scholarly journals A Visual Approach for Solving Problems with Fractions

2021 ◽  
Vol 11 (11) ◽  
pp. 727
Author(s):  
Ana Barbosa ◽  
Isabel Vale
Keyword(s):  
Problem Solving ◽  
Elementary Education ◽  
Teaching Experience ◽  
Future Teachers ◽  
Visual Component ◽  
Before And After ◽  
Visual Approach ◽  
Mathematical Problems ◽  
Analytical Approaches ◽  
Didactics Of Mathematics

This article discusses the importance of visual models in problem solving, in the scope of rational numbers. We seek to highlight the potential of this approach, as a structuring theme in the mathematical development of students in elementary education and the connections it allows to establish. In order for students to be mathematically competent and creative, they must be able not only to solve traditional computational problems but also to use models/visual representations when solving all types of mathematical problems, including those in which the visual component is not evident. We developed a qualitative study based on a didactical experience involving 14 future teachers who were attending a Didactics of Mathematics unit course that included a module about problem solving with emphasizes in visual approaches. The main purpose of the study was to identify the strategies used by the future teachers when solving problems with multiple solutions, before and after that module. Data was collected through observation and the written productions of the participants. It was possible to conclude that they tended to privilege analytical approaches before the intervention and, after the teaching experience, they started to value visual approaches, which generated an increase of the productions involving this type of solutions.

scholarly journals Characteristics of Students’ Intuitive Thinking in Solving Mathematical Problems

2019 ◽  
Vol 3 ◽  
pp. 48-57
Author(s):  
Maria Ulpah
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Teaching Experience ◽  
Mathematical Problem Solving ◽  
Problem Solution ◽  
Important Thing ◽  
Cognitive Mediation ◽  
Intuitive Thinking ◽  
Mathematical Problems ◽  
Alternative Solutions

Intuition is one of important thing in the process of solving mathematical problems. It works as cognitive mediation. In this understanding, intuition can be made as a bridge to students' understanding so that it can be accessed in linking imagined objects with the desired alternative solutions. In other words, students can determine what strategies or steps should be taken to get a problem solution, especially contextual problems that have completion steps that cannot be accessed directly. Intuitive thinking often occurs in mathematical problem solving. This was also seen in the mathematical students of IAIN Purwokerto. Based on the teaching experience so far, it was found that many students gave spontaneous answers without analyzing first. So, the researcher studied how characteristics of students’ intuitive thinking are. This research used qualitative with descriptive-exploratory type of research and used test to identify the characteristics of students’ intuitive thinking in solving mathematical problems. Results showed that students’ characteristics consisted of extrapolative, implicitly, persistently, coercively, and the power of synthesis.

Meningkatkan Kemampuan Pengajuan Masalah Serta Penyelesaian Masalah Matematika Melalui Pembelajaran Berbasis Masalah Pada Mahasiswa Jurusan Pendidikan Matematika STKIP “Tapanuli Selatan” Padang Sidempuan

2014 ◽  
Vol 3 (2) ◽  
pp. 165-172
Author(s):  
Sinar Depi Harahap
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Strong Association ◽  
Mathematics Problems ◽  
New Information ◽  
Learning Mathematics ◽  
Before And After ◽  
Mathematical Problems ◽  
Mathematical Relationships ◽  
Math Problems

Learning mathematics should be able to improve the abilityand creativity in learning mathematics, especially in solving mathematical problems. To improve theability of anappropriate learning need sand learning mathematical problem submissionis in accordance with the needs of students in facilitating the completion of (solution) of the mathematical problem significantly. To obtain data submission capability math problem students, the research for mulated the problemas follows: (a) How does the ability filing math problems before and after the learning seen from the stage before and during problem solving?,(b) How is the level of complexity of the questions asked of students according to the structure of language and mathematical relationships?, (c) how associations filing capability math problems with the ability of the settlement (solving) the mathematical problem?.To answer this problem conducted experimental research on mathematics semester students majoringin STKIP "Tapanuli Selatan" Padangsidimpuan. Results showed that (a) the ability of the student submission mathematical problemsseen from the stage before and during the settlement of problems inproblem-based learningis quite good, as shown by the large percentage of math questions that can be solved either with new information and without any new information. (b) Differences filing capabilities grade math problems and problem-based learning class conventional learningis significant. (c) the ability filing math problems with the ability of the settlement (solving) the strong association of students of mathematics problems.

