Bridging powerful knowledge and lived experience: Challenges in teaching mathematics through COVID-19

Pythagoras ◽  
2021 ◽  
Vol 42 (1) ◽  
Author(s):  
Karin Brodie ◽  
Deepa Gopal ◽  
Julian Moodliar ◽  
Takalani Siala
Keyword(s):  
Lived Experience ◽  
Mathematical Knowledge ◽  
Teacher Practices ◽  
School Experiences ◽  
Task Design ◽  
Teaching Mathematics ◽  
Disciplinary Knowledge ◽  
Productive Disciplinary Engagement ◽  
Powerful Knowledge ◽  
Out Of School

The coronavirus disease 2019 (COVID-19) pandemic supported an investigation of ongoing challenges as to whether and how to make mathematics relevant to learners’ lifeworlds. Given that COVID-19 created major disruptions in all learners’ lives, we developed and taught tasks that attempted to make links between their experiences of the pandemic and disciplinary mathematical knowledge. We located our investigation in current debates about the extent to which disciplinary knowledge can be linked to learners’ out-of-school experiences. We developed and analysed two tasks about COVID-19 that could support link-making and productive disciplinary engagement, and analysed one Grade 10 teacher teaching these tasks. We found that linking mathematics to learners’ lifeworlds is both possible and extremely difficult in relation to task design and how the teacher mediates the tasks. In relation to task design, we argue that teachers cannot do it alone; they need to be supported by the curriculum and textbooks. In relation to mediation, we saw that teacher practices are difficult to shift, even in the best of circumstances. We articulate the complexities and nuances involved in bridging powerful knowledge and lived experience and thus contribute to debates on how to teach powerful knowledge in relation to learners’ lifeworlds.

scholarly journals Ciclo de estudo e desenho de tarefasStudy and Task Design Cycle

2021 ◽  
Vol 22 (3) ◽  
pp. 666-697
Author(s):  
Tânia Cristina Rocha Silva Gusmão ◽  
Vicenç Font
Keyword(s):  
Mathematical Knowledge ◽  
Research Method ◽  
Mathematics Learning ◽  
Task Design ◽  
Mathematical Tasks ◽  
Teaching Mathematics ◽  
Pedagogical Practice ◽  
Design Cycle ◽  
Sobre Todo ◽  
And Task

ResumoEste artigo apresenta o Ciclo de Estudo e Desenho de Tarefas (CEDT) como um método de pesquisa dirigido ao estudo e desenho de tarefas matemáticas para orientar, sobretudo, o trabalho do professor em sala de aula. Fundamentado na junção de ferramentas teóricas da perspectiva do Desenho de Tarefas e dos Critérios de Idoneidade Didática, o CEDT resulta em uma ferramenta potente e interessante para orientar o trabalho com tarefas matemáticas e tem se configurado como um espaço privilegiado para estudos e discussões em torno do conhecimento didático e matemático; aquisição de experiências e conhecimentos e reflexões para mudanças na prática pedagógica. Subjaz a esse artigo a intenção de divulgar os resultados das pesquisas desenvolvidas com o CEDT, a fim de fomentar discussões sobre a temática.Palavras-chave: tarefas, desenho de tarefas, critério de idoneidade didática, ensino de matemática, aprendizagem de matemática.AbstractThis article presents the of Study and Task Design Cycle (STDC) as a research method aimed at the study and design of mathematical tasks to guide, above all, the work of the teacher in the classroom. Based on the combination of theoretical tools from the perspective of Task Design and Didactic Suitability Criteria, the STDC results in a powerful and interesting tool to guide working with mathematical tasks and has been configured as a privileged space for studies and discussions around didactic and mathematical knowledge; acquisition of experiences and knowledges and reflections for changes in pedagogical practice. This article is based on the intention of disseminating the results of the research developed with the STDC, in order to foster discussions on the issue in question.Keywords: tasks, task design, didactic suitability criterion, mathematics teaching, mathematics learning.                                                         ResumenEste artículo presenta el Ciclo de Estudio y Diseño de Tareas (CEDT) como un método de investigación orientado al estudio y diseño de tareas matemáticas para guiar, sobre todo, el trabajo del profesor en el aula. Basado en la combinación de herramientas teóricas desde la perspectiva del Diseño de Tareas y Criterios de Adecuación Didáctica, el CEDT da como resultado una poderosa e interesante herramienta para guiar el trabajo con tareas matemáticas y ha sido un espacio privilegiado para estudios y discusiones en torno al conocimiento didáctico y matemático; adquisición de experiencias; conocimientos y reflexiones para los cambios en la práctica pedagógica. También tiene la intención de este artículo difundir los resultados de la investigación trabajando con el CEDT con el fin de fomentar los debates sobre la temática.Palabras clave: tareas, diseño de tareas, criterio de adecuación didáctica, enseñanza de matemáticas, aprendizaje matemático.

