Mathematical reasoning is gaining increasing significance in mathematics education. It has become part of school curricula and the numbers of empirical studies are growing. Researchers investigate mathematical reasoning, yet, what is being under inve...
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these models to...
Mathematical reasoning is an essential ability that students must have in every mathematics lesson. However, student behavior during the process of mathematical reasoning has yet to be widely studied. This research explores the mathematical reasoning...
This study develops and empirically evaluates a multilevel analytical framework linking AI-generated mathematical reasoning, students’ diagnostic reasoning, and mathematics achievement in AI-supported mathematical problem solving. A classroom i...
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 betw...
Recent studies have provided convincing evidence highlighting the strong relationship between spatial reasoning and mathematical performance. However, there is a limited body of research exploring the contributions of different spatial reasoning cons...
This article explores what impact a program of IT programming (Scratch and Python) activities has on the logical-mathematical reasoning of high school children. The sample comprised a group of 388 high school students, spanning first-year compulsory...
Large language models (LLMs) are increasingly used in applied intelligent systems, but mid-sized models still lag on mathematical reasoning, partly because reliable step-level supervision is scarce. Many existing remedies rely on costly human annotat...
For children with persistent mathematics difficulties, research and practice espouses that an altered kind of mathematics instruction is necessary due to sustained performance differences. Yet, a critical issue in mathematics education rests in the q...
Statistics education has investigated how to promote formal inferential reasoning from informal inferential reasoning. Nevertheless, there is still a need for proposals that explore and progressively develop inferential reasoning of students and teac...
This study explores how to support Turkish–American secondary school students to co-develop covariational reasoning (CR) and representational fluency (RF) in solving contextually based quadratic function tasks in an after-school community cente...
The sustainability of education systems depends on teachers’ capacity to adapt to changing curriculum expectations and diverse student needs. However, there is limited information on how adaptive design reasoning develops in the iterative proce...
Large language models and vision–language models already achieve strong results on reasoning tasks, but their reliability under controlled assessment-style conditions remains insufficiently characterized. This paper presents a benchmark study o...
The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problem...
This paper poses, discusses, but does not definitively answer, the following questions: What sorts of reasoning machinery could the ancient mathematicians, and other intelligent animals, be using for spatial reasoning, before the discovery of modern...
Large language models (LLMs) have shown great potential in solving complex mathematical problems, but their performance in university-level mathematics is still underexplored. This study provides a systematic evaluation of eleven state-of-the-art LLM...
The paper focuses on the cognitive and epistemic characterization of backward reasoning in strategy games resolution. It explores the use of abstraction in context (AiC) theory as a tool for the analysis of the epistemic actions involved in these pro...
5 December 2021
Research suggests that integrated STEM activities can best support students in developing their mathematical and scientific understanding. On one hand, while science provides mathematics with real-life authentic problems to investigate, mathematics p...
A cross-sectional qualitative study examined how different pattern types accounted for wide variation in children’s Awareness of Mathematical Pattern and Structure (AMPS), illustrating how spatial and patterning skills are interrelated. An inte...
Remote learning has reduced the mathematical performance of students. Mathematical reasoning is the critical skill that enables students to make use of all other mathematical skills. The aim of the present study was (1) to develop the mathematical re...
Large language models (LLMs) have recently improved their problem-solving abilities and can solve complex mathematical problems with an increasing accuracy, necessitating the development of more challenging benchmarks. Over the years, the performance...
Large Language Models (LLMs) show promise for supporting formative assessment by generating feedback on students’ written mathematical reasoning. However, practical use in educational settings remains constrained by the need to manually curate...
The topic of similarity plays an essential role in developing students’ deductive reasoning. However, knowing how to teach similarity and understanding how to incorporate deductive reasoning and proof along with plane geometry remain a challenge to b...
This study explored individual differences among senior high school students in detecting and correcting logical errors in mathematical reasoning. Eight participants with high and average mathematical abilities each were recruited from a key high sch...
Computational thinking is considered a set of skills necessary for living and working in today’s society. It has recently become part of mathematics curricula in several European countries. In this study, we offer a glimpse into the informal cl...
Supporting teachers to transfer their learnings from innovative professional development settings to the classroom is challenging. In this paper, we investigate a novel approach to teacher learning, in which teachers from seven US districts taught in...
Creating learning models that can exhibit sophisticated reasoning abilities is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this direction...
