Reconceptualizing a mathematical domain on the basis of student reasoning: Considering teachers’ perspectives about integers

Hawthorne, Casey; Philipp, Randolph A.; Lamb, Lisa; Bishop, Jessica Pierson; Whitacre, Ian; Schappelle, Bonnie P.

doi:10.1016/j.jmathb.2021.100931

Cited by 5 publications

(3 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Foundational mathematics skills are important predictors of secondary and postsecondary success for students (Varma & Schwartz, 2011). In early mathematics classrooms, students often struggle when they encounter negative integers (Bossé et al, 2016;Hawthorne et al, 2022). Negative integers, unlike positive integers, are not easily modeled by teachers.…”

Section: Relevance For Mathematics Teaching and Learningmentioning

confidence: 99%

Mathematics MOVES Me: Digital Solutions for Coordinating Enactive and Symbolic Perspectives—The Case of Basic Arithmetic With Positive and Negative Integers

Anton,

Cosentino,

Gelsomini

et al. 2023

Preprint

View full text Add to dashboard Cite

We present an innovative educational design for basic arithmetic that responds to students’ documented difficulties with adding and subtracting single-digit positive and negative numbers. The design utilizes MOVES, a technological architecture that combines floor- and wall-projected interactive interfaces. Students enact arithmetic operations, e.g., “3 - (-2)” by walking along a projected body-scale number line, while their actions are captured and analyzed to provide in-the-moment feedback on elements of their solution procedure. Next, a screen-based avatar is introduced who mimics their whole-body movements. Finally, analogous problems are presented on a tablet that utilizes tangible interaction, where students walk the avatar, now as an action-figure, along a standard-sized number line. Our theoretical framework, design conjecture, product evaluation, and data analysis all pertain to fostering conceptual understanding through coordinating full-body egocentric experiences on a body-scale number line with the allocentric experience of “puppeting” the avatar along the desk-scale number line. Based on pilot trials, we speculate on the nature and type of supports students require to coordinate these perspectives and discuss implications for future iterations of the design.

show abstract

Section: Relevance For Mathematics Teaching and Learningmentioning

confidence: 99%

Mathematics MOVES Me: Digital Solutions for Coordinating Enactive and Symbolic Perspectives—The Case of Basic Arithmetic With Positive and Negative Integers

Anton,

Cosentino,

Gelsomini

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Este enfoque consiste en plantear a los estudiantes problemas desafiantes que les obliguen a pensar de forma lógica y sistemática para llegar a una solución. Mediante la práctica repetida, los alumnos pueden empezar a reconocer patrones y relaciones, mejorando su capacidad para identificar y aplicar el razonamiento lógico en situaciones de resolución de problemas (Hawthorne et al, 2022).…”

Section: Enseñanza Del Razonamiento Lógico Matemático Mediante La Res...unclassified

Métodos de enseñanza del razonamiento lógico matemático para estudiantes universitarios

