Algebraic Skills Research Articles

“Which Proof for Which Class?” Factors Influencing the Selection of Mathematical Proofs for Teaching

Selecting a proof for teaching is a frequent task for teachers. However, it is so far unclear, which factors are considered by teachers when selecting proofs. Is the selection based on task and proof characteristics such as the didactical type of proof? Or based on class characteristics such as students’ algebraic skills? Or do teachers’ characteristics such as their proof skills govern their decision? Or is the selection too non-generic for these characteristics to show a meaningful impact?To address these questions, a quasi-experimental study with N = 183 pre-service teachers was conducted to evaluate the influence of each of these factors on their selection of proofs for teaching. Results highlight several significant effects of the abovementioned characteristics and underline that—even at the pre-service level—the selection of proofs is more nuanced than often assumed in prior research and that teachers deliberately and adaptively select proofs for their teaching based on these factors.

Exploring the Effect of Mathematics Skills on Student Performance in Physics Problem-Solving: A Structural Equation Modeling Analysis

AbstractStudents’ success in physics problem-solving extends beyond conceptual knowledge of physics, relying significantly on their mathematics skills. Understanding the specific contributions of different mathematics skills to physics problem-solving can offer valuable insights for enhancing physics education. Yet such studies are rare, particularly at the high school level. This study addresses the underexplored area of this topic in secondary education by investigating the associations between physics problem-solving performance using a robust methodological framework. We applied exploratory factor analysis (EFA) to identify latent sub-mathmetics skills relevant to physics problem-solving and employed structural equation modeling (SEM) to examine the causal impact of these skills on students’ performance in physics. The study analyzed data from a municipal-wide assessment involving 1,878 grade 12 students in Southern China. The results demonstrate that mathematics skills impacting high school students’ physics problem-solving performance can be categorized into two sub skills, algebraic skills and geometric skills. It also indicates that algebraic skills have a stronger direct effect on physics problem-solving performance compared to geometric skills in high school setting. These findings suggest that integrating focused algebraic training within physics education can significantly improve student outcomes in STEM fields. We recommend that educators design curricula and instructional strategies that emphasize the development of algebraic skills necessary for solving complex physics problems. Additionally, these findings have important implications for policymakers, who should consider integrating targeted mathematics training within physics curricula to foster interdisciplinary learning and better prepare students for challenges in STEM education.

Diagnostic study of mathematical reasoning in novice university students

This paper presents the results of a study aimed at diagnosing how newly enrolled mathematics majors reason from a mathematical standpoint when they are required to perform inductive and deductive processes and validate or refute claims of a general nature. The theoretical framework underpinning this research comprises studies and investigations related to mathematical reasoning. The results of this diagnostic reveal that students lack mathematical reasoning skills that would allow them to justify statements of a general nature. In addition, they face difficulties in the development of deductive reasoning, are prone to generalize based on specific cases and lack skills in mathematical argumentation. On the other hand, they lack basic algebra skills such as developing square binomials and factoring. These findings highlight the need to design and implement a didactic proposal that fosters the development of reasoning and argumentation in students.

Enhancing number and algebra skills of primary students with learning disabilities or low mathematics achievement through a smartphone application

Enhancing number and algebra skills of primary students with learning disabilities or low mathematics achievement through a smartphone application

Procedural flexibility on fraction arithmetic and word problems predicts middle-schoolers’ differential algebra skills.

Procedural flexibility on fraction arithmetic and word problems predicts middle-schoolers’ differential algebra skills.

О ПРИВЛЕЧЕНИИ СТУДЕНТОВ К ИЗУЧЕНИЮ АБСТРАКТНОЙ АЛГЕБРЫ (НА ПРИМЕРЕ ОДНОЙ ЗАДАЧИ ТЕОРИИ ГРУПП И ЕЕ ПРИЛОЖЕНИЯХ)

The authors analize the alterations in the content of the algebra course, which is a conventional part of the university curriculum aimed at training maths teachers. The changes in the algebra skills development resulting from the overhaul of the education system are highlighted. The importance of general algebra is underlined. The problem is considered to be the impossibility to create conditions for mastering abstract algebra under existing approaches to the algebra study. Given general educational guidelines and the significance of the general algebra component, the authors propose to apply a methodology-based solution to the stated problem. The authors notice some options for motivating actions in these aspects of developing the general algebra content in the course of mathematics teacher training. One of such options is the selection of a series of problems (ranging from educational to research related), which makes it possible to discover the methods of general algebra, formulate some concepts of abstract algebra and consider their applications. The article describes a proposed solution to a well-known problem for schoolchildren from the Kvant magazine. The description of the (main) problem is given. A set of exercises is proposed enabling one to achieve a solution to the main problem. The solution to the proposed tasks is of greatest interest. A discussion of these solutions with students of mathematics at a pedagogical university makes it possible to introduce new group-theoretic concepts, which is illustrated in the text of the article. In a certain sense, the algebraic operation ‘*’ artificially introduced on a set of natural numbers allows us to define a group, being it Abelian and periodic, which is isomorphic to the direct sum of two-element groups. These properties allow us to consider a number of applications, in particular, the game of nim. The material presented in the article was tested at the Pitirim Sorokin Syktyvkar State University in the course of mathematics teacher training.