This study is based on an interdisciplinary teaching experience in two 2nd-grade classes, integrating Visual Arts and Mathematics through the use of Pop-Up cards. It aimed to identify how these activities foster disciplinary and interdisciplinary lea...
In this article we analyze the current state of the didactics of mathematics in the U.S. as it relates to research on equity. The sociopolitical turn in U.S. mathematics education resulted in a push for critical mathematics pedagogies (CMPs) in which...
Geometric problem-solving (GPS) has been a long-standing challenge in the fields of formal mathematics and artificial intelligence. To address the limitations of unidirectional approaches, we developed a neuro-symbolic system that integrates forward...
We tested the mathematical literacy (ML) proficiency of 204 grade 10 “advanced track” students in the United Arab Emirates (UAE) using 34 questions from the Programme for International Student Assessment (PISA) 2012 released items. Using...
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 deeper, more...
This paper explores the performance of ChatGPT and GeoGebra Discovery when dealing with automatic geometric reasoning and discovery. The emergence of Large Language Models has attracted considerable attention in mathematics, among other fields where...
Robust Arithmetic Word Problem (AWP) solving is important for applying mathematical reasoning systems in educational scenarios, where problem statements may contain changed numerical values, paraphrased descriptions, or irrelevant distracting informa...
Human-like automatic deductive reasoning has always been one of the most challenging open problems in the interdisciplinary field of mathematics and artificial intelligence. This paper is the third in a series of our works. We built a neural-symbolic...
Understanding rate of change requires reasoning about measurable quantities and how one quantity changes relative to another. To support this kind of reasoning, teachers should develop the ability to notice students’ quantitative and covariatio...
18 February 2023
The relevance of cognitive performance during adolescence requires further studies that analyze potential associated factors. This study aimed to analyze inductive reasoning, reading comprehension, and mathematical thinking (problem-solving and numbe...
Large Language Models (LLMs) generate fluent text but often struggle with reliable multi-step reasoning, factual grounding, and stable use of long context, especially when inputs are incomplete, inconsistent, or imprecise. To address these challenges...
Manipulative materials are widely considered valuable resources in geometry education because they may support visualization, spatial reasoning, and conceptual understanding when implemented within appropriate instructional contexts. However, many ex...
The armed forces of major nations have utilized modeling and simulation technologies to develop weapon systems corresponding to changing modern battlefields and reducing the development cycle. However, model design is complex owing to the characteris...
This paper presents an initial output of the project “Augmented Intelligence in Mathematics Education through Modeling, Automatic Reasoning and Artificial Intelligence (IAxEM-CM/PHS-2024/PH-HUM-383)”. The starting hypothesis of this proje...
Spatial reasoning (SR) skills are inherent to our daily interactions with the world and essential to young children’s learning in science, technology, engineering, arts, and mathematics (STEAM) domains. Most simply, SR skills allow humans to me...
Neurosymbolic AI (NeSy AI) seeks to integrate the strengths of symbolic reasoning with computational learning methods, addressing fundamental challenges of each paradigm in isolation. Existing surveys have primarily organized this growing body of res...
The fuzzy logic reasoning based on the “If... then...” rule is not the inaccurate reasoning of AI against ambiguity because fuzzy reasoning is antilogical. In order to solve this problem, a redundancy theory for discriminative weight filt...
This research proposes to evaluate the difference in essential mathematical competencies of middle school students transitioning to high school level under pandemic conditions (COVID-19) using the PreparaTec platform and Programme for International S...
Since the introduction of Carol Dweck’s landmark work in mindset, many scholars have studied the impact of a change in mindset on learning, behavior, and health. National and international large-scale studies have validated the consistent corre...
The present article focuses on the role that the artificial teaching and learning of mathematics could play for education in the forthcoming era of a new industrial revolution that will be characterized by the development of an advanced Internet of t...
This study aims to document the extent to which the use of digital technology enhances and extends high school teachers’ problem-solving strategies when framing their teaching scenarios. The participants systematically relied on online developments s...
The main objective of this study is to investigate the impact of a proposed mathematical enrichment program based on the Programme for International Student Assessment (PISA) framework for mathematical literacy. Mathematical literacy is essential bec...
Dyslexia has been linked to an altered perception of metrical structures in language, but no study to date has explored the link between reading impairments and other forms of metrical thinking (e.g., proportional reasoning). In the present study, we...
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