Graphs in Primary School: Playing with Technology

Ferrarello, Daniela

doi:10.1007/978-3-319-51380-5_8

Cited by 3 publications

(8 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This agrees with the ideas of different authors claiming that the teaching of graph theory should go from the global to the local aspects. For instance, Gibson (2012) designs a sequence of tasks that initially present graphs as integral wholes and sequentially focus on their parts, thus making students pay attention to local concepts such as subgraphs or minimal paths (see also the work of Ferrarello (2017)). Hart and Martin (2018) also emphasize students' ability to detach from the irrelevant characteristics of graphs in order to give more importance to their combinatorial aspects.…”

Section: Discussionmentioning

confidence: 99%

Characterizing Levels of Reasoning in Graph Theory

González

Gallego

Izquierdo

et al. 2021

EURASIA J Math Sci Tech Ed

View full text Add to dashboard Cite

This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We thus obtain four levels of reasoning: an initial level of visual character in which students perceive graphs as a whole; a second level, analytical in nature in which students distinguish parts and properties of graphs; a pre-formal level in which students can interrelate properties; and a formal level in which graphs are handled as abstract mathematical objects. Our results, which are supported by a review of the literature on the teaching and learning of graph theory, might be very helpful to design efficient data collection instruments for empirical studies aiming to analyze students' thinking in this field of mathematics.

show abstract

Section: Discussionmentioning

confidence: 99%

Characterizing Levels of Reasoning in Graph Theory

González

Gallego

Izquierdo

et al. 2021

EURASIA J Math Sci Tech Ed

View full text Add to dashboard Cite

show abstract

“…The next two sessions offer an original approach which differs from those found in previous work [11][12][13][14]. In the second session, we use star polygons to practice Eulerian cycles.…”

Section: Discussionmentioning

confidence: 99%

“…The reasoning stage is mainly devoted to deepening the understanding of Eulerian paths and cycles; Hamiltonian graphs appear briefly in the last session. We finally explain the definition of Eulerian cycle and propose to the participants some activities to distinguish Eulerian and non-Eulerian cycles before presenting the Köningsberg bridges problem, which is frequently used in the literature to introduce graphs [12][13][14].…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In Italy, some teaching experiments have been performed. About fifty 8-9 year old students participated in 12 sessions, one weekly meeting along 3 months, involving Eulerian and semi-Eulerian graphs, Hamiltonian graphs, planar graphs and graph coloring [12]. Using the laboratorian methodology, the authors propose activities such as problems to be solved with the help of paper and pencil, and online games such as YED Graph Editor.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Graph Theory for Primary School Students with High Skills in Mathematics

Blanco

García-Moya

2021

Mathematics

View full text Add to dashboard Cite

Graph theory is a powerful representation and problem-solving tool, but it is not included in present curriculum at school levels. In this study we perform a didactic proposal based in graph theory, to provide students useful and motivational tools for problem solving. The participants, who were highly skilled in mathematics, worked on map coloring, Eulerian cycles, star polygons and other related topics. The program included six sessions in a workshop format and four creative sessions where participants invented their own mathematical challenges. Throughout the experience they applied a wide range of strategies to solve problems, such as look for a pattern, counting strategies or draw the associated graph, among others. In addition, they created as challenges the same type of problems posed in workshops. We conclude that graph theory successfully increases motivation of participants towards mathematics and allows the appearance and enforcement of problem-solving strategies.

show abstract

Graph Theory in Primary, Middle, and High School

Ferrarello

Mammana

2017

ICME-13 Monographs

View full text Add to dashboard Cite

Graphs in Primary School: Playing with Technology

Cited by 3 publications

References 4 publications

Characterizing Levels of Reasoning in Graph Theory

Characterizing Levels of Reasoning in Graph Theory

Graph Theory for Primary School Students with High Skills in Mathematics

Graph Theory in Primary, Middle, and High School

Contact Info

Product

Resources

About