scholarly journals Different Perspectives on Success in Solving Stand-Alone Problems by 14 to 15-Year-Old Students / Različite prespektive o uspješnosti 14 i 15-godišnjaka u rješavanju izoliranoga problema

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Nives Baranović ◽  
Branka Antunović-Piton
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Secondary School ◽  
Mathematical Task ◽  
Mathematical Concepts ◽  
Urban Elementary Schools ◽  
8Th Grade ◽  
Verbal Problem ◽  
Set Up ◽  
Problem Solving Process

The paper defines a special type of problem tasks and considers its didactic potential, as well as the success of students in solving the selected problem. The research instrument used is a geometrical task from the National Secondary School Leaving Exam in Croatia (State Matura). The geometrical task is presented in three versions: as a verbal problem, as a verbal problem with a corresponding image and as a problem in context. The material analysed in the present paper was collected from 182 students in 7th and 8th grade of Croatian urban elementary schools. The didactic potential is considered from the aspect of use of mathematical concepts and connections. The success of students in problem-solving is considered from the aspect of implementation of the problem-solving process and producing correct answers, depending on the manner in which the tasks are set up. The results show that the stand-alone problem, as a special type of problem task, has considerable didactic potential. However, the students’ skills of discovering and connecting mathematical concepts and their properties are underdeveloped. In addition, the manner in which the tasks are set up considerably affects the process of solving the task and consequently the success of that process. Based on the results of the research, proposals are given for application of stand-alone problems in teaching mathematics.Key words: isolated problem; mathematical task; problem solving; problem evaluation.  --- U radu se definira posebna vrsta problemskoga zadatka te se razmatra njegov didaktički potencijal kao i uspješnost učenika u rješavanju odabranoga problema. Instrument istraživanja je geometrijski zadatak s državne mature koji se postavlja u tri inačice: kao tekstualni problem, kao tekstualni problem uz odgovarajuću sliku te kao zadatak u kontekstu. U istraživanju je sudjelovalo 182 učenika 7. i 8. razreda hrvatskih gradskih osnovnih škola. Didaktički potencijal razmatra se s aspekta iskoristivosti matematičkih koncepata i veza, a uspješnost učenika u rješavanju problema razmatra se s aspekta provedbe procesa rješavanja i otkrivanja točnoga rješenja ovisno o načinu postavljanja zadatka. Rezultati pokazuju da promatrani problem kao posebna vrsta problemskoga zadatka ima veliki didaktički potencijal, ali da učenici imaju nedovoljno razvijene vještine otkrivanja i povezivanja matematičkih koncepata i njihovih svojstava. Osim toga, način postavljanja zadatka značajno utječe na proces rješavanja, a posljedično i na uspješnost određivanja rješenja. Na temelju rezultata daju se prijedlozi primjene opisane vrste problema u nastavi Matematike.Ključne riječi: izolirani problem; matematički zadatak; rješavanje problema; vrednovanje problema

scholarly journals Resolución de problemas matemáticos en GeoGebra

2020 ◽  
Vol 9 (1) ◽  
pp. 26-42
Author(s):  
William Enrique Poveda Fernández
Keyword(s):  
Costa Rica ◽  
Problem Solving ◽  
Secondary School ◽  
Secondary School Teachers ◽  
Mathematical Reasoning ◽  
Mathematical Thinking ◽  
School Teachers ◽  
Mathematical Objects ◽  
Problem Solving Strategies ◽  
Problem Solving Process

