scholarly journals ANALYSIS OF STUDENTS MATHEMATICAL CONNECTION ERRORS IN TRIGONOMETRIC IDENTITY PROBLEM SOLVING

2020 ◽  
Vol 17 (35) ◽  
pp. 825-836
Author(s):  
Budi MARDIYANA USODO ◽  
. BUDIYONO ◽  
Anisa Astra JINGGA ◽  
Dwi FAHRUDIN
Keyword(s):  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Arithmetic Operation ◽  
Critical Role ◽  
Trigonometric Identity ◽  
Mathematical Connections ◽  
Learning Mathematics ◽  
Algebraic Concepts ◽  
Algebraic Concept ◽  
Trigonometric Identities

The trigonometric identity is essential in learning Mathematics because it requires students to think critically, logically, systematically, and thoroughly. Solving trigonometric identity problems requires students to relate conceptual knowledge or procedural knowledge, which then used in questions. This study involved grade X students of senior high school, which were examined to find out the types of mathematical connections errors and causes of the errors. Before task-based interviews were conducted, 36 students were first given a test. Based on several considerations, seven students ( three males and four females) were selected to undergo a task-based interview. This research employed a qualitative research method with a case study design. The results of the analysis indicate that the errors in connecting to conceptual knowledge are most commonly the mistake of connecting the algebraic concept. On the other hand, 86.11% of students experienced errors in connecting to procedural knowledge. This error happened when the students worked on problems with trigonometric identities, which they had rarely encountered in exercises. Errors in mathematical connections in trigonometric identity are caused by the lack of understanding of the algebraic arithmetic operation, emphasis on the concept, and strategic knowledge. It shows that students need a variety of problems to be able to master various forms of trigonometric identities. This research's result also reinforces the critical role of algebraic concepts as prior knowledge in studying trigonometric identity.

Why Is the Midpoint an Average?

2013 ◽  
Vol 106 (7) ◽  
pp. 514-519 ◽  
Author(s):  
Lingguo Bu
Keyword(s):  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Learning Mathematics ◽  
Mathematics For Teaching ◽  
The Relationship

The relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching.

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.

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.

Mathematical Approaches and Strategies

2016 ◽  
pp. 145-169
Author(s):  
Lorelei R. Coddington
Keyword(s):  
United States ◽  
Student Performance ◽  
Mathematics Teachers ◽  
Conceptual Knowledge ◽  
Teaching And Learning ◽  
The United States ◽  
Inclusive Classroom ◽  
Learning Mathematics ◽  
Improve Student Performance ◽  
Support Students

Recent shifts in standards of instruction in the United States call for a balance between conceptual and procedural types of teaching and learning. With this shift, an emphasis has also been placed on ensuring teachers have the knowledge and tools to support students to improve student performance. Since many struggle in learning mathematics, teachers need practical ways to support students while also building their conceptual knowledge. Research has highlighted many promising approaches and strategies that can differentiate instruction and provide needed support. This chapter highlights various examples found in the research and explains how the approaches and strategies can be used to maximize student learning in the inclusive classroom.

The Functional Neuroanatomy of Thematic Role and Locative Relational Knowledge

2007 ◽  
Vol 19 (9) ◽  
pp. 1542-1555 ◽  
Author(s):  
Denise H. Wu ◽  
Sara Waller ◽  
Anjan Chatterjee
Keyword(s):  
Conceptual Knowledge ◽  
Visual Motion ◽  
Critical Role ◽  
Temporal Cortex ◽  
Functional Neuroanatomy ◽  
Thematic Role ◽  
Point Of Entry ◽  
Relational Knowledge ◽  
Relational Concepts ◽  
The Relationship

Lexical-semantic investigations in cognitive neuroscience have focused on conceptual knowledge of concrete objects. By contrast, relational concepts have been largely ignored. We examined thematic role and locative knowledge in 14 left-hemisphere-damage patients. Relational concepts shift cognitive focus away from the object to the relationship between objects, calling into question the relevance of traditional sensory-functional accounts of semantics. If extraction of a relational structure is the critical cognitive process common to both thematic and locative knowledge, then damage to neural structures involved in such an extraction would impair both kinds of knowledge. If the nature of the relationship itself is critical, then functional neuroanatomical dissociations should occur. Using a new lesion analysis method, we found that damage to the lateral temporal cortex produced deficits in thematic role knowledge and damage to inferior fronto-parietal regions produced deficits in locative knowledge. In addition, we found that conceptual knowledge of thematic roles dissociates from its mapping onto language. These relational knowledge deficits were not accounted for by deficits in processing nouns or verbs or by a general deficit in making inferences. Our results are consistent with the hypothesis that manners of visual motion serve as a point of entry for thematic role knowledge and networks dedicated to eye gaze, whereas reaching and grasping serve as a point of entry for locative knowledge. Intermediary convergence zones that are topographically guided by these sensory-motor points of entry play a critical role in the semantics of relational concepts.

