Long-Term Relationships Between Mathematics Instructional Time During Teacher Preparation and Specialized Content Knowledge

Author:
Julien Corven University of Delaware

Search for other papers by Julien Corven in
Current site
Google Scholar
PubMed
Close
,
Joseph DiNapoli Montclair State University, NJ

Search for other papers by Joseph DiNapoli in
Current site
Google Scholar
PubMed
Close
,
Laura Willoughby University of Delaware

Search for other papers by Laura Willoughby in
Current site
Google Scholar
PubMed
Close
, and
James Hiebert University of Delaware

Search for other papers by James Hiebert in
Current site
Google Scholar
PubMed
Close

We investigated how the time elementary preservice teachers (PSTs) spent studying certain mathematics topics during teacher education coursework was related to performance on teaching-related tasks administered after graduation. In two studies, participants completed tasks assessing their specialized content knowledge (SCK) for teaching 12 mathematical topics addressed to varying degrees in the preparation program. We found that instructional time was positively associated with SCK demonstrated both immediately postgraduation and 2 years later. Several possible confounding factors were assessed; one, entering PSTs’ average SCK for topics, appeared to influence the relationship. Accounting for professional learning postgraduation, such as attending professional development, did not change the underlying relationship. Considering these findings, we identify policy implications for the mathematics curriculum of PST education.

Footnotes

Preparation of this article was supported by the National Science Foundation (Grant No. DRL-1420578). The opinions expressed in the article are those of the authors and not necessarily those of the Foundation. The authors gratefully acknowledge the assistance of Dawn Berk, PI of the grant project, during the design and management of this project; Henry May and Joe Glutting for consultations regarding statistical methodology; and the mathematics education faculty and doctoral students at the University of Delaware for feedback throughout the project.

Contributor Notes

Julien Corven, School of Education, University of Delaware, Newark, DE 19716; jcorven@udel.edu

Joseph DiNapoli, Department of Mathematics, Montclair State University, Montclair, NJ 07043; dinapolij@montclair.edu

Laura Willoughby, School of Education, University of Delaware, Newark, DE 19716; lwilloug@udel.edu

James Hiebert, School of Education, University of Delaware, Newark, DE 19716; hiebert@udel.edu

  • Collapse
  • Expand
Journal for Research in Mathematics Education
  • Ahn, S., & Choi, J. (2004, April 12–16). Teachers’ subject matter knowledge as a teacher qualification: A synthesis of the quantitative literature on students’ mathematics achievement [Paper presentation]. Annual Meeting of the American Educational Research Association, San Diego, CA, United States. https://eric.ed.gov/?id=ED490006

    • Search Google Scholar
    • Export Citation
  • Arbaugh, F., Ball, D. L., Grossman, P., Heller, D. E., & Monk, D. (2015). Dean’s corner: Views on the state of teacher education in 2015. Journal of Teacher Education, 66(5), 435445. https://doi.org/10.1177/0022487115602314

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Armstrong, K. D. (2013). The impact of teacher content knowledge in mathematics and teacher efficacy on fifth graders’ achievement in mathematics [Doctoral dissertation, Trevecca Nazarene University]. ProQuest Dissertations and Theses. https://www.proquest.com/dissertations-theses/impact-teacher-content-knowledge-mathematics/docview/1697500077/se-2

    • Search Google Scholar
    • Export Citation
  • Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. https://amte.net/standards

  • Ball, D. L., Sleep, L., Boerst, T. A., & Bass, H. (2009). Combining the development of practice and the practice of development in teacher education. The Elementary School Journal, 109(5), 458474. https://doi.org/10.1086/596996

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389407. https://doi.org/10.1177/0022487108324554

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Beckmann, S., & Izsák, A. (2021). Focusing on mathematical structure and sensemaking in courses for future teachers. In Y. Li, R. E. Howe, W. J. Lewis, & J. J. Madden (Eds.), Developing mathematical proficiency for elementary instruction (pp. 131164). Springer. https://doi.org/10.1007/978-3-030-68956-8_6

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Begle, E. G. (1979). Critical variables in mathematics education: Findings from a survey of the empirical literature. Mathematical Association of America & National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • Berk, D., & Hiebert, J. (2009). Improving the mathematics preparation of elementary teachers, one lesson at a time. Teachers and Teaching: Theory and Practice, 15(3), 337356. https://doi.org/10.1080/13540600903056692

