Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

Johnson, Heather L.; Coles, Alf; Clarke, David

doi:10.1007/s11858-017-0894-0

Cited by 43 publications

(22 citation statements)

References 29 publications

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“…Tasks encompass more than just observable artifacts; they include the intentions of the task designers, the students working on the task and the teacher/researchers implementing the task (Johnson et al 2017a). First, we share design elements of our task sequences, then we explain our theoretical and conceptual bases for design.…”

Section: A Dual Approach To Digital Task Designmentioning

confidence: 99%

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Johnson

McClintock

Gardner

2020

Digit Exp Math Educ

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We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students' reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton's variation theory and Patrick Thompson's theory of quantitative reasoning, we designed digital task sequences, in which students were to create different graphs linked to the same video animations. We report results of a qualitative study of thirteen secondary students (aged 15-17), who participated in digital, taskbased, individual interviews. We investigated two questions: (1) How do students conceive of what graphs represent when engaging with digital task sequences? (2) How do student conceptions of graphs shift when working within and across digital task sequences? Two conceptions were particularly stablerelationships between quantities and literal motion of an object. When students demonstrated conceptions of graphs as representing change in a single quantity, they shifted to conceptions of relationships between quantities. We explain how a critical aspect: What graphs should represent, intertwined with students' graph-sketching. Finally, we discuss implications for digital task design to promote students' conceptions of mathematical representations, such as graphs. Keywords Digital task design. Variation theory. Quantitative reasoning. Graphs By means of digital technology, students have opportunities to sketch and interpret dynamic graphs linked to video animations (Kaput 1994; Kaput and Roschelle 1999; Schorr and Goldin 2008). Yet, such opportunities are only a starting point. Instead of promoting reasoning, student interactions with digital technology may focus on skills and recall (Kitchen and Berk 2016). We developed digital task sequences that center on Digital Experiences in Mathematics Education

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Section: A Dual Approach To Digital Task Designmentioning

confidence: 99%

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Johnson

McClintock

Gardner

2020

Digit Exp Math Educ

Self Cite

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“…Una de las ventajas de un SGD es que nos provee de una habilidad para retener el contexto o esencia de una configuración geométrica mientras podemos traer al frente aquellas partes dinámicas de toda la configuración que nos interesan. Esto es, podemos visualizar el estudio de la variación de un aspecto de la configuración mientras mantenemos otros aspectos constantes, La Resolución de Problemas Matemáticos y el Uso de Tecnología Digital en el Diseño de Libros Interactivos Manuel SantoS-trigo y MatíaS CaMaCho-MaChín Johnson et al (2017) mencionan que las tareas o problemas son esenciales y representan el medio para que los estudiantes desarrollen y muestren un pensamiento matemático consistente con el quehacer de la disciplina. Así, un problema puede utilizarse para introducir un contenido matemático nuevo, consolidar un procedimiento enseñado, generar oportunidades para que los estudiantes apliquen un concepto o procedimiento en una situación nueva, evaluar la comprensión de un concepto, o crear condiciones para que los estudiantes desarrollen y muestren habilidades genéricas y de colaboración para resolver problemas.…”

Section: El Movimiento De Las Figuras Y Objetos Matemáticos Y Los Libunclassified

“…También es común que en sus tareas académicas revise materiales en línea, interactúe con sus pares y comparta ideas sobre cómo resolver un problema o comprender algún concepto matemático. Johnson, Coles & Clarke (2017) afirman que las tareas matemáticas que trabajan los estudiantes moldean y caracterizan su aprendizaje. También sugieren que las oportunidades que tengan los estudiantes para desarrollar un pensamiento matemático dependen del tipo de tareas que se trabaje y lo que se valore y se promueva durante el proceso de resolución de las tareas.…”

Section: Introductionunclassified

La Resolución de Problemas Matemáticos y el Uso de Tecnología Digital en el Diseño de Libros Interactivos

Trigo

Machín

2018

Educatio

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Los libros de texto y los materiales de un curso de matemáticas siguen siendo un recurso importante para los estudiantes. En general, estos materiales ayudan a los estudiantes a revisar y extender sus conocimientos acerca de los temas que se estudian en la clase. Incluyen explicaciones de conceptos, definiciones y formas de resolver problemas, además deuna lista de problemas variados que los estudiantes tienen que resolver. Los desarrollos de la tecnología digital están transformando el diseño y uso de los libros de texto en términos de ofrecer un material interactivo donde el estudiante pueda consultar vídeos que expliquen conceptos, revisar otros recursos en línea o compartir y discutir sus acercamientos con otros a través de aplicaciones usando una tableta o un teléfono móvil. En este artículo se presenta un marco, que incluye episodios que caracterizan el proceso de resolver problemas, para el diseño de materiales interactivos donde los estudiantes tienen la oportunidad de representar y explorar problemas dinámicamente, formular conjeturas y relaciones y buscar argumentos que validen o sustenten esas relaciones. Textbooks are an essential resource that teachers use to organize and guide their students’ learning of mathematics. In general, textbooks help students review and extend their knowledge of the themes that they study in their courses. Digital technology developments are transforming the ways in which textbooks are designed since this technology fosters the inclusion of interactive activities where students can consult videos to review and extend concepts, access and discuss online materials and share and discuss ideas or problem solving approaches within a learning community that include their peers or other students. In this article, we present a framework that aims to help teachers design interactive textbooks via the identification of main problem solving episodes such as understanding the problem statement and the construction of dynamic representations, looking for different ways to solve the problem, extending the initial problem, and communicating results.

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“…Oleh karenanya, perancangan RPP harus menjadi perhatian karena menjadi tonggak awal keberlangsungan proses belajar mengajar. Gambar 2 merupakan perluasan dari tetrahedron model of the didactical situation (Rezat & Straßer, 2012) dan (Johnson, et. al., 2017).…”

Section: Pembahasanunclassified

Rencana Pelaksanaan Pembelajaran Matematika Di Sekolah Menengah Kejuruan

Fatimah¹,

Amam²

2018

JPPM Untirta

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This study aims to describe the lesson plan in vocational high schools. The analysis of lesson plan is based on: (1) conformity with the principles of lesson plan formulation in regulation of education and culture minister No. 22 of 2016 about standard of basic and intermediate education process; (2) conformity with the characteristics of learners, vocational mathematics knowledge, and learning activities in vocational education. Based on the analysis, it is necessary to develop lesson plan of vocational high schools tailored to the needs of learners and vocational mathematics knowledge in the work in the field of expertise both contextually and practically which will have implications for the design of mathematics tasks.

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Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

Cited by 43 publications

References 29 publications

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

La Resolución de Problemas Matemáticos y el Uso de Tecnología Digital en el Diseño de Libros Interactivos

Rencana Pelaksanaan Pembelajaran Matematika Di Sekolah Menengah Kejuruan

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