scholarly journals A New Model of Mathematics Education: Flat Curriculum with Self-Contained Micro Topics

Philosophies ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 76
Author(s):  
Miklós Hoffmann ◽  
Attila Egri-Nagy
Keyword(s):  
Mathematics Education ◽  
Teaching Methods ◽  
Mathematics Anxiety ◽  
Mathematical Knowledge ◽  
Teaching Mathematics ◽  
Hierarchical Relationship ◽  
Learning Mathematics ◽  
Entry Points ◽  
Recent Developments ◽  
Monolithic Structure

The traditional way of presenting mathematical knowledge is logical deduction, which implies a monolithic structure with topics in a strict hierarchical relationship. Despite many recent developments and methodical inventions in mathematics education, many curricula are still close in spirit to this hierarchical structure. However, this organisation of mathematical ideas may not be the most conducive way for learning mathematics. In this paper, we suggest that flattening curricula by developing self-contained micro topics and by providing multiple entry points to knowledge by making the dependency graph of notions and subfields as sparse as possible could improve the effectiveness of teaching mathematics. We argue that a less strictly hierarchical schedule in mathematics education can decrease mathematics anxiety and can prevent students from ‘losing the thread’ somewhere in the process. This proposal implies a radical re-evaluation of standard teaching methods. As such, it parallels philosophical deconstruction. We provide two examples of how the micro topics can be implemented and consider some possible criticisms of the method. A full-scale and instantaneous change in curricula is neither feasible nor desirable. Here, we aim to change the prevalent attitude of educators by starting a conversation about the flat curriculum alternative.

Do the Standards Go Far Enough? Power, Policy, and Practice in Mathematics Education

1992 ◽  
Vol 23 (5) ◽  
pp. 412-431 ◽  
Author(s):  
Michael W. Apple
Keyword(s):  
Mathematics Education ◽  
Educational Reform ◽  
Mathematical Knowledge ◽  
Mathematics Curriculum ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Policy And Practice ◽  
Conservative Movement ◽  
Evaluation Standards

Although NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) are generating considerable interest, there has been little discussion of their ideological and social grounding and effects. By placing the Standards within the growing conservative movement in education, this paper raises a number of crucial issues about the documents, including the depth of the financial crisis in education and its economic and ideological genesis and results; the nature of inequality in schools; the role of mathematical knowledge in our economy in maintaining these inequalities; the possibilities and limitations of a mathematics curriculum that is more grounded in students' experiences; and the complicated realities of teachers' lives. Without a deeper understanding of these issues, the Standards will be used in ways that largely lend support only to the conservative agenda for educational reform.

scholarly journals UPDATING MATHEMATICAL KNOWLEDGE WHEN SOLVING PROBLEMS

2020 ◽  
Vol 70 (2) ◽  
pp. 90-96
Author(s):  
U.A. Kosybayeva ◽  
◽  
N.K Shamataeva ◽  
A.K Tleubergen ◽  
◽  
...  
Keyword(s):  
Secondary Schools ◽  
General Education ◽  
Teaching Methods ◽  
Mathematics Teaching ◽  
Mathematical Knowledge ◽  
Heuristic Method ◽  
Teaching Mathematics ◽  
Teaching Tools ◽  
Article Analyse

The article deals with the issue of improving the methodology of teaching mathematics using new teaching methods in General education schools in the conditions of updated education. The authors characterize the implementation of the principles of didactics through teaching tools and their functions used in teaching mathematics in modern secondary schools. Among these methods, for example, the heuristic method analyzes several tasks from pages of school textbooks as an example and demonstrates learning results achieved in the same way. Using these examples, it is important for the student to analyze the problem depending on the topic of each lesson. In addition, the authors of this article analyse some peculiarities of mathematics teaching.

scholarly journals Online Learning during Covid-19: What is the Most Effective Platform for Teaching and Learning Mathematics?

2021 ◽  
Vol 4 (1) ◽  
pp. 166-178
Author(s):  
Mela Aziza
Keyword(s):  
Online Learning ◽  
Teaching Methods ◽  
Teaching And Learning ◽  
Teaching Mathematics ◽  
Islamic State ◽  
Online Questionnaire ◽  
State Institute ◽  
Strong Signal ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

The purpose of this research was to find how the first online learning implementation in the Department of Mathematics Education in The Islamic State Institute of Bengkulu during the Covid-19 pandemic. This research was qualitative research which was conducted in July as an evaluation of the first online learning from March until July. 90 students were chosen by purposive sampling and then given an online questionnaire. The results showed that there were some mathematical courses students took in the Even Semester 2019/2020. The platforms used by lecturers while teaching Mathematics were 39.6% WhatsApp Group, 22% Google Classroom, 13.2% Cisco Webex, and 25.2 % others. Platforms that were felt effective as online learning applications were 52.7% Cisco Webex, 26.4 % WhatsApp Group, 9.9% Zoom meeting, 5.5% Google Classroom, and 5.5% others. This is felt to be effective because it does not consume a lot of data packages, has a strong signal, and can be accessed at any time (WhatsApp Group and Google Classroom). In addition, this platform can be used for live conferencing / video calls using whiteboards which are deemed effective for teaching math material (Cisco Webex). However, several obstacles were found during the implementation of online learning, namely difficulties in obtaining sufficient internet data packages; limited network; difficult assignments and assessments; less effective teaching methods; and use of multiple applications.