Knowledge Acquisition in Computer-Based Learning Environments among Elementary Children

1997 ◽  
Vol 26 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Andrew S. Chirwa
Keyword(s):  
Learning Environments ◽  
Learning Strategies ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Learning Strategy ◽  
High Order ◽  
Factual Knowledge ◽  
Computer Based Learning ◽  
Computer Based ◽  
Computer Based Learning Environments

The need to understand how children acquire knowledge in computer-based learning environments led the researcher to undertake this study. The purpose was to develop a conceptualization of what learning strategies children frequently use to process conceptually demanding material. The goal was to expose children to different categories of courseware that featured multimedia, drill and practice, simulations, tutorials, spreadsheets, and databases; and to determine learning strategies including elaboration, organization, integration, and recall. The object was to compare the types of learning strategy and nature of knowledge forms acquired during the process of learning the given material in a subject area. The study was conducted at Washington Elementary School; and participants were children in the third through sixth grades. Data was collected by using surveys, formal observations, and formative and summative evaluation procedures. Results show that 80 percent of the time the students had attention focused on the learning material and gained an elevated level of awareness. The learning strategies imagery, exemplifying, and networking were used 70 percent of the time as means to gain conceptual knowledge, factual knowledge, procedural knowledge, and develop high order thinking. The learning strategies covert practice, overt practice, and identifying key ideas were used 60 percent of the time to gain conceptual knowledge, factual knowledge, procedural knowledge, and rules in the subject areas. The learning strategy categorization was used 40 percent of the time as means to gain conceptual knowledge, factual knowledge, procedural knowledge, and rules. The learning strategies sentence elaboration and anticipation were used 30 percent of the time to gain conceptual knowledge, factual knowledge, procedural knowledge, rules, high-order rules, and develop high order thinking. These findings have implications to learning and knowledge acquisition in computer-based learning environments, instructional design, program development and improvement, and technology and teacher education.

scholarly journals THE EFFECT ON STUDENTS’ ARITHMETIC SKILLS OF TEACHING TWO DIFFERENTLY STRUCTURED CALCULATION METHODS

2020 ◽  
Vol 78 (2) ◽  
pp. 167-195
Author(s):  
Margareta Engvall ◽  
Joakim Samuelsson ◽  
Rickard Östergren
Keyword(s):  
Mathematics Teaching ◽  
Conceptual Knowledge ◽  
Decomposition Method ◽  
Intervention Study ◽  
Procedural Knowledge ◽  
Empirical Support ◽  
Factual Knowledge ◽  
Calculation Methods ◽  
Traditional Algorithm ◽  
Development Of Students

Mastering traditional algorithms has formed mathematics teaching in primary education. Educational reforms have emphasized variation and creativity in teaching and using computational strategies. These changes have recently been criticized for lack of empirical support. This research examines the effect of teaching two differently structured written calculation methods on teaching arithmetic skills (addition) in grade 2 in Sweden with respect to students’ procedural, conceptual and factual knowledge. A total of 390 students (188 females, 179 males, gender not indicated for 23) were included. The students attended 20 classes in grade 2 and were randomly assigned to one of two methods. During the intervention, students who were taught and had practiced traditional algorithms developed their arithmetic skills significantly more than students who worked with the decomposition method with respect to procedural knowledge and factual knowledge. These results provided no evidence that the development of students' conceptual knowledge would benefit more from learning the decomposition method compared to traditional algorithm. Keywords: arithmetic skills, decomposition method, intervention study, mathematics education, traditional algorithm, written calculation.

scholarly journals Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction is Important to Teachers

2021 ◽  
Vol 46 (2) ◽  
pp. 57-71
Author(s):  
Derek Hurrell ◽  
Keyword(s):  
Mathematics Teaching ◽  
Conceptual Knowledge ◽  
Teacher Educators ◽  
Procedural Knowledge ◽  
Insight Into

The terms conceptual knowledge and procedural knowledge are often used by teachers and never more so than when discussing how teachers teach, and children learn mathematics. This paper will look at literature regarding conceptual and procedural knowledge and their place in the classroom, to offer teachers and teacher educators’ advice on some of the more pressing issues and understandings around them. A thorough synthesis of extant and seminal literature will provide advice to teachers and teacher educators on how a deeper insight into conceptual and procedural knowledge could improve the quality of mathematics teaching.

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