scholarly journals Advantages of discussion and cognitive conflict as an instructional method in contemporary teaching of mathematics

2012 ◽  
Vol 44 (1) ◽  
pp. 92-110
Author(s):  
Irena Misurac-Zorica ◽  
Maja Cindric
Keyword(s):  
Conceptual Knowledge ◽  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Descriptive Analysis ◽  
Cognitive Conflict ◽  
Construction Of Knowledge ◽  
Teaching And Learning Mathematics ◽  
Starting Point ◽  
Teaching Of Mathematics ◽  
Decimal Numbers

Contemporary theories of teaching and learning mathematics emphasise the importance of learner?s active participation in the teaching process, in which discovery and logical reasoning lead to the construction of student?s knowledge. In this form of teaching, it is important to detect students? misunderstandings and errors that can occur during learning. Uncovered tacit and false conceptions of students? knowledge can greatly contribute to the opposite effect in the construction of knowledge. In teaching mathematics, there are many situations which leave students with ambiguities and misunderstandings, and create an impression in children that teaching of mathematics and mathematical knowledge itself is something that is not possible. Discussion and cognitive conflict are methods which have their starting point in the theory of constructivism. The aim of our study has been to determine whether application of the method of discussion and cognitive conflict in learning to divide decimal numbers leads to the enhancement of student?s procedural knowledge and conceptual knowledge about the division of decimal numbers. Longitudinally, we monitored two groups of 117 pupils of the fifth grade. In the first group, which was taught according to the guidelines of contemporary mathematics education, students engaged in discussion, discovering their misunderstandings and errors, and the cognitive conflict resulted in correct concepts. The second group of students were taught traditionally, learning the procedure and then practicing it. The paper presents a descriptive analysis of the process of teaching and quantitative analysis of the performance based on the comparison of conceptual and procedural knowledge of both groups. Results of our work show that the application of contemporary methods of discussion and cognitive conflict affects the increase of procedural and conceptual knowledge of the division of decimal numbers.

scholarly journals The Effect of Geogebra on Students’ Conceptual and Procedural Knowledge: The Case of Applications of Derivative

2017 ◽  
Vol 7 (2) ◽  
pp. 67 ◽  
Author(s):  
Mehmet Fatih Ocal
Keyword(s):  
Conceptual Knowledge ◽  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Dynamic Geometry ◽  
The Other ◽  
Control Group ◽  
Other Hand ◽  
Significant Difference ◽  
Before And After ◽  
Post Test

Integrating the properties of computer algebra systems and dynamic geometry environments, Geogebra became an effective and powerful tool for teaching and learning mathematics. One of the reasons that teachers use Geogebra in mathematics classrooms is to make students learn mathematics meaningfully and conceptually. From this perspective, the purpose of this study was to investigate whether instruction with Geogebra has effect on students’ achievements regarding their conceptual and procedural knowledge on the applications of derivative subject. This study adopted the quantitative approach with pre-test post-test control group true experimental design. The participants were composed of two calculus classrooms involving 31 and 24 students, respectively. The experimental group with 31 students received instruction with Geogebra while the control group received traditional instruction in learning the applications of derivative. Independent samples t-test was used in the analysis of the data gathered from students’ responses to Applications of Derivative Test which was subjected to them before and after teaching processes. The findings indicated that instruction with Geogebra had positive effect on students’ scores regarding conceptual knowledge and their overall scores. On the other hand, there was no significant difference between experimental and control group students’ scores regarding procedural knowledge. It could be concluded that students in both groups were focused on procedural knowledge to be successful in learning calculus subjects including applications of derivative in both groups. On the other hand, instruction with Geogebra supported students’ learning these subjects meaningfully and conceptually.

