Validity of critical thinking skills instrument on prospective Mathematics teachers

This study aims to describe the process of validity of critical thinking skills on prospective mathematics teachers. This research used a quantitative approach with a survey method. Data were collected from 245 prospective mathematics teachers from 19 Mathematics education study programs at 19 higher education institutions in Indonesia. The data were collected using a questionnaire given via Google Form and analyzed by the Rasch Model analysis using Winstep software and Confirmatory Factor Analysis (CFA) using JASP. The results show that the instrument of critical thinking skills with indicators such as open-mindedness, inquisitiveness, systematicity, truth-seeking, analyticity, and self-confidence is valid and reliable, although it has to consider eliminating items and person misfit.

Communication and Mathematic reasoning: Theory of planned behavior and inquiry

The purpose of this study is to investigate the aspects of communication and mathematical reasoning. In investigating the aspects of mathematical communication with an inquiry approach, of course there are several things observed related to learning mathematics. The focus of the material aims at observing communication and mathematical reasoning within the framework of inquiry, and the theory of planned behavior (TPB) is geometry and algebra. The research method used a qualitative research by looking at case studies with research subjects consisting of 31 prospective mathematics teachers in Semarang city. From the aspect of communication and mathematical reasoning that exists, it can be seen from the answers of 31 prospective mathematics teachers with an authentic point of view of inquiry and a theory of planned behavior for problem solving. From the observation, several cognitive processes are adapted to the authentic framework of inquiry and the theory of planned behavior for algebra and geometry material. In reasoning, a wedge appears between mathematical reasoning and communication adapted to the framework of inquiry and the theory of planned behavior. The contribution of this study is to determine the communication framework and mathematical reasoning from the theoretical aspects of planned behavior and inquiry. It is important to know aspects of communication and mathematical reasoning from a different perspective.

Making the Pedagogical Elements Used by Prospective Mathematics Teachers Visible in Teaching: Scenario Writing Activities

Introduction: In the reflective writing process, teachers make identification, information, explanation and evaluation activities (Spanneberg, 2009). It is thought that the scenarios written by the teacher candidates in order to teach a certain subject can give them an opportunity to think deeply. However, these teaching scenarios can be a valuable tool for reflective thinking in terms of educational matters such as teaching methods, pedagogy, and beliefs. Methods: In this study, it was investigated whether script writing is an effective tool to make pedagogical elements visible in the prospects of mathematics teachers. Case study pattern, which is one of the qualitative research patterns, was used in the research. For this purpose, thirty prospective mathematics teachers who participated in the study were asked to write two scenarios. The first one is called as “car travel” and the other one is called as “triangles and similarity” scenario. Before the study, some basic frameworks were defined for both scenarios. These are explained to prospective teachers. The “car travel” scenario in this research was given within the scope of the theme which includes only two people and a limited environmental interaction. The second scenario is the triangles and the similarity scenario. In the second scenario, the role of a teacher who conducts applied and real-life education outside of school is defined. Results: In general, it is concluded that script writing activities are very useful in training teachers. The data obtained from both scenarios reveal that the pedagogical elements constructed during the scenario writing activities become concrete in the minds of the prospective teachers. Discussion: It is observed that prospective teachers often include the structure of teaching related to real life in their scenarios. It is stated that teaching in the context of real life increases academic success and students’ interest in the lesson, and thus, the content is learned perceptibly by the students (Acar & Yaman, 2011). Another cognitive element that prospective teachers include in their scenarios is the use of available materials. It is noteworthy that the prospective teachers used real-life tools and materials as materials in the place chosen for the scenarios of their scripts. Limitations: This research is limited to script texts written by thirty prospective teachers. Conclusions: Thanks to this visibility, feedback can be given on the pedagogical elements that the prospective teacher will use in the future.

Exploring the Prospective Mathematics Teachers Computational Thinking in Solving Pattern Geometry Problem

This research aims to describe the characteristic of mathematics prospective teacher's computational thinking (CT) in solving the geometric pattern problem. The subject consists of 65 preservice mathematics teachers in Universitas in Madiun. The instrument was used in this research are geometric pattern problem tests and interview guidelines. The result shows that are three types of mathematics prospective teachers in solving the problem. First, CT substantial, i.e. prospective mathematics teachers use the conceptual knowledge who collaborated with procedural knowledge exactly. They use mathematics iteration to find the pattern and express them to the general form easily. Second, CT Nominal, i.e. prospective mathematics teachers, use manual ways to solve the pattern problem. They count using numeric, not symbolic, of solving the pattern formed. They can understand the design but can't express it to the mathematics model. Third, CT procedural, i.e. mathematics prospective teacher using the procedural knowledge only, not an expert in concept, and following the steps who teaches from experience before. The recommendation for future research is to develop the research to find the other characters in other mathematics subjects, in other students, to develop the learning models who can embody CT.

Prospective Mathematics Teachers Understanding of Classical and Frequentist Probability

Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist approaches to probability. To achieve this goal, content analysis was used to categorize the prospective teachers’ answers to a questionnaire with open-ended tasks in which they had to estimate and justify the composition of an urn, basing their answers on the results of 1000 extractions from the urn. Most of the sample proposed an urn model consistent with the data provided; however, the percentage that adequately justified the construction was lower. Although the majority of the sample correctly calculated the probability of an event in a new extraction and chose the urn giving the highest probability, a large proportion of the sample forgot the previously constructed urn model, using only the frequency data. Difficulties, such as equiprobability bias or not perceiving independence of trials in replacement sampling, were also observed for a small part of the sample. These results should be considered in the organisation of probabilistic training for prospective teachers.