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 Improving the Conceptual and Procedural Knowledge of Prospective Teachers through Multisensory Approach: Experience from Indonesia

2018 ◽  
Vol 3 (2) ◽  
pp. 106 ◽  
Author(s):  
Yurniwati Yurniwati
Keyword(s):  
Prospective Teachers ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Research Study ◽  
Learning Activities ◽  
State University ◽  
Mathematics Problems ◽  
Hands On ◽  
Mathematics Understanding ◽  
Concrete Materials

Abstract. In mathematics, there is conceptual and procedural knowledge. Conceptual knowledge is about ideas or mathematics understanding but procedural knowledge is about procedure to solve mathematics problems. Multisensory approach involve many senses like kinaesthetic,  visual and auditory to gain knowledge. This research aims to find information about how to apply multisensory approach to improve conceptual and procedural knowledge of prospective teacher in Jakarta State University. This action research study used Kemmis and Taggart model and implemented in two cycles. The data were collected through questionnaires and observation sheets. Then, the data was analyzed descriptively.  The research results showed that the multisensory approach can enhance the conceptual and procedural knowledge of the prospective teachers. The Kinaesthetic approach was implemented in hands-on activity using concrete materials while the visual using images. The concrete materials and image provide different presentation but it helped to constructed concepts and abstraction. Furthermore, the auditory approach was developed along learning activities trough discussion to produce and clarify the ideas. Keywords: Conceptual knowledge, Procedural knowledge, Multisensory approach  

scholarly journals Exploring the Prospective Mathematics Teachers Computational Thinking in Solving Pattern Geometry Problem

2021 ◽  
Vol 13 (3) ◽  
pp. 1756-1767
Author(s):  
Swasti Maharani ◽  
Zeni Fadlila Agustina ◽  
Muhammad Noor Kholid
Keyword(s):  
Mathematics Teachers ◽  
Prospective Teachers ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Computational Thinking ◽  
Future Research ◽  
Mathematics Model ◽  
Geometric Pattern ◽  
Prospective Mathematics Teachers ◽  
Pattern Problem

This research aims to describe the characteristic of mathematics prospective teacher's computational thinking (CT) in solving the geometric pattern problem. The subject consists of 65 preservice mathematics teachers in Universitas in Madiun. The instrument was used in this research are geometric pattern problem tests and interview guidelines. The result shows that are three types of mathematics prospective teachers in solving the problem. First, CT substantial, i.e. prospective mathematics teachers use the conceptual knowledge who collaborated with procedural knowledge exactly. They use mathematics iteration to find the pattern and express them to the general form easily. Second, CT Nominal, i.e. prospective mathematics teachers, use manual ways to solve the pattern problem. They count using numeric, not symbolic, of solving the pattern formed. They can understand the design but can't express it to the mathematics model. Third, CT procedural, i.e. mathematics prospective teacher using the procedural knowledge only, not an expert in concept, and following the steps who teaches from experience before. The recommendation for future research is to develop the research to find the other characters in other mathematics subjects, in other students, to develop the learning models who can embody CT.

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.

scholarly journals Improving the Conceptual and Procedural Knowledge of Prospective Teachers through Multisensory Approach: Experience from Indonesia

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Yurniwati Yurniwati
Keyword(s):  
Prospective Teachers ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Research Study ◽  
Learning Activities ◽  
State University ◽  
Mathematics Problems ◽  
Hands On ◽  
Mathematics Understanding ◽  
Concrete Materials

Abstract. In mathematics, there is conceptual and procedural knowledge. Conceptual knowledge is about ideas or mathematics understanding but procedural knowledge is about procedure to solve mathematics problems. Multisensory approach involve many senses like kinaesthetic,  visual and auditory to gain knowledge. This research aims to find information about how to apply multisensory approach to improve conceptual and procedural knowledge of prospective teacher in Jakarta State University. This action research study used Kemmis and Taggart model and implemented in two cycles. The data were collected through questionnaires and observation sheets. Then, the data was analyzed descriptively.  The research results showed that the multisensory approach can enhance the conceptual and procedural knowledge of the prospective teachers. The Kinaesthetic approach was implemented in hands-on activity using concrete materials while the visual using images. The concrete materials and image provide different presentation but it helped to constructed concepts and abstraction. Furthermore, the auditory approach was developed along learning activities trough discussion to produce and clarify the ideas. Keywords: Conceptual knowledge, Procedural knowledge, Multisensory approach  

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.

