**Source:** Teaching and Teacher Education Volume 102

*(Reviewed by the Portal Team)*

This research aims to examine the following research questions:

1. What effect does a sequence of instructor-led transmission and transactional teaching practices and a PBL teaching strategy in a secondary school mathematics preservice methods course have on secondary school mathematics preservice teacher efficacy?

2. What effect on their their attitudes and beliefs towards their teaching and students’ learning?

**Methodology**

A sequential four-phase mixed methods design was used for this study.

The four phases used for this study align with data collection that occurred pre- and post-instructor-led transmission and transactional teaching practice instruction (T1 and T2 respectively) and pre- and post-PBL as a professional learning model (T3 and T4 respectively).

At each phase data was collected from the preservice teachers using a questionnaire that included demographic information, quantitative data (30 Likert-scale response questions chosen to measure teachers’ sense of efficacy and mathematical beliefs) and qualitative data (two short answer questions used to gain insight into teacher orientation and current teacher concerns).

The data was then analyzed separately, and then purposefully mixed in order to gain a better understanding of the impact PBL had on preservice teachers’ learning and beliefs.

**Participants**

The participants for this study were 47 preservice teachers in a post-graduate secondary mathematics education methods course at one mid-sized Canadian university.

**Course context**

In its entirety, the mathematics education methods course was comprised of 36 classes.

Of these 36 classes, the first 10 were taught using instructor-led transmission and transactional teaching practices, the next 16 classes being taught using the structure of PBL as a professional learning model, and the last 8 classes a blend of instructor-led activities and preservice teacher-led small group workshops.

The 16 PBL classes were separated into four PBL cycles, each having its own unique problem of practice for preservice teachers to work on.

Data was captured using a questionnaire administered at four unique time points; pre-learning in the instructor-led transmission and transactional teaching block (T1), post-learning in the instructor-led transmission and transactional teaching block (T2), pre-PBL structured teaching block (T3) and post-PBL structured teaching block (T4).

At each time period of data collection, the same questionnaire was distributed and completed by the preservice teachers.

The questionnaire was comprised of a set of demographic questions, the short form of the Teachers’ Sense of Efficacy Scale (TSES) (Tschannen-Moran & Woolfolk Hoy, 2001), a subset of the Beliefs About Mathematics Problem Solving (BMPS) questionnaire (Kloosterman & Stage, 1992), and two short answer questions used to gain an understanding of the concerns of preservice teachers at each specific point in time.

The demographic questions provided information regarding gender and the preservice teachers’ additional teaching subject.

The two short answer questions given to preservice teachers were “what is the most important thing to date that you feel has contributed to your learning about, and ability to, teach secondary school mathematics” and “what is the greatest concern you have at the present moment about teaching secondary school mathematics?”

**Results and discussion**

For the quantitative results, the first notable result is the increase in teacher efficacy from T3 to T4.

This is notable as it correlates with the implementation of PBL, as Selçuk (2010) found with preservice physics teachers.

The incorporation of problems of practice based in an obvious teaching context offers preservice teachers the ability to place themselves in the role of a teacher while still being in a safe and low-risk environment of the mathematics education course.

From the results of the first open-ended question the authors see a trend where preservice teachers move from a reliance on prior knowledge, experiences, and raw mathematical content knowledge as a main factor in their ability to teach mathematics to a reliance on pedagogical experience and pedagogical knowledge, a move from a self-concern to task-concern (Fuller & Brown, 1975).

This is to be expected as preservice teachers begin to “see behind the curtain” of teaching and begin to comprehend the unseen work that goes into teaching.

After the implementation of PBL, preservice teachers report PBL to be the main contributor to their learning about and ability to teach mathematics.

This result is promising as it shows preservice teachers becoming aware of the learning model they are experiencing, and the value preservice teachers put in learning through PBL.

From the results of the second open-ended question the authors note that student disinterest is a reoccurring theme across all four time periods.

This comes as no surprise as this is a common concern regarding teaching mathematics, especially in the secondary school context (Frank & Williams, 2016).