Hernández Dávila,

Velastegui Hernández,

Mayorga Ases

et al. 2023

View full text Add to dashboard Cite

Introducción. El razonamiento lógico matemático es el proceso de utilizar principios lógicos para llegar a conclusiones válidas y resolver problemas matemáticos. Es crucial para desarrollar el pensamiento crítico y la capacidad de resolver problemas. Tiene diversas aplicaciones en campos como la informática, la educación y la criptografía. Enseñar razonamiento lógico matemático a estudiantes universitarios puede ser todo un reto ya que los educadores pueden ayudar a los estudiantes a desarrollar una comprensión más profunda del razonamiento lógico matemático y aplicarlo a diversos contextos. Objetivo. Facilitar la comprensión del aprendizaje del razonamiento lógico matemático a estudiantes universitarios. Metodología. Incluye un examen exhaustivo de la bibliografía existente sobre el tema, así como un análisis de los métodos de enseñanza actuales y de su eficacia. Se centra en la evaluación de las necesidades de cada estudiante y en la adaptación de la enseñanza a sus estilos y capacidades de aprendizaje específicos. Al dominar conceptos básicos, los alumnos estarán mejor preparados para abordar temas más complejos de lógica y razonamiento matemáticos. Finalmente, al proporcionar a los estudiantes una base sólida en lógica proposicional, los educadores pueden ayudarles a desarrollar las habilidades de pensamiento crítico necesarias para tener éxito en la educación superior y más allá. Resultados. Se ha presentado los siguientes resultados: 1. Enseñanza del razonamiento lógico matemático mediante la resolución de problemas. 2. Uso de la tecnología en la enseñanza del razonamiento lógico matemático. 3.Estrategias de aprendizaje activo para la enseñanza del razonamiento lógico matemático. 4. Integración de aplicaciones del mundo real en la enseñanza del razonamiento lógico matemático. 5. Desarrollo de las capacidades de pensamiento crítico mediante el razonamiento lógico matemático. 6. Ayudar a los alumnos con dificultades en el razonamiento lógico matemático. 7. Evaluación de las capacidades de razonamiento lógico matemático. Conclusión. La enseñanza del razonamiento lógico matemático a los estudiantes universitarios es un aspecto crucial de su desarrollo académico y profesional, también, la enseñanza del razonamiento lógico matemático mediante la resolución de problemas, el uso de la tecnología, las estrategias de aprendizaje activo, la integración de aplicaciones del mundo real y el desarrollo de habilidades de pensamiento crítico puede mejorar la comprensión del razonamiento lógico matemático por parte de los estudiantes. Área de estudio general: Matemática. Área de estudio específica: Razonamiento lógico matemático.

show abstract

“…Reasoning abilities can help students connect systematic facts or data, explore ideas, and identify solutions to produce conclusions from relevant knowledge in a mathematical context (Abidin et al, 2020). Students' reasoning abilities help them understand what they are doing, not just remembering facts, rules, or procedures but also using their reasoning abilities to make predictions based on experience to understand related concepts (Hawthorne et al, 2022;Qomariyah & Darmayanti, 2023). An analogy is one of the many methods of reasoning (Agusantia & Juandi, 2022;Maghfiroh & Rosyidi, 2021).…”

Section: Introductionmentioning

confidence: 99%

Mathematical analogical reasoning ability based on the thinking style of junior high school students on flat surface of solid figures

Fazrianti

Yusmin

Suratman

2022

JASME

View full text Add to dashboard Cite

Analogical reasoning ability teaches students how to translate abstract concepts into a concrete ones. Students can receive and process information from this knowledge according to their thinking style. Therefore, this study aims to determine students' mathematical analogical reasoning ability at SMP Negeri 1 Sungai Raya based on their thinking style. The research method used in this research is quantitative descriptive analysis, with data analysis assisted by Anates V4 software. The subjects in this study were 29 class IX A students at SMP Negeri 1 Sungai Raya. Data collection techniques used in this study include measurement and direct and indirect communication. The instruments used were mathematical analogical reasoning tests, thinking style tests, and interview guidelines. The results showed that students who had a concrete sequential thinking style obtained an average value of mathematical analogical reasoning ability of 46.25 in the good category, while the average value of students with abstract sequential mathematical analogical reasoning ability was 31.50, concrete random 27.83, and random abstract 32.07 in the medium category. The findings mean that the classroom learning pattern needs to be maintained while improving students' mathematical analogical reasoning abilities. In addition, students are expected to maximize their potential according to the character of their thinking style.

show abstract

Reconceptualizing a mathematical domain on the basis of student reasoning: Considering teachers’ perspectives about integers

Cited by 5 publications

References 18 publications

Mathematics MOVES Me: Digital Solutions for Coordinating Enactive and Symbolic Perspectives—The Case of Basic Arithmetic With Positive and Negative Integers

Mathematics MOVES Me: Digital Solutions for Coordinating Enactive and Symbolic Perspectives—The Case of Basic Arithmetic With Positive and Negative Integers

Métodos de enseñanza del razonamiento lógico matemático para estudiantes universitarios

Mathematical analogical reasoning ability based on the thinking style of junior high school students on flat surface of solid figures

Contact Info

Product

Resources

About