Studying the school algebra course in the conditions of distance education

Distance learning is becoming more and more relevant in today's educational environment, particularly for learning complex subjects such as algebra. The article examines the challenges and opportunities teachers and students face when learning a school algebra course in distance learning conditions. The author considers various methods, tools, and strategies to effectively learn the material, increase motivation, and support interaction between the teacher and the student in a virtual learning environment. The study also considers the impact of distance learning on academic performance and the development of students' algebra skills. The results of the study can determine the optimal strategies for the successful study of algebra in the conditions of distance learning and contribute to the further improvement of the pedagogical process.

Applying APOS Theory to Enhance Algebraic Logic Skills: Comparing Traditional Teaching and Computer-Assisted Instruction

This study aims to assess how effectively applied science students use equations to express connectivity in algebraic logic and understand their cognitive framework. This research measures students' understanding of mathematical logic connectors in line with the polytechnic curriculum and uses APOS theory as a basis. It compares the effectiveness of traditional teaching methods with the computer-assisted instruction (CAI) approach. The results show that students learning with CAI perform better in applying connectivity equations. These findings underscore the importance of students' cognitive schemes in understanding the relationship between algebra and logic. Students with a more mature conceptual understanding tend to overcome conceptual application difficulties better. For future research, it is suggested to explore the application of CAI methods in various learning contexts and other disciplines, as well as to assess its long-term impact on students' cognitive skills and mathematical understanding. Additionally, it is essential to compare the effectiveness of CAI with other innovative learning methods to determine the best approach to developing students' logic and algebra skills.

An Exploration of Grade 12 Learners’ Misconceptions on Solving Calculus Problem: A Case of Limits

This case study explored Grade 12 learners’ misconceptions in limits of functions. The study aimed at understanding problems that learners face in learning the concepts of limit by analyzing misconceptions that learners have and identifying the possible sources of these misconceptions to take remedial action. An exploratory research design was adopted, and purposive sampling employed to select 35 Grade 12 learners (21 females and 14 males) who wrote a test on limits. From the 35 learners who wrote the test, five learners were interviewed guided by their written responses. Theoretically, the study was guided by the constructivism theory and used a systematic error conceptual framework to categories the learners` misconceptions according to extrinsic and intrinsic calculus misconceptions. The study sought to answer the questions: (a) What type of misconceptions do Grade 12 learners exhibit in responding to limit questions? (b) What are the possible sources of these misconceptions? The study found that Learners exhibited misconceptions on the limit concept and related symbolism. Learners who had a flawed understanding of algebraic concepts struggled to apply limits correctly. The weak foundation on algebraic skills impacted negatively on their learning of new concepts on limits. The study recommends that, educators should always check and make sure that learners have appropriate prior knowledge before the teaching of new concepts in calculus. It is recommended that that teaching and learning approaches need to be adjusted to give equal weight to both the procedural and the conceptual understanding of mathematical knowledge in learners.

Design of an adaptive hypermedia system to strengthen algebra learning skills of high school students

The national and international parameters of educational evaluation have provided a frame of reference to analyze and compare the performance of the students, however, in Mexico these results show a low educational level. Therefore, it is important to implement tools to reduce educational deficiencies. The objective of this work is to develop an Adaptive Hypermedia System (SHA), which considers the individual characteristics of students in order to adapt and present content based on competencies, for the development of algebra skills. This research project was carried out in three phases: Phase 1. The Protocol Test was applied to identify the academic entry profile of 185 high school students who were studying algebra. Phase 2. The learning strategies contained in the SHA were designed, taking into account two key approaches: research-action-development and the ESEAC scale. Finally, in Phase 3, the SHA was used as support for students who presented low performance in the subject of algebra that they are currently studying in their high school training, and thus determine the impact and effectiveness of this system.

Developing and Reporting Psychometric Evidence of Prerequisite Algebra Skills Instrument

Developing and Reporting Psychometric Evidence of Prerequisite Algebra Skills Instrument

The effect of learning with a realistic mathematical approach on students mathematical communication skills in the material algebra

The effect of learning with a realistic mathematical approach on students mathematical communication skills in the material algebra

Supplementary Files for Santiago & Oller

The Excel file presented here contains the exact records used in computing the various statistical results reported in the paper by Santiago and Oller at DOI https://doi.org/10.56098/ijvtpr.v3i1.73. They have not been changed in any way except to remove elements added to blank cells, evidently by Medicare authorities. Also, 37 antirely blank records had to be deleted in order to make the counting functions and ordinary scrolling and data sorting functions work as they normally do in Excel. The Medicare data for Connecticut showing up to 7 doses of COVID-19 injectable fluids were sorted and stacked in such a manner as to enable the counting and statistical comparisons across the various subsamples referred to in the Santiago and Oller paper. Those computational processes were applied only to make the normal Excel functions for ordinary scrolling, counting, creating tables, and charting results feasible. Again, Santiago and Oller express gratitude to Steve Kirsch and his anonymous source(s) for the Medicare data published here. All of the results reported by Santiago and Oller were obtained from these data and are easily replicable by anyone with the requisite statistical and algebraic skill set.