A Framework for Investigating Qualities of Procedural and Conceptual Knowledge in Mathematics—An Inferentialist Perspective

2020 ◽  
Vol 51 (5) ◽  
pp. 574-599
Author(s):  
Per Nilsson
Keyword(s):  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Theoretical Perspective ◽  
Mathematical Discussions ◽  
Teaching Of Mathematics

This study introduces inferentialism and, particularly, the Game of Giving and Asking for Reasons (GoGAR), as a new theoretical perspective for investigating qualities of procedural and conceptual knowledge in mathematics. The study develops a framework in which procedural knowledge and conceptual knowledge are connected to limited and rich qualities of GoGARs. General characteristics of limited GoGARs are their atomistic, implicit, and noninferential nature, as opposed to rich GoGARs, which are holistic, explicit, and inferential. The mathematical discussions of a Grade 6 class serve the case to show how the framework of procedural and conceptual GoGARs can be used to give an account of qualitative differences in procedural and conceptual knowledge in the teaching of mathematics.

Teaching Toward the Big Ideas of Algebra

2000 ◽  
Vol 6 (4) ◽  
pp. 226-231
Author(s):  
Sonia Woodbury
Keyword(s):  
Problem Solving ◽  
Conceptual Knowledge ◽  
Middle Grades ◽  
Procedural Knowledge ◽  
Conceptual Structure ◽  
Algebraic Manipulation ◽  
Relational Understanding ◽  
The Past ◽  
Starting Point ◽  
Big Ideas

IN WHAT WAYS DO WE WANT MIDDLE-GRADES STUDENTS TO UNDERSTAND ALGEBRA? Hiebert and Carpenter (1992) describe the need for students to gain both procedural knowledge and broadly connected conceptual knowledge to understand mathematics. A knowledge of rules and procedures provides students with tools for efficient problem solving. However, in learning the procedures of algebraic manipulation, for example, students often develop what Skemp (1978) calls an “instrumental understanding” of algebra. He explains, “It is what I have in the past described as ‘rules without reasons,’ without realizing that for many pupils… the possession of such a rule, and the ability to use it, was what they meant by ‘understanding’ ” (p. 9). Skemp contrasts instrumental understanding with “relational understanding,” which “consists of building up a conceptual structure (schema) from which its possessor can (in principle) produce an unlimited number of plans for getting from any starting point within his schema to any finishing point” (p. 14).

scholarly journals Maths concepts in teaching: Procedural and conceptual knowledge

Pythagoras ◽  
2005 ◽  
Vol 0 (62) ◽  
Author(s):  
Caroline Long
Keyword(s):  
Prospective Teachers ◽  
School Environment ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Teaching Practice ◽  
Teaching Of Mathematics

In teaching a general course on mathematics for prospective teachers, I have found the theoretical distinction between conceptual knowledge and procedural knowledge (Hiebert & Lefevre, 1986) a useful focus for teaching practice. The constructs provide a scaffold for the learning of mathematics by the students and for thinking about the teaching of mathematics in the school environment. These theoretical insights uncover in part the processes for acquiring knowledge and provide a tool for addressing problematic areas of learning.

scholarly journals Analisis Keperluan Bagi Pembangunan Modul Untuk Pengekalan Pengetahuan Konseptual Dan Prosedural Matematik Tingkatan 1

2020 ◽  
Vol 8 (2) ◽  
pp. 86-99
Author(s):  
Teh Guan Leong ◽  
Raja Lailatul Zuraida Raja Maamor Shah ◽  
Nor’ashiqin Mohd Idrus
Keyword(s):  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Descriptive Analysis ◽  
Descriptive Statistics ◽  
Learning Module ◽  
Need Analysis ◽  
Algebraic Expressions ◽  
Learning Mathematics ◽  
Questionnaire Form ◽  
Very High