scholarly journals Digital Representations of Mathematical Objects in the Context of Various Forms of Representation of Mathematical Knowledge

2020 ◽  
pp. 58-86
Author(s):  
Semjon F. Adlaj ◽  
◽  
Sergey N. Pozdniakov ◽  
Keyword(s):  
Comparative Analysis ◽  
Digital Media ◽  
Mathematical Knowledge ◽  
Information Environment ◽  
Teaching Mathematics ◽  
Mathematical Concepts ◽  
Mathematical Objects ◽  
Computer Tools ◽  
Digital Representations ◽  
The Impact

This article is devoted to a comparative analysis of the results of the ReMath project (Representing Mathematics with digital media), devoted to the study of digital representations of mathematical concepts. The theoretical provisions and conclusions of this project will be analyzed based on the theory of the information environment [1], developed with the participation of one of the authors of this article. The analysis performed in this work partially coincides with the conclusions of the ReMath project, but uses a different research basis, based mainly on the work of Russian scientists. It is of interest to analyze the work of the ReMath project from the conceptual positions set forth in this monograph and to establish links between concepts and differences in understanding the impact of computer tools (artifacts) on the process of teaching mathematics. At the same time, the authors dispute the interpretation of some issues in Vygotsky’s works by foreign researchers and give their views on the types and functions of digital artifacts in teaching mathematics.

scholarly journals "If you don't have an education, you are no one": Understanding the School Experiences of Youth Involved in Drug-Related Crime in Ciudad Juárez and Medellín

2020 ◽  
Vol 6 (1) ◽  
pp. 148
Author(s):  
Cirenia Chavez Villegas ◽  
Elena Butti
Keyword(s):  
Educational Experiences ◽  
School Experiences ◽  
Drop Out ◽  
Ciudad Juarez ◽  
Urban Centers ◽  
Male Youth ◽  
Youth Delinquency ◽  
Depth Interviews ◽  
Out Of School

The relation between being out of school and participating in criminal economies is widely documented in the literature on youth delinquency. However, the complex connection between these two phenomena has not yet been fully unpacked. This paper draws from two studies that we, the authors, conducted separately to explore the role educational experiences play in shaping the delinquent trajectories of male youth who participate in the drug business in urban centers located in Mexico and Colombia. The first consists of in-depth interviews and surveys conducted in Ciudad Juárez, Mexico, while the second is based on long-term ethnographic engagement in Medellín, Colombia. We provide unique insights into the educational experiences of this hard-to-reach population and find that economic hardship does not wholly explain why these young people leave school and engage in delinquent activities. These youth do not "drop out" of school in search of money; rather, they are "pushed out" by a vicious cycle of stigmatization, segregation, punishment, and exclusion. By exploring these dynamics in two cities that have waged long drug wars, this article furthers understanding of the nexus between crime-related violence and educational experiences, thus making an important contribution to the field of education in emergencies.

Developing Program Around Out-of-School Experiences

1974 ◽  
Vol 58 (382) ◽  
pp. 171-176
Author(s):  
Franklin J. Thompson
Keyword(s):  
School Experiences ◽  
Out Of School

scholarly journals What Does Social Realism Have to Offer for Research on Teacher Identity in Mathematics Education?

