An exploration of reflection and mathematics confidence during problem solving in senior phase mathemetics
Empowerment through proficiency in mathematics could better not only one’s life, but also one’s chances in study and work. The current study is an exploration of what reflection and mathematics confidence entail during mathematics problem solving. Reflections on experiences with mathematics create awareness of the individual’s level of confidence in the social, psychological and intellectual domains. Personal, strategic and task knowledge enhances meaning and promotes the understanding of mathematics tasks during problem solving. The level of mathematics confidence can be described as either fearful or fearless when solving mathematics problems. Reflecting on achievement, with or without fear, is regarded as vital for higher-order reasoning by means of metacognitive processes, moderates mathematic confidence and fosters achievement. Although research in metacognition is increasing, literature involving mathematics confidence and reflection is scarce. The current study explores this link between reflection and mathematics confidence by focusing on metacognitive reflective skills. A mixed-method design consisting of positivist and interpretivist paradigms is employed. Merging of the quantitative and qualitative findings indicates that metacognitive strategies include reflecting on task, personal and strategic awareness. Regulating understanding, planning, monitoring and evaluating during problem solving occurs in accordance with these active internal processes. Mathematics confidence during problem-solving emerges from experiences relating to a variety of contexts involving mathematics. The findings confirm the dimensionality of mathematics confidence and present sources of participants’ mathematics confidence and metacognitive skills as reflected upon. The schools in the sample represent single-gender (all-boys and all-girls) and co-ed schools and findings should not be generalised to all schools. Reflection on metacognitive knowledge and regulation deepens the awareness of the level of confidence and promotes, to some extent, a knowing of knowledge. The study therefore evaluates the role reflection and mathematics confidence play during problem solving in senior phase mathematics.
- Education