This study explored teachers' beliefs about mathematical problem-solving. It involved 36 identified teachers of Kayonza District in Rwanda via an explanatory mixed-method approach. The findings indicate that most teachers show a positive attitude towards advancing problem-solving in the mathematics classroom. However, they expose different views on its implementation. Role of problem-solving, Mathematical problems, and Problem-solving in Mathematics were identified as main themes. Problem-solving was highlighted as an approach that helps teachers use time adequately and helps students develop critical thinking and reasoning that enable them to face challenges in real life. The study recommends teacher professional development initiatives with their capacity to bring problem-solving to standard.

Developing problem-solving abilities is a major objective of learning mathematics at school. However, learners’ problem-solving abilities are still critical. The main purpose of this study was to investigate how the problem-based learning model could enhance learners’ problem-solving abilities in mathematics. The study used quasi-experimental research with one group pre-test-post-test design. The population in this study consisted of fifty-four grade eleven learners (aged between 16 to 19 years old) from one school in Kayonza District in Rwanda. Data were collected using mathematical problem-solving tests and interviews and were analysed using paired t-tests for dependent sample means and descriptive analysis. The study results indicate that problem-based learning potentially impacts learners’ problem-solving abilities. It is shown from learners’ work in problem-solving that all indicators of problem-solving abilities, namely understanding the problem, planning ways to approach the problem, monitoring the progress while tackling the problem and reviewing the solution process, emerged as being fairly well improved. In addition, based on the interview results from some learners and their teachers, they like the PBL model because embedded tasks helped them to apply the knowledge that can improve their reasoning, creativity and thinking capability. The study recommends that schools encourage teachers to adopt PBL for enhancing learners’ problem-solving abilities. Additionally, researchers are urged to use findings from this study as a reference for further research. Furthermore, researchers could conduct similar research on a large scale using different methodologies.

<span>Interactive teaching practices in mathematics classrooms are encouraged to meet the learning potential. However, how it is applied in the classroom is still challenging. This paper uses evidence gathered from a large research project to contribute to the understanding of teacher-student interactions. It followed an interventional approach with two teachers and 82 students of two grade 11 classes from one school of Kayonza District in Rwanda. Data were collected through observations, video recordings, and field notes. Results revealed that there is a variety of ways to facilitate and keep interactive learning. These include asking purposeful questions and giving feedback. The quality of teacher facilitation (52%) and students' engagement (60%) were moderately high. However, there was little guidance from teachers in the problem-solving process and the classroom discourse. It is argued that the role of instructional language in communication hinders the quality of teacher-student interactions. This leads us to advise an exploration of language supportive pedagogy in the Rwandan context.</span>

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