Conceptual and Procedural Knowledge of Students of Nepal in Algebra: A Mixed Method Study

Abstract

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.

A brickworker becomes transformative STEAM educator: Journey of resistance, advocacy, and envisioning

“…Students are likely to be passive receivers and reproducers of knowledge and skills within this education system without developing transversal skills. Students develop routine problem-solving skills by using given and algorithmic procedures, rules, and strategies which leads to the production of procedural fluency (Rittle-Johnson, 2019; Manandhar et al, 2022), wherein they cannot solve the complex and real-world problems. In the controlled environment, students did not get the opportunities to discuss, communicate, share, question, and explore the world beyond the four walls of the classroom.…”

The effect of assessment for learning on prospective teachers’ learning of algebra through a professional development program

“…This finding agrees with the argument of Black and Wiliam (2010), which states that although AfL can benefit all students, it is especially beneficial to low achievers since it focuses on specific faults with their work and provides them with a clear grasp of what is wrong and how to fix it. Manandhar et al (2022) in their study indicated that students were influenced and encouraged by textbooks, teachers, and learning activities to develop procedural skills, memorize formulae, and solve problems. They further noted that lack of well-trained teachers, poor management of teacher training and PD programs, a heavy number of contents, large number of students, etc., affect the implementation of students-cantered approaches, though they found that students can learn mathematics concepts when they play with problems related to their day-to-day life using more contextual examples which this study tried to incorporate.…”

A Textbook Problem-Solving Student Becomes Transformative Contextualized Mathematics Teacher: Journey of Learning and Teaching

“…This followed the statement of Hunt and Andreasen (2011) who suggested for instructional method that is based on real-life context, in order for the teachers/educators to make their mathematics classroom better engaging. So, use of studentcentric instructional approach such as Activity Based Learning 5 (ABL) assist students in regards to their enhancement of CK of mathematics (Manandhar et al, 2022), which is based on the hypothesis that when learners indulge actively in the learning process, then they learn best (Festus, 2013). The students creatively demonstrated the connection of particular mathematical concepts/ideas to surroundings using locally available materials, as illustrated in story 2 of episode 3.…”