Eliciting Learner Errors and Misconceptions in Simplifying Rational Algebraic Expressions to Improve Teaching and Learning

Purpose The purpose of this paper is to report how the use of a direct and an inverse task gave students an opportunity to discern the structure of a distributive law that they could apply to expand or to factorise algebraic expressions. The paper discusses a teaching sequence (of about 40 minutes) in a Grade 8 (14-15 year-olds) algebra class and it focusses on how the use of inverse tasks opens the dimension of variation. For instance, if the distributive law has always been used as a(b+c), factorising the expressions ab+ac means opening up the dimension of distributive law. The analysis showed that two central processes, transformation and variation, improved communication in the classroom. Design/methodology/approach The data used come from a longitudinal study conducted in Sweden. The methodology is grounded in educational design research. Two secondary school teachers conducted a lesson with variation theory as a guiding principle, supervised by a researcher. The relationship between teaching and learning was analysed in the enacted object of learning. The critical aspect for students’ learning was identified by asking questions to probe the students’ understanding. Findings The use of a direct and an inverse task gave the students an understanding of the structure of the distributive law that they could apply to expand or to factorise algebraic expressions. The teacher opened up a dimension of variation by similarity that gave the students the opportunity to discern the commonality in direct and inverse tasks as well as to relate the direct and inverse tasks to each other. Without an identification of similarity that might help students to compare underlying meanings, or to match one representation to another, students may not experience variations because there is not concordance among the relationships between the representations. Research limitations/implications Teachers can produce new knowledge as well as communicate successfully in the classroom when creating teaching activities that promote the discernment of similarity and difference that might help students to compare underlying meanings, or to match one representation to another. Practical implications The study represents an example of research which has the aim of improving teachers’ practices by using research results from mathematics education whilst keeping in mind that learning must be improved. Social implications The central educational problem is to have students make sense of sophisticated ways of reflecting on the general laws used in mathematics in relation to the algebraic ways of acting and reflecting. Variation theory sees learning as the ability to discern different features or aspects of what is being learned. It postulates that the conception one forms about the object of learning is related to the aspects of the object one notices and focusses upon. Originality/value The commutative law for algebraic generalisations is not characterised by the use of notations but, rather, by the way the general is dealt with. Algebraic generalisations entail: the grasping of a commonality related to the discernment of whole-parts relationships, the generalisation of this commonality to two types of transformations: treatments and conversions, and the formation of direct and inverse tasks that allows one to discern the relationship between the whole, the parts, the relations between the parts, the transformation between the parts and the relationship between the parts and the whole.

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Eliciting Learner Errors and Misconceptions in Simplifying Rational Algebraic Expressions to Improve Teaching and Learning

International Journal of Educational Sciences ◽

10.1080/09751122.2016.11890408 ◽

2016 ◽

Vol 12 (1) ◽

pp. 16-28 ◽

Cited By ~ 1

Author(s):

Judah P. Makonye ◽

Nzima Stepwell

Keyword(s):

Teaching And Learning ◽

Algebraic Expressions

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La implementación del taller “Juguemos con Álgebra” para la mejora del rendimiento académico en el tema de expresiones algebraicas y la resolución de ecuaciones lineales, así como la conceptualización de la materia de matemáticas de los estudiantes de 3° de secundaria / The Implementation of the Workshop “Let’s Play with Algebra” for the Improvement of Academic Performance in the Field of Algebraic Expressions and Linear Equations Solving Sills as well as the Conceptualization of Maths of 3rd Year of Secondary School Students

Revista Internacional de Educación y Aprendizaje ◽

10.37467/gka-revedu.v2.600 ◽

2014 ◽

Vol 2 (2) ◽

Author(s):

Ana Laura Núñez Rodríguez ◽

Alma Minerva Aguilar Martínez ◽

Mireya Sarahí Abarca Cedeño ◽

Jesús Antonio Larios Trejo

Keyword(s):

