Abstract
Beliefs about problem solving are very important because they form the basis for learning mathematics. This research describes beliefs of prospective mathematics teachers toward mathematical problem solving. Participants of this research consisted of 157 prospective mathematics teachers at a private University in Semarang. Participants have sufficient background in the field of mathematics and pedagogy study in learning. Data were collected through semi-structured interviews and beliefs questionnaire on problem solving with answer choices. Questionnaire we used was to investigate the beliefs of prospective teachers about mathematical problem solving, while the interview process that we used was to obtain qualitative data. Based on the results of the questionnaire, each one of the prospective teacher students who had instrumentalist, platonic and constructivist beliefs was interviewed for their beliefs in mathematical problems, problem solving and problem solving processes. The results of the research show that most of prospective teacher tended to have platonist beliefs in every statement of mathematical problems and mathematical problem solving. But on the statement of the problem solving process, the most of prospective teachers tended to have constructivist beliefs. The belief perspective is built to help teachers understand and develop mathematical knowledge needed in solving mathematical problems.
Highlights
Problem solving has become an important issue that is discussed deeply in mathematics education
Students learn mathematical concepts and procedures, and how to interact in the classroom, they learn about a set of beliefs, and they learn how to behave in math lessons
The statement of 'mathematical problem maker' indicated that 25.4% of prospective teachers believed that mathematical problems should be made by teachers 'spontaneously' in accordance with textbooks, 51% of prospective teachers believed that mathematical problems should be specially designed by teachers in accordance with material needs lessons that were appropriate to textbooks, and 23.6% of prospective teachers believed that mathematical problems should be specially designed by the teachers according to the material needs and problems that were made by the students themselves
Summary
Problem solving has become an important issue that is discussed deeply in mathematics education. Students are directed to develop their skills such as building new mathematical knowledge, solving problems in various contexts related to mathematics, applying the necessary strategies and reflecting the process of mathematical solution (Anderson, White and Sullivan, 2005; Chapman, 2015; Muhtarom, Juniati, & Siswono, 2017a; Nizaruddin, Muhtarom, & Murtianto, 2017). Mkomange & Ajagbe (2012) conclude that most mathematics prospective teachers have positive beliefs about the importance of understanding mathematical problems, problems with some completion ways and the type of mathematical learning emphasized by contemporary principles. The instrumentalist's beliefs are consistent with the inadequate knowledge of problem solving, while platonist and constructivist teacher beliefs are consistent with their knowledge of problem solving (Muhtarom et al, 2017b; Siswono et al, 2017). Our research aimed to express the beliefs of prospective teachers toward mathematical problem solving
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