The Effects of Flipped Classroom Strategy Based on “Addie Model” for Algebraic Skill Development

The Effects of Flipped Classroom Strategy Based on “Addie Model” for Algebraic Skill Development

Development of Proof Skills in Abstract Algebra Through Learning Communities

Development of Proof Skills in Abstract Algebra Through Learning Communities

The effect of assessment for learning on pre-service mathematics teachers higher-order thinking skills in algebra

The effect of assessment for learning on pre-service mathematics teachers higher-order thinking skills in algebra

The cognition of programming: logical reasoning, algebra and vocabulary skills predict programming performance following an introductory computing course

ABSTRACT In the current study we aimed to determine which cognitive skills play a role when learning to program. We examined five cognitive skills (pattern recognition, algebra, logical reasoning, grammar learning and vocabulary learning) as predictors of course-related programming performance and their generalised programming performance in 282 students in an undergraduate introductory programming course. Initial skills in algebra, logical reasoning, and vocabulary learning predicted performance for generalised programming skill, while only logical reasoning skills predicted course-related programming performance. Structural equation modelling showed support for a model where the cognitive skills were grouped into a language factor and an algorithmic/mathematics factor. Of these two factors, only the algorithmic/mathematics factor was found to predict generalised and course-related programming skills. Our results suggested that algorithmic/mathematical skills are most relevant when predicting generalised programming success, but also showed a role for memory-related language skills.

Ethnomathematics in Sundanese Culture from Scopus Database: Systematic Literature Review

Ethnomathematics has also been shown to have a positive impact on students' academic development, including improved creative thinking, understanding of geometry, and algebraic skills. However, there are challenges in implementing ethnomathematics in Sundanese culture, and more research is needed to understand these difficulties and potential solutions. This literature review aims to examine the current state of research on Sundanese ethnomathematics, including definitions and characteristics of ethnomathematics used in previous studies, as well as methodological challenges and potential applications. The review is based on a systematic search of leading mathematics education journals. This research explores the use of Sundanese ethnomathematics in education and cultural understanding, utilizing a variety of research objectives and methods, including didactic design analysis, instructional design research, and ethnographic field study. The results indicate that incorporating cultural context and traditional practices, such as the use of religious symbols and specialized teaching materials, can improve students' understanding and learning of mathematics. It is suggested that educators consider incorporating elements of Sundanese ethnomathematics into their teaching practices and that further research be conducted on the impact of ethnomathematics on students' academic, social, and physical development, as well as the effectiveness of different teaching methods in various cultural settings.

Richard Newland Dixon. 25 December 1930—25 May 2021

Richard Newland Dixon began his independent scientific career as a molecular spectroscopist in Sheffield, where he demonstrated new ways to measure, analyse and interpret the electronic spectra of small gas phase species. He later moved to the chair of theoretical chemistry at the University of Bristol, where he embraced new experimental methods, particularly techniques enabled by continuous wave and pulsed lasers, and honed his theoretical skills in angular momentum algebra and time-dependent quantum mechanics. This blend of experimental and theoretical expertise allowed him to make pioneering contributions in the field of gas phase molecular photodissociation dynamics. Richard will be remembered as a polite and modest man, and a very sharp scientist. Among his many lasting scientific achievements, he will be remembered for developing strategies for determining state-resolved correlations between the vectorial properties of the products of molecular photofragmentation processes, and for being one of the first to recognize the near ubiquitous importance of non-adiabatic couplings between potential energy surfaces in rationalizing the dynamics of such dissociations.

Unravelling the numerical and spatial underpinnings of computational thinking: a pre-registered replication study

ABSTRACT Background Key to optimizing Computational Thinking (CT) instruction is a precise understanding of the underlying cognitive skills. Román-González et al. (2017) reported unique contributions of spatial abilities and reasoning, whereas arithmetic was not significantly related to CT. Disentangling the influence of spatial and numerical skills on CT is important, as neither should be viewed as monolithic traits. Objective This study aimed (1) to replicate the results of a previous study by Román-González et al. (Computers in Human Behaviour 72), and (2) to extend this research by investigating other theoretically relevant constructs. Specifying the contribution of reasoning (i.e. numerical, figural), numerical skills (i.e. arithmetic, algebra), and spatial skills (i.e. visualization, mental rotation, short-term memory) helps to better understand the cognitive mechanisms underlying CT. Method We investigated a sample of 132 students from Grades 7–8 (age range 12–15 years). Participants completed the Computational Thinking test, as well as a variety of psychometric assessments of reasoning, numerical, and spatial skills. To determine which cognitive skills are relevant for CT, we calculated bivariate correlations and performed a linear regression analysis. Findings Results confirmed unique contributions of figural reasoning and visualization. Additional variance was explained by algebraic skills. Implications We conclude that CT engages cognitive mechanisms extending beyond reasoning and spatial skills.