scholarly journals Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2257
Author(s):  
Janka Medová ◽  
Kristína Ovary Bulková ◽  
Soňa Čeretková
Keyword(s):  
Teaching And Learning ◽  
Combinatorial Problem ◽  
Secondary Mathematics ◽  
Complex Problem ◽  
Algebraic Thinking ◽  
Special Focus ◽  
Secondary Mathematics Education ◽  
Algebraic Generalization ◽  
Upper Secondary ◽  
Mathematical Problems

Algebraic thinking, combinatorial thinking and reasoning skills are considered as playing central roles within teaching and learning in the field of mathematics, particularly in solving complex open-ended mathematical problems Specific relations between these three abilities, manifested in the solving of an open-ended ill-structured problem aimed at mathematical modeling, were investigated. We analyzed solutions received from 33 groups totaling 131 students, who solved a complex assignment within the mathematical contest Mathematics B-day 2018. Such relations were more obvious when solving a complex problem, compared to more structured closed subtasks. Algebraic generalization is an important prerequisite to prove mathematically and to solve combinatorial problem at higher levels, i.e., using expressions and formulas, therefore a special focus should be put on this ability in upper-secondary mathematics education.

scholarly journals Uses of Technology in Upper Secondary Mathematics Education

2017 ◽  
Author(s):  
Stephen Hegedus ◽  
Colette Laborde ◽  
Corey Brady ◽  
Sara Dalton ◽  
Hans-Stefan Siller ◽  
...  
Keyword(s):  
Mathematics Education ◽  
Secondary Mathematics ◽  
Secondary Mathematics Education ◽  
Upper Secondary

scholarly journals Uses of Technology in Upper Secondary Mathematics Education

2016 ◽  
pp. 1-36 ◽  
Author(s):  
Stephen Hegedus ◽  
Colette Laborde ◽  
Corey Brady ◽  
Sara Dalton ◽  
Hans-Stefan Siller ◽  
...  
Keyword(s):  
Mathematics Education ◽  
Secondary Mathematics ◽  
Secondary Mathematics Education ◽  
Upper Secondary

scholarly journals Analyzing the Teaching and Learning of Mathematical Reasoning Skills in Secondary School

2017 ◽  
Vol 13 (12) ◽  
pp. 167 ◽  
Author(s):  
E. Elvis Napitupulu
Keyword(s):  
Public Schools ◽  
Secondary School ◽  
Secondary Students ◽  
Teaching And Learning ◽  
Mathematical Reasoning ◽  
Upper Secondary ◽  
Teachers And Students ◽  
Mathematical Problems ◽  
Reasoning Skills ◽  
D Model

The paper reports part of a study aimed at developing teaching materials in inculcating upper secondary students’ mathematical reasoning skills (MRS). To develop the materials, the researcher implemented the Four-D Model. The study took subjects from five public schools in Province of North Sumatera, Indonesia. The researcher designed and developed students’ work sheet (SWS) and instrument to measure MRS. Along the teaching ran, which applied problem-based learning model, the researcher observed teachers’ and students’ activities while nurturing and applying MRS in the frame of solving mathematical problems. Of the four indicators laid to measure the MRS, students lack most in use of pattern relationship to analyse situation, to make analogy, or to generalize. The ways support student’s progress in achieving MRS are if (i) the problem faced is much mimicked the task solved in the classroom, (ii) more various problems given to solve under guidance, and (iii) intensive scaffolding is given.

scholarly journals Frame shifting as a challenge to integrating computational thinking in secondary mathematics education

2020 ◽  
Author(s):  
Wendy Huang
Keyword(s):  
Teaching And Learning ◽  
Computational Thinking ◽  
Secondary Mathematics ◽  
Secondary Mathematics Education ◽  
12Th Grade ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Subject Specific ◽  
And Mathematics

In this study, we adapted the notion of framing, a theoretical construct that refers to a person’s expectations about social spaces (Goffman, 1974), to investigate whether teachers viewed computational thinking (CT) according to subject-specific frames. This case study aimed to understand how teachers make connections between CT and subjects targeted for integration. Epistemological framing contributed new insights on why teachers connected CT in different ways to different subjects: frame shifting focused teachers’ attention on goals and activities specific to each subject. As teachers attended to a subject’s particularities, they drew upon different epistemic resources to construct their descriptions of CT. Our participants (n=6) were teachers who taught 7th-12th grade computing and mathematics as individual subjects. Qualitative coding of interview transcripts revealed that teachers' ideas about CT in computing were strongly influenced by computer programming while their ideas about CT in mathematics corresponded with familiar ways of teaching and learning mathematics. However, rather than accepting the fragmentation of CT as the price of integration into individual subjects, we propose limiting the scope when defining CT. We explain how this non-intuitive strategy can preserve the coherence of CT and how it might be used in CT professional development (PD) for mathematics teachers.