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Blömeke, S., Paine, L., Houang, R. T., Hsieh, F.-J., Schmidt, W. H., Tatto, M. T., Bankov, K., Cedillo, T., Cogan, L., Han, S. I., Santillan, M., & Schwille, J. (2008). Future teachers’ competence to plan a lesson: First results of a six-country study on the efficiency of teacher education. ZDM, 40(5), 749762. https://doi.org/10.1007/s11858-008-0123-y

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194222. https://doi.org/10.2307/749118

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Boyd, D. J., Grossman, P. L., Lankford, H., Loeb, S., & Wyckoff, J. (2009). Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, 31(4), 416440. https://doi.org/10.3102/0162373709353129

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brown, B. W., & Saks, D. H. (1986). Measuring the effects of instructional time on student learning: Evidence from the Beginning Teacher Evaluation Study. American Journal of Education, 94(4), 480500. https://doi.org/10.1086/443863

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H., DePiper, J. N., Frank, T. J., Griffin, M. J., & Choi, Y. (2014). The relationship between teachers’ mathematical content and pedagogical knowledge, teachers’ perceptions, and student achievement. Journal for Research in Mathematics Education, 45(4), 419459. https://doi.org/10.5951/jresematheduc.45.4.0419

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chapin, S. H., Gibbons, L. K., Feldman, Z., Callis, L. K., & Salinas, A. (2021). The Elementary Mathematics Project: Supporting preservice teachers’ content knowledge for teaching mathematics. In Y. Li, R. E. Howe, W. J. Lewis, & J. J. Madden (Eds.), Developing mathematical proficiency for elementary instruction (pp. 89113). Springer. https://doi.org/10.1007/978-3-030-68956-8_4

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cochran-Smith, M., Stern, R., Sánchez, J. G., Miller, A., Keefe, E. S., Fernández, M. B., Chang, W.-C., Carney, M. C., Burton, S., & Baker, M. (2016). Holding teacher preparation accountable: A review of claims and evidence. National Education Policy Center. https://files.eric.ed.gov/fulltext/ED574703.pdf

    • Search Google Scholar
    • Export Citation
  • Cochran-Smith, M., Villegas, A. M., Abrams, L., Chavez-Moreno, L., Mills, T., & Stern, R. (2015). Critiquing teacher preparation research: An overview of the field, part II. Journal of Teacher Education, 66(2), 109121. https://doi.org/10.1177/0022487114558268

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cohen, D. K., & Hill, H. C. (2001). Learning policy: When state education reform works. Yale University Press. https://doi.org/10.12987/yale/9780300089479.001.0001

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155159. https://doi.org/10.1037/0033-2909.112.1.155

  • Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II. American Mathematical Society & Mathematical Association of America. https://doi.org/10.1090/cbmath/017

    • Search Google Scholar
    • Export Citation
  • Copur-Gencturk, Y. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers’ knowledge and instruction. Journal for Research in Mathematics Education, 46(3), 280330. https://doi.org/10.5951/jresematheduc.46.3.0280

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Copur-Gencturk, Y., Plowman, D., & Bai, H. (2019). Mathematics teachers’ learning: Identifying key learning opportunities linked to teachers’ knowledge growth. American Educational Research Journal, 56(5), 15901628. https://doi.org/10.3102/0002831218820033

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Darling-Hammond, L. (2017). Teacher education around the world: What can we learn from international practice? European Journal of Teacher Education, 40(3), 291309. https://doi.org/10.1080/02619768.2017.1315399

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Darling-Hammond, L., & Lieberman, A. (Eds.). (2012). Teacher education around the world: Changing policies and practices. Routledge. https://doi.org/10.4324/9780203817551

    • Search Google Scholar
    • Export Citation
  • Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181199. https://doi.org/10.3102/0013189X08331140

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Desimone, L. M., & Garet, M. S. (2015). Best practices in teachers’ professional development in the United States. Psychology, Society, & Education, 7(3), 252263. https://doi.org/10.25115/psye.v7i3.515

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Desimone, L. M., Porter, A. C., Garet, M. S., Yoon, K. S., & Birman, B. F. (2002). Effects of professional development on teachers’ instruction: Results from a three-year longitudinal study. Educational Evaluation and Policy Analysis, 24(2), 81112. https://doi.org/10.3102/01623737024002081

