ARITHMETICAL AND ALGEBRAIC THINKING lN PROBLEM-SOLVINGl (original) (raw)

Arithmetical and Algebraic Thinking in Problem-Solving

Bednarz, N., Radford, L., Janvier, B. and Lepage A. (1992). In W. Geeslin and K. Graham (eds.), Proceedings of the 16th Conference of the International Group for the Psychology of Mathematics Education (PME-16), University of New Hampshire, USA, 1, 65-72., 1992

The fact that students have difficulty acquiring and developing algebraic procedures in problem-solving. considering the arithmetical experience that they have acquired over years. calls for a didactic reflection on the nature of the conceptual changes which mark the transition from one mode of treatment to the other. In this perspective. our study seeks ID characterize the spontaneous problem-solving strategies used by Secondary III level students (14-and-15-year-olds), what have already taken one algebra course. when solving different problems. The analysis of the problem-solving procedures developed by these students reveals the differences between the conceptual basis which underlie the two modes of thought.

Algebraic Problem Solving and Learning Strategies in Compulsory Secondary Education

Procedia - Social and Behavioral Sciences, 2012

This paper accounts for a study to analyze of the influence of algebra as a procedure for problem solving among compulsory secondary education students. The investigation aims to examine the procedures chosen by compulsory secondary education students to solve mathematical problems which can be solved both by algebraic and arithmetic methods. Furthermore, it also pursues to relate the methodological tendency identified with these learning strategies. The research has been conducted in different public schools located in The Basque Country (Spain) and collects data from 215 students using a questionnaire that comprised of three mathematical problems which could be solved by both arithmetic and algebraic procedures and, additionally, the Motivated Strategies Learning Questionnaire. The conclusions highlight the role that contextual situation plays to encour age students to use algebraic procedures and the relationship between the learning strategies and the tendency to utilize algebraic methods.

Algebraic Thinking Profiles of Junior High Schools’ Pupil in Mathematics Problem Solving

International Journal of Trends in Mathematics Education Research

Algebra is one of concept that must be learned by pupils. It is because the algebraic concept can be used in all areas of mathematics. One of the ways that is used to develop pupils' algebraic abilities is to think algebraically. While one of the ways to develop pupils' algebraic thinking skills is to adapt pupils with mathematical problem solving. The purpose of this study is describing algebraic thinking profiles of junior high school pupils in mathematical problem solving. The description of pupils' algebraic thinking profiles is explained based on six indicators namely generalization, abstraction, analytic thinking, dynamic thinking, modeling and organization. This research is a qualitative study using test and interview methods. The research subjects consisted of one student in each student with high mathematical abilities, medium mathematical abilities and low mathematical abilities. The results showed that there were differences in algebraic thinking of junior ...

Students' Strategies and Reasoning in School Mathematics Problems Solving

2015

Although there has been many studies carried out considering different teaching and learning approaches on different perspectives and contexts, the aspects regarding influence of the student reasoning and choice of adequate strategies and procedures in solving problems still be influential to their achievement in mathematics tests. Though, based on this consideration, the purpose of this study was to explore Mozambican students' engagement with algebraic symbolism and their achievement in school mathematics. With a stronger focus on what is specific to 'algebraic thinking', as one aspect of thinking and reasoning employed in mathematical work, making generalizations and expressing generality, the aim of the study touch a variety of fields that have been researched in mathematics education. As findings, there were seen cases or situation that learners do not strictly the formal strategies because of some linguistic or scientific constraints as they do not translate correc...

Examining Algebraic Habits of the Mind through a Problem Solving: Elementary School Example

2022

In this study, it is aimed to determine the algebraic thinking habits of two eighth grade school students through the answers they gave in the process of solving mathematical problems. The algebraic habits of mind (ZCA) theoretical framework developed by Driscoll (1999) was used to reveal these thinking habits. The research design of this study is a case study and the participants consist of two eighth grade students. The data were analyzed using Driscoll (1999)'s ZCA framework, which is algebraic habits of mind. Descriptive analysis was used in the analysis of the data. When we look at the findings obtained from the research; It is seen that both students can do describing a rule and justifying a rule in the solutions of the problems. In addition, it is seen that computational shortcuts, equivalent expressions and symbolic expressions come to the fore in the solutions of students' problems. On the other hand, the habit of undoing in solving problems was not encountered very rarely in both students. In the light of the findings obtained, the reasons for the existing and non-existent algebraic habits of mind are discussed. As a result of this discussion, it is thought that it is effective to include guide questions to create and develop algebraic thinking habits in students in classroom teaching practices of teachers.

Analysis of student difficulties on algebra problem solving in junior high school

Journal of Physics: Conference Series, 2019

Algebra is one of the mathematical sciences studied in junior high school. Some students may have difficulty learning algebra. This study aims to determine the difficulties experienced by students in solving the problem of algebraic operations. The type of this research is qualitative research with case study approach. Subjects in this study are students of grade 8D 1 Salam Magelang junior high scchool, Central Java in the semester of the year 2016/2017 academic year. Methods of data collection used include algebraic operations tests, open questionnaires, and documentation. Data analysis techniques through data reduction, data presentation, and conclusions. The result of the research that there are students’ difficulties in doing algebraic problems related to concept and principle. Students difficulties experienced related to the concept of difficulty in determining variables and constants including but not understanding the definitions of variables and constants, and difficulties i...

Problem Solving - Purpose and Means of Learning Mathematics in School

Procedia - Social and Behavioral Sciences, 2015

Of all school subjects, mathematics introduces and develops the "problem-solving" concept, as fundamental component of school learning with a strong formative effect on students. In mathematics, solving problems represents the most effective concept to contextualization and re-contextualization of concepts, to operational and basic mathematical knowledge transfer to ensure a sustainable and meaningful learning. The resolvent conduct of the student also involves, in addition to the cognitive factors, factors aiming the affectivity and the experience of the student. In this context, the study conducted on a significant group of students at the end of the secondary school aimed at knowing the importance given by students to solving problems, the preferred type of problems and the performance level achieved by the students in solving math problems. Taking into account the complex intellectual activity, the nature of difficulties which the student faces in solving problems is varied, ranging from perceptual difficulties to those concerning his cognitive self-regulation.

A Commognitive Framework: The Process of Solving Mathematical Problems of Middle School Students

International Journal of Learning, Teaching and Educational Research, 2019

This study aims to describe students' ability to solve mathematical problems from a commognitive point of view, It will describe their word use, visual mediators, narratives, and routines. This type of research is qualitative research with a descriptive approach. The research method is comprised of four steps: (1) preparation, (2) collecting data, (3) transcribing the data, and (4) analyzing the data. The results of the study showed that the subject manifested visual markers of algebraic expressions in verbal terms and used words symbolically. The subject used sketching as a visual mediator, and the sketch was divided into parts. Narrative was used by students in relation to broad rectangular theorems and the concepts of addition, subtraction, and multiplication. The subject carried out a routine to solve the problem, which consisted of writing down what was known, dividing the problem into several parts, identifying the purpose of the problem, and making a sketch to determine how much fabric remained unused.

STUDENTS' DIFFICULTIES IN SOLVING MATHEMATICAL PROBLEMS

The purpose of this study is to analyze the ability and students' difficulties in solving mathematical problems. This study is a qualitative research with the number of participants-32 students consisting of 16 male students and 16 female students with an age range of 12-13 years. Data were collected by observation, interviews, and tests of social arithmetic problems. The results showed that junior high school students have low ability in solving mathematical problems. The low ability of students' mathematical problem solving is caused by several factors, namely (1) students can not understand the keyword of social arithmetic problem; (2) students can not develop problem solving strategy based on problem in question; (3) students easily give up in the face of every difficulty and error; (4) students do not like to read long and unclear questions in reading questions; (5) students are not careful in the calculation process; (6) the student is wrong in taking and determining the concept or strategy of completion; and (7) the students did not verify either in terms of concepts, strategies, calculations, and answers. In subsequent research, our objective is to focus more on student activities in solving mathematical problems.