This study aims to describe the types of explanations made by pre-service teachers in mathematics learning. In this research, the types of explanations are used to describe the explanatory trends used by pre-service teachers in mathematics teaching. The descriptive qualitative research was chosen in this research. The research subjects are pre-service teacher as the students of Mathematics Education of PGRI Madiun University and Madura University who are studying Field Experience Practice. Of the 105 mathematics student, five students with a cumulative grade achievement of more than 3.50 were observed during the teaching practice at the school for approximately five meetings. The research data was obtained from observation, video recording, and interview. Data analysis was done through data condensation, data presentation, and conclusion/verification focused on pre-service teacher explanation on mathematics learning activity. The research findings indicate that the explanation used by the pre-service teacher in the mathematics learning starting from the most frequently used is the descriptive explanation (51,7%), giving of reason (36,2%) and interpretative (12,1%). Descriptive explanations are used to describe mathematical procedures. The type of reason-giving explanation is used to explain reasons based on mathematical principles. Furthermore, the interpretative explanation is used to explain the concepts and facts of mathematics.

This case study aims to explore how male and female Indonesian mathematics teachers enact decision-making processes in teaching High-Order Thinking Skills (HOTS). Non-random purposive sampling technique was used to select the participants. The participants involved in this study were two Indonesian mathematics teachers who teach HOTS in their classrooms. The participants were chosen from 87 Indonesian mathematics teachers in 23 secondary schools in East Java, Indonesia, who were invited to our survey and confirmed that they taught HOTS and underwent classroom observation. Data were collected from classroom teaching and interview sessions. The data of classroom teaching consisted of a video-audio recording of two meetings and field notes of observation. In the interview session, we recorded the teachers’ responses during semi-structured interviews. We coded and explained our interpretation for each code. We also conducted investigator triangulation by comparing coding and interpretation made by two researchers and discussing them to find the best representation of the meaning of the data. Our findings indicate that both male and female teachers performed four steps of decision making, consisting of giving problems, asking students to solve, checking, and obtaining new ideas. The difference of male and female teachers’ decision-making process is observed in the process of giving problem (non-contextual vs contextual), how they ask students to solve and check the solution (individual vs group), and the criteria of the new idea of problem-solving (correct vs the best solution). The study findings can be a catalyst for enacting decision-making steps in teaching HOTS. Also, these can be a reflective practice for mathematics teachers to improve their teaching quality.

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Problem Posing approach is necessary for teacher training students. Problem Posing can train students to create questions/problems and their solutions. Make problem then solve it is part of student’s creative thinking ability. Differential equations problem is one of the materials that learned in mathematics education courses. Every teacher training student of mathematics has diverse skills. This diversity certainly brings various creative thinking skills as well. The purpose of this study is to determine the ability of student’s creative thinking in mathematical education courses, differential equation problem posing. This study uses a qualitative approach with descriptive methods. Sources of data in this study are the students of mathematics education consist of one student of each with high, medium, and low begining math ability. The data collection was conducted by using observation, testing, and interviews. Technique authenticity of data using a triangulation method. Data analysis technique done in stages, data reduction, data presentation, drawing conclusions, and verification. The result of this study were (1) Students with high initial capability not have fluency and flexibility of thought, but it shows the novelty think that qualifies as a Creative Thinking Ability Level (CTAL) 2 is creative enough, (2) Students with prior knowledge currently have the fluency of thought, but do not have the flexibility and novelty think that qualifies as a Level capabilities creative thinking (CTAL) 1 is less creative, (3) Students with prior knowledge low yet has grace, eloquence, and the novelty of thought that goes into the criteria of creative thinking ability Level (CTAL) 0 is not creative.