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 relationship between grade 11 learners’ procedural and conceptual knowledge of algebra

2021 ◽  
Vol 6 (4) ◽  
pp. 368-387
Author(s):  
Munyaradzi Chirove ◽  
Ugorji Iheanachor Ogbonnaya
Keyword(s):  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Descriptive Statistics ◽  
Gauteng Province ◽  
Problem Solving Skills ◽  
Positive Linear Relationship ◽  
Research Findings ◽  
Low Levels ◽  
The Relationship ◽  
Grade 11

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners’ procedural and conceptual knowledge of algebra has not been well explored. This research paper examined the relationship between Grade 11 learners’ procedural and conceptual knowledge of algebra. Data for the study was collected using an algebra test administered to 181 grade 11 learners in Gauteng province, South Africa. Descriptive statistics and Pearson’s correlation coefficient were used to analyse the data in SPSS. The study revealed that the learners have low levels of both procedural and conceptual knowledge of algebra. However, they displayed better procedural knowledge than the conceptual knowledge of algebra. In addition, a statistically significant moderate positive linear relationship was found between the learners’ procedural and conceptual knowledge of algebra.

Review: Missing Links

1987 ◽  
Vol 18 (2) ◽  
pp. 158-159
Author(s):  
Larry Sowder
Keyword(s):  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
The Relationship

The purpose of this book is to move toward describing the relationship between conceptual knowledge and procedural knowledge.

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.

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.

scholarly journals ANALISIS MINAT SISWA TERHADAP PELAJARAN MATEMATIKA DAN KEMAMPUAN MENYELESAIKAN MASALAH MATEMATIKA

2017 ◽  
Vol 1 (1) ◽  
pp. 32
Author(s):  
Dewi - Kartikasari
Keyword(s):  
Descriptive Analysis ◽  
Student Interest ◽  
Spearman Correlation ◽  
Learning Mathematics ◽  
Eighth Grade Students ◽  
Mathematical Problems ◽  
Class Viii ◽  
The Relationship ◽  
Math Students ◽  
Range Of Values

This minor thesis aims to determine whether or not a significant influence anatara student interest and student's ability in solving mathematical problems in class VIII MTsN Karangrejo Tulungagung. The method used in this thesis is a qualitative approach - quantitative and descriptive study. Alar analysis used is descriptive analysis and correlation using Spearman correlation. Based on the results of the discussion showed that: (1) the level of interest in learning mathematics eighth grade students MTsN Karangrejo Tulungagung in the medium category, it is shown on the third indicator of interest are two indicators shows the results being, (2) ability of solving math students in both categories, it is shown from the results of the students' work is based on four indicators Polya get a range of values in both categories, (3) while for relations interest in learning and the ability to problem-solving mathematics were analyzed using spearman correlation correlation values 0.414 with significance of 0.000 which indicates that the relationship between the interest and ability to solve problems in mathematics has a moderate correlation

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.

scholarly journals Analysis of 5th Grade Science Learning Outcomes and Exam Questions According to Revised Bloom Taxonomy

2020 ◽  
Vol 6 (1) ◽  
pp. 58
Author(s):  
Seraceddin Levent Zorluoğlu ◽  
Çağrı Güven
Keyword(s):  
Learning Outcomes ◽  
Conceptual Knowledge ◽  
Science Curriculum ◽  
Descriptive Analysis ◽  
Factual Knowledge ◽  
Analysis Technique ◽  
Level Of Understanding ◽  
Bloom Taxonomy ◽  
The Relationship ◽  
5Th Grade

In this study, the relationship between the levels of 5th grade science course exam questions and the 5th class learning outcomes of the science curriculum in the revised Bloom taxonomy was examined. The research was carried out using document analysis method. Since the revised Bloom taxonomy categories were used for the analysis, the data obtained were analyzed with the descriptive analysis technique. The study included 967 science questions and 40 learning outcomes in the 2017-2018 academic year. These questions and learning outcomes were analyzed. At the end of analysis, the relationship between the learning outcomes and exam questions was determined. The inter-rater reliability computing has been made in the analysis of questions-learning outcomes. The reliability co-efficient was calculated .81 for learning outcomes and .77 for questions, indicating an acceptable reliability. According to the results of the analysis, it was determined that the most learning outcomes were in the conceptual knowledge dimension and the most questions were included in the factual knowledge dimension. In the cognitive processes dimension, it was determined that most learning outcomes are at the level of understanding, and the most questions are at the level of remembering. It is understood that 37% of the exam questions are at the level of learning outcomes. In addition, it was determined that there were no questions about some learning outcomes (24%).

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