Scientific Problem Solving in a Virtual Laboratory: A Comparison Between Individuals and Pairs

2008 ◽  
Vol 67 (2) ◽  
pp. 71-83 ◽  
Author(s):  
Yolanda A. Métrailler ◽  
Ester Reijnen ◽  
Cornelia Kneser ◽  
Klaus Opwis
Keyword(s):  
Visual Search ◽  
Problem Solving ◽  
Process Data ◽  
Scientific Problem ◽  
Domain Specific ◽  
Scientific Problem Solving ◽  
Before And After ◽  
Verbal Data ◽  
Psychological Knowledge ◽  
Problem Solving Task

This study compared individuals with pairs in a scientific problem-solving task. Participants interacted with a virtual psychological laboratory called Virtue to reason about a visual search theory. To this end, they created hypotheses, designed experiments, and analyzed and interpreted the results of their experiments in order to discover which of five possible factors affected the visual search process. Before and after their interaction with Virtue, participants took a test measuring theoretical and methodological knowledge. In addition, process data reflecting participants’ experimental activities and verbal data were collected. The results showed a significant but equal increase in knowledge for both groups. We found differences between individuals and pairs in the evaluation of hypotheses in the process data, and in descriptive and explanatory statements in the verbal data. Interacting with Virtue helped all students improve their domain-specific and domain-general psychological knowledge.

scholarly journals Students’ suspension of sense making in problem solving

ZDM ◽  
2021 ◽  
Author(s):  
Gemma Carotenuto ◽  
Pietro Di Martino ◽  
Marta Lemmi
Keyword(s):  
Problem Solving ◽  
Qualitative Study ◽  
Word Problem ◽  
Word Problems ◽  
Mathematical Problem ◽  
Critical Issue ◽  
Mathematical Problem Solving ◽  
Sense Making ◽  
Mathematical Problems

AbstractResearch on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the presence of words and expressions having many and sometimes opposite meanings. Significant examples are the terms ‘realistic’ and ‘modeling’ associated with word problems in school. Understanding how these terms are used is important in research, because this issue relates to the design of several studies and to the interpretation of a large number of phenomena, such as the well-known phenomenon of students’ suspension of sense making when they solve mathematical problems. In order to deepen our understanding of this phenomenon, we describe a large empirical and qualitative study focused on the effects of variations in the presentation (text, picture, format) of word problems on students’ approaches to these problems. The results of our study show that the phenomenon of suspension of sense making is more precisely a phenomenon of activation of alternative kinds of sense making: the different kinds of active sense making appear to be strongly affected by the presentation of the word problem.

scholarly journals Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

2016 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Jackson Pasini Mairing
Keyword(s):  
Problem Solving ◽  
Procedural Knowledge ◽  
Mental Image ◽  
Research Subjects ◽  
Maximum Score ◽  
Mathematical Problems ◽  
Problem Solving Strategies ◽  
Thinking Process ◽  
Problem Solvers ◽  
Holistic Rubric

Solving problem is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe the thinking process of naive problem solvers based on heuristic of Polya. The researcher gave two problems to students at grade XI from one of high schools in Palangka Raya, Indonesia. The research subjects were two students with problem solving scores of 0 or 1 for both problems (naive problem solvers). The score was determined by using a holistic rubric with maximum score of 4. Each subject was interviewed by the researcher separately based on the subject’s solution. The results showed that the naive problem solvers read the problems for several times in order to understand them. The naive problem solvers could determine the known and the unknown if they were written in the problems. However, they faced difficulties when the information in the problems should be processed in their mindsto construct a mental image. The naive problem solvers were also failed to make an appropriate plan because they did not have a problem solving schema. The schema was constructed by the understanding of the problems, conceptual and procedural knowledge of the relevant concepts, knowledge of problem solving strategies, and previous experiences in solving isomorphic problems.

Problem solving with the Sneetches

2016 ◽  
Vol 23 (5) ◽  
pp. 282-283
Author(s):  
James Russo ◽  
Toby Russo
Keyword(s):  
Problem Solving ◽  
Multiple Solutions ◽  
Mathematical Concepts ◽  
Mathematical Problems

Math by the Month features collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes four activities each for grade bands K–2, 3–4, and 5–6. In this issue, teachers read the classic Dr. Seuss book The Sneetches and other stories with their class and get students to engage with these associated mathematical problems. The problems, many of which are open-ended or contain multiple solutions or solution pathways, cover a range of mathematical concepts.

Teaching Personal Finance Mathematical Problem Solving to Individuals With Moderate Intellectual Disability

2016 ◽  
Vol 40 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Jenny Root ◽  
Alicia Saunders ◽  
Fred Spooner ◽  
Chelsi Brosh
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Functional Relation ◽  
Personal Finance ◽  
Future Research ◽  
School Students ◽  
Problem Solving Skills ◽  
Mathematical Problems ◽  
Based Instruction ◽  
Multiple Probe

The ability to solve mathematical problems related to purchasing and personal finance is important in promoting skill generalization and increasing independence for individuals with moderate intellectual disabilities (IDs). Using a multiple probe across participant design, this study investigated the effects of modified schema-based instruction (MSBI) on personal finance problem solving skills, purchasing an item on sale or leaving a tip, and using a calculator or iDevice (i.e., iPhone or iPad) for three middle school students diagnosed with a moderate ID. The results showed a functional relation between MSBI using a calculator on the participant’s ability to solve addition and subtraction personal finance word problems and generalize to iDevices. The findings of this study provide several implications for practice and offer suggestions for future research.

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