RESUMENEn este artículo se analizan y discuten las ventajas y oportunidades que ofrece GeoGebra durante el proceso de resolución de problemas. En particular, se analizan y documentan las formas de razonamiento matemático exhibidas por ocho profesores de enseñanza secundaria de Costa Rica, relacionadas con la adquisición y el desarrollo de estrategias de resolución de problemas asociadas con el uso de GeoGebra. Para ello, se elaboró una propuesta de trabajo que comprende la construcción y la exploración de una representación del problema, y la formulación y la validación de conjeturas. Los resultados muestran que los profesores hicieron varias representaciones del problema, examinaron las propiedades y los atributos de los objetos matemáticos involucrados, realizaron conjeturas sobre las relaciones entre tales objetos, buscaron diferentes formas de comprobarlas basados en argumentos visuales y empíricos que proporciona GeoGebra. En general, los profesores usaron estrategias de medición de atributos de los objetos matemáticos y de examinación del rastro que deja un punto mientras se arrastra.Palabras claves: GeoGebra; Resolución de problemas; pensamiento matemático. RESUMOEste artigo analisa e discute as vantagens e oportunidades oferecidas pelo GeoGebra durante o processo de resolução de problemas. Em particular, as formas de raciocínio matemático exibidas por oito professores do ensino médio da Costa Rica, relacionadas à aquisição e desenvolvimento de estratégias de resolução de problemas associadas ao uso do GeoGebra, são analisadas e documentadas. Para isso, foi elaborada uma proposta de trabalho que inclui a construção e exploração de uma representação do problema, e a formulação e validação de conjecturas. Os resultados mostram que os professores fizeram várias representações do problema, examinaram as propriedades e atributos dos objetos matemáticos envolvidos, fizeram conjecturas sobre as relações entre esses objetos e procuraram diferentes formas de os verificar com base em argumentos visuais e empíricos fornecidos pelo GeoGebra. Em geral, os professores utilizaram estratégias para medir os atributos dos objetos matemáticos e para examinar o rasto que um ponto deixa enquanto é arrastado.Palavras-chave: GeoGebra; Resolução de problemas; pensamento matemático. ABSTRACTThis article analyzes and discusses the advantages and opportunities offered by GeoGebra during the problem-solving process. In particular, the mathematical reasoning forms exhibited by eight secondary school teachers in Costa Rica, related to the acquisition and development of problem solving strategies associated with the use of GeoGebra, are analyzed and documented. The proposal was developed that includes the elements: construction and exploration of a representation of the problem and formulation and validation of conjectures. The results show that teachers made several representations of the problem, examined the properties and attributes of the mathematical objects involved, made conjectures about the relationships between such objects, and sought different ways to check them based on visual and empirical arguments provided by GeoGebra. In general, the teachers used strategies to measure the attributes of the mathematical objects and to examine the trail that a point leaves while it is being dragged.Keywords: GeoGebra; Problem Solving; Mathematical Thinking.

Focus-Fight-Finalize (3F): Problem-Solving Steps Extracted From Behavioral Patterns in Block Based Programming

2020 ◽  
Vol 58 (7) ◽  
pp. 1279-1310 ◽  
Author(s):  
Ünal Çakıroğlu ◽  
Suheda Mumcu
Keyword(s):  
Problem Solving ◽  
Secondary School ◽  
Secondary School Students ◽  
Learning Experience ◽  
Behavioral Patterns ◽  
School Students ◽  
Programming Environments ◽  
Public Secondary School ◽  
Block Based ◽  
Problem Solving Process

This exploratory study attempts to determine problem solving steps in block based programming environments. The study was carried out throughout one term within Code.org. Participants were 15 6th grade secondary school students enrolled in an IT course at a public secondary school. Observations, screenshots and interviews were analyzed together to find out what students do and what they think during problem solving process. As a result, three main steps (focus, fight and finalize) were extracted from students’ behavioral patterns. The results suggest that three steps occur in linear or cyclic manner with regard to the programming constructs required for the solution of the problem. Implications for instructors who desire to provide a better learning experience on problem solving through block-based programming are also included.

scholarly journals TEKNIK POLYA DALAM PENYELESAIAN MASALAH GEOMETRI

Sigma ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 114
Author(s):  
Rahma Wahyu
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Qualitative Approach ◽  
High Ability ◽  
Story Problems ◽  
Story Problem ◽  
Study Results ◽  
Mathematical Problems ◽  
Problem Solving Process ◽  
Low Ability

This study aims to analyze the steps for solving mathematical problems by students' understanding of the geometric material in story problems based on the Polya technique. This research was conducted in one of the Islamic elementary schools in Batu City on six students in grade 6. The approach taken is to use a descriptive qualitative approach. The research was carried out using triangulation methods, namely observing the problem-solving process, interviews, and reviewing documents (students' work). Interviews in this study were conducted with several students, namely two high ability people, two low ability people, and two medium ability people. The analysis was carried out by concluding the data obtained based on the observations that have been made. The study results showed that the Polya technique showed different results on the results of solving the problems of each category of students in solving story problems about the area of squares and rectangles. Based on these results, it can be seen that students' understanding of the geometry material on the story problem.

