Learners bring prior knowledge to their learning environments. This prior knowledge is said to have an effect on how they encode and later retrieve new information learned. This research aimed at exploring ‘A’ level mathematics learners’ understanding of the determinant concept of 3×3 matrices. A problem-solving approach was used to determine learners' conceptions and errors made in calculating the determinant. To identify the conceptions; a paper and pencil test, learner interviews, and learner questionnaires were used. Ten learners participated in the research and purposive sampling was used to select learners who are doing the syllabus 6042/2 Zimbabwe School Examination Council (ZIMSEC). Data was analyzed qualitatively through an analysis of each learners' problem-solving performance where common themes were identified amongst the learners’ work. Results from the themes showed that Advanced level learners faced some challenges in calculating the determinant of 3×3 matrices. Learners were having challenges with the place signs used in 3×3 matrices, especially when using the method of cofactors. The findings reveal that learners had low levels of engagement with the concepts and the abstract nature of the concepts was the major source of these challenges. The study recommends that; teachers should engage learners for lifelong learning and apply some mathematical definitions in real-world problems. Teachers should address the issues raised in this research during the teaching and learning process. In addition, teachers should engage learners more through seminars where learners get to mingle with others from other schools.

This paper reports an exploratory study on the pre-service teachers’ content knowledge on school calculus. A calculus instrument assessing the pre-service teachers’ iconic thinking, algorithmic thinking and formal thinking related to various concepts in school calculus was administered to a group of pre-service mathematics teachers. Their performance on five of the items is reported in this paper. Other than their good performance in the iconic recognition of stationary points, their recognition on points of inflexion, differentiability and notion of minimum points was relatively poor. In addition, they appeared to lack the algorithmic flexibility in testing the nature of stationary points and the formal thinking about definition of an extremum point. The implications of the findings are discussed.  

Mathematical connection ability is very important to be mastered by prospective mathematics teacher students as competency to teach in secondary schools. However, the facts show that there are still many students who have weak mathematical connection abilities. This qualitative descriptive study aimed to explore how the process, and product of the mathematical connection made by prospective mathematics teacher students when solving the integral calculus problems based on their prior knowledge. The research subjects were 58 students who were prospective high school mathematics teachers at the University of Jember, Indonesia. Data were collected using documentation, questionnaire, test, and interview methods. After the test results of all subjects were analyzed, six students were interviewed. To find the match between the results of the written test and the results of the interview, a triangulation method was carried out. Data analysis used descriptive qualitative analysis with steps of data categorization, data presentation, interpretation, and making conclusions. The results show that the research subjects have connected and used mathematical ideas in the form of procedures, facts, concepts/principles, and representations in solving integral calculus problems. Students with high prior knowledge abilities can make better mathematical connections than students with moderate and low prior abilities. From these results, it is recommended that lecturers need to improve students' prior knowledge and train the students more intensely to solve integral calculus problems so all students can develop their mathematical connection abilities into very strong categories.

The diversity of definitions of science literacy has resulted in a diversity of measurement tools. However, adult science literacy is mainly assessed on short standardized and non-contextualized questions, thus making the study of adult science literacy more qualitative than quantitative. Here we describe the rationale, development, and validation of a questionnaire that associates the use of science in the specific science-related setting of parents of hard of hearing children with general and topic-specific science knowledge. The questionnaire went through four developmental steps: (1) gathering input from hearing rehabilitation experts and parents, (2) testing the close-ended questionnaire (n=10), (3) open-ended questionnaire (n=24), (4) online close-ended questionnaire (n=91). These all assessed general science knowledge, contextual science knowledge in the field of hearing and parents' advocacy knowledge and attitudes. These steps and the resulting assessment tool can thus inform the further development of measures of adult science literacy in context. The findings suggest that although general science knowledge enables the application of science to everyday science-related problems it only explained a small proportion of the variance in contextual science knowledge. Thus, the results strongly point to the importance of measuring adults' science literacy in a context that is relevant to the responders. The findings also underscored the disappointing outcomes of secondary science education, in that formal scientific background predicted general science knowledge but did not account for contextual science knowledge at all. This should elicit concern as to the ability of students to use science knowledge in future personally important science related contexts.