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dick, L. K. (2017). Investigating the relationship between professional noticing and specialized content knowledge. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 339358). Springer. https://doi.org/10.1007/978-3-319-46753-5_20

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feuer, M. J., Floden, R. E., Chudowsky, N., & Ahn, J. (2013). Evaluation of teacher preparation programs: Purposes, methods, and policy options. National Academy of Education. https://files.eric.ed.gov/fulltext/ED565694.pdf

    • Search Google Scholar
    • Export Citation
  • Fuchs, L. S., & Malone, A. S. (2021). Can teaching fractions improve teachers’ fraction understanding? Insights from a causal-comparative study. The Elementary School Journal, 121(4), 656673. https://doi.org/10.1086/713975

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gansle, K. A., Noell, G. H., & Burns, J. M. (2012). Do student achievement outcomes differ across teacher preparation programs? An analysis of teacher education in Louisiana. Journal of Teacher Education, 63(5), 304317. https://doi.org/10.1177/0022487112439894

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(4), 915945. https://doi.org/10.3102/00028312038004915

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Guskey, T. R. (1994). Results-oriented professional development: In search of an optimal mix of effective practices. Journal of Staff Development, 15(4), 4250.

    • Search Google Scholar
    • Export Citation
  • Harnischfeger, A., & Wiley, D. E. (1976). The teaching–learning process in elementary schools: A synoptic view. Curriculum Inquiry, 6(1), 543. https://doi.org/10.1080/03626784.1976.11075510

    • Search Google Scholar
    • Export Citation
  • Hiebert, J., Berk, D., Miller, E., Gallivan, H., & Meikle, E. (2019). Relationships between opportunity to learn mathematics in teacher preparation and graduates’ knowledge for teaching mathematics. Journal for Research in Mathematics Education, 50(1), 2350. https://doi.org/10.5951/jresematheduc.50.1.0023

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hiebert, J., Wieman, R. M., & Berk, D. (2018). Designing systems for continuously improving instruction: The case of teacher preparation mathematics courses. In R. P. Ferretti & J. Hiebert (Eds.), Teachers, teaching, and reform: Perspectives on efforts to improve educational outcomes (pp. 116139). Routledge. https://doi.org/10.4324/9781315186559-7

    • Search Google Scholar
    • Export Citation
  • Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430511. https://doi.org/10.1080/07370000802177235

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hill, H. C., & Charalambous, C. Y. (2012). Teacher knowledge, curriculum materials, and quality of instruction: Lessons learned and open issues. Journal of Curriculum Studies, 44(4), 559576. https://doi.org/10.1080/00220272.2012.716978

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371406. https://doi.org/10.3102/00028312042002371

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 1130. https://doi.org/10.1086/428763

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Levine, A. (2006). Educating school teachers. The Education Schools Project. https://files.eric.ed.gov/fulltext/ED504144.pdf

  • Lorah, J. (2018). Effect size measures for multilevel models: Definition, interpretation, and TIMSS example. Large-Scale Assessments in Education, 6(8). https://doi.org/10.1186/s40536-018-0061-2

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum. https://doi.org/10.4324/9781410602589

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Monk, D. H. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13(2), 125145. https://doi.org/10.1016/0272-7757(94)90003-5

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morris, A. K., & Hiebert, J. (2017). Effects of teacher preparation courses: Do graduates use what they learned to plan mathematics lessons? American Educational Research Journal, 54(3), 524567. https://doi.org/10.3102/0002831217695217

    • Crossref
    • Search Google Scholar
    • Export Citation
  • National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. http://www.corestandards.org

    • Search Google Scholar
    • Export Citation
  • National Research Council. (2010). Preparing teachers: Building evidence for sound policy. National Academies Press. https://doi.org/10.17226/12882

    • Search Google Scholar
    • Export Citation
  • Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3rd ed.). McGraw-Hill.

  • Peshkin, A. (1988). In search of subjectivity—One’s own. Educational Researcher, 17(7), 1721. https://doi.org/10.3102/0013189X017007017

    • Search Google Scholar
    • Export Citation
  • Rathouz, M., & Rubenstein, R. N. (2009). Supporting preservice teachers’ learning: A fraction operations task and its orchestration. In D. S. Mewborn & H. S. Lee (Eds.), Scholarly practices and inquiry in the preparation of mathematics teachers (pp. 85103). Information Age.

