Many elementary teacher education programs seek to prepare candidates to enact ambitious mathematics instruction that supports students in engaging in rigorous, conceptually rich mathematics tasks. Extant literature suggests that preparedness to engage in ambitious elementary mathematics instruction is multifaceted and includes teaching candidates’ mathematical knowledge for teaching (MKT), self-efficacy with regard to teaching mathematics, and pedagogical beliefs about mathematics. Prior research has produced findings that provide discrete, and at times conflicting, information about teacher preparation.
Purpose/Objective/Research Question/Focus of Study
This study examined how elementary candidates’ learning opportunities in mathematics content courses, mathematics methods courses, and student teaching were moderated by their reports about the quality of their experiences in courses and field placements to seem to affect their MKT, self-efficacy, and beliefs.
Population/Participants/Subjects
The study participants were 220 elementary teaching candidates who were in their final year of teacher preparation at four universities in three states.
Research Design
We employed multivariate path analysis, an approach that is purposefully designed to probe heterogeneity in teaching candidates’ experiences in courses and clinical placements.
Data Collection and Analysis
We administered two surveys to each study participant: an elementary teaching candidate survey, which included measures of mathematics teaching self-efficacy and pedagogical beliefs about mathematics, and an MKT survey.
Findings/Results
The number of mathematics content courses that elementary candidates took was positively associated with their MKT and mathematics teaching self-efficacy only when they also reported having positive experiences learning mathematics. When candidates reported increased opportunities to engage with representations, decompositions, and approximations of mathematics teaching practices in mathematics methods courses, this was associated with higher MKT scores and pedagogical beliefs about mathematics. When candidates reported that their cooperating teacher was a high-quality mentor, increased opportunities to observe, attempt, and receive feedback on mathematics teaching practices during their field experience were associated with mathematics teaching self-efficacy and pedagogical beliefs about mathematics.
Conclusions/Recommendations
The findings from this multivariate path analysis, which account for both the reported quantity and the perceived quality of elementary teaching candidate experiences, may shed light on conflicting findings in prior literature. There is little agreement in extant literature about associations between facets of teacher preparation and candidate knowledge, self-efficacy, or beliefs. Explaining the positive associations in some samples and lack of associations in others may have more to do with the quality of teaching candidate experiences than with whether a candidate was exposed to a particular opportunity to learn.
Get full access to this article
View all access options for this article.
References
1.
BallD. L., & BassH. (2002). Toward a practice-based theory of mathematical knowledge for teaching. In Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 3–14). Canadian Mathematics Education Study Group.
2.
BallD. L., & ForzaniF. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 605, 497—511.
3.
BallD. L.LubienskiS. T., & MewbornD. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In RichardsonV. (Ed.), Handbook of research on teaching (4th ed., pp. 433—456). Macmillan.
4.
BeilockS. L.GundersonE. A.RamirezG., & LevineS. C. (2010). Female teachers’ math anxiety affects girls’ math achievement. Proceedings of the National Academy of Sciences, 1075, 1860—1863.
5.
BlömekeS.BuchholtzN.SuhlU., & KaiserG. (2014). Resolving the chicken-or-egg causality dilemma: The longitudinal interplay of teacher knowledge and teacher beliefs. Teaching and Teacher Education, 37, 130—139.
6.
BoerstT. A.SleepL.BallD. L., & BassH. (2011). Preparing teachers to lead mathematics discussions. Teachers College Record, 11312, 2844—2877.
7.
BorkoH., & MayfieldV. (1995). The roles of the cooperating teacher and university supervisor in learning to teach. Teaching and Teacher Education, 115, 501—518.
8.
BoydD. J.GrossmanP. L.LankfordH.LoebS., & WyckoffJ. (2009). Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, 314, 416—440.
9.
CampbellP. F., & MalkusN. N. (2014). The mathematical knowledge and beliefs of elementary mathematics specialist-coaches. ZDM, 462, 213—225.
10.
CharalambousC. Y. (2015). Working at the intersection of teacher knowledge, teacher beliefs, and teaching practice: A multiple-case study. Journal of Mathematics Teacher Education, 185, 427—445.
11.
CharalambousC. Y.PanaouraA., & PhilippouG. (2009). Using the history of mathematics to induce changes in pre-service teachers’ beliefs and attitudes: Insights from evaluating a teacher education program. Educational Studies in Mathematics, 712, 161—180.
12.
CliftR. T., & BradyP. (2005). Research on methods courses and field experiences. In Cochran-SmithM., & ZeichnerK (Eds.), Studying teacher education: The report of the AERA Panel on Research and Teacher Education (pp. 309—424). Routledge.
13.
DragesetO. G. (2010). The interplay between the beliefs and the knowledge of mathematics teachers. Mathematics Teacher Education and Development, 121, 30—49.
14.