Towards Flipped Learning in Upper Secondary Mathematics Education

2020 ◽  
Vol 5 (1) ◽  
pp. 1-15
Author(s):  
Robert Weinhandl ◽  
Zsolt Lavicza ◽  
Stefanie Schallert
Keyword(s):  
Secondary Education ◽  
Mathematics Education ◽  
Mathematics Learning ◽  
Flipped Learning ◽  
Educational Innovations ◽  
Design Based Research ◽  
Secondary Mathematics Education ◽  
Upper Secondary Education ◽  
Mathematics Classrooms ◽  
Upper Secondary

Challenges for students in the 21st century, such as acquiring technology, problem-solving and cooperation skills, also necessitates changes in mathematics education to be able to respond to changing educational needs. One way to respond to these challenges is utilising recent educational innovations in schools, for instance, among others are flipped learning (FL) approaches. In this paper, we outline our explorative educational experiment that aims to investigate key elements of mathematics learning in FL approaches in upper secondary education. We describe the methodologies and findings of our qualitative study based on design-based research to discover key elements of FL approaches in upper secondary education. Analysing the data collected over ten months suggested categories (a) confidence when learning; (b) learning by working; and (c) flexibility when learning could be essential to understand FL approaches practices in mathematics classrooms.

scholarly journals Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 518
Author(s):  
Natividad Adamuz-Povedano ◽  
Elvira Fernández-Ahumada ◽  
M. Teresa García-Pérez ◽  
Jesús Montejo-Gámez
Keyword(s):  
Teaching And Learning ◽  
Number Sense ◽  
Methodological Approach ◽  
Number System ◽  
Algebraic Thinking ◽  
First Year ◽  
Symbolic Language ◽  
Decimal Number ◽  
Language Characteristic ◽  
Theoretical Foundations

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

scholarly journals The System Analysis in Language Teaching and Learning for Technical Students in Russia

2015 ◽  
Vol 10 (5) ◽  
pp. 22 ◽  
Author(s):  
Tatiana Sidorenko ◽  
Vladimir Yampolsky
Keyword(s):  
Language Proficiency ◽  
Teaching And Learning ◽  
System Analysis ◽  
Foreign Languages ◽  
Special Focus ◽  
Engineering Programs ◽  
Technical Students ◽  
Language Courses ◽  
University Level ◽  
Personal Skills

Integration of the Russian system of engineering education into the global educational domain compelled Russian universities to enhance the importance of humanities in engineering programs with a special focus on foreign languages. However, it must be admitted that the system of language training in Russia at a university level comes up against serious problems of historical, economic or political backgrounds, for which reason there are processes in the system that hamper a solution of the tasks set before the university and the society. The solution requires strong and decisive initiatives capable to improve the situation with the language proficiency among the graduators. Therefore, there is a rapid need in essentially new approaches to teaching foreign languages attain the desired outcomes for engineers, which reflect not only subject-oriented knowledge but also personal skills and the ability to effectively communicate with an opponent or a partner. The need to identify barriers towards high-quality language courses at a university level motivated the authors to carry out a special research based on the methods that are typical to system analysis.

scholarly journals Innovative Teaching and Learning Pathways for Responsible Use of Resources Focusing on the ESEE Region

2022 ◽  
Vol 5 (1) ◽  
pp. 95
Author(s):  
Mariaelena Murphy ◽  
Corina Pacher
Keyword(s):  
Teaching And Learning ◽  
Raw Materials ◽  
Knowledge Exchange ◽  
Special Focus ◽  
Cultural Perspective ◽  
Innovative Teaching ◽  
Life Long Learning ◽  
Use Of Resources ◽  
Knowledge Triangle ◽  
Learning Pathways

In a world depicted by rapid growth and consumerism, where pressing societal issues such as, the critical climate crises, resources exploitation in developing countries and much more, it is essential to educate all citizens about raw materials, their uses and about responsible production and consumption. Developing life-long learning wider society programmes is an essential tool to educate the population starting with the youngest members of society (pre-school) to adulthood (life-long learning) with a special focus on the life-world orientation from a learners’ perspective. The wider society learning flagship project, ‘Raw Matters Ambassadors at Schools’ (RM@Schools), is an innovative programme funded by the European Institute of Innovation & Technology (EIT) which promotes science education and careers in the raw materials sector. Since the project’s commencement in 2016, it has gained stronger European representation with a current total of 32 partners from 18 countries. This includes the consortium members from a parallel funded programme, RM@SchoolsESEE. This project aims at extending best practices and diversifying the current portfolio to East and Southeast European countries. What makes this project so innovative is in the programme and individual learning pathways. Considering a multidisciplinary and cultural perspective, a framework was developed to assist in forming raw materials ambassadors through engaging programmes for school pupils from aged 10 up to 19 years old and through the development of educational hands-on toolkits that range from experiments to game-based tools and much more. In particular, and as a way to increase impact, the project aims to mentor teenagers from all educational disciplines between the ages of 14–19 years old to become ‘Young RM Ambassadors’. This approach utilises state-of-the-art teaching and learning methods resulting in peer-to-peer knowledge exchange and dissemination. Built into the programme is a continuous feedback loop that involves stakeholders from all sides of the knowledge triangle: educators, pupils, professionals and researchers.

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