scholarly journals TEORI KOGNITIF BRUNER DALAM PEMBELAJARAN MATEMATIKA

2021 ◽  
Vol 5 (2) ◽  
pp. 87
Author(s):  
Ahmad Hatip ◽  
Windi Setiawan
Keyword(s):  
Learning Theory ◽  
Mathematics Teachers ◽  
Mathematical Knowledge ◽  
Cognitive Theory ◽  
Mathematics Learning ◽  
Cognitive Learning ◽  
Teaching Mathematics ◽  
Learning Mathematics ◽  
Cognitive Learning Theory

ABSTRAK Artikel ini menganalisis bagaimana mengaplikasikan teori kognitif Bruner dalam pengajaran matematika berdasar teori pembelajaran penemuan. Melalui analisis pembelajaran kasus matematika, tujuan dari pengajaran matematika adalah untuk memungkinkan siswa menguasai struktur pengetahuan matematika secara komprehensif. Guru matematika harus aktif menciptakan kondisi dalam mengajar, dan membimbing siswa untuk menemukan dan belajar aktivitas langsung, pemikiran dan representasi. Dari akuisisi pasif pengetahuan menjadi penemuan aktif mandiri, sehingga siswa menjadi objek utama belajar matematika. Kata kunci : Kognitif Bruner,  Teori Belajar, Pembelajaran Matematika ABSTRACT This article analyzes how to apply Bruner's cognitive theory of discovery in teaching based on learning theory. Through the analysis of mathematics case learning, the aim of teaching mathematics is to help students master mathematical knowledge comprehensively. Mathematics teachers must actively create conditions in teaching, and guide students to discover and learn direct activity, thinking and representation. From the acquisition of knowledge to independent active discovery, so that students become the main object of learning mathematics. Keywords : Bruner's Cognitive, Learning Theory, Mathematics Learning

scholarly journals Empowering the Disadvantaged Students in Mathematics Education: Relevance of Social Justice, Equity and Mainstreaming

2019 ◽  
Vol 29 ◽  
pp. 132-145
Author(s):  
Bed Prasad Dhakal
Keyword(s):  
Mathematics Education ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Phenomenological Study ◽  
Mathematics Classroom ◽  
Secondary Level ◽  
Learning Mathematics ◽  
Contextualized Teaching And Learning ◽  
And Mathematics ◽  
Mind Set

Mathematical knowledge is indubitable in various sectors, but diversity in culture and tradition in society causes inequality, injustice and backwardness among the students learning mathematics. Study of cultural heritage, customs, behavior in mathematics education is the demand of post-modern paradigm. Efforts of self-organization and co-construction in the initiation of students and teachers through their active participation, interaction and mathematics classroom discourses could be instrumental towards the generation of mathematical knowledge in classroom – which can support to reduce the western domination in mathematics education; and societal negative mind-set about mathematics education will also be minimized in this way. Ethno-mathematics, diversified mathematical strategies, culturally responsive mathematics classroom and enhancing equity in learning mathematics are the major dimensions that mathematics professionals need to exercise for the effective, reflective and contextualized teaching and learning of mathematics. This is a phenomenological study conducted among secondary level mathematics teachers. Using written interview and informal sharing of participants’ experiences towards teaching and learning mathematics, three major themes were developed and discussed. This article primarily shows that there exists the intertwined relation among these themes; and it is essential to properly address these themes for more effective learning of mathematics in the context of Nepalese secondary level classrooms.

scholarly journals How To Learn To Understand Mathematics?

2017 ◽  
Vol 10 (2) ◽  
pp. 114
Author(s):  
Raymond Duval
Keyword(s):  
Mathematics Education ◽  
Cognitive Factors ◽  
Mathematical Tasks ◽  
Education For All ◽  
Teaching Mathematics ◽  
Mathematical Activity ◽  
Crucial Issue ◽  
Semiotic Representations ◽  
Learning Mathematics ◽  
Insight Into

The cognitive core process of mathematical activity is the recognition of a same object in two semiotic representations whose respective contents have nothing in common with each other. It is also the recurrent and insuperable difficulty of comprehension in learning mathematics and the main impediment to solving problems for most students. The theory of registers provides a cognitive analysis of the way of working and thinking in mathematics. It highlights the key cognitive factors to be taken into account in Mathematics Education for all students up to the age of 16. To give an insight into the theory this paper focuses on two topics. How to introduce letters and elementary algebra? How to learn to solve problems in mathematics? And to avoid the confusion of words arising in Mathematics Education whenever we talk about « theories », we shallshow how to analyze in terms of registers the mathematical tasks related to these two topics. This allow us to identify the cognitive thresholds to be crossed to understand and to solve problems in mathematics. Analyzing mathematical activity in terms of registers is quite different from the prevailing mathematical view. This concerns the hidden face of mathematical activity and not its exposed face. We are broaching here the crucial issue about teaching mathematics to all students up to the age of 16. What should be its objectives and priority areas?Keywords: Register. Transformation of Semiotic Representation. Conversion. Treatment. Discursive operation.

