Developing learning materials supporting teachersr understanding on mathematics problem-solving knowledge for teaching

Abstract

This study aims to develop a set of learning materials supporting teachers' understanding of mathematics problem-solving knowledge for teaching (MPSKT). The MPSKT implemented in the learning materials consist of problem-solving content knowledge (PSCK) (knowledge of problems, nature of problem-solving, problem-posing), pedagogical problem-solving knowledge (PPSK) (knowledge of students as problem solvers, instructional practice for problem-solving), and affective factors and beliefs (beliefs about nature of mathematics, mathematics teaching, and mathematics learning). The learning materials, consisting of lesson plan and teaching book, were developed by following two stages, i.e. preliminary stage and prototyping using formative evaluation: one-to-one, self-evaluation, small group, and field test. There were 41 teachers involved to examine the validity, practicality, and effectiveness of the learning materials. Results indicate that prototype of the learning materials were revised along the formative evaluation stages, in which it was proved valid and practical according to the revision based on experts' review and teachers' suggestion. Also, it was effective to improve teachers' understanding of MPSKT and beliefs about teaching and learning mathematics. In the future studies, we encouraged to develop learning materials which include these two components more explicitly as well as a more comprehensive and complete component of MPSKT characterizing a complex network of interdependent knowledge among the components.

Learning models that can improve elementary school students' creative thinking ability

“…Haylock, 1997;D. W. Haylock, 1987;Kamalasari et al, 2019;Kaufmann, 1988;Leung, 1997;Maier, 1970;Pramestika et al, 2020;Septian et al, 2019;Shella et al, 2018;Silver, 1997;Siswono, 2010aSiswono, , 2010bSiswono, , 2016Siswono, , 2018Novitasari, 2007;Weisberg, 1988;Yuliati &;Lestari, 2019) The interaction between formulating a problemsolving plan and solving a problem can be seen as a creative process that takes place. This statement can be supported that in one of the (Polya, 2004)syntax of problem solving there is a process of sharing ideas and solving a problem or choosing the right solution to be used as a solution to a problem.…”

“…The process of solving problems or divergent processes is in accordance with indicators of creative thinking, namely solving problems. There are several indicators of creative thinking ability, including (Silver, 1997;Siswono, 2010aSiswono, , 2016Siswono, , 2018Novitasari, 2007) Explanation of syntax that can impro students' creative thinking ability ); Then proceed to produce other, different solutions to the problem (Polya, 2004;Silver, 1997;Novitasari, 2007) 2.…”

“…Problem Posing ((Ayllón et al, 2016;Bonotto & Santo, 2015;Kontorovich et al, 2011;Leung, 1997;Shriki, 2013;Silver, 1997;Siswono, 2005Siswono, , 2010aSiswono, , 2010bSiswono, , 2018van Problemsolving is an activity task that leads to a critical and creative attitude. Because in submitting problems students are asked to make questions from the information provided.…”