Academic Performance ◽

Teaching And Learning ◽

Linear Equations ◽

Mathematics Students ◽

School Students ◽

Grade Group ◽

Algebraic Expressions ◽

Training Approach ◽

The Subject ◽

The Impact

ABSTRACTOften, the design of dynamic and engaging activities for teaching mathematics is one of the main challenges faced by teachers of the subject, because the Studies Program 2011 of Mexican Educational System considers that is the teacher who should promote teaching situations to arouse interest in students, promoting the development of skills, by working both individually and as a collective. Looking to design and validate experiences that promote the teaching and learning of mathematics, was conducted this research, which aimed to assess the impact of the workshop “Juguemos con Álgebra” in the conceptualization of the subject of mathematics students of 3rd grade group A, of high school Alberto Larios Villalpando, as well as the impact on academic performance in the area of algebraic expressions and solving linear equations. The workshop implemented the Program of Studies 2011, that is, work-based training approach, which is to problematize students to discuss and analyze their procedures and results, supporting this with the game, as a resource for teaching of algebra.RESUMENCon frecuencia, el diseño de actividades dinámicas y atractivas para la enseñanza de las matemáticas es uno de los principales retos a los que se enfrentan los profesores de dicha materia, debido a que el Programa de Estu-dios 2011 del Sistema Educativo Mexicano considera que es el docente quien debe propiciar situaciones didácticas para despertar el interés en los alumnos; promoviendo el desarrollo de ciertas habilidades, tanto a través del trabajo individual y autónomo como colectivo. Buscando diseñar y validar experiencias que favorezcan el proceso de enseñan-za-aprendizaje de las matemáticas, se llevó a cabo la presente investigación, la cual tuvo como objetivo evaluar el impacto del taller “Juguemos con Álgebra” en la conceptualización de la materia de matemáticas en alumnos de 3° grupo A de la escuela secundaria Alberto Larios Villalpando, turno vespertino, así como también el impacto en el rendimiento académico en el tema de expresiones algebraicas y resolución de ecuaciones lineales. En dicho taller se puso en práctica lo propuesto en el Programa de Estudios 2011, es decir, trabajar con base en un enfoque didáctico, el cual consiste en problematizar a los alumnos para que discutan y analicen sus procedimientos y resultados, apoyando esto con el juego, como recurso para la enseñanza del álgebra. Contacto principal: [email protected]

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Understanding How Students Learn: Preparing Students to Become Professionals

Perspectives on Issues in Higher Education ◽

10.1044/ihe12.1.16 ◽

2009 ◽

Vol 12 (1) ◽

pp. 16-23

Author(s):

Lizbeth Curme Stevens

Keyword(s):

Service Learning ◽

Teaching And Learning ◽

Communication Disorders ◽

Learning Opportunities ◽

Graduate Courses ◽

Speech Language Pathologists ◽

Community Partners ◽

Scholarship Of Teaching ◽

Academic Service Learning

Abstract The intent of this article is to share my research endeavors in order to raise awareness of issues relative to what and how we teach as a means to spark interest in applying the scholarship of teaching and learning to what we do as faculty in communication sciences and disorders (CSD). My own interest in teaching and learning emerged rather abruptly after I introduced academic service-learning (AS-L) into one of my graduate courses (Stevens, 2002). To better prepare students to enter our profession, I have provided them with unique learning opportunities working with various community partners including both speech-language pathologists (SLPs) and teachers who supported persons with severe communication disorders.

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The Use of Supplementary Podcasting as an Instructional Tool in an Online Classroom Setting

Perspectives on Issues in Higher Education ◽

10.1044/ihe11.2.61 ◽

2008 ◽

Vol 11 (2) ◽

pp. 61-66

Author(s):

Jennifer C. Friberg

Keyword(s):

Continuing Education ◽

Teaching And Learning ◽

Classroom Setting ◽

Educational Tool ◽

Instructional Tool ◽

Online Classroom ◽

Potential Applications ◽

Education Tool ◽

Professional Learners ◽

Professional Disciplines

Abstract The use of podcasting is incredibly widespread, with experts estimating that 60 million Americans will be using podcasting in some form by 2010. The use of podcasting has grown beyond entertainment to become an educational tool, showing promise as a way to disseminate information and create networks of professional learners. However, despite the growing clinical and educational uses of podcasting in other professional disciplines, podcasting is being used primarily as a continuing education tool for speech-language pathologists and audiologists at this time. This article provides guidelines and examines the potential applications for use of podcasting in teaching and learning in communication sciences and disorders.

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