EnochsL. G.SmithP. L., & HuinkerD. (2000). Establishing factorial validity of the mathematics teaching efficacy beliefs instrument. School Science and Mathematics, 1004, 194—202.
15.
ErnestP. (1989). The impact of beliefs on the teaching of mathematics. In ErnestP. (Ed.)., Mathematics teaching: The state of the art (pp. 249—254). Falmer Press.
16.
EvansB. R. (2011). Content knowledge, attitudes, and self-efficacy in the mathematics New York City Teaching Fellows (NYCTF) program. School Science and Mathematics, 1115, 225—235.
17.
Feiman-NemserS., & BuchmannM. (1985). Pitfalls of experience in teacher preparation. Teachers College Record, 871, 53—65.
18.
FennemaE.FrankeM. L.CarpenterT. P., & CareyD. A. (1993). Using children's mathematical knowledge in instruction. American Educational Research Journal, 303, 555—583.
19.
FrancisD. C.RapackiL., & EkerA. (2014). The individual, the context, and practice: A review of the research on teachers’ beliefs related to mathematics. In FivesH., & GillM. G. (Eds.), International handbook of research on teachers’ beliefs (pp. 336—352). Routledge.
20.
FrykholmJ. A. (1998). Beyond supervision: Learning to teach mathematics in community. Teaching and Teacher Education, 143, 305—322.
21.
GeistE. (2015). Math anxiety and the “math gap”: How attitudes toward mathematics disadvantages students as early as preschool. Education, 1353, 328—336.
22.
GhousseiniH., & HerbstP. (2016). Pedagogies of practice and opportunities to learn about classroom mathematics discussions. Journal of Mathematics Teacher Education, 191, 79—103.
23.
GreshamG. (2007). A study of mathematics anxiety in pre-service teachers. Early Childhood Education Journal, 352, 181—188.
24.
GrossmanP.HammernessK., & McDonaldM. (2009). Redefining teaching, reimagining teacher education. Teachers and Teaching: Theory and Practice, 152, 273—289.
25.
HammernessK. (2006). From coherence in theory to coherence in practice. Teachers College Record, 1087, 1241—1265.
26.
HammernessK.Darling-HammondL.BransfordJ.BerlinerD.Cochran-SmithM.McDonaldM., & ZeichnerK. (2005). How teachers learn and develop. In Darling-HammondL., & BransfordJ. (Eds.), Preparing teachers for a changing world: What teachers should learn and be able to do (pp. 358—389). Jossey-Bass.
27.
HiebertJ., & GrouwsD. A. (2007). The effects of classroom mathematics teaching on students’ learning. In LesterF. K. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371—404). Information Age.
28.
HillH. C. (2010). The nature and predictors of elementary teachers’ mathematical knowledge for teaching. Journal for Research in Mathematics Education, 415, 513—545.
29.
HillH. C.BallD. L., & SchillingS. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 394, 372—400.
30.
HillH. C.BlazarD., & LynchK. (2015). Resources for teaching: Examining personal and institutional predictors of high-quality instruction. AERA Open, 14. https://doi.org/10.1177/2332858415617703
31.
HillH. C.CharalambousC. Y., & ChinM. J. (2019). Teacher characteristics and student learning in mathematics: A comprehensive assessment. Educational Policy, 337, 1103—1134.
32.
HillH. C.RowanB., & BallD. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 422, 371—406.
33.
HillH. C.SchillingS. G., & BallD. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. Elementary School Journal, 1051, 11—30.
34.
HillH. C.UmlandK.LitkeE., & KapitulaL. R. (2012). Teacher quality and quality teaching: Examining the relationship of a teacher assessment to practice. American Journal of Education, 1184, 489—519.
35.
HuL. T., & BentlerP. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 61, 1—55.
36.
JacksonK., & CobbP. (2010, April 30–May 4). Refining a vision of ambitious mathematics instruction to address issues of equity. Paper presented at the annual meeting of the American Educational Research Association, Denver, CO, United States.
37.
JacksonK. J.ShahanE. C.GibbonsL. K., & CobbP. A. (2012). Launching complex tasks. Mathematics Teaching in the Middle School, 181, 24—29.
38.
JongC., & HodgesT. E. (2015). Assessing attitudes toward mathematics across teacher education contexts. Journal of Mathematics Teacher Education, 185, 407—425.
39.
KazemiE.FrankeM., & LampertM. (2009). Developing pedagogies in teacher education to support novice teachers’ ability to enact ambitious instruction. In Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 12—30). MERGA.
40.
KennedyM. (1999). The role of preservice teacher education. In Darling-HammondL., & SykesG. (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 54—85). Jossey-Bass.
41.
KleickmannT.RichterD.KunterM.ElsnerJ.BesserM.KraussS., & BaumertJ. (2013). Teachers’ content knowledge and pedagogical content knowledge: The role of structural differences in teacher education. Journal of Teacher Education, 641, 90—106.
42.
KlineR., (2005). Principles and practice of structural equation modeling (3rd ed.). Guilford Press.
