scholarly journals Measuring Conceptual Understanding, Procedural Fluency and Integrating Procedural and Conceptual Knowledge in Mathematical Problem Solving

2020 ◽  
Vol 8 (05) ◽  
pp. 1334-1350
Author(s):  
Thi Minh Phuong Ho
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Structural Equation ◽  
Conceptual Knowledge ◽  
Mathematical Problem ◽  
Linear Functions ◽  
Equation Modeling ◽  
Mathematical Problem Solving ◽  
Procedural Fluency ◽  
Mathematical Proficiency

The main aim of this paper is to meassure students’ mathematical proficiency on conceptual understanding and procedural fluency, and their ability of integrating procedural and conceptual knowledge in problem solving. Based on the PCK taxonomy (Ho 2018), we design a questionnaire consisting of 12 questions with 22 tasks whose content is focus on linear functions and equations. The collected data is analysed by the statistical software IBM SPSS Statistics 22. Moreover, we use the structural equation modeling (SEM) to study the correlation between these two components of mathematical proficiency and the ability of integrating procedural and conceptual knowledge in problem solving, implemented in IBM SPSS AMOS 24. The findings show that students’ mathematical proficiency on procedural fluency on linear functions and equations is higher than that of conceptual understanding, and their ability of integrating procedural and conceptual knowledge is very low. Moreover, these categories have a bi-directional relationship, in which the affection of mathematical proficiency on conceptual understanding to the ability of integrating procedural and conceptual knowledge in problem solving is stronger than on procedural fluency.

scholarly journals A modeling study to explain mathematical problem-solving performance through metacognition, self-efficacy, motivation, and anxiety

2019 ◽  
Vol 63 (1) ◽  
pp. 116-134 ◽  
Author(s):  
Zeynep Çiğdem Özcan ◽  
Aynur Eren Gümüş
Keyword(s):  
Problem Solving ◽  
Mathematics Anxiety ◽  
Self Efficacy ◽  
Mathematical Problem ◽  
Equation Modeling ◽  
Mathematical Problem Solving ◽  
And Mathematics ◽  
Metacognitive Experience ◽  
Noncognitive Constructs ◽  
Mathematics Self Efficacy

Many noncognitive constructs affect mathematical problem-solving performance. The aim of the present study is to investigate the direct and indirect effects of a number noncognitive constructs such as mathematics self-efficacy, mathematics anxiety, and metacognitive experience on the mathematical problem solving of middle-school students. The sample consisted of 517 seventh-grade Turkish students of whom 252 were male (49%) and 265 were females (51%). The instruments used in this study were a mathematical problem-solving performance test, a mathematics self-efficacy scale, a mathematics anxiety scale, a metacognitive experience scale, and a mathematics motivation scale. Two-stage structural equation modeling was used to examine the relationships between the noncognitive contructs and problem solving. Metacognitive experience was the only noncognitive construct, which had a direct effect on mathematical problem-solving performance; it also mediated the effects of self-efficacy, motivation, and mathematics anxiety on performance. Motivation and mathematics anxiety had an indirect effect on mathematical problem-solving performance through self-efficacy.

scholarly journals Students’ agency, creative reasoning, and collaboration in mathematical problem solving

2021 ◽  
Author(s):  
Ellen Kristine Solbrekke Hansen
Keyword(s):  
Problem Solving ◽  
Driving Forces ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Linear Functions ◽  
Shared Understanding ◽  
Interaction Patterns ◽  
Collaborative Processes ◽  
Mathematical Properties ◽  
Shared Agency

AbstractThis paper aims to give detailed insights of interactional aspects of students’ agency, reasoning, and collaboration, in their attempt to solve a linear function problem together. Four student pairs from a Norwegian upper secondary school suggested and explained ideas, tested it out, and evaluated their solution methods. The student–student interactions were studied by characterizing students’ individual mathematical reasoning, collaborative processes, and exercised agency. In the analysis, two interaction patterns emerged from the roles in how a student engaged or refrained from engaging in the collaborative work. Students’ engagement reveals aspects of how collaborative processes and mathematical reasoning co-exist with their agencies, through two ways of interacting: bi-directional interaction and one-directional interaction. Four student pairs illuminate how different roles in their collaboration are connected to shared agency or individual agency for merging knowledge together in shared understanding. In one-directional interactions, students engaged with different agencies as a primary agent, leading the conversation, making suggestions and explanations sometimes anchored in mathematical properties, or, as a secondary agent, listening and attempting to understand ideas are expressed by a peer. A secondary agent rarely reasoned mathematically. Both students attempted to collaborate, but rarely or never disagreed. The interactional pattern in bi-directional interactions highlights a mutual attempt to collaborate where both students were the driving forces of the problem-solving process. Students acted with similar roles where both were exercising a shared agency, building the final argument together by suggesting, accepting, listening, and negotiating mathematical properties. A critical variable for such a successful interaction was the collaborative process of repairing their shared understanding and reasoning anchored in mathematical properties of linear functions.

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