Exploring of Student’s Algebraic Thinking Process Through Pattern Generalization using Similarity or Proximity Perception

Students' algebraic thinking skills must continue to be developed because they can support success in mathematics. Algebraic thinking relates to generalizing patterns learned at the junior secondary level. During the process of generalizing students use the perception of similarity or proximity. Therefore, the purpose of this study is to describe the algebraic thinking process of junior high school students in generalizing patterns. The approach used is qualitative with 3 research subjects who have different algebraic thought processes. The results showed that junior high school students carried out algebraic thought processes by perceiving images, representing, looking for functional relationships, making generalizations, and applying general formulas. The difference in perception is used early in the activity and in the search for functional relationships. The results of this study can be used in developing mathematics learning strategies so that students' algebraic thinking skills develop. AbstrakKemampuan berpikir aljabar siswa harus terus dikembangkan karena dapat mendukung kesuksesan dalam matematika. Berpikir aljabar generalisasi dengan generalisasi pola yang dipelajari pada tingkat SMP. Pada saat proses melakukan generalisasi siswa menggunakan persepsi similarity atau proximity. Oleh sebab itu, tujuan penelitian ini yaitu mendeskripsikan proses berpikir aljabar siswa SMP dalam melakukan generalisasi pola. Pendekatan yang digunakan yaitu kualitatif dengan 3 subjek penelitian yang memiliki proses berpikir aljabar yang berbeda. Hasil penelitian menunjukkan bahwa siswa SMP melakukan proses berpikir aljabar dengan mempersepsikan gambar, merepresentasikan, mencari hubungan fungsional, melakukan generalisasi, dan mengaplikasikan rumus umum. Perbedaannya persepsi digunakan di awal kegiatan dan pada kegiatan pencarian hubungan fungsional. Hasil penelitian ini dapat digunakan dalam mengembangkan strategi pembelajaran matematika agar kemampuan berpikir aljabar siswa berkembang.

The Algebraic Thinking Process in Solving Hots Questions Reviewed from Student Achievement Motivation

This research is a preliminary study that aims to describe the algebraic thinking process of prospective mathematics teachers. This research is a qualitative descriptive study. Subjects were grouped into two categories based on high and low achievement motivation. Data is obtained based on the results of tests conducted in the algebra process. Research subjects (S1) and (S2) with high achievement motivation and subjects (S3) and (S4) with low achievement motivation using different algebraic thought processes. Subjects (S1) are able in the process of thinking algebra until crashing indicators assess understanding with understanding of the concept wrong in solving Higher Order Thinking Skills (HOTS) problems, whereas, (S2) the process of thinking algebra is only capable of chunking information (pieces of information), (S3) able in the process of thinking algebra until indicators of change with wrong answers, and the subject (S4) is able in the process of thinking algebra only until chunking information (pieces of information). Factors that cause subjects S1, S2, S3, and S4 are still unable to solve HOTS questions in algebraic thinking processes are questions of knowledge on HOTS material and difficulty understanding concepts in working on algebra need special handling in improving understanding of concepts in algebra.

Improving Mathematics Students’ Learning Motivation with the Guidelines Method of Household Engineering Techniques in Vocational School

This research is motivated by the observations of researchers when teaching, it was found that there are still many students who experience obstacles when solving row problems. This type of research is qualitative research with descriptive research type. The approach and type of study were chosen according to the researcher's goal which is to describe the students' algebraic thought processes in solving the problem of ranks. The findings in this study, namely high ability students can go through each stage of problem-solving as well as doing the algebraic thinking process well, while moderate and low ability students still often ignore the stage of looking back. They also still have difficulty doing the algebraic thought process. The algebraic thinking process of high-ability students is more complex than students of medium and low ability. Highly capable students experience the process of gathering ideas, clarifying ideas, evaluating ideas, and making decisions over and over again in the thought process he does in solving problems. Besides that, in the process of thinking, high-ability students also observe patterns, make generalizations, use meaningful symbols, use functions, and make mathematical models.

Algebra Thinking Process on Vocational School Students in Completing Line Problems

This research is motivated by the observations of researchers when teaching, it was found that there are still many students who experience obstacles when solving row problems. This type of research is qualitative research with descriptive research type. The approach and type of study were chosen according to the researcher's goal which is to describe the students' algebraic thought processes in solving the problem of ranks. The findings in this study, namely high ability students can go through each stage of problem-solving as well as doing the algebraic thinking process well, while moderate and low ability students still often ignore the stage of looking back. They also still have difficulty doing the algebraic thought process. The algebraic thinking process of high-ability students is more complex than students of medium and low ability. Highly capable students experience the process of gathering ideas, clarifying ideas, evaluating ideas, and making decisions over and over again in the thought process he does in solving problems. Besides that, in the process of thinking, high-ability students also observe patterns, make generalizations, use meaningful symbols, use functions, and make mathematical models.

A importância da função discursiva de designações de relações algébricas para o desenvolvimento do pensamento algébricoThe importance of the discursive function of algebraic relations designations for the development of algebraic thought

A investigação contou com um instrumento de coleta de dados subsidiadas pelas ideias de Raymond Duval relacionadas à aprendizagem da álgebra, aplicado a 115 alunos do 7º e 8º anos de escolas do estado do Paraná no Brasil. Foi analisada uma das questões do instrumento relacionada à ideia de que não são as letras que são importantes, mas as operações discursivas de designação dos objetos feitas por meio da língua natural ou formal. Os resultados encontrados revelaram formas de designação e redesignação diretas e verbais em linguagem natural, numérica ou algébrica ou indiretas e descritivas que implicaram na utilização de letras com utilização de léxicos associativos e, dessa forma, a identificação da atribuição de significação à essas letras pelos alunos. The present research used a data collection instrument subsidized by some of Raymond Duval's ideas related to learning algebra. The instrument was applied to 115 students from the 7th and 8th years in the state of Paraná, in Brazil. One of the questions of the instrument was analyzed in relation to the idea that it is not the letters that are important, but the discursive operations of designating objects, which are made through natural or formal languages. The results revealed specific forms of direct and verbal designation and reassignment in natural, numerical or algebraic language or, indirect and descriptive that implied the use of letters through a process of associative lexicons and, therefore, the assignment of meaning to such letters by students.

The Growth of Algebraic Thought in Sixteenth-Century Europe

This chapter traces the growth of algebraic thought in Europe during the sixteenth century. Equations of the third and fourth degrees sparked quite a few algebraic fireworks in the first half of the century. Their solutions marked the first major European advances beyond the algebra contained in Fibonacci's thirteenth-century Liber abbaci. By the end of the century, algebraic thought—through work on the solutions of the cubics and quartics but, more especially, through work aimed at better contextualizing and at unifying those earlier sixteenth-century advances—had grown significantly beyond the body of knowledge codified in Luca Pacioli's fifteenth-century compendium, the Summa de arithmetica, geometria, proportioni, e proportionalita. Algebra during this period was evolving in interesting ways.