Student Teachers’ Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools

Published: 
Sep. 01, 2014

Source: Journal of Mathematics Teacher Education, Volume 17, Issue 4, (2014), p. 331–368.

(Reviewed by the Portal Team)

Based on findings from a semester-long study, this paper examines the development of Samoan prospective primary teachers’ (PPTs) mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems.
The authors were also interested in assessing the impact of using the innovative tools, mental computations and creative authentic investigations on PPTs attitudes towards mathematics.

Methodology
The participants were prospective teachers (PPTs) had enrolled for the second time (having failed their first attempt), in the first-year mathematics methods (FYMM ) course of a 2-year Diploma of Education (Primary) programme.
The group also included those enrolled in the Diploma of Education (Early Childhood and Special Needs) programmes, who recognizing their own limited understanding of mathematics would ordinarily shy away from opportunities for improvement.

Data were collected through mathematics diagnostic tests, course tests and assessment tasks.
Furthermore, a pre-questionnaire was administered at the beginning of Week 1 of the semester with a post-questionnaire administered after PPTs’ teaching practicum, in Week 14.
In addition, interviews with some PPTs were conducted during Week 14 of the semester and with some held in the first semester of the following year due to non-availability of PPTs.

Discussion

In addition to the usual course assessment tasks of course tests and written assignments, the PPTs applied innovative metacognitive tools to working mathematically processes, mental computations and problem-solving strategies whilst conducting their authentic mathematical investigations.
The findings showed that the two highest item estimates were those describing the importance of remembering concepts learnt in previous classes and mathematics being their most favourite subject.
Through the application of working mathematically processes, mental computations and multiple problem-solving strategies, PPTs were supported and scaffolded as they learnt to strategically identify and meaningfully understand and appreciate mathematical ideas, their interconnections and various applications in selecting appropriate methods in solving mathematical tasks or conducting investigations.

The findings reveal that positive attitudinal variations by the end of the study suggested PPTs’ expressed positive feelings of liking, interest, enjoyment, great satisfaction when individually successful in solving a problem and strong agreement that mathematics was their most favourite subject.
Secondly, PPTs thought positively about the utilitarian value and relevance of mathematics skills to daily living and cross-curricular applications.
Thirdly, when faced with challenging problems, one of the strategies they would consider included the use of diagrams and/or models to clarify their thinking.
Fourthly, positive attitudinal variations demonstrated PPTs’ personal beliefs and perceived confidence about their capacity and competence as mathematics learners to use existing knowledge to solve problem/s and a willingness to improve their mathematical understanding.

In addition, PPTs’ explanations and responses were analysed for possible factors influencing their mathematics attitudes.
Four themes, namely motivational factors, self-improvement, personal perceptions of mathematics and course feedback, were identified from PPTs’ explanations of why they would continue taking another mathematics course in the following year.
The first two themes collectively demonstrated PPTs’ good intentions to persevere and succeed in passing their mathematics courses so that they graduate.

Furthermore, the participants faced challenges, which made it difficult to cope with the mathematical and cognitive demands of the FYMM course.
These concerns were categorized under the third theme: personal perceptions of primary mathematics.

As aforementioned, a national need exists to offer innovative, constructivist and socioculturally driven learning programmes to target the development of students’ critical thinking.
Further highlighted by the fourth theme from PPTs’ open responses is another concern regarding the need for upgrading professional learning and development opportunities for existing, practicing teachers to familiarize themselves with the new Curriculum.
Finally, PPTs’ perceptions of the FYMM content also provided constructive feedback to appropriately revise and rearrange the course structure and sequencing of learning experiences and assessment opportunities to optimize future PPTs’ learning experiences and skills development in better meeting the demands of the new Curriculum.

By the end of the study, the main findings included the overall cohort’s mathematics attitudes and more detailed trends of paired PPTs’ attitudinal estimate changes and the nature of variations in item estimates.
Both the positive and negative variations, including PPTs’ open and interview responses, suggested that learning experiences in the FYMM course influenced general perceptions about mathematics learning and therefore, one’s actions when confronted with problems to solve.
These findings contribute to the mathematics education literature on attitudes and innovation in general and in particular to the scarce literature in mathematics teaching and learning in Samoan educational institutions.

Implications

The main findings of the study have implications for teacher education and ongoing professional learning and development programmes.
This new pedagogical approach requires: the ongoing implementation/application of working mathematically processes is both a philosophical and conceptual mind shift for prospective and practicing teachers to recognize, acknowledge and accept as an integral part of the new mathematics curriculum.
The main findings from this study provided empirical evidence of some areas such as sufficient provision of time for both teachers and students to become familiar in applying and practicing the new approach before being able to work effectively and efficiently with it.

Updated: Dec. 09, 2015
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