    • Search Google Scholar
    • Export Citation
  • Rowan, B., Correnti, R., & Miller, R. J. (2002). What large-scale, survey research tells us about teacher effects on student achievement: Insights from the prospectus study of elementary schools. Consortium for Policy Research in Education. https://repository.upenn.edu/cpre_researchreports/31

    • Search Google Scholar
    • Export Citation
  • Schack, E. O., Fisher, M. H., & Wilhelm, J. A. (Eds.). (2017). Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks. Springer. https://doi.org/10.1007/978-3-319-46753-5

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schilling, S. G., Blunk, M., & Hill, H. C. (2007). Test validation and the MKT measures: Generalizations and conclusions. Measurement: Interdisciplinary Research and Perspectives, 5(2–3), 118128. https://doi.org/10.1080/15366360701487146

    • Search Google Scholar
    • Export Citation
  • Schmidt, W. H., Cogan, L., & Houang, R. (2011). The role of opportunity to learn in teacher preparation: An international context. Journal of Teacher Education, 62(2), 138153. https://doi.org/10.1177/0022487110391987

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sleep, L., & Eskelson, S. L. (2012). MKT and curriculum materials are only part of the story: Insights from a lesson on fractions. Journal of Curriculum Studies, 44(4), 537558. https://doi.org/10.1080/00220272.2012.716977

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Speidel, M., Drechsler, J., & Jolani, S. (2020). The R package hmi: A convenient tool for hierarchical multiple imputation and beyond. Journal of Statistical Software, 95(9), 148. https://doi.org/10.18637/jss.v095.i09

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stallings, J. (1980). Allocated academic learning time revisited, or beyond time on task. Educational Researcher, 9(11), 1116. https://doi.org/10.3102/0013189X009011011

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Stein, M. K., Baxter, J. A., & Leinhardt, G. (1990). Subject-matter knowledge and elementary instruction: A case from functions and graphing. American Educational Research Journal, 27(4), 639663. https://doi.org/10.3102/00028312027004639

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Supovitz, J. A., & Turner, H. M. (2000). The effects of professional development on science teaching practices and classroom culture. Journal of Research in Science Teaching, 37(9), 963980. https://doi.org/10.1002/1098-2736(200011)37:9<963::AID-TEA6>3.0.CO;2-0

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Suppa, S. (2018). Supporting novice mathematics teacher educators to teach ambitiously via continuously improved curriculum materials [Doctoral dissertation, University of Delaware]. UDSpace. https://udspace.udel.edu/handle/19716/23994

    • Search Google Scholar
    • Export Citation
  • Swars, S., Hart, L. C., Smith, S. Z., Smith, M. E., & Tolar, T. (2007). A longitudinal study of elementary pre-service teachers’ mathematics beliefs and content knowledge. School Science and Mathematics, 107(8), 325335. https://doi.org/10.1111/j.1949-8594.2007.tb17797.x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76(2), 141164. https://doi.org/10.1007/s10649-010-9269-y

    • Crossref
    • Search Google Scholar
    • Export Citation
  • TeachingWorks. (n.d.). High-leverage content. http://www.teachingworks.org/work-of-teaching/high-leverage-content

  • Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually, part I: A teacher’s struggle. Journal for Research in Mathematics Education, 25(3), 279303. https://doi.org/10.2307/749339

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Travers, K. J. (1992). Overview of the longitudinal version of the Second International Mathematics Study. In L. Burstein (Ed.), The IEA study of mathematics III: Student growth and classroom processes (pp. 114). Pergamon. https://doi.org/10.1016/B978-0-08-041371-6.50009-2

    • Crossref
    • Search Google Scholar
    • Export Citation
  • U.S. Department of Education. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. https://files.eric.ed.gov/fulltext/ED500486.pdf

    • Search Google Scholar
    • Export Citation
  • Wayne, A. J., & Youngs, P. (2003). Teacher characteristics and student achievement gains: A review. Review of Educational Research, 73(1), 89122. https://doi.org/10.3102/00346543073001089

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wilson, S. M., Floden, R. E., & Ferrini-Mundy, J. (2001). Teacher preparation research: Current knowledge, gaps, and recommendations. Center for the Study of Teaching and Policy. https://www.education.uw.edu/ctp/sites/default/files/ctpmail/PDFs/TeacherPrep-WFFM-02-2001.pdf

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 2868 1738 367
Full Text Views 503 65 2
PDF Downloads 793 163 3
EPUB Downloads 0 0 0