However, while student disinterest is a consistent theme, it is also seen that over time the preservice teachers begin to attribute more and more conscious effort into understanding pedagogical knowledge and pedagogical content knowledge.

A focus on students’ disinterest and an emerging focus on instructional strategies aligns with teacher efficacy subscales of student engagement and instructional strategies in which these teacher efficacies increase over time with learning and classroom experience.

Looking at the qualitative and quantitative data together paints an interesting picture of the shift of preservice teacher beliefs throughout the mathematics education course.

The authors see a deliberate shift in orientation away from personal and anecdotal mathematical experiences to formal pedagogical knowledge, as is seen in the progression from self-concern to task-concern (Fuller & Brown, 1975).

This shift towards critically thinking about the learning and teaching of mathematics sets preservice teachers up for the meaningful and productive conversations during their PBL instruction (T3 to T4) because they are less concerned with the survival skills of being in a classroom, and can instead focus on their teaching skills.

In Time 3, which is after their teaching practicum and at the start of the PBL section of the mathematics education course, the Instructional Strategies efficacy is now correlated with the Usefulness and Understanding beliefs.

Additionally, the preservice teacher concern for their students’ disinterest in the preservice teachers’ lesson is less important than thoughts of pedagogical knowledge and pedagogical content knowledge.

The preservice teachers believed that their ability to teach effectively is tied to being able to maintain student interest and engagement, not necessarily being strong in mathematical content knowledge.

Now the preservice teachers are looking ahead to other concerns, such as task concerns, and this change in belief is reflected in the increasing statistical significances with teacher efficacy.

The PBL learning environment is useful as it helps preservice teachers build on their pedagogical skills as it emulates teaching contexts.

**Conclusions**

This study puts forward results indicating that the design of transmission and transactional instruction of teaching practices at the beginning of learning followed by the structure of PBL as instruction in a preservice secondary school mathematics education course is not detrimental for preservice teacher learning.

It is argued that there are clear benefits to preservice teacher knowledge of teaching and an increasing awareness and appreciation of pedagogical content knowledge.

Learning the “survival skills” or seminal ideas of teaching secondary school mathematics and then building on these foundations by having rich and meaningful discussions in the PBL instruction phase focuses preservice teacher learning on anticipated teacher concerns.

It also helps preservice teachers become more self-aware of their beliefs and the need for critical thinking, which in turn builds preservice teachers’ abilities to critically think about their teaching practice and move from thinking about how to teach mathematics the way we do to why we teach mathematics the way we do.

It is also argued that these results show preliminary evidence that preservice teacher beliefs may dramatically increase more in a PBL structured teaching environment, and that necessary teacher efficacy is integrally a focus and a support for these increases in beliefs about mathematics and the teaching and learning of mathematics.

A professional learning model that accentuates one’s ownership of learning, provides a purposeful collaborative structure to learning together, and uses authentic problems of practice, enhances the engagement in and acquisition of learning goals and improves cognitive and affective outcomes (i.e., the learner likes who they are as a learner and who they are becoming as a professional).

**References**

Frank, T. J., & Williams, M. A. (2016). Pre-service secondary mathematics teachers’ perceptions of ability, engagement, and motivation during field experiences. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the north American chapter of the international group for the psychology of mathematics education. Tucson, AZ: The University of Arizona.

Fuller, F. F., & Brown, O. H. (1975). Becoming a teacher. In K. Ryan (Ed.), Teacher education (74th yearbook of the national society for the study of education, Part II) (pp. 25-52). Chicago: University of Chicago Press.

Kloosterman, P., & Stage, F. K. (1992). Measuring beliefs about mathematical problem solving. School Science & Mathematics, 92(3), 109-115.

Selçuk, G. S. (2010). The effects of problem-based learning on pre-service teachers’ achievement, approaches and attitudes towards learning physics. International Journal of the Physical Sciences, 5(6), 711-723.

Tschannen-Moran, M., & Woolfolk Hoy, A. (2001). Teacher efficacy: Capturing an elusive construct. Teaching and Teacher Education, 17, 783-805.