In design and development study, a need analysis needs to be carried out to ensure that the learning module for retention of conceptual and procedural knowledge to be developed can meet the needs of the study target. A need analysis has been conducted to identify the Form 1 topics that students find difficult, moderate difficult and most difficult to learn, examine students’ perceptions on the difficulties they encounter in learning Mathematics and examine students’ perceptions on the characteristics of module that they want into retaining conceptual and procedural knowledge of Form 1 Mathematics topics learnt. The respondents of this study consisted of 150 Form 1 students and 150 Form 2 students. Data collection was done using questionnaire form. The results of descriptive statistics analysis showed Linear Equation as the most difficult topic, Algebraic Expressions as moderate difficult topic and Linear Inequality as difficult topic to be learnt in Form 1 Mathematics. As for the difficulties students encounter in learning Mathematics, the results of descriptive analysis found that students faced difficulties in terms of procedural and conceptual knowledge mastery, remembering and recalling. In addition, characteristics of module that students want into retaining conceptual and procedural knowledge of Form 1 Mathematics topics learnt indicated that the respondents’ consent level were Very High for most of the proposed module features. The implication of this study informed the researcher on what to consider when developing a learning module to retain conceptual and procedural knowledge of Form 1 Mathematics topics.

A Model of Designing Online Assignments Based on the Revision of Bloom's Taxonomy

2016 ◽  
pp. 186-193 ◽  
Author(s):  
Congwu Tao
Keyword(s):  
Online Teaching ◽  
Conceptual Knowledge ◽  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Bloom's Taxonomy ◽  
Factual Knowledge ◽  
Revised Bloom's Taxonomy ◽  
Bloom’S Taxonomy ◽  
Online Assignments ◽  
Online Instructor

Online assignments play an important role in online teaching and learning, and the revised Bloom's Taxonomy has been proved to be valuable for real teaching and learning. But few research efforts are put into combining online assignment design with the revised Bloom's Taxonomy. This chapter is to propose a model of designing online assignments based on the revised Bloom's Taxonomy, which can be used as a guide for online instructor to design a comprehensive online assignment with helping the students to master the four types of knowledge–factual knowledge, conceptual knowledge, procedural knowledge and metacognitive knowledge–and at the same time help the students develop the six-stage cognitive process.

scholarly journals A Constructivist Approach to the Teaching of Mathematics to Boost Competences Needed for Sustainable Development

2018 ◽  
Vol 39 (334) ◽  
pp. 1-7 ◽  
Author(s):  
Anna Vintere
Keyword(s):  
Sustainable Development ◽  
Mathematics Education ◽  
Teaching And Learning ◽  
Mathematics Learning ◽  
Educational Process ◽  
Constructivist Approach ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Teaching Of Mathematics ◽  
Study Process

Abstract The constructivist approach is based on the idea that knowledge can never be passed from one person to another. The only way to acquire knowledge is to create or construct them. The constructivist approach changes also the role of the teacher in the educational process, the task of them is to organize the environment so that the student himself can construct the cognitive forms that teacher wants to give him. In the paper, the nature of the constructivist approach is identified, different aspects regarding mathematics education are analysed as well as the potential impact on the development of mathematical competences in the context of sustainable development is discussed. The study process and learning methods appropriate to constructivist approach also were studied. In order to illustrate the need for a constructivist approach in mathematics education, the survey of students from Latvia University of Life Science and Technologies (LLU) and Riga Technical University (RTU) were carried out, the results of which proved that mathematics learning at universities has to be changed. The current study proved that the constructivist approach radically changes the process of teaching and learning mathematics, connecting it with daily life, rather than teaching only abstract formulas and using a creative approach to mathematical tasks solving. This study shows that using constructivist approach to the teaching of mathematics, the competences needed for sustainable development are boosted.

scholarly journals TAXONOMY OF LEARNING OBJECTIVES AT ELEMENTARY LEVEL

2020 ◽  
Author(s):  
Mara Cotič ◽  
◽  
Darjo Felda ◽  
Amalija Žakelj ◽  
Keyword(s):  
Conceptual Knowledge ◽  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Learning Objectives ◽  
Elementary Level ◽  
Complex Thinking ◽  
Centre Of Gravity ◽  
Complex Process ◽  
Cognitive Knowledge

