]  Catherine A. Brown,et al.  Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give Up Too Easily? , 1992 .

[50]  Ronald F. Ferguson.  Paying for public education: New evidence on how and why money , 1991 .

[51]  G. Leinhardt,et al.  Expertise in mathematics instruction: Subject matter knowledge. , 1985 .

[52]  L. Darling-Hammond,et al.  Does Teacher Certification Matter? Evaluating the Evidence , 2001 .

[53]  L. Shulman.  Those Who Understand: Knowledge Growth in Teaching , 1986 .

[54]  David H. Monk,et al.  Subject area preparation of secondary mathematics and science teachers and student achievement , 1994 .

[55]  Eric A. Hanushek,et al.  Throwing money at schools , 1981 .

[56]  John B. Willett,et al.  Understanding correlates of change by modeling individual differences in growth , 1985 .

[57]  D. Ball,et al.  Developing Measures of Teachers’ Mathematics Knowledge for Teaching , 2004, The Elementary School Journal.

[58]  R. Strauss,et al.  Some new evidence on teacher and student competencies , 1986 .