Academic Articles & Research Papers

Knowing and Teaching Elementary Mathematics

Chinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers--11 to 12 years of schooling versus 16 to 18 years of ...

Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention

The Psychology of Learning Mathematics

This classic text presents problems of learning and teaching mathematics from both a psychological and mathematical perspective. The Psychology of Learning Mathematics, already translated into six languages (including Chinese and Japanese),...

Problem-Based Tasks in Mathematics Learning: Opportunities and Challenges for Teachers

Mathematics education and teaching should not only include routine tasks; but tasks that need practice and memorization are mathematically more prosperous and more difficult because they promote problem-solving, investigation, and the disco...

Conceptual Mathematics

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning s...

ANALISIS KLASTER KEMISKINAN KABUPATEN KOTA DI PROVINSI BANTEN MENGGUNAKAN METODE K-MEANS

Poverty is a special problem that needs to be discussed in Indonesia. Because poverty that occurs in a certain area will have an impact on development in Indonesia. Banten province has a percentage of 6.04 percent with a total poverty of 57...

Mathematical Reasoning

Contents: Preface. Part I: Introduction. L.D. English, Analogies, Metaphors, and Images: Vehicles for Mathematical Reasoning. Part II: Cognitive Foundations for a Mind-Based Mathematics. G. Lakoff, R.E. Nunez, The Metaphorical Structure of ...

The Emergence of Mathematical Meaning

Contents: Preface. P. Cobb, H. Bauersfeld, Introduction: The Coordination of Psychological and Sociological Perspectives in Mathematics Education. P. Cobb, E. Yackel, T. Wood, The Teaching Experiment Classroom. P. Cobb, Mathematical Learnin...

Mathematical Ideas in Biology

This is a lucid introduction to some of the mathematical ideas which are useful to biologists. Professor Maynard Smith introduces the reader to the ways in which biological problems can be expressed mathematically, and shows how the mathema...

Mathematics as a science of patterns

Mathematics as a Science of Patterns is the definitive exposition of a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has ...

Solar heat transport analysis of Falkner Skan Casson ternary hybrid nanoparticles over a permeable wedge

Abstract In the modern era, energy has become a vital concern across all sectors, while efficient energy generation remains a significant challenge for scientists and engineers. To overcome this issue, researchers have developed ternary hyb...

Changing Movements in a Changing World: Modelling Early Pleistocene and Early Middle Pleistocene Climatic and Ecological Environments and Influences on Hominin Dispersal in Eurasia

In a world of drastic climatic and ecological changes, our knowledge of how the environment influenced hominin behaviour is of the utmost importance. Archaeology plays a key role in this domain, as it is the only discipline that studies emp...

Theories of Mathematical Learning

Contents: Preface. Part I: P. Cobb, Sociological and Anthropological Perspectives on Mathematics Learning. P. Cobb, B. Jaworski, N. Presmeg, Emergent and Sociocultural Views of Mathematical Activity. J. Voigt, Negotiation of Mathematical Me...

Skills underlying mathematics: The role of executive function in the development of mathematics proficiency

The successful learning and performance of mathematics relies on a range of individual, social and educational factors. Recent research suggests that executive function skills, which include monitoring and manipulating information in mind (...

System 2 Thinking in OpenAI’s o1-Preview Model: Near-Perfect Performance on a Mathematics Exam

The processes underlying human cognition are often divided into System 1, which involves fast, intuitive thinking, and System 2, which involves slow, deliberate reasoning. Previously, large language models were criticized for lacking the de...

Mathematical Capabilities of ChatGPT

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In...

On Mathematical Problem Posing.

In mathematics classes at all levels of schooling in all countries of the world, students can be observed solving problems. The quality and authenticity of these mathematics problems has been the subject of many discussions and debates in r...

The Nature of Mathematical Knowledge

Abstract The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the available accounts of a priori mathematical kno...

The Handbook of Mathematical Cognition

Part 1: Cognitive Representations for Number and Mathematics. M. Fayol, X. Seron, About Numerical Representations: Insights from Neuropsychological, Experimental and Developmental Studies. M. Brysbaert, Number Recognition in Different Forma...

Realism, Mathematics and Modality

Fictionalism, epistemology and modality realism and anti-realism about mathematics is mathematical knowledge just logical knowledge? on conservativeness and incompleteness Platonism for cheap? - Crispin Wright on Frege's context principle c...