Conceptual Understanding, Procedural Knowledge and Problem-Solving Skills in Mathematics: High School Graduates Work Analysis and Standpoints

Abstract

This study measures the mathematical abilities high school graduates" in Bahrain. Mathematical abilities encompass conceptual understanding, procedural knowledge and problem-solving skills in the five content domains which are Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. While procedural understanding focusses on performing facts and algorithms, conceptual understanding reflects a student's ability to reason and comprehend mathematical concepts, operations and relations which will be helpful in solving non-routine problems. A test consisting of questions from the five content domains was administered to students where they demonstrated conceptual understanding and procedural knowledge which enabled them to solve problems in various real-life situations. Structured interviews were also conducted to test their mathematical abilities and suggest ways to improve proficiency in mathematics and eliminate misconceptions. The results show that conceptual understanding and problem-solving skills are positively correlated. This research also endeavors to correlate students" performance in this test with their high school GPA. Contribution/Originality:This study explores the relationship between mathematical abilities: conceptual understanding, procedural knowledge and problem-solving skills in high school graduates in the five mathematics content domains: number and operations, algebra, geometry, measurement, and data analysis and probability. INTRODUCTIONEven after graduating from high school, it is apparent that students do not possess an appropriate level of conceptual understanding in the five content domains. This adversely impacts on their problem solving capabilities.Problem solving is one of the major processes defined in the National Council of Teachers of Mathematics (NCTM) Standards for School Mathematics (National Council of Teachers of Mathematics, 2000). Problem solving involves students applying four processes: reasoning, communication, connections, and representation. Problem solving can also provide opportunities for students to apply content knowledge in all five mathematic domains. Problem solving provides a window into children"s mathematical thinking and is consequently a major vehicle for assessment.Learning with understanding is essential to enable students to solve emergent problems throughout their lives.

Analysis of the Relationship Between Concept Mastery and Problem-Solving Skills of Pre-Service Biology Teachers in Human Physiology Courses

“…This causes the students' mastery of concepts to be low (Mulyani, et al, 2020). In order to improve students' mastery of concepts, lecturers must prepare as much learning as possible (Shi, 2011;Mutawah, et al, 2019). Students who have mastery of deep concepts will have the ability to 1) identify problems, 2) analyze and evaluate data or events, 3) design research, 4) use and manipulate tools, materials or procedures; and 5) solving problems in order to understand facts about nature and the changes that occur in life (Pantiwati, et al, 2020;Surif, et al, 2012).…”

Learner-generated drawings by students with mathematical learning difficulties in finishing open number sentences

“…Meanwhile, changes in the learner-generated drawings of MLD students indicate the development of student understanding towards a better direction in interpreting symbolic representations into visual representations. (Al-Mutawah et al, 2019;Barmby et al, 2012;Martin, 2008). Further research is recommended to use mixed-methods to provide a numerical measurement of the significance of the effect of tasks in the form of open number sentences questions on adding and subtracting integer operations to the types of drawings and learner-generated drawings changes of MLD students.…”

The Ability of Students’ Conceptual Understanding in Completing Story Problems on Mathematics

“…Even students are less able to understand the concepts on their notes when they are given practice questions (Al-Mutawah et al, 2019). If this continues, students will be trained to be spoiled students and have a negative impact on learning outcomes (Al-Mutawah et al, 2019 (Hakim & Ramlah, 2019;Fajar et al, 2019;Aminah and Ayu Kurniawati, 2018 ) learning is being carried out at this time with the pattern of providing material, explanation of examples and exercises, students only record each concept without understanding it.…”