Listening to the Experiences and Concerns of Pre-Service Teachers During Teaching Practice Programme

2021 ◽  
pp. 14-27
Author(s):  
Darshana Sharma
Keyword(s):  
Teacher Education ◽  
Student Teachers ◽  
Prospective Teachers ◽  
Teacher Educators ◽  
Teaching Practice ◽  
Group Discussion ◽  
Education Programme ◽  
Practical Training ◽  
Teacher Education Programme ◽  
Practice Teaching

Teaching Practice is widely recognised as the sine-qua-non of any teacher education programme. It is a component in the teacher preparation programme where prospective teachers are provided with an opportunity to put their theoretical studies into practice, get feedback, reflect on practice and consequently further improve their teaching skills. As teaching practice is an important component of a teacher education programme, considerable attention must be given to make it more effective and fruitful. This paper is based on a research study conducted to know pre-service teachers' experiences of the quality of teaching practice and the common concerns they have during teaching practice. On the basis of focussed group discussion a total of five themes were identified, these are (1) usefulness of teaching practice (2) experiences/concerns with pupils' behaviour (3) experiences/concerns with own behaviour (4) experiences/concerns with supervisors' behaviour (5) experiences/concerns with institutional and personal adjustments. The outcome of the focussed group discussion was used to prepare a structured questionnaire. Among other things, the study recommended rigorous practical training in lesson planning, demonstration lessons by teacher educators, simulated teaching before the commencement of practice teaching, school orientation programmes, a separate internship of two weeks and writing a journal by student teachers during teaching practice.

Pupils' Creative Self-Expression in Visual Art

2021 ◽  
Vol 12 (3) ◽  
pp. 29-37
Author(s):  
Daiga Kaleja-Gasparovica
Keyword(s):  
Prospective Teachers ◽  
Visual Art ◽  
Teaching Practice ◽  
Basic Education ◽  
Research Problem ◽  
Study Process ◽  
Pupil Learning ◽  
The Individual ◽  
Creative Self ◽  
Teaching Learning

The study is devoted to the organization of the teaching/learning content of visual art and self-expression process in practice. The article, based on theory, explains creative self-expression in the context of pupil's meaningful learning, based on the new education policy and the developed guidelines in basic education. The individual experience of prospective primary school teachers and their understanding of self-expression in visual art has been clarified during the reflection and pedagogical observation in the study process in methods of teaching visual art which led to stating the research problem. The theoretical account offered in the article reveals pedagogical possibilities for prospective teachers to organize purposefully self-expression classes in visual art during the teaching practice so that the pupil, learning visual art without professional literacy in art, improved his/her transversal skills acquiring the experience of self-guided learning, critical thinking and problem-solving, innovation, cooperation, and civic participation.

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.

scholarly journals Three levels of naturalistic knowledge

2019 ◽  
Author(s):  
Andreas Stephens
Keyword(s):  
Semantic Memory ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Dual Process ◽  
Long Term Memory ◽  
Cognitive Ethology ◽  
System 2 ◽  
System 1 ◽  
Level Of Analysis

A recent naturalistic epistemological account suggests that there are three nested basic forms of knowledge: procedural knowledge-how, conceptual knowledge-what, and propositional knowledge-that. These three knowledge-forms are grounded in cognitive neuroscience and are mapped to procedural, semantic, and episodic long-term memory respectively. This article investigates and integrates the neuroscientifically grounded account with knowledge-accounts from cognitive ethology and cognitive psychology. It is found that procedural and semantic memory, on a neuroscientific level of analysis, matches an ethological reliabilist account. This formation also matches System 1 from dual process theory on a psychological level, whereas the addition of episodic memory, on the neuroscientific level of analysis, can account for System 2 on the psychological level. It is furthermore argued that semantic memory (conceptual knowledge-what) and the cognitive ability of categorization are linked to each other, and that they can be fruitfully modeled within a conceptual spaces framework.

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