Qualified learning materials is needed in the efforts to improve the quality of teaching-learning mathematics. Qualified learning materials can be obtained through development research. Learning materials in this study were learning materials that were developed based on guided discovery learning model. The learning materials was also developed by integrating local culture into a guided learning model. The local culture in this study was adapted to the local culture of the students, namely the Batak Toba. Learning materials in this study were developed using the development model of Thiagarajan et al. (1974). The result of second trial showed that learning materials based guided discovery learning with Batak Toba context improved students' mathematical problem solving ability and self-efficacy significantly. Based on the results of the study, it was suggested that mathematics teachers make an effort qualified learning materials and integrate local culture in mathematics learning.

Algebra is a crucial subject in the study of mathematics. However, many junior high school students, such as grade 9 students, who are the unit of analysis for this study, need help with this topic. Exploration of the factors causing these difficulties will aid in unravelling the problem and making the solution more effective and efficient. This study tried to investigate these factors. This research employs a qualitative approach with a case study approach. The data was gathered through observation, interviews, and documentation, and it was then analyzed using the Creswell and Creswell qualitative data analysis model (2018). The findings revealed that the following factors hampered students' understanding of algebra lack of motivation in mathematics, self-efficacy, basic skills and knowledge, social skills, and learning development.

Inspiration plays a significant role in sparking or enhancing the learning motivation of prospective mathematics teachers (PMTs). Inspiration will also influence the mathematical identity of PMTs’ when they become professional mathematics teachers. A mathematics teacher educator (MTE) can be a source of inspiration for PMTs; hence, a study must identify and explain why an MTE is considered inspiring. This study attempts to develop the theory of inspiring MTEs profiles based on the experience of PMTs. This study included 21 students and 7 lecturers of the Mathematics Education Department in a public university in Indonesia. This qualitative research was conducted employing a grounded theory constructivist approach. The findings revealed that inspiring MTEs possessed the following characteristics: “creating a sense of comfort, being knowledgeable, being motivating, providing fun and enjoyable learning, imparting new insights and comprehension, and being disciplined and authoritative.” According to this theory, an inspiring MTE creates a sense of comfort through their gracious, friendly, humble, and humorous personality. Fun and enjoyable learning in this study is learning that provide a sense of comfort, fun learning, interactive learning, and carrying out evaluations. MTEs give new insight and understanding by explaining in detail, systematically, and easily understood, sharing creative ideas, and providing scaffolding. Implications of this finding are discussed.

Combinatorics is a branch of mathematics that is very important, but this topic has not received serious attention in educational research compared to other branches of mathematics such as geometry, calculus and algebra in Indonesia. Meanwhile, in secondary and undergraduate education, existing research reports that students’ combinatorial thinking ability tend to be low. Efforts to improve students’ combinatorial thinking ability in one of the Vocational Schools in Medan, Indonesia, are carried out through the development of the Numbered Heads Together (NHT). NHT is one cooperative learning structure. The result showed that NHT learning improved students’ combinatorial thinking ability.