43.
KunterM.KlusmannU.BaumertJ.RichterD.VossT., & HachfeldA. (2013). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology, 1053, 805—820.
44.
LampertM. (2001). Teaching problems and the problems of teaching. Yale University Press.
45.
LampertM.FrankeM. L.KazemiE.GhousseiniH.TurrouA. C.BeasleyH.CunardA., & CroweK. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 643, 226—243.
46.
LampertM., & GrazianiF. (2009). Instructional activities as a tool for teachers’ and teacher educators’ learning. The Elementary School Journal, 1095, 491—509.
47.
LortieD. C. (1975). Schoolteacher: A sociological study. University of Chicago Press.
48.
MaL. (2010). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Routledge.
49.
MaasC. J., & HoxJ. J. (2005). Sufficient sample sizes for multilevel modeling. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 13, 86—92.
50.
MaaszJ., & SchlöglmannW. (Eds.). (2009). Beliefs and attitudes in mathematics education. Sense.
51.
McDonaldM.KazemiE., & KavanaghS. S. (2013). Core practices and pedagogies of teacher education: A call for a common language and collective activity. Journal of Teacher Education, 645, 378—386.
52.
MewbornD. S. (2000). Learning to teach elementary mathematics: Ecological elements of a field experience. Journal of Mathematics Teacher Education, 31, 27—46.
53.
MunterC. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 455, 584—635.
54.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education.
55.
NurluÖ. (2015). Investigation of teachers’ mathematics teaching self-efficacy. International Electronic Journal of Elementary Education, 81, 21—40.
56.
PajaresM. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 623, 307—332.
57.
PetersonP. L.FennemaE.CarpenterT. P., & LoefM. (1989). Teacher's pedagogical content beliefs in mathematics. Cognition and Instruction, 61, 1—40.
58.
PhilippR. A. (2007). Mathematics teachers’ beliefs and affect. In LesterF. K. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257—315). Information Age.
59.
QianH., & YoungsP. (2016). The effect of teacher preparation programs on future elementary mathematics teachers’ knowledge: A five-country analysis using TEDS-M data. Journal of Mathematics Teacher Education, 194, 371—396.
60.
RaudenbushS. W., & BrykA. (2002). Hierarchical linear models: Applications and data analysis methods (Vol. 1). SAGE.
61.
RenL., & SmithW. M. (2017). Teacher characteristics and contextual factors: Links to early primary teachers’ mathematical beliefs and attitudes. Journal of Mathematics Teacher Education, 214, 321—350.
62.
RonfeldtM. (2012). Where should student teachers learn to teach? Effects of field placement school characteristics on teacher retention and effectiveness. Educational Evaluation and Policy Analysis, 341, 3—26.
63.
RonfeldtM., & ReiningerM. (2012). More or better student teaching?Teaching and Teacher Education, 288, 1091—1106.
64.
SchmidtW. H.BlömekeS., & TattoM. T. (2011a). Teacher education matters: A study of middle school mathematics teacher preparation in six countries. Teachers College Press.
65.
SchmidtW. H.HouangR., & CoganL. S. (2011b). Preparing future math teachers. Science, 3326035, 1266—1267.
66.
SleeterC. E. (2001). Preparing teachers for culturally diverse schools: Research and the overwhelming presence of whiteness. Journal of Teacher Education, 522, 94—106.
67.
SmithM. E.SwarsS. L.SmithS. Z.HartL. C., & HaardörferR. (2012). Effects of an additional mathematics content course on elementary teachers’ mathematical beliefs and knowledge for teaching. Action in Teacher Education, 344, 336—348.
68.
SolomonY.EriksenE.SmestadB.RodalC., & BjerkeA. H. (2017). Prospective teachers navigating intersecting communities of practice: Early school placement. Journal of Mathematics Teacher Education, 202, 141—158.
69.
StaubF. C., & SternE. (2002). The nature of teachers’ pedagogical content beliefs matters for students’ achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 942, 344—355.
70.
SwarsS. L.SmithS. Z.SmithM. E., & HartL. C. (2009). A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs. Journal of Mathematics Teacher Education, 121, 47—66.
71.
TattoM. T. (1996). Examining values and beliefs about teaching diverse students: Understanding the challenges for teacher education. Educational Evaluation and Policy Analysis, 182, 155—180.
72.
WilkinsJ. L. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 112, 139—164.
73.
WilsonM., & CooneyT. (2002). Mathematics teacher change and developments. In LederG. C.PehkonenE., & TörnerG. (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127—147). Springer.
74.
ZeichnerK. (2010). Rethinking the connections between campus courses and field experiences in college-and university-based teacher education. Journal of Teacher Education, 611–2, 89—99.
75.
ZeichnerK.PayneK. A., & BraykoK. (2015). Democratizing teacher education. Journal of Teacher Education, 662, 122—135.