scholarly journals UNDERSTANDING OF BASIC CONCEPTS FOR MASTERING COMPETENCES OF SCHOOL MATHEMATICS

2016 ◽  
Vol 2 ◽  
pp. 330
Author(s):  
Anita Sondore ◽  
Elfrīda Krastiņa ◽  
Pēteris Daugulis ◽  
Elga Drelinga
Keyword(s):  
Elementary Schools ◽  
Problem Solving ◽  
Life Quality ◽  
School Failure ◽  
School Mathematics ◽  
Mathematical Concepts ◽  
Mathematics Courses ◽  
Mathematical Competence ◽  
Basic Concepts ◽  
University Level

Mathematical competence as a universal and fundamental competence is essential for everyone as a problem solving and life quality improving tool. It is also essential for future teachers who will implement competence based teaching processes starting from elementary schools and preschools. The goal of this research is to discuss typical errors about certain basic mathematical concepts which are taught in school. Failure to grasp these concepts cause problems for learning subsequent mathematics courses and dealing with practical problems. This research will help to improve studies at university level. Experience analysis of university educators related to oral and written answers of students in tests is used in this research. Observations show that many errors get repeated year by year.

Reasoning as an Associative Process: II. “Direction” in Problem Solving as a Function of Prior Reinforcement of Relevant Responses

1956 ◽  
Vol 2 (3) ◽  
pp. 501-507 ◽  
Author(s):  
Abe J. Judson ◽  
Charles N. Cofer ◽  
Sidney Gelfand
Keyword(s):  
Problem Solving ◽  
Problem Solution ◽  
Complex Response ◽  
Associative Process ◽  
Response Systems ◽  
Verbal Problem ◽  
A Chain ◽  
Set Up

Several studies are described in which relevant patterns of verbal associations, set up by learning in the first stage of the experiment, are shown to be associated with the frequencies of certain types of solution in the Maier two string and hat rack problems. It is also shown, in the case of a simple verbal problem, that problem solution requiring choice of members of a chain of free associations is affected by prior reinforcement of one member of the chain. These investigations are interpreted as giving support to and indicating the fruitfulness of a conception of set or direction in problem solving as consisting of complex response systems or habit families.

A course of Elementary Probability Course

2020 ◽  
Author(s):  
Gane Samb LO ◽  
Aladji Babacar Niang ◽  
Lois Chinwendu Okereke
Keyword(s):  
Probability Theory ◽  
Problem Solving ◽  
Secondary School ◽  
Mathematical Statistics ◽  
Mathematical Concepts ◽  
Foundations Of Probability ◽  
Counting Methods ◽  
General Chapter ◽  
Mathematical Foundations ◽  
Present Text

This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability theory. The theory is preceded by a general chapter on counting methods. Then, the theory of probabilities is presented in a discrete framework. Two objectives are sought. The first is to give the reader the ability to solve a large number of problems related to probability theory, including application problems in a variety of disciplines. The second is to prepare the reader before he takes course on the mathematical foundations of probability theory. In this later book, the reader will concentrate more on mathematical concepts, while in the present text, experimental frameworks are mostly found. If both objectives are met, the reader will have already acquired a definitive experience in problem-solving ability with the tools of probability theory and at the same time he is ready to move on to a theoretical course on probability theory based on the theory of Measure and Integration. The book ends with a chapter that allows the reader to begin an intermediate course in mathematical statistics.

Experimental projects and research: The use of programed instruction in teaching an advanced mathematical topic

1962 ◽  
Vol 9 (3) ◽  
pp. 160-162
Author(s):  
Robert Kalin
Keyword(s):  
Elementary Schools ◽  
Secondary School ◽  
Sixth Grade ◽  
Intermediate Grade ◽  
Mathematical Concepts ◽  
Mathematical Content ◽  
Considerable Evidence ◽  
Mathematical Topic

Considerable evidence bas been accumulating that intellectually superior fifth-and sixth-grade pupils have both the ability and the desire to learn important mathematical concepts normally not taught until secondary school. But elementary schools have generally been unable to include advanced mathematical content in their courses of study for their more capable intermediate-grade pupils.

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