2019 ◽  
Vol 18 (7) ◽  
pp. 1229-1247 ◽  
Author(s):  
Lise Westaway ◽  
Gabriele Kaiser ◽  
Mellony Graven
Keyword(s):  
Primary School ◽  
Teacher Identity ◽  
Mathematical Knowledge ◽  
Social Constructionist ◽  
Social Realism ◽  
Teaching Mathematics ◽  
School Teachers ◽  
Primary School Teachers ◽  
Knowledge And Skills ◽  
Made In

Abstract Research that focuses on teacher identity is gaining traction as researchers argue that teachers mediate more than mathematical knowledge and skills in the classroom. This research tends to be underpinned by a social constructionist orientation, which foregrounds epistemology over ontology. This orientation is limiting for research that wishes to understand the base conditions that enable or constrain the expression (i.e. both communication and action) of teacher identity in teaching primary mathematics. The paper suggests that this requires research that explores the interaction between structure, culture and agency in the expression of teacher identity in teaching mathematics in primary school. The study argues that a social realist orientation is of value to research on teacher identity. From this perspective, teacher identity is defined as the manner in which teachers express their roles as teachers. As the paper is primarily theoretical, the exemplification is limited to two primary school teachers’ expression of only one role namely effective communicator of mathematics. It demonstrates what social realism enables, that is, not illuminated in research underpinned by a social constructionist orientation. The argument made in this paper elucidates how social realism supports a deep analysis of the structural and agential conditions that enable and constrain teacher identities.

Let's Do It: Using Geometry Tiles As a Manipulative for Developing Basic Concepts

1983 ◽  
Vol 30 (8) ◽  
pp. 8-15
Author(s):  
Virginia M. Horak ◽  
Willis J. Horak
Keyword(s):  
Young Children ◽  
School Experiences ◽  
Elementary Grades ◽  
Spatial Relationships ◽  
Geometric Shapes ◽  
Geometrical Concepts ◽  
Basic Concepts ◽  
Out Of School

Many of the out-of-school experiences young children have deal with geometrical concepts and understandings. Thus children have an intuitive feeling for much of the geometry content introduced in the lower elementary grades. The “geometry tile” described in this article can be used to develop and extend these beginning concepts. Through the use of handson materials like these tiles, children are better able to visualize geometric shapes and to communicate the involved spatial relationships. They are also able to begin dealing with measurement in a very concrete manner.

Do the Standards Go Far Enough? Power, Policy, and Practice in Mathematics Education

1992 ◽  
Vol 23 (5) ◽  
pp. 412-431 ◽  
Author(s):  
Michael W. Apple
Keyword(s):  
Mathematics Education ◽  
Educational Reform ◽  
Mathematical Knowledge ◽  
Mathematics Curriculum ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Policy And Practice ◽  
Conservative Movement ◽  
Evaluation Standards

Although NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) are generating considerable interest, there has been little discussion of their ideological and social grounding and effects. By placing the Standards within the growing conservative movement in education, this paper raises a number of crucial issues about the documents, including the depth of the financial crisis in education and its economic and ideological genesis and results; the nature of inequality in schools; the role of mathematical knowledge in our economy in maintaining these inequalities; the possibilities and limitations of a mathematics curriculum that is more grounded in students' experiences; and the complicated realities of teachers' lives. Without a deeper understanding of these issues, the Standards will be used in ways that largely lend support only to the conservative agenda for educational reform.

Implementing The Professional Standards for Teaching Mathematics: Linking Teaching, Learning, and Assessment

1994 ◽  
Vol 41 (9) ◽  
pp. 550-552
Author(s):  
Jeane M. Joyner
Keyword(s):  
Learning Environment ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Professional Standards ◽  
Teaching Mathematics ◽  
Other Information ◽  
Teaching Learning ◽  
Analysis Of Teaching

The sixth standard in the Professional Standards for Teaching Mathematics (NCTM 1991) focuses on analyzing and interconnecting teaching and learning. The standard calls for the analysis of teaching and learning to be ongoing by “[o]bserving, listening to, and gathering other information about students to assess what they are learning.” Teachers examine the “[e]ffects of the tasks, discourse, and learning environment on students' mathematical knowledge, skills, and dispositions.”

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