International Portal of Teacher Education

Source: Teacher Development, 23:5, 529-548

(Reviewed by the Portal Team)

The author examines the mathematical content knowledge (MCK) (Lowrie and Jorgensen 2016) of pre-service middle school teachers in an Australian university and links this to their confidence to do and to teach middle school mathematics.
The key aims of this research are:
(1) Document the starting content knowledge of a cohort of participants.
This provides empirical non-proximal evidence as a reference point for confidence and self-efficacy.
(2) Document the starting confidence to do specific middle school mathematics.
(3) Document the starting self-efficacy to teach specific middle school mathematics concepts.
The relationships between these variables are explored in this study with the intention to discuss the implications of the results in terms of the structuring of mathematics curriculum courses for pre-service teachers.

Method
The research methods used to answer the research aims involve surveying pre-service teachers’ mathematical content knowledge (MCK), confidence and self-efficacy at the commencement of a middle school mathematics curriculum course.
The method examines associations between MCK, confidence and self-efficacy.
The calculated correlation coefficient is a measure of the strength of the relationship between the variables.

Participants
The participants were enrolled in a well-ranked Australian university in a school of education.
The program and courses the Australian students studied were accredited by the state regulatory body.
There were 114 enrolments across two campuses with 87% (N = 99) participating in the study.

Data-collection instruments
Mathematical content knowledge (MCK) - Participants were assessed on their MCK via a one-hour closed-book test.
In total there were 24 MCK questions totalling 31 marks.

Confidence and self-efficacy
The measurement of confidence and self-efficacy in this study was based on the logic of Bandura (2006) and Bleicher (2004), in that these attributes were measured in the context of specific situations and distinct realms of functioning.
After each of the 24 questions in the MCK tool, the participants responded on a 5-point Likert scale rating their confidence in understanding the mathematics.
As accepted in the literature reviewed, self-efficacy was seen as the individual having confidence/belief that he/she can effect an outcome or, in the case of teaching, ‘I know the steps necessary to teach (concept area) . . . effectively’ (Bleicher 2004, 391).
Thus, as was the case in assessing confidence, after each of the 24 MCK questions the students were asked to respond using a 5-point scale.
In effect, the self-efficacy scale is a measure of pre-service teachers’ faith in their specific mathematics pedagogical content knowledge (MPCK).

Findings and discussion
The findings of this study indicate that many of the participants enrolled in the mathematics curriculum course with very low levels of MCK.
That is, they could not do much of the mathematics they were soon to be certified to teach, with a significant proportion of the participants struggling with lower middle years content.
Success became more elusive as the mathematics became more abstract in the higher year levels.
Such findings prompted the re-orientation of the mathematics curriculum courses in the study institution to take greater account of relevant MCK and the associated MPCK.
A further finding was that when presented with the specific mathematics to be taught, most participants could discern which questions they could and could not do, but they tended to be optimistic with respect to their capability, particularly with more abstract mathematics.
The overall mean confidence of the sample (3.2/5 variance = .164) suggests that the participants lacked confidence in their mathematical content as assessed by this scale, especially as the MCK became increasingly abstract. In this regard, the present results add to the findings of earlier authors who have commented on secondary school teacher confidence in Australia (e.g. Beswick, Watson, and Brown 2006; Callingham and Watson 2014).
The very different confidence that participants recorded for different levels of questions supports the practice of asking about confidence within narrow content domains.
The findings regarding self-efficacy to teach specific mathematics were a mirror of confidence in doing the mathematics, except that self-efficacy lagged confidence. the low levels of self-efficacy are a matter of concern since teacher self-efficacy has been linked to developing this attribute in school students and has been associated with greater success with ‘hard to teach’ students (Ross 2013, 266). it is noteworthy that the participants were consistent in over-estimating their capacity to do mathematics and similarly over-confident about teaching it with minimal additional intervention.
The high correlation between confidence and specific self-efficacy was anticipated, since those who believed they could do the problem also believed they could implement effective teaching.
A further consideration of the finding of a strong correlation between confidence and self-efficacy is that some pre-service teachers may have a naïve view of the relationship between knowing how to do the mathematics and knowing how to teach it.
While not knowing the content almost certainly places significant limits on capacity to teach the content, being able to scaffold effective learning is a significant extension on simply knowing how to attain the correct solution (e.g. Gess-Newsome 2013).
The findings have methodological implications.
As is the case for confidence, there seems to be a need to question the virtue in asking generic questions about self-efficacy (at least with respect to mathematics teaching), a common practice in earlier research (e.g. Schwarzer and Jerusalem 1995; Sherer et al. 1982).
The data lend evidence to extend the argument put forward by Bandura (2006), Bleicher (2004) and Callingham and Watson (2014) that content-specific probing has merit, especially in the case of mathematics teaching.
Pre-service teachers had very different levels of confidence and self-efficacy associated with different mathematical tasks.
In general, they were more confident with simple, lower year level (e.g. Year 7) procedural mathematics and less so on more abstract mathematics (e.g. Year 10 algebra).
By asking generic questions, this detail is lost.

References
Bandura, A. 2006. “Guide for Constructing Self-Efficacy Scales.” In Self-Efficacy Beliefs of Adolescents, edited by F. Pajares and T. Urdan, 307–337. Greenwich, CT: Information Age Publishing.
Beswick, K., J. Watson, and N. Brown. 2006. “Teacher’s Confidence and Their Beliefs and Students’ Attitudes to Mathematics.” Accessed 25 March 2017. https://www.researchgate.net/publication/228943793_Teachers'_confidence_...
Bleicher, R. 2004. “Revisiting the STEBI-B: Measuring Self-efficacy in Preservice Elementary Teachers.” School Science and Mathematics 104 (8): 383–392
Callingham, R., and J. Watson. 2014. “Teachers’ Confidence in Teaching Statistical Ideas.” In Sustainability in Statistics Education. Proceedings of the Ninth International Conference on Teaching Statistics, edited by K. Makar, B. de Sousa, and R. Gould. Flagstaff, AZ: International Statistical Institute
Gess-Newsome, J. 2013. “Pedagogical Content Knowledge.” In International Guide to Student Achievement, edited by J. Hattie and E. Anderman, 257–259. New York: Routledge.
Ross, J. 2013. “Teacher Efficacy.” In International Guide to Student Achievement, edited by J. Hattie and E. Anderman, 266–267. New York: Routledge.
Schwarzer, R., and M. Jerusalem. 1995. “Generalized Self-Efficacy Scale.” In Measures in Health Psychology: A User’s Portfolio. Causal and Control Beliefs, edited by J. Weinman, S. Wright, and M. Johnston, 35–37. Windsor, UK: NFER-Nelson
Sherer, M., J. E. Maddux, B. Mercandante, S. Prentice-Dunn, B. Jacobs, and R. Rogers. 1982. “The Self-Efficacy Scale: Construction and Validation.” Psychological Reports 51: 663–671.