Mathematical knowledge has been defined in several ways in the literature of mathematics education. Procedural knowledge (PK) and conceptual knowledge (CK) or both types of knowledge are the emphasis of knowledge construction. This is a research-based paper extracted from a dissertation of MEd in mathematics education of the first author under the supervision of the remaining two authors. In this context, this explanatory mixed method research study was carried out to find students' level of PK and CK in algebra and explore why students develop such knowledge. In the quantitative part, the survey was conducted among 360 students of grade eight of 9 public schools of Kathmandu Metropolitan City. The study revealed that students have a lower level of CK (x̅ =8.56) but a higher level of PK (y̅ =14.05) out of 20 and a moderate positive correlation (r=+0.559, p<0.05) between PK and CK. The regression equation was: CK=3.716+0.345(PK). Similarly, PK was dependent, but CK was independent upon the gender of the respondents. In the qualitative part, a two-phase interview was conducted with six participants followed by a group discussion with four mathematics teachers teaching at the same level. This phase concluded that students are weak in reasoning, critical thinking, representational knowledge and comparing algebraic quantities. The reason is because students seemed to be forced/encouraged to develop procedural fluency because of teachers' methods of teaching which oftentimes neglect the progressive pedagogical approaches. The research is useful for everyone who is working on educational reform to emphasize meaningful learning.
The process of constructing knowledge in mathematics education is critical in developing it as a discipline with an impact on the field of teaching, learning, and assessment based on theory and practice. How do mathematics educators perceive the processes of knowledge construction in mathematics education? It may have an implication in the methods of teaching, learning, and researching to enrich this discipline. In this context, the purpose of this study was to explore the Nepali mathematics educators’ perspectives on critical conscience for the construction of knowledge in mathematics education. The research participants were five university-level mathematics educators who participated in in-depth interviews on critical conscience in mathematics education. The qualitative thematic analysis of the interview data unveiled four major thematic groups in terms of four idiographic passes– culture, communication, collaboration, and context (4Cs); discourse, dedication, deliberation, and development (4Ds); equity, engagement, elaboration, and extension (4Es); and formation, fusion, frame of reference, and faculty of cognition (4Fs). The thematic interpretations of critical conscience may portray the paradigmatic assumptions of ontological, epistemological, and axiological primacy of mathematics education from the participants’ views. Policy and pedagogical implications of the themes have been discussed.
The objectives of this study are to determine students’ understanding about different methods of proof in mathematics and compare their understanding with respect to their previous degree in education and other majors within the framework of a post-positivist research paradigm. Forty-two purposively selected students in the sample were selected. Their understanding of different methods of proof was determined with the help of a test paper consisting of 30 mathematical statements with proof. The study concluded that students are familiar with the methods of proofs used in verifying a mathematical statement. In addition, it is found that students with a previous degree in education and other majors differ in the level of understanding of different methods of proof in mathematics.
The major objective of the study is to identify the perception of mathematics teachers towards the use of instructional materials in teaching mathematics for the students of secondary level and to compare their perceptions on the basis of their teaching experience. The study has adopted descriptive survey design. A set of the questionnaire with 24 statements regarding the use of instructional materials in teaching mathematics was the tool for collecting the data. The statements in the questionnaire were categorized into four categories as availability, appropriateness, self-confidence in using instructional materials, and motivation to use it. The questionnaire forms were distributed to 68 secondary school mathematics teachers of public schools. The data were collected, tabulated, ordered, compared, calculated and analyzed by using different statistical tools. Finally, it was found that teachers have negative attitudes towards the statements under the subheadings availability which indicates teachers do not feel comfortable in gathering the instructional materials in teaching mathematics and they were found to have positive towards the statements under the subheadings appropriateness, self-confidence in using, and motivation which means mathematics teachers are in the favor of appropriate use instructional materials in teaching mathematics, and they were found confident in using instructional materials. And also teachers are found motivated to use instructional materials in teaching mathematics at secondary level. The study also concluded that the perception of the teachers regarding the use of instructional materials in teaching mathematics at secondary level differs according to the teaching experience of the teachers. Interestingly, the teacher with less teaching experience were found more positive in using instructional materials in teaching mathematics at secondary level.
Teaching mathematics at the university level expects a more complex form of algorithmic and theoretical exploration which sometimes could not be delivered as enough as the curriculum demands. In this context, this study primarily focused on exploring the opportunities and challenges of online classes while teaching-learning mathematics at the university level. It is an ethnographic study in which three students and a teacher who had a long experience in online teaching-learning practices were taken as the key respondents. The key informants were requested for writing the reflection about their experiences of learning mathematics through online mode. And, the responses of the students were analyzed and presented in different themes. Based on the responses of the key respondent students, poor networking, unavoidable disturbance, teacher’s artificial pretending, negligence of the teachers, and less ICT-friendly curriculum & teachers were found as the major challenges for the online class. From the perspective of teachers' preparing documents for teaching, students’ negligence, ICT being used only as a means of sharing, taking more time to complete the course, less interactive class, and evaluating the students were found as the major challenges. However, online education provided the teachers and student both with a friend in crisis, sitting home reaching school, reducing unnecessary expenditures, and utilizing video records of the classes. Similarly, for teachers; providing opportunities for professional development, web browsing, any time anywhere teaching-learning, and developing the skills for designing different online evaluation tools have been observed as the major opportunities. Based on these conclusions, even having many challenges of using ICT in teaching university mathematics, its appropriate use leads for the deeper and wider understanding of mathematical contents.
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