The impact of problem-based learning on pre-service teachers’ development and application of their mathematics pedagogical content knowledge

The main aim of this study was to investigate the effectiveness of problem-based learning (PBL) compared to a traditional teacher-led instructional approach on pre-service teachers’ mathematics pedagogical content knowledge (PCK) and their ability to apply that knowledge. Predictors of teacher effectiveness in relation to student achievement are based on defined attributes, for example: (a) the ability to use a range of evidence-based teaching strategies (Dean, Hubbell, Pitler, & Stone, 2012; Hattie, 2009), such as those encompassed in the PBL framework as described by Hmelo-Silver and Barrows (2015) and Savery (2015); (b) the ability of a teacher to enact the PCK he or she possesses (Hattie, 2009; Hill, Ball, & Schilling, 2008; Hill, Rowan, & Ball, 2005; Shulman, 1986; Tatto & Senk, 2011) and (c) the level of confidence, and/or self-efficacy, a teacher maintains in his or her ability to teach (Bandura, 1977; Schunk, 1991; Tschannen-Moran & Hoy, 2001). Teachers who have high self-efficacy may also maintain the expectation that they can influence positive academic outcomes for their students (Bandura, 1986; Enochs, Smith, & Huinker, 2000). This type of cognitive belief is identified by Bandura (1977) as outcome expectancy. Although studies on PBL are numerous, an inspection of the literature did not reveal any which examined the specific characteristics noted above in pre-service teachers when PBL was introduced to the teaching context. As a result, this study aimed to investigate the impact specifically that closed loop PBL had in a tertiary mathematics education subject, compared to using a traditional teacher-led approach, on pre-service teachers’ mathematics PCK, their ability to enact their PCK, their self-efficacy for teaching mathematics and their mathematics teaching outcome expectancy. To measure pre-service teachers’ knowledge of mathematics PCK and their self-beliefs for teaching mathematics, a Mathematics Pedagogical Content Knowledge Instrument (MPCKI) and a Mathematics Teaching Efficacy Belief Instrument (MTEBI) were developed and used in a pilot study. The instruments were administered pre-intervention and post-intervention to both a control group (n=15), who received traditional instruction, and a treatment group (n=15) who were instructed using the closed loop PBL teaching method (the intervention). The outcomes of the pilot study provided insight into the need for additional data to be collected from pre-service teachers’ end-of-semester exam questions (N=37) to measure specifically their ability to enact their mathematics PCK. Qualitative data were also collected in the form of semi-structured interview responses. The interviews, which were conducted at the end of the intervention, asked questions of the treatment group participants (n=17) relating to the impact PBL had on the development of their mathematics PCK, the ability to enact their PCK and their teaching beliefs. The analysis of the results of the MPCKI, which was designed as a multiple-choice survey instrument, did not demonstrate a significant difference between the two groups’ mathematics PCK. However, the analysis of the pre-service teachers’ constructed responses to the end-of-semester exam mathematics PCK-specific questions did demonstrate a significant difference between the two groups ability to enact their mathematics PCK. Furthermore, the qualitative data collected from the interview responses from the PBL treatment group indicated a unanimous satisfaction with being taught by the PBL method and a unanimous affirmative response when asked if they felt the closed loop PBL teaching method was more effective than traditional instruction in developing their mathematics PCK and their ability to enact their PCK. The results of the MTEBI analysis did not demonstrate a significant difference between the two groups’ self-efficacy for teaching and teaching outcome expectancy. However, an analysis of the interview transcripts from the PBL group of pre-service teachers revealed a new sense of confidence and teacher effectiveness, which, they felt will positively impact on their students’ academic success. It was hypothesised that the closed loop PBL method is a more effective pedagogical approach in teacher education compared to traditional teacher-led instruction for mathematics education. As the aim of teacher education is to enhance graduate teachers’ abilities to enact their mathematics PCK, simply put to be better mathematics teachers, it was concluded that closed loop PBL is a useful pedagogical strategy to afford them the confidence and skills to enact their personal mathematics PCK. Although the findings returned mixed results, most of the evidence supports closed loop PBL’s potential as a more effective pedagogical approach for developing pre-service teachers’ ability to enact mathematics PCK.