scholarly journals MATHEMATICAL CHARACTERISTICS OF THE CHILDREN THAT SHOWN ABOVE/BELOW AVERAGE SUCCESS AT THE MATHEMATICAL EDUCATION

2019 ◽  
Vol 9 (1) ◽  
pp. 88-98
Author(s):  
Sead Rešić ◽  
◽  
Edisa Korda ◽  
Ahmed Palić ◽  
Maid Omerović ◽  
...  
Keyword(s):  
Mathematics Anxiety ◽  
Self Esteem ◽  
Situational Interest ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
Learning Mathematics ◽  
Motivation For Learning ◽  
Fourth Grade Students ◽  
Descriptive Method ◽  
Mathematical Characteristics

In this study, we analyzed the emotional and conative characteristics of fourth grade students of elementary school as follows: motivation for learning math, situational interest in learning mathematics during teaching, mathematics anxiety, self-esteem in relation to academic achievement and attributions of success and failure in mathematics. In a sample of 200 students and 20 teachers were analyzed emotional and conative characteristics capable of above-average and below average in math-age students. The study used the descriptive method, a questionnaire and a test. The research results are presented graphically and in tabular form with an explanation and discussion. In the conclusion are set the directions which should further improve this insufficiently studied area.

scholarly journals Understanding and Organizing Mathematics Education as a Design Science–Origins and New Developments

2020 ◽  
pp. 265-285
Author(s):  
Erich Christian Wittmann
Keyword(s):  
Mathematics Education ◽  
Teaching And Learning ◽  
Design Science ◽  
List Type ◽  
Developmental Research ◽  
New Developments ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Recent Developments ◽  
Natural Foundation

AbstractThe objective of this paper is to revisit briefly the conception of mathematics education as a design science as it has been evolving alongside the developmental research in the project Mathe 2000 from 1987 to 2012 to report in some detail on recent developments, as concerns both conceptual and practical issues. The paper is a plea for appreciating and (re-)installing “well-understood mathematics” as the natural foundation for teaching and learning mathematics.

scholarly journals The constructive methods of teaching mathematics

2021 ◽  
Vol 47 ◽  
Author(s):  
Eglė Jasutienė
Keyword(s):  
Teaching Methods ◽  
Teaching And Learning ◽  
Mathematics Curriculum ◽  
Teaching Mathematics ◽  
Geometer's Sketchpad ◽  
Constructive Methods ◽  
Teaching Mathematic ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Mathematics Teaching Methods

The problem of teaching mathematics in Lithuanian schools envisaged in this article. The teachers often use the teaching methods of behaviourism. The widely used teachingmethods of constructivionism in the world are appearing in Lithuanian schools too. There is talked how mathematics teachers can easier start to use new progressivemethods by using IT in this article. There is reviewing how start to use constructive mathematics teaching methods by using Geometer’s Sketchpad in this article. There was appeared some problems for teachers by using Geometer’s Sketchpad in schools. So these problems help to find new step of investigating Geometer’s Sketchpad in teaching mathematics – to built the various sets of dynamic sketches for teaching and learning mathematics in basic schools. More than 800 dynamic sketches have been developed within 9th and 10th grades mathematics curriculum. Now is preparing set of sketches for 11th and 12th grades. Some constructive methods of teaching mathematic by using these sets of sketches are discussed in this article.The methods of comparative analyze and of synthesis of scientificworks are used in this article.

scholarly journals Teaching mathematics to Business and Enterprise students in a module based around Excel

2016 ◽  
Vol 15 (1) ◽  
pp. 22
Author(s):  
Claire Cornock
Keyword(s):  
Data Analysis ◽  
Teaching Methods ◽  
Classroom Environment ◽  
Mathematics Anxiety ◽  
Teaching Mathematics ◽  
Financial Mathematics ◽  
Information Analysis ◽  
Video Tutorials ◽  
Short Video

Within this paper, a case study of a mathematics module ‘Information Analysis’ for Business and Enterprise students will be presented. The assessment for the module consists of four coursework assignments that are all done within Excel. The content of the module, which includes financial mathematics and data analysis, was carefully selected to be relevant and useful to the students further on in their degree and beyond. The module is based around the development of skills such as IT and communication. The students are required to pay attention to how they use Excel, how they present their work and their explanations. Comments from students are generally positive about the opportunity to develop skills within the module and they recognise the benefits surrounding employability. In addition to lectures and computer tutorials, the students have access to a collection of short video tutorials which contain examples of the Excel techniques. In this case study, the challenges of teaching this module will be explored, including teaching students with different abilities, the limitations of the classroom environment and the problem of mathematics anxiety. Details of the content of the module will be provided along with descriptions of the assessment methods and the teaching methods. 

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