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

Johnson, Heather L.; McClintock, Evan; Gardner, Amber

doi:10.1007/s40751-020-00061-9

Cited by 17 publications

(5 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Results of empirical research provided backing for this approach. Johnson et al (2020) engaged 13 secondary students with the Cannon Man and Toy Car tasks, and found that students discerned critical aspects of graphs themselves, what graphs "should" represent. To illustrate, one student distinguished between a convention, where an attribute was represented in a Cartesian plane (i.e., distance traveled on the vertical axis), and where she imagined that attribute in the physical world (on the ground).…”

Section: Discussionmentioning

confidence: 99%

“…Figure 1 (Cannon Man) and Figure 2 (Toy Car) show a screenshot of the end of each video animation (dotted lines provide an approximate trace of each object's motion) and computergenerated sketches of the two graphs in each task. For a more detailed description of the tasks, see Johnson et al (2020).…”

Section: Variation Theory In Task Design For Graphs: Different Forms mentioning

confidence: 99%

See 1 more Smart Citation

Task design for graphs: rethink multiple representations with variation theory

Johnson

2020

Mathematical Thinking and Learning

Self Cite

View full text Add to dashboard Cite

It is well known that students benefit from opportunities to interpret and create different representations (e.g., diagrams, graphs, tables, symbols) of mathematical ideas. Employing Marton's Variation theory as a lens, I argue for an expansion of the use of multiple representations in task design for graphs: Incorporate two different forms of the same type of graph to represent a relationship between variables in a situation. With this approach, designers, teachers, and researchers can engineer opportunities for students to discern, or separate, features of representation systems, such as the Cartesian coordinate system, and in turn, promote students' mathematical reasoning.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Variation Theory In Task Design For Graphs: Different Forms mentioning

confidence: 99%

Task design for graphs: rethink multiple representations with variation theory

Johnson

2020

Mathematical Thinking and Learning

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, Lingefjärd and Farahani (2017) identified three categories: (1) intuitive and iconic interpretations, (2) scientifically grounded interpretations and (3) a combination with influences from both 1 and 2. Similarly, Johnson et al (2019) included an iconic category and three other categories: motion of objects, individual quantities, and relationship between quantities. Our categories resemble these earlier categorizations.…”

Section: Discussionmentioning

confidence: 99%

Supporting primary school students’ reasoning about motion graphs through physical experiences

Duijzer

Heuvel–Panhuizen

Veldhuis

et al. 2019

ZDM Mathematics Education

View full text Add to dashboard Cite

Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper addresses the issue of how these 21st century skills of interpreting and creating graphs can be supported in a six-lesson teaching sequence about graphing motion. In this teaching sequence, we focused on the potential of an embodied learning environment to facilitate the development of primary school students' reasoning about motion graphs by having primary school students (9-11 years) 'walk' graphs in front of a motion sensor to generate distance-time graphs. We asked: How does students' reasoning about graphing motion develop over a six-lesson teaching sequence within an embodied learning environment? Based on the collected data, we examined changes in students' level of reasoning on graph interpretation and graph construction tasks using a repeated measurement design. Additionally, we present two teaching episodes showing instances of how perceptual-motor experiences during the lessons aided students' reasoning about graphical representations of motion. Results show that students went from iconic understanding towards understanding in which they reasoned based on one or two variables when interpreting and constructing graphical representations of motion events. At these higher levels of reasoning these students showed understanding of modelling motion in line with the intended 21st century skills of generating, refining, and evaluating graphs.

show abstract

“…One is an FLC and a local classroom community. Another is different theoretical communities, because there are different theoretical perspectives informing the design of the techtivites (Johnson et al, 2020). Our use of variation theory (Kullberg et al, 2017;Marton, 2015) underlies our decision to incorporate variation against a background of invariance.…”

Section: The Techtivities: Five Design Principlesmentioning

confidence: 99%

“…Each techtivity has four main elements (Johnson et al, 2020). First, students are to view a video animation and then consider attributes in the animation that may be possible to measure.…”

Section: Elements Of a Techtivitymentioning

confidence: 99%

Boundary Transitions Within, Across, and Beyond a Set of Digital Resources: Brokering in College Algebra

Johnson

Olson

Tsinnajinnie

et al. 2022

Digit Exp Math Educ

Self Cite

View full text Add to dashboard Cite

We address a problem of promoting instructional transformation in early undergraduate mathematics courses, via an intervention incorporating novel digital resources (“techtivities”), in conjunction with a faculty learning community (FLC). The techtivities can serve as boundary objects, in order to bridge different communities to which instructors belong. Appealing to Etienne Wenger’s Communities of Practice theory, we theorise a role of the instructor as a broker, facilitating “boundary transitions” within, across, and beyond a set of digital resources. By “boundary transition”, we mean a transition that is also a brokering move; instructors connect different communities as they draw links between items in their instruction. To ground our argument, we provide empirical evidence from an instructor, Rachel, whose boundary transitions served three functions: (1) to position the techtivities as something that count in the classroom community and connect to topics valued by the broader mathematics community; (2) to communicate to students that their reasoning matters more than whether they provide a correct answer, a practice promoted in the FLC; (3) to connect students’ responses to mathematical ideas discussed in the FLC, in which graphs represent a relationship between variables. Instructors’ boundary transitions can serve to legitimise novel digital resources within an existing course and thereby challenge the status quo in courses where skills and procedures may take precedence over reasoning and sense-making.

show abstract

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

Cited by 17 publications

References 23 publications

Task design for graphs: rethink multiple representations with variation theory

Task design for graphs: rethink multiple representations with variation theory

Supporting primary school students’ reasoning about motion graphs through physical experiences

Boundary Transitions Within, Across, and Beyond a Set of Digital Resources: Brokering in College Algebra

Contact Info

Product

Resources

About