Looking for an answer to the question what knowledge represents the centre of gravity in teaching and learning and thus also in testing and assessing knowledge, as well as in the interpretation of students’ achievements taxonomies of learningobjectives for the cognitive area can be of assistance. In education sciences there are several taxonomies of cognitive knowledge (Bloom, Marzano, Gagne). Taxonomy is derived from basic cognitive – mental processes that are arranged in a hierarchic relationship, namely from the lowest – the simplest to the highest – the most complex process. The present paper represents an introduction to Bloom’s, Gagne’s, and Marzano’s taxonomies. Bloom’s taxonomy is one of the best known classifications of learning objectives, where Bloom and associates have formed a taxonomy of cognitive, conative, and psycho-motoric learning objectives. In the cognitive area the following degrees have been defined: remembering, understanding, applying, analysing, synthesising, and evaluating. Gagne’s classification of knowledge classifies the achievements of learners into: basic and conceptual knowledge, procedural knowledge, and problem solving knowledge. Marzano’s taxonomy distinguishes between content and lifelong or process knowledge, which are further divided into complex thinking, data processing, communication, cooperation in the group, and development of mental habits.

scholarly journals Methodical Scheme for Introduction of Combinatorial Compounds in Mathematics Education

TEM Journal ◽  
2021 ◽  
pp. 414-420
Author(s):  
Ivan Georgiev ◽  
Ivo Andreev
Keyword(s):  
Mathematics Education ◽  
Teaching And Learning ◽  
Mathematics Curriculum ◽  
Short Review ◽  
Combinatorial Problems ◽  
Innovative Methods ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Alternative Approach ◽  
Teaching Of Mathematics

The article is structured as follows. In section 1, the Introduction, a historical summary on the arising of the combinatorics is given. Next, a short review of the part of the combinatorics in the teaching of mathematics in Bulgaria is presented. At the beginning of section 2, combinatorial compounds, included in the Mathematics curriculum in Bulgaria, are reviewed. A new methodical scheme for the introduction of basic combinatorial compounds is proposed. Then, an alternative approach for solving combinatorial problems in teaching and learning mathematics is analyzed in detail. The innovative methods are illustrated with four particular sample tasks in section 3. Certain conclusions on the specific issues are drawn at the end of the article.

scholarly journals INCOMPREHENSION OF THE INDONESIAN ELEMENTARY SCHOOL STUDENTS ON FRACTION DIVISION PROBLEM

2019 ◽  
Vol 8 (1) ◽  
pp. 57 ◽  
Author(s):  
Yoppy Wahyu Purnomo ◽  
Chairunnisa Widowati ◽  
Syafika Ulfah
Keyword(s):  
Elementary School ◽  
Elementary School Students ◽  
Conceptual Knowledge ◽  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Mathematics Classroom ◽  
Division Problem ◽  
School Students ◽  
Descriptive Case Study ◽  
Fraction Division

The purpose of the study is to investigate the Indonesian students’ performance in solving fraction division case including the difficulties, relations, and implications for classroom instruction. This study employed a descriptive case study to achieve it. The procedures of data collecting were initiated by giving a context-based problem to 40 elementary school students and it then according to the test result was selected three students for semi-structure interviewed. The findings of the study showed that the tendency of students’ procedural knowledge dominated to their conceptual knowledge in solving the fraction division problem. Furthermore, it was found several mistakes. First, the students were not accurate when solving the problem and unsuccessful to figure out the problem. Second, students’ conceptual knowledge was incomplete. The last was is to apply the laws and strategies of fraction division irrelevant. These findings emphasized other sub-construct of fractions instead of part-to-whole in the teaching and learning process. Teaching and learning of fraction in the mathematics classroom should take both conceptual and procedural knowledge into account as an attempt to prevent faults and misconceptions. In conclusion, it was substantial to present context-based problems at the beginning of the lesson in order for students to be able to learn fraction division meaningfully.

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