Youngsters Solving Mathematical Problems with Technology

Carreira, Susana; Jones, Keith; Amado, Nélia; Jacinto, Hélia; Nobre, Sandra

doi:10.1007/978-3-319-24910-0

Cited by 23 publications

(15 citation statements)

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“…Given that all the students were attending the fifth and sixth grades, their learning of formal logic in school is inexistent, and logical reasoning is very limited in their mathematics lessons, as it is delayed to more advanced school levels in the Portuguese curriculum. However, over several years of implementation of the mathematical problem-solving competition, it was observed that analytical reasoning problems, compared with several other non-routine problems proposed, were among the competitors' favorites, apparently because they incite their curiosity and appeal to their cleverness [9]. This suggests that such problems deserve new attention from school mathematics concerning the development of deductive reasoning.…”

Section: Analytical Reasoning Problems As Deductive Reasoning Problemsmentioning

confidence: 99%

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

2020

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The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problems are adequate tasks to engage the solver in deductive reasoning, as they require rule checking and option elimination, for which chains of inferences based on premises and rules are accomplished. Focusing on the solutions of children aged 10–12 to an analytical reasoning problem proposed in two separate settings—a web-based problem-solving competition and mathematics classes—this study aims to find out what forms of deductive reasoning they undertake and how they express that reasoning. This was done through a qualitative content analysis encompassing 384 solutions by children participating in a beyond-school competition and 102 solutions given by students in their mathematics classes. The results showed that four different types of deductive reasoning models were produced in the two venues. Moreover, several representational resources were found in the children’s solutions. Overall, it may be concluded that moderately complex analytical reasoning tasks can be taken into regular mathematics classes to support and nurture young children’s diverse deductive reasoning models.

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Section: Analytical Reasoning Problems As Deductive Reasoning Problemsmentioning

confidence: 99%

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

2020

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“…Each solution should be submitted electronically and include a complete explanation of the processes followed. A selection of exemplary solutions was published on the website, portraying different approaches or representations, or showing the use of different tools (Carreira et al, 2016). Within this empirical context, our research aimed to understand the role of the tools chosen to solve and express mathematical problems, particularly when developing a conceptual model of the problem situation.…”

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confidence: 99%

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Jacinto

Carreira

2021

J. Math. Educ.

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This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

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“…Based on the findings of the research, learning space geometry using GeoGebra further improves problem solving skills than conventional learning. Carreira, Jones, Amado, Jacinto, and Nobre (2016) also explained that problem solving is the kind of activity that requires experimentation, exploration, investigation, testing, reflection, and discussion. The results also found that students were able to solve problems very well.…”

Section: Resultsmentioning

confidence: 99%

Implementation of Space Geometry Learning Using Geogebra to Improve Problem Solving Skills

Pamungkas

Nugroho

2020

mapan

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Prospective mathematics teachers must be equipped with problem solving skills because it has a very important place in the mathematics curriculum. The purpose of this research is to get an overview of improving the problem solving skills of prospective mathematics teachers by implementing GeoGebra on space geometry learning. The research was conducted in Study Program of Mathematics Education, Tidar University in the second semester students. This research uses quasi-experimental method, with nonequivalent control group pretest-posttest design using two groups, namely experimental group consisting of 36 students got GeoGebra-based space geometry learning and control group consisting of 35 students got conventional space geometry learning. Research instruments in the form of observation sheets and test instruments in the form of pretest and posttest to measure achievements of problem solving skills improvement. The data obtained is then processed and analyzed by calculating the percentage of learning implementation and calculating the average normalized gain score (N-Gain). The results showed that GeoGebra-based Space Geometry learning can improve problem solving skills. In the experimental group, problem solving skills were improved in high category, while in the control group the improvement of problem solving skills in moderate category.

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Youngsters Solving Mathematical Problems with Technology

Cited by 23 publications

References 0 publications

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Implementation of Space Geometry Learning Using Geogebra to Improve Problem Solving Skills

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