An Analysis of Middle School Mathematics Textbooks from the Perspective of Fostering Algebraic Thinking through Generalization

doi:10.12738/estp.2017.6.0506

Cited by 6 publications

(7 citation statements)

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“…Conceptualization of arithmetic as rational numbers in student learning and its transformation into algebra has been recognized as a crucial and difficult issue in student mathematical learning. This study illustrates that students' arithmetic pre-knowledge (Zazkis & Liljedahl, 2002;Kieran & Martínez-Hernández, 2022), and their pre-knowledge of rational numbers (Ni & Zhou, 2005;Gözde & Dilek, 2017) play an important role for in student achievement of algebraic equations and problem solving, and more generally in student learning of the abstract nature of algebra, expressed in symbols (Carraher et al, 2006).…”

Section: Resultsmentioning

confidence: 70%

“…Learning of rational numbers is a matter of conceptual meaning (Ni & Zhou, 2005;Gözde & Dilek, 2017) from multiplication to fractions and more, a process that successively presupposes adequate prerequisite knowledge of algebra. According to Vygotsky (1986), mathematics is a social construct that implies an ability for abstract thinking.…”

Section: Student Pre-knowledgementioning

confidence: 99%

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Arithmetic and Algebraic Knowledge in Student Learning of Concepts

2023

Education and New Developments

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Current research deals with students' arithmetical and algebraical knowledge, with a focus on a conceptual connection, and the relationship between two aspects of knowledge. The content in question is rational numbers, rational equations, and problem-solving in terms of proportion and ratio in grades 7, 8 and 9. The method contains three tests given to 400 students in grades 7-9. Tools for analysis were theories of generalizing arithmetic into algebra (Kieran, 2004), and the relationship between arithmetic and algebra in a conceptual context (Kaput, 2008). Current research shows that student knowledge of algebra and arithmetic often has a limited conceptual connection, and a weak relationship. Their knowledge of arithmetic operations and solving rational equations used to be just procedural, and reliant on formulas learnt in a procedural way, and often mixed up. The study also shows that student procedural strategies for finding formulas suitable for solving the equations, as well as carrying out the corresponding calculations, were often insufficient. The study investigates shortcomings in students' conceptualization of arithmetic operations with rational numbers, and how to apply them to solving rational equations. One reason for this, is lack of continuity in instruction and learning.

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Section: Resultsmentioning

confidence: 70%

Section: Student Pre-knowledgementioning

confidence: 99%

Arithmetic and Algebraic Knowledge in Student Learning of Concepts

2023

Education and New Developments

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“…When the research's chosen analytic methodologies were examined, qualitative analysis was shown to be the most popular. Document analysis (Ayber & Tanisli, 2017) and content analysis (Papadopoulos & Patsiala, 2019), on the other hand, have been recognized as analytical tools in qualitative approaches. While inferential statistics are preferred in quantitative techniques, latent class analysis, cluster analysis, and test development analysis are used depending on the study design.…”

Section: Discussionmentioning

confidence: 99%

“…• It is a mathematical modeling process (Ayber & Tanisli, 2017). Kriegler (2007), on the other hand, examined algebraic thinking under two main headings, as seen in Figure 3.…”

Section: Contribution To the Literaturementioning

confidence: 99%

“…In this process, to define algebraic relations by selecting the necessary information from the available situations; reasoning proportionally; It is important to present mathematical information using different representations in order to Figure 3. Components of algebraic thinking (Kriegler, 2007) 6 / 15 internalize concepts such as variable, equality, pattern, and function (Ayber & Tanisli, 2017).…”

Section: Contribution To the Literaturementioning

confidence: 99%

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A Systematic Review on Algebraic Thinking in Education

Sibgatullin

Korzhuev

Khairullina

et al. 2022

EURASIA J Math Sci Tech Ed

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Algebraic thinking is a method of solving math problems that stresses the significance of general connections. Excellent algebraic thinking necessitates strong symbolization and generalization ability. Students aged 7 to 15 are at the Piaget thinking stage's formal operational stage. Teachers, especially those working with secondary school students, must be aware of how kids think and reason algebraically. A detailed literature review provides an overview of research on algebraic thinking. The goal of this study was to compile a list of full-text papers that presented empirical research on algebraic thinking. The "algebraic thinking" search phrase was used to search the ERIC and Scopus databases. A total of 36 studies were included in the review. The educational levels, participants, nations, research methodologies, study objectives, data collecting tools, and analytic approaches have all been considered in studies on algebraic thinking. The number of studies published has risen over time. 2019 was the year with the most studies. The majority of the research was carried out in the United States of America. The majority of the participants in the study were elementary and secondary school pupils. Teachers' knowledge, elements impacting algebraic thinking, relations, and comprehension, as well as measuring categories, were determined when the study was grouped according to the study's topic. The algebraic thinking exam was the most popular data gathering instrument. The qualitative technique was used in the study of algebraic thinking. The most common method was found to be qualitative analysis. While inferential statistics are preferred in quantitative techniques, latent class analysis, cluster analysis, and test development analysis are used depending on the study design. According to the results, it was stated that in-service or pre-service teacher training is needed for the development of algebraic thinking and non-routine activities such as games should be used in the classroom. In addition, it has been determined that teaching strategies such as geometry representation, multiple representation strategies, mental computational activity also improve algebraic thinking.

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How Students Use Cognitive Structures to Process Information in the Algebraic Reasoning?

Abdul¹,

Waluya²,

Dwijanto³

et al. 2025

EUROPEAN J ED RES

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<p style="text-align: justify;">Cognitive processes are procedures for using existing knowledge to combine it with new knowledge and make decisions based on that knowledge. This study aims to identify the cognitive structure of students during information processing based on the level of algebraic reasoning ability. This type of research is qualitative with exploratory methods. The data collection technique used began by providing a valid and reliable test instrument for algebraic reasoning abilities for six mathematics education student programs at the Islamic University of Sultan Agung Indonesia. Subjects were selected based on the level of upper, middle, and lower algebraic reasoning abilities. The results showed that (1) students with the highest level of algebraic reasoning ability meet the logical structure of Logical Reasoning which shows that students at the upper level can find patterns and can generalize; (2) Students at the intermediate level understand the cognitive structure of Symbolic Representations, where students can make connections between knowledge and experience and look for patterns and relationships but have difficulty making rules and generalizations; (3) students at lower levels understand the cognitive structure of Comparative Thinking, where students are only able to make connections between prior knowledge and experience.</p>

show abstract

An Analysis of Middle School Mathematics Textbooks from the Perspective of Fostering Algebraic Thinking through Generalization

Cited by 6 publications

References 12 publications

Arithmetic and Algebraic Knowledge in Student Learning of Concepts

Arithmetic and Algebraic Knowledge in Student Learning of Concepts

A Systematic Review on Algebraic Thinking in Education

How Students Use Cognitive Structures to Process Information in the Algebraic Reasoning?

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