Comparing Model-Building Process: A Model Prospective Teachers Used in Interpreting Students’ Mathematical Thinking

Abstract

Mathematical thinking is an important aspect of mathematics education and, therefore, also needs to be understood by prospective teachers. Prospective teachers should have the ability to analyze and interpret students’ mathematical thinking. Comparing model is one of the interpretation models from Wilson, Lee, and Hollebrands. This article will describe the prospective teacher used the model of the building process in interpretation students' mathematical thinking. Subjects selected by considering them in following the students’ strategies in solving the Building Construction Problem. Comparing model is a model of interpretation in which a person interprets student thinking based on student work. There are two types comparing model building process prospective teacher use in interpreting students’ mathematical thinking ie. comparing work and comparing knowledge. In comparing works, prospective teachers use an external representation rubric. This is used to analyze student activities in order to provide an interpretation that is comparing the work of students with their own work. In comparing knowledge, prospective teachers use internal representation rubrics to provide interpretation by comparing the students' work with their knowledge or thought.

Characteristics of Continuing Professional Learning Provisions for School Mathematics Teachers in Zimbabwe

“…It appeared for the majority of the teachers that motivation was generated in big part as a reaction to poor material work environments. Again, relative frequency distribution of the teachers' responses on their motivators is consistent with this: career progression (44), accessibility of the training (26), higher qualifications (11), and personal fulfillment (11). A ministry district officer attributed low motivation of teachers to "….…”

“…Mathematics teachers and CPD providers can be seen as 'multipliers' because they interact in professional learning processes through, for instance, sharing their knowledge, often collaboratively, in specific CPD activities according to Roesken-Winter, Hoyles, and Bl meke [9] Thus, a major aim for engaging in CPD learning is to raise an individual's selfefficacy, defined by Bandura [10] as "belief in one's capabilities to organize and execute the courses of action to produce given attainments." Such capabilities include the ability to analyze and interpret students' thinking as suggested by Sapt et al [11]. Abreh [5] writes that improved interpretation of practice in turn influences learning outcomes.…”

The Effectiveness of Think-Talk-Write (TTW) Learning Strategy in the Critical Thinking and Mathematical Communication

“…After that, the researcher and the teacher gave a pretest in the form of questions to students. The obstacles that occurred at the first meeting were as follows: (1) there were some students who did not concentrate on paying attention to learning and thought that mathematics, especially Trigonometry, was a difficult material; (2) there are some students who are not enthusiastic about asking their peers, so that group work becomes slow in completing group assignments; (3) students lack confidence to convey the results of their work to other friends.…”

“…(1) The application of the Think-Talk-Write (TTW) learning strategy is effective, while the application of conventional learning is not effective in terms of critical thinking skills and mathematical communication. (2) The application of the Think-Talk-Write (TTW) learning strategy is more effective than the application of conventional learning in terms of critical thinking skills and mathematical communication.…”

“…Meanwhile, the average scientific literacy of students in Indonesia is still low, namely 382 points compared to OECD countries, which is 501 points. Accessing students thinking when students solve problems is essensial to get information potensial and also difficulties [2].…”