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

Lucy Cragg, Camilla K. Gilmore • Trends in Neuroscience and Education (2014)

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 (...

OPENALEX cc-by DOI: https://doi.org/10.1016/j.tine.2013.12.001

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

Joost C. F. de Winter, Dimitra Dodou, Yke Bauke Eisma • Computers (2024)

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...

DOAJ Open Access (DOAJ) DOI: 10.3390/computers13110278

Mathematical Capabilities of ChatGPT

Simon Frieder, Luca Pinchetti, Chevalier Chevalier, Ryan-Rhys Griffiths et al. • neural information processing systems (2023)

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...

OPENALEX Open Access DOI: https://doi.org/10.52202/075280-1205

On Mathematical Problem Posing.

Edward A. Silver • for the learning of mathematics (1994)

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...

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The Nature of Mathematical Knowledge

Philip Kitcher (1985)

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...

OPENALEX DOI: https://doi.org/10.1093/0195035410.001.0001

The Handbook of Mathematical Cognition

Jamie I. D. Campbell • Psychology Press eBooks (2005)

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...

OPENALEX DOI: https://doi.org/10.4324/9780203998045

Realism, Mathematics and Modality

Hartry H. Field • Philosophical Topics (1988)

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...

OPENALEX DOI: https://doi.org/10.5840/philtopics19881613

The Mathematical Brain

Brian L. Butterworth • UCL Discovery (University College London) (1999)

The concept of numbers and the ability to recognize and process them is innate, part of everyone's intellectual apparatus whether they've had formal education or not. This instinct is not dependent on basic intelligence or general knowledge...

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Introduction to Mathematical Philosophy

Bertrand Russell, Michael Potter • Routledge eBooks (2022)

"The philosophy of mathematics will naturally be expected to deal with questions at the frontier of knowledge, as to which comparative certainty is not yet attained. But separation of such questions is hardly likely to be fruitful unless th...

OPENALEX DOI: https://doi.org/10.4324/9781003308881

Mathematics, mathematicians, and mathematics education

Hyman Bass • Bulletin of the American Mathematical Society (2005)

I am one of a growing number of research mathematicians who are substantially engaged with school mathematics education. Such outreach has a long and honor-able tradition. In this lecture, I illustrate some of the ways that I think this can...

OPENALEX public-domain DOI: https://doi.org/10.1090/s0273-0979-05-01072-4

Teachers of Mathematics

Howard F. Fehr • Mathematics Teacher Learning and Teaching PK-12 (1948)

There are persons who do not like to teach who are conducting classes in our schools. There are persons who do not like mathematics who have been assigned to handle algebra classes and to instruct in arithmetic. There are men and women who ...

OPENALEX DOI: https://doi.org/10.5951/mt.41.6.0270

Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study

Heather C. Hill, Merrie Blunk, Charalambos Y. Charalambous, Jennifer M. Lewis et al. • Cognition and Instruction (2008)

This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the ma...

OPENALEX Open Access DOI: https://doi.org/10.1080/07370000802177235

Health Technologies: Transforming Scientific Knowledge into Human Health

Hüseyin Okan Durmuş • Zenodo (CERN European Organization for Nuclear Research) (2026)

Health technologies are commonly associated with medical devices, digital health platforms, robotics, and artificial intelligence. However, this perspective captures only the most visible dimension of a much broader concept. This study exam...

OPENALEX cc-by DOI: https://doi.org/10.5281/zenodo.21826977

Translational research in health technologies: A scoping review

Nadja N. V. Mayrink, Luís Alcoforado, Arthur Chioro, Felipe Ricardo dos Santos Fernandes et al. • Frontiers in Digital Health (2022)

Introduction: The current debate on the process of technological innovation points out as a challenge for universities consolidation of competencies that allow the generation and transfer of knowledge to society. The Translational Research ...

OPENALEX cc-by DOI: https://doi.org/10.3389/fdgth.2022.957367 PMC: 9385029

HEALTH TECHNOLOGY ASSESSMENT IN THE UNITED KINGDOM

Steven H. Woolf, Chris Henshall • International Journal of Technology Assessment in Health Care (2000)

The National Health Service (NHS) provides universal health coverage for all British citizens. Most services are free of charge, although modest copayments are sometimes applied. About 11% of the population also has private insurance. Gener...

OPENALEX DOI: https://doi.org/10.1017/s0266462300101175

Health Technology Assessment

Lise Lund Håheim, Berit Mørland • IGI Global eBooks (2011)

Scientific publications in medical fields are rapidly increasing and are overwhelming in numbers. This poses a challenge to health authorities, and health professionals who need knowledge to make informed decisions in finding the best evide...

OPENALEX DOI: https://doi.org/10.4018/978-1-60566-988-5.ch003