Negative Instances and Mathematical Concept Formation: A Preliminary Study

1971 ◽  
Vol 2 (3) ◽  
pp. 218-227
Author(s):  
Richard J. Shumway
Keyword(s):  
Mathematics Achievement ◽  
Concept Formation ◽  
Inductive Reasoning ◽  
Mathematical Concept ◽  
Syllogistic Reasoning ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Common Error ◽  
The Common ◽  
Preliminary Study

Are there measurable differences in general mathematics achievement, inductive reasoning, syllogistic reasoning, perceptual speed, and tendency to overgeneralize between groups learning mathematical concepts through the use of positive instances (C groups), and groups learning mathematical concepts through the use of both positive and negative instances (E groups)? 84 eighth grade mathematics students in 4 classes served as subjects for 65 days. Analysis of variance and covariance of pre- and posttest means yielded significant differences (p<.05) indicating that the E groups tended to overgeneralize less frequently than the C groups. No other differences in means were significant (p<.05). It appears that the use of negative instances may be a means for controlling the common error of overgeneralization.

The Effect of User Experience on Designing Interactive Tool: A Case Study of Learning Images Compression

2021 ◽  
Vol 9 (10) ◽  
pp. 1312-1320
Keyword(s):  
User Experience ◽  
Real Life ◽  
Mathematical Concept ◽  
Design Principles ◽  
Mathematical Explanation ◽  
Mathematical Concepts ◽  
Learning Platform ◽  
Learning Mathematics ◽  
The Common ◽  
Value Decomposition

Technology has significantly emerged in various fields, including healthcare, government, and education. In the education field, students of all ages and backgrounds turn to modern technologies for learning instead of traditional methods, especially under challenging courses such as mathematics. However, students face many problems in understanding mathematical concepts and understanding how to benefit from them in real-life. Therefore, it can be challenging to design scientific materials suitable for learning mathematics and clarifying their applications in life that meet the students’ preferences. To solve this issue, we designed and developed an interactive platform based on user experience to learn an advanced concept in the idea of linear algebra called Singular Value Decomposition (SVD) and its applicability in image compression. The proposed platform considered the common design principles to map between the provider in terms of clear mathematical explanation and the receiver in terms of matching good user experience. Twenty participants between the ages of 16 and 30 tested the proposed platform. The results showed that learning using it gives better results than learning traditionally in terms of the number of correct and incorrect actions, effectiveness, efficiency, and safety factors. Consequently, we can say that designing an interactive learning platform to explain an advanced mathematical concept and clarify its applications in real-life is preferable by considering and following the common design principles.

scholarly journals PENERAPAN METODE PENEMUAN TERBIMBING DALAM UPAYA MENINGKATKAN KEMAMPUAN PEMAHAMAN KONSEP MATEMATIKA DI KELAS VIII SMP NEGERI 1 AJIBATA

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Mariani . Manik ◽  
Mukhtar . .
Keyword(s):  
Mathematical Concept ◽  
Learning Activity ◽  
Average Score ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Guided Discovery ◽  
Class Viii ◽  
Level Of Understanding ◽  
High Level ◽  
Discovery Method

ABSTRAK Penelitian ini bertujuan untuk mengetahui peningkatan kemampuan pemahaman konsep matematika siswa di kelas VIII SMP Negeri 1 Ajibata setelah diterapkan metode Penemuan Terbimbing dan mengetahui aktivitas belajar siswa  ketika diterapkan metode Penemuan Terbimbing. Penelitian ini adalah penelitian tindakan kelas yang dilaksanakan dalam 2 siklus yang masing-masing siklus dilaksanakan dalam 2 kali pertemuan. Subjek dalam penelitian ini adalah siswa kelas VIII-A yang berjumlah 30 orang. Objek dalam penelitian ini adalah upaya meningkatkan kemampuan pemahaman konsep matematika siswa pada materi Prisma dan Limas. Data diperoleh dari tes pemahaman konsep matematika siswa pada akhir setiap siklus dan lembar observasi untuk setiap kali pertemuan. Hasil penelitian menunjukkan bahwa kemampuan Pemahaman konsep matematika siswa mengalami peningkatan. Ini dapat dilihat dari nilai rata-rata pemahaman konsep matematika siswa pada tes awal yaitu 58,83 dengan tingkat pemahaman rendah. Secara klasikal dari 30 siswa hanya 2 siswa (6,67%) yang mencapai peningkatan kemampuan pemahaman konsep (mencapai nilai  75). Setelah pelaksanaan tindakan pada siklus I, nilai rata-rata pemahaman konsep matematika siswa meningkat menjadi 70,91 dengan tingkat pemahaman sedang dan jumlah siswa yang mencapai peningkatan sebanyak 14 siswa (46,67%). Selanjutnya setelah pelaksanaan tindakan pada siklus II, nilai rata-rata pemahaman konsep matematika siswa meningkat menjadi 81,91 dengan tingkat pemahaman tinggi dan sebanyak 26 siswa (86,67%) mencapai peningkatan, serta telah mencapai indicator keberhasilan penelitian. Berdasarkan hasil penelitian dapat disimpulkan bahwa metode Penemuan Terbimbing dapat meningkatkan kemampuan pemahaman konsep matematika siswa pada materi Prisma dan Limas.Kata Kunci   : Kemampuan Pemahaman Konsep, Metode Penemuan Terbimbing, Prisma dan Limas.ABSTRACT This study aims to determine the improvement of the ability to understand the concepts of mathematics students in class VIII SMP Negeri 1 Ajibata after applied Guided Discovery method and to know the student's learning activity  when applied method of Guided Discovery. This study is a classroom action research conducted in 2 cycles, each cycle is held in 2 meetings. Subjects in this study were students of class VIII-A  which amounted to 30 people. Objects in this research is an effort to improve the ability of students' understanding of mathematical concepts on Prism and Limas material in class VIII-A SMP Negeri 1 Ajibata academic year 2016/2017. The data were obtained from a comprehension test of students' mathematical concepts at the end of each cycle and an observation sheet for each meeting. The results showed that the ability to understand the concept of mathematics students have increased. This can be seen from the average score of understanding of mathematical concepts of students on the initial test that is 58.83 with low understanding level. Classically of 30 students only 2 students (6.67%) who achieved improvement of concept comprehension ability (reaching value ≥75). After the implementation of the action on the first cycle, the average score of students' mathematical concepts comprehension increased to 70.91 with a moderate level of understanding and the number of students who achieved an increase of 14 students (46.67%). Furthermore, after the implementation of the action in cycle II, the average score of understanding of mathematical concepts of students increased to 81.91 with a high level of understanding and as many as 26 students (86.67%) achieved improvement, and has achieved the indicator of research success. Based on the result of the research, it can be concluded that Guided Discovery method can improve students' mathematical concept comprehension on Prism and Limas materialKeywords: Ability to Understand Concepts, Guided Discovery Methods, Prisms and Limas. 

Mathematics and Cognition

2017 ◽  
Author(s):  
Roi Wagner
Keyword(s):  
Mental Representation ◽  
Concept Formation ◽  
Cognitive Theory ◽  
History Of Mathematics ◽  
Mathematical Practice ◽  
Mathematical Concept ◽  
Mathematical Cognition ◽  
Mathematical Concepts ◽  
Cognitive Theories ◽  
History Of

This chapter introduces the notion of embodied mathematical cognition by reviewing some neuro-cognitive theories of mathematical concept formation. It first considers the neuro-cognitive debate on the mental representation of numbers, focusing on Stanislas Dehaene's notion of “number sense” and Vincent Walsh's ATOM (acronym for a theory of magnitude), before presenting the cognitive theory of mathematical metaphor and relating it to Water J. Freeman III's theory of meaning. It also examines Gilles Deleuze's Logic of Sensation in the context of mathematical practice, the link between the history of mathematics and neuro-cognition through an analysis of theories that explicitly engage the formation of higher mathematical concepts, and some challenges to the theory of mathematical metaphors.

scholarly journals PERBEDAAN KEMAMPUAN PEMAHAMAN KONSEP MATEMATIKA SISWA DENGAN MODEL PEMBELAJARAN KONTEKSTUAL DAN MODEL PEMBELAJARAN INVESTIGASI KELOMPOK KELAS VIII SMP NEGERI 1 PANCUR BATU

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
Arif . Hidayat ◽  
Humuntal . Banjarnahor
Keyword(s):  
Mathematical Concept ◽  
Learning Model ◽  
Contextual Learning ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Purposive Sampling ◽  
Average Value ◽  
Class 1 ◽  
Class Viii ◽  
Better Than

ABSTRAKPenelitian ini bertujuan untuk melihat bahwa kemampuan pemahaman konsep matematika siswa menggunakan model pembelajaran kontekstual (CTL) lebih baik daripada menggunakan model pembelajaran investigasi kelompok (Group Investigation) di kelas VIII SMP Negeri Pancur Batu. Jenis penelitian ini adalah eksperimen semu. Populasi dalam penelitian ini adalah seluruh kelas VIII SMP Negeri 1 Pancur Batu yang terdiri dari 7 kelas. Pengambilan sampel dilakukan dengan menggunakan purposive sampling dan diambil kelas VIII-6 sebagai kelas eksperimen 1 dengan 34 siswa, serta kelas VIII-7 sebagai kelas eksperimen 2 dengan 32 siswa. Penelitian ini menggunakan intrumen berbentuk uraian yaitu posttest yang digunakan untuk mengetahui kemampuan pemahaman konsep matematika siswa. Dari hasil penelitian setelah diberikan perlakuan berbeda yaitu kelas eksperimen 1 menggunakan model pembelajaran kontekstual (CTL) dan kelas eksperimen 2 menggunakan model pembelajaran investigasi kelompok (Group Investigation) diperoleh nilai rata-rata 77,171 untuk kelas eksperimen 1 dan 70,685 untuk kelas eksperimen 2. Hasil uji hipotesis memberikan nilai thitung = 1,734252 dan ttabel = 1,6693 dengan dk = 64 dan taraf signifikan  = 0,05 sehingga terlihat yang berarti bahwa Ho ditolak dan Ha diterima. Sehingga disimpulkan bahwa kemampuan pemahaman konsep matematika siswa yang diajar menggunakan model pembelajaran kontekstual (CTL) lebih tinggi daripada kemampuan pemahaman konsep matematika siswa yang diajar menggunakan model pembelajaran Investigasi Kelompok (Group Investigation).Kata Kunci : Pemahaman Konsep Matematika Siswa, Model Pembelajaran Konteskstual (CTL), Model Pembelajaran Investigasi Kelompok.ABSTRACT This study aims to see that the ability to understand students' mathematical concepts using contextual learning model (CTL) is better than using Group Investigation model in Grade VIII SMP Negeri Pancur Batu. This type of research is a quasi experiment. The population in this study is the entire class VIII SMP Negeri 1 Pancur Batu which consists of 7 classes. Sampling was done by using purposive sampling and taken class VIII-6 as experiment class 1 with 34 students, and class VIII-7 as experiment class 2 with 32 students. This study uses the intrument in the form of a description of posttest used to determine the ability to understand the concept of mathematics students. From the result of the research after being given different treatment that is experiment class 1 using contextual learning model (CTL) and experimental class 2 using Group Investigation study model obtained the average value 77,171 for experiment class 1 and 70,685 for experiment class 2. Test result Hypothesis gives tcount = 1,734252 and ttable = 1,6693 with dk = 64 and significant level a = 0.05 so it looks t_hitung (1.734252)> t_tabel (1,6693) which means that Ho is rejected and Ha accepted. It is concluded that the students' understanding of mathematical concepts taught using contextual learning model (CTL) is higher than the ability to comprehend the concepts of mathematics students taught using Group Investigation model. Keywords: Understanding Mathematical Concept, Contextual Learning Model (CTL), Model of Group Investigation Learning.

Note on Suppes' "Mathematical concept formation."

1967 ◽  
Vol 22 (5) ◽  
pp. 400-401 ◽  
Author(s):  
Lawrence T. Frase
Keyword(s):  
Concept Formation ◽  
Mathematical Concept

scholarly journals Is There a Place for Theoretical Frameworks in Qualitative Research?

2021 ◽  
Vol 20 ◽  
pp. 160940692098795
Author(s):  
Casey M. Garvey ◽  
Rachel Jones
Keyword(s):  
Qualitative Research ◽  
Conceptual Understanding ◽  
Inductive Reasoning ◽  
Theoretical Framework ◽  
Theoretical Frameworks ◽  
Common Sense Model ◽  
Rich Description ◽  
The Common ◽  
The Rich ◽  
Qualitative Analyses

Qualitative research proceeds from the position that there is no one observable reality. Researchers utilizing qualitative methods build findings inductively, from raw data to a conceptual understanding. Theoretical frameworks may be utilized to guide qualitative analyses by suggesting concepts and relationships to explore. The framework may provide a sense of the story emerging from the analyses. And concurrently, the rich description provided by the analyses may allow the framework to be more deeply appreciated. However, there is a risk that using a theoretical framework may stifle inductive reasoning or result in findings incongruent to the data. The following is a discussion of the application of a theoretical framework in a qualitative study. This study, guided by the Common-Sense Model, explores the choice to undergo treatment for Hepatitis C Virus among veterans. Examples from the analyses are provided to facilitate discussion on the utilization of a theoretical framework. Techniques to optimize the use of a theoretical framework, as well as mitigate risks of such use, are presented. When utilized alongside rigorous data analyses and introspection, a theoretical framework may serve as a valuable tool to navigate data in qualitative research.

Borges on Replication and Concept Formation

2017 ◽  
Author(s):  
Yemima Ben-Menahem
Keyword(s):  
Philosophy Of Mind ◽  
Philosophy Of Language ◽  
Concept Formation ◽  
Jorge Luis Borges ◽  
Ancient Greece ◽  
Broad Sense ◽  
Common Theme ◽  
Contemporary Philosophy ◽  
Complex Picture ◽  
The Common

This chapter examines three stories by Jorge Luis Borges: “Funes: His Memory,” “Averroës's Search,” and “Pierre Menard, Author of the Quixote.” Each of these highlights the intricate nature of concepts and replication in the broad sense. The common theme running through these three stories is the word–world relation and the problems this relation generates. In each story, Borges explores one aspect of the process of conceptualization, an endeavor that has engaged philosophers ever since ancient Greece and is still at the center of contemporary philosophy of language and philosophy of mind. Together, Borges's stories present a complex picture of concepts and processes of conceptualization.

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