Solving Algebra Word Problems Research Articles

Analysis of Students Mathematical Reasoning Ability in Solving Algebra Word Problems in terms of Learning Styles

This study aims to describe students' mathematical reasoning abilities in solving algebra word problems in terms of learning styles. This type of research is descriptive qualitative research. The research subjects were class VII A students of SMPN 1 Pasrepan for the 2022/2023 academic year. The subjects in this study were 2 students with a visual learning style, 2 students with an auditory learning style, and 2 students with a kinesthetic learning style. Data collection techniques in this study were learning style questionnaires, mathematical reasoning ability tests, and interviews. Triangulation in this study uses triangulation techniques. The results of this study indicate that subjects with a visual learning style have high mathematical reasoning abilities with a percentage of 78.75%, subjects with an auditory learning style have high mathematical reasoning abilities with a percentage of 93.75%, and subjects with a kinesthetic learning style have reasoning abilities moderate mathematics with a percentage of 60%.

Boys' advantage in solving algebra word problems is mediated by spatial abilities and mathematics anxiety.

Adolescents' (n = 342, 169 boys) general algebra and algebra word problems performance were assessed in 9th grade as were intelligence, academic achievement, working memory, and spatial abilities in prior grades. The adolescents reported on their academic attitudes and anxiety and their teachers reported on their in-class attentive behavior in 7th to 9th grade. There were no sex differences on the general algebra measure or for mathematics achievement, but boys had an advantage on the algebra word problems measure (d = .51) and for spatial abilities (ds = .29 to .58). Boys had higher mathematics self-efficacy (d = .24 to .33), lower mathematics anxiety (ds = -.31 to -.53) and were less attentive in classrooms (ds = -.28 to -.37). A series of structural equation models revealed the sex difference for algebra word problems was mediated by spatial abilities and mathematics anxiety, controlling myriad confounds. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

The Use of Representations when Solving Algebra Word Problems and the Sources of Solution Errors

In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of the algebraic solving method, were useful in the construction of situation and/or problem models. However, this did not entail a higher rate of correct solutions, because students made errors in the subsequent conversion to equations due to misconceptions about the notion of equation. Teaching implications are discussed.

An Alternative Approach to Solving Algebra Word Problems: Singapore Bar Model Method

Bu çalışmada, yedinci sınıf öğrencilerinin cebir problemlerini çözmede tercih ettikleri yöntemleri ve öğrencilerin Singapur çubuk model yöntemi hakkındaki görüşleri incelenmiştir. Tek durum çalışması olarak tasarlanan çalışmada, yedinci sınıf öğrencilerinden cebir problemlerinin sorulduğu ön değerlendirme testinin cevaplarına göre seçilen 10 öğrenci ile klinik görüşmeler yapılmıştır. Öğrenciler ders saatlerinde yedinci sınıf matematik öğretim programına uygun olarak cebirsel denklem kurma yöntemi ile problem çözmeyi öğrenmiştir. Buna ek olarak, öğrencilere okul sonrasında üç saatlik Singapur bar/çubuk model eğitimi verilmiştir. Eğitimden sonra yapılan bire bir klinik görüşmelerde öğrencilerin tercih ettikleri çözüm yöntemleri, nitel veri kodlaması yoluyla analiz edilmiştir. Çalışmanın bulguları, öğrencilerin ilk tercihlerinin çubuk model yöntemi olduğunu göstermiştir. Öğrencilerin, çubuk modeli özellikle problemde verilen bilinmeyen nicelikleri anlamlandırmak amacıyla kullandıkları görülmüştür. Öğrencilerin büyük çoğunluğu probleme uygun doğru çubuk modeli çizerek doğru cevaba ulaşabilmiş ve sonrasında da çubuk modelden yararlanarak cebirsel denklem oluşturabilmiştir. Dolayısıyla, çubuk model öğrencilerin problemi anlamasına yardımcı olurken cebirsel denklem kurmaları için de bir ara basamak görevi görmüştür. Öğrenciler, çubuk modeli “daha anlaşılır” bulduklarını, problem çözme sürecini zevkli hale getirdiğini ve diğer matematik problemlerini de bu yöntemle çözmek istediklerini belirtmiştir. Bu bulgu da, çubuk modelin öğrencilerin problem çözmeye karşı motivasyonlarına katkı sağladığını göstermektedir. Bu çalışma, öğrencilerin zorlandıkları cebir problemlerinde ve denklem kurma sürecinde görsel bir araç olan çubuk modelin etkisini ortaya koymuştur. Bu anlamda, matematik öğretmenlerine, öğretmen eğitimcilerine ve matematik eğitimi alanındaki araştırmacılara katkı sağlaması beklenmektedir.

Learning and solving algebra word problems: The roles of relational skills, arithmetic, and executive functioning.

Although algebra is a prerequisite for higher mathematics, few studies have examined the mathematical and cognitive capabilities that contribute to the development of algebra word problems solving skills. We examined changes in these relations from second to ninth grades. Using a cross-sequential design that spanned 4 years, children from 3 cohorts (Mage = 7.85, 10.05, and 12.32) were administered annual tests of algebra word problems, mathematical skills (mathematical relational tasks, arithmetic word problems), and cognitive capabilities (working memory, updating, inhibitory, task switching, and performance intelligence). The cross-sectional findings showed that ability to solve mathematical relational problems was associated strongly with performance in algebra word problems. Working memory and updating explained variance in the relational, but not the algebra problems. Using an autoregressive cross-lagged model with structured residuals to analyze the longitudinal data, we found relational and arithmetic performance predicted independently algebra performance from one year to the next. The strength of these relations was consistent across grades. These findings point to the importance of developing skills in relational problems as one of the tools for improving algebra performance. (PsycINFO Database Record

Conceptual and Procedural Knowledge During Strategy Construction: A Complex Knowledge Systems Perspective

ABSTRACTThis article elaborates a new direction for studying the construction of novel strategies that enables researchers to model the conceptual underpinnings of students' observable strategic actions during episodes of mathematical problem solving. The nature of the relationship between conceptual and procedural knowledge has been persistently debated for decades. Recently, there has been mounting empirical evidence that conceptