scholarly journals STAGES IN PARTIAL FUNCTIONAL THINKING IN THE FORM OF LINEAR FUNCTIONS: APOS THEORY

2020 ◽  
Vol 8 (3) ◽  
pp. 536-544
Author(s):  
Suci Yuniati ◽  
Toto Nusantara ◽  
Subanji ◽  
I Made Sulandra
Keyword(s):  
Mathematics Education ◽  
Linear Functions ◽  
Apos Theory ◽  
Functional Thinking ◽  
Mathematical Problems ◽  
Thinking Processes

Purpose of the study: The purpose of this study is to describe students' partial functional thinking processes in solving mathematical problems based on APOS Theory. The problem in this study was formulated into the question, what are the stages of students' partial functional thinking in solving mathematical problems based on APOS Theory?. Methodology: This study was conducted by with 44 students from the Department of Mathematics Education. The subjects of this study were asked to solve mathematical problems developed from (Wilkie, 2014). Then some of them were interviewed to learn their functional thinking processes. The subjects’ partial functional thinking processes were analyzed using APOS theory. Main Findings: The results showed that, based on APOS theory, the students’ partial functional thinking consisted of several stages: 1) identifying the problem, 2) organizing the data, 3) determining the recursive patterns, 4) determining the covariational relationships, 5) generalizing the relationships between variations in quantities (correspondence), and 6) re-checking the generalization results. In this case, the students generalized the relationships between variations in the form of functions done partially using the arithmetic formula . Applications of this study: The findings of this study can help teachers understand the stages in students' thinking processes in solving problems about functions and the difficulty faced by the students in understanding the functions. Novelty/Originality of this study: The researchers identified stages in students' partial functional thinking in solving mathematical problems in the form of functions based on APOS Theory.

scholarly journals INTUISI SEBAGAI SALAH SATU SOLUSI MERAIH PRESTASI BELAJAR MATEMATIKA

2020 ◽  
Vol 2 (1) ◽  
pp. 28-33
Author(s):  
Sofia Sa’o
Keyword(s):  
Cognitive Process ◽  
Research Method ◽  
Qualitative Method ◽  
Intuitive Thinking ◽  
Analytical Thinking ◽  
Mathematical Problems ◽  
Thinking Processes ◽  
Conventional Methods ◽  
Math Problems ◽  
Descriptive Qualitative

Mathematical problems are often solved without using conventional methods but using intuition thinking. Intuitive thinking is a cognitive process that leads to ideas as strategies for making decisions that produce spontaneous answers in solving problems. Spontaneous answers are written and spoken expressions that help a person solve math problems without using analytical thinking. This study aims to describe the various forms of intuition that arise when students solve math problems. The research method used is descriptive qualitative method to describe students' intuitive thinking processes through test instruments and interviews. The results showed that the form of intuitive thinking that emerged was (1) affirmatory intuition, namely direct cognition to understand the problem and (2) perceptual and global components, because students made perceptions of the answer solutions to be generated, then resolved until they got the results. In addition, it was also found that intuitive thinking that is raised as a strategy in making decisions is based on feelings, intrinsics and interventions to produce answers to solving the problems faced

scholarly journals Not all Equals are Equal: Decoupling Thinking Processes and Results in Mathematical Assessments

2019 ◽  
pp. 631-636
Author(s):  
Stephen Woodcock
Keyword(s):  
Mathematics Education ◽  
Specific Question ◽  
Transferable Skills ◽  
Mathematical Thought ◽  
Initial Work ◽  
Thinking Processes ◽  
Positive Integers ◽  
Mathematical Assessments

One of the greatest challenges in mathematics education is in fostering an understanding of what mathematicians would recognise as “mathematical thought.” We seek to encourage students to develop the transferable skills of abstraction, problem generalization and scalability as opposed to simply answering the specific question posed. This difference is perhaps best illustrated by the famous – but likely apocryphal – tale of Gauss’s school days and his approach to summing all positive integers up to and including 100, rather than just summing each sequentially. Especially with the rise of technology-enabled marking and results-focussed tutoring services, the onus is on the educator to develop new types of question which encourage and reward the development of mathematical processes and deprioritise results alone. Some initial work in this area is presented here.

scholarly journals The Effect of Realistic Mathematics Education on Sixth Grade Students’ Statistical Thinking

2021 ◽  
Vol 14 (1) ◽  
pp. 76-90
Author(s):  
Bedriye ALTAYLAR ◽  
Sibel KAZAK
Keyword(s):  
Mathematics Education ◽  
Sixth Grade ◽  
Control Group ◽  
Realistic Mathematics Education ◽  
Statistical Thinking ◽  
Mathematics Textbook ◽  
Realistic Mathematics ◽  
Sixth Grade Students ◽  
Quasi Experimental ◽  
Thinking Processes

Abstract: Purpose of the study is to investigate the effectiveness of the use of Realistic Mathematics Education (RME) approach on sixth grade students’ statistical thinking levels. Mooney’s (2002) statistical thinking framework describing four thinking levels across four different statistical thinking processes was used. This study utilized a quasi-experimental pretestposttest design. In the experimental group, the data handling unit was taught using RME approach whereas in the control group lessons were taught traditionally using a mathematics textbook and direct instruction. A statistical thinking test composed of seven open-ended questions was prepared and applied to both groups as pretest and posttest. The change of students’ statistical thinking levels in pretest and posttest were analyzed and compared in both groups as well as between groups. The data analysis showed that the overall growth at Level 4 across statistical thinking processes was higher for the students who were taught using the RME approach than for those taught traditionally.

scholarly journals Mathematics Education for Engineering Technology Students �?? A Bridge Too Far?

2013 ◽  
Vol 3 (S2) ◽  
pp. 33
Author(s):  
Noraishiyah Abdullah
Keyword(s):  
Mathematics Education ◽  
Engineering Technology ◽  
Apos Theory ◽  
Technology Students ◽  
The World ◽  
The Future ◽  
Life Curriculum ◽  
The Right

Trying to decide what is best suited for someone or something is an ever enduring task let alone trying to prepare students with the right engineering mind. So ‘how do you build an engineer?’ if that is the right word. What is the right ingredient? Mathematics has been said as the most important foundation in engineers’ life. Curriculum has been developed and reviewed over the years to meet this target. This work explores how much or lack of it has the curriculum prepares the future technologist to face the world of engineering technology as far as mathematics is concerned. Analysis of mathematics lectures, interviews of engineering technologist students and engineering technology subject lecturer is undertaken. Understand what each contributes help in understanding the picture that the current education is painting. Based on the theory of learning, APOS theory helps in explaining how students bridge their knowledge of mathematics when it comes to solving engineering technology problems. The question is, is it a bridge too far? 

Activities: Iterating Linear Functions—An Introduction to Dynamical Systems

1997 ◽  
Vol 90 (2) ◽  
pp. 122-136
Author(s):  
Jonathan Choate
Keyword(s):  
Mathematics Education ◽  
Dynamical Systems ◽  
Numerical Methods ◽  
Mathematics Curriculum ◽  
Secondary Mathematics ◽  
Linear Functions ◽  
Exponential Functions ◽  
Numerical Iteration ◽  
Symbolic Methods ◽  
And Mathematics

The arrival of computers has caused some major changes in both mathematics and mathematics education. One of the biggest shifts has been from an emphasis on symbolic methods to one on numerical methods. One field of mathematics, dynamical systems, requires considerable number crunching and is just coming into its own because we currently have the ability to perform extensive calculations easily. This article introduces students to this new field. The study of sequences created by using numerical iteration provides interesting new ways to approach many of the concepts central to the secondary mathematics curriculum, such as functions in general and linear and exponential functions in particular.

scholarly journals The Analysis of Pre-service Math Teachers’ Level of Understanding the Derivative Concept within the Context of APOS Theory

2018 ◽  
Vol 48 ◽  
pp. 01064
Author(s):  
Selin Urhan ◽  
Şenol Dost
Keyword(s):  
Mathematics Education ◽  
Geometric Dimension ◽  
Secondary Mathematics ◽  
Apos Theory ◽  
Secondary Mathematics Education ◽  
Math Teachers ◽  
University Mathematics ◽  
Education Community ◽  
Action Process ◽  
Level Of Understanding

APOS (Action-Process-Object-Schema) learning theory is the result of the studies of a mathematics education research group named Research in Undergraduate Mathematics Education Community (RUMEC), whose aim is to examine students’ level of comprehending university mathematics subjects. This study aimed to investigate how secondary mathematics education pre-service teachers in a public university structured the geometric dimension of the concept of derivative in their minds in the context of the components of the APOS theory. As data collection tools, questions developed by Çekmez [1] based on the genetic decomposition of Asiala, Dubinsky, Cottrill and Schwingendorf [2] for the geometric dimension of derivatives were used. The study revealed that secondary mathematics education pre-service teachers did not have the mental structures related to this topic and could not learn it at the desired level.

scholarly journals The Use of Realistic Mathematics Education (RME) to Help Indonesian 5th-Grade Students to Learn Multiplication and Division

2020 ◽  
Vol 10 (1) ◽  
pp. 41-53
Author(s):  
Nanang Setiadi
Keyword(s):  
Mathematics Education ◽  
Learning Process ◽  
Mathematics Teaching ◽  
Realistic Mathematics Education ◽  
Realistic Mathematics ◽  
Alternative Approach ◽  
Mathematical Problems ◽  
Teaching Learning ◽  
Mastery Criteria ◽  
5Th Grade

Abstract                                                              This paper discusses the use of Realistic Mathematics Education (RME) as an alternative approach to enhance Indonesian 5th-grade students’ ability in multiplication and division. It presents the analysis of Indonesian 5th-grade students’ difficulties in applying stacking method for multiplication and division. Furthermore, it describes a mathematics teaching learning practice to stimulate students constructing their strategies, mathematical models and number sense in solving mathematical problems that involve multiplication and division. The teaching learning practice aims to apply RME for helping students develop their multiplication and division ability.Findings shows that stacking methods for multiplication and division are difficult for the students. The main students’ problem in multiplication and division stacking methods is in reapplying the steps of the methods. The steps taken to improve the learning process by implementing RME are: (1) analyze in detail the difficulties of students in multiplication and division stacking methods, (2) provide contexts of mathematical problems that can stimulate students to think mathematically, (3) hold a class mathematics congress, and (4) conduct a test to measure students’ achievement.            Based on the students’ achievement, there has been several improvements. After RME, there were more students whose grades passed the Minimum Mastery Criteria. Moreover, there was a student who got 100. Then, the average test was higher. Meanwhile, there were only 3 children whose grades were 0. Thus, the application of RME has helped the 5th-grade students to improve their ability in multiplication and division.         

scholarly journals Realistic mathematics education: Mathematical reasoning and communication skills in rural contexts

2021 ◽  
Vol 10 (2) ◽  
pp. 522
Author(s):  
Anderson Leonardo Palinussa ◽  
Juliana Selvina Molle ◽  
Magy Gaspersz
Keyword(s):  
Mathematics Education ◽  
Communication Skills ◽  
Mathematical Reasoning ◽  
Mathematics Learning ◽  
Realistic Mathematics Education ◽  
Realistic Mathematics ◽  
Mathematical Problems ◽  
Geographical Position ◽  
Rural Context

Mathematics learning has always been a problem in the world of education in Indonesia especially in the Province of Maluku, which is a thousand island area. The geographical position of Maluku, which is an area of the archipelago, is quite extensive, affecting the quality of students in mathematics. One approach that is recommended to overcome mathematical problems of rural island-based students is realistic mathematics education (RME). The purpose of this study was to analyze the effect of RME on mathematical reasoning and communication skills in a rural context. The research design used was quasi experiment. The sample size was 130 students from several junior high schools in Central Maluku Regency. The instrument developed was in the form of problem descriptions to measure students' mathematical reasoning and communication skills. The findings prove that RME has a significant influence on students' mathematical reasoning and communication skills. Thus, RME can be recommended in improving students' mathematical reasoning and communication skills in the island-based rural context.

scholarly journals E-Learning of Mathematics- A New Trend of Learning in 21st Century During Covid-19 Pandemic

2021 ◽  
Vol 9 (12) ◽  
pp. 736-739
Author(s):  
Reenu Kumari
Keyword(s):  
Mathematics Education ◽  
Problem Solving ◽  
Teaching And Learning ◽  
Qualitative Methodology ◽  
Mathematics Learning ◽  
Mathematical Activity ◽  
Online Mode ◽  
Mathematical Problems ◽  
Private And Public ◽  
E Learning

Abstract: The goal of this study is to highlight current breakthroughs in digital technology research in the subject of mathematics education. The Covid-19 outbreak in 2020 turned both private and public life on its head. Higher education institutions all across the world were forced to switch their teaching and learning online on very short notice. As a result, many types of software like Google Meet, MS teams, Zoom and WebEx, etc. have been developed to help teachers and students communicate more effectively. Problem-solving is a characteristic of mathematical activity and an essential component of the development of mathematical and analytical skills. The capacity to answer a broad variety of complicated mathematical problems is a major goal of mathematics education and learning. However, the process of problem-solving in online mode has not received the attention it deserves, because many professors are uncomfortable with it. As a result, problemsolving as a method and skill is not taught as an intrinsic component of the mathematics learning process by instructors. Qualitative methodology is a technique used for this study. The purpose of this study is to reveal the roles and significance of mathematics teaching and learning via the use of technology applications (E-learning). Keywords: Mathematics, COVID-19, E-learning, Education

scholarly journals Thinking Process of Concrete Student in Solving Two-Dimensional Problems

2020 ◽  
Vol 14 (2) ◽  
pp. 117-128
Author(s):  
Sri Adi Widodo ◽  
Ambar Dana Pangesti ◽  
Istiqomah Istiqomah ◽  
Krida Singgih Kuncoro ◽  
Tri Astuti Arigiyati
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Two Dimensional ◽  
Research Subjects ◽  
Student Work ◽  
Logical Operations ◽  
Mathematical Problems ◽  
Thinking Process ◽  
Thinking Processes

The purpose of this research was to find out the thinking processes of a concrete student in solving two-dimensional problems. The research method used is descriptive qualitative. The research subjects were two students taken using purposive sampling. The instrument used was the Test of Logical Operations and problem-solving tests. Stages of data analysis used are researching all data, making a cognitive classification of students, choosing concrete students to be used as research subjects, reviewing the results of concrete student work in solving mathematical problems, verify data and data sources that have been classified and transcribed in the presentation or exposure of data. The results showed that at the stage of understanding the problem and re-checking the answers, concrete students use the assimilation at the stage of planning to solve the problem of doing the disequilibration. At the stage of carrying out a plan to solve a problem, concrete students carry out the accommodation. During this study, it was found that students 'habits in mathematical problem-solving did not plan to solve problems, did not re-examine answers, and there were students' habits by interpreting the final results of problems. It can be concluded that the students' concrete thinking processes in solving two-dimensional problems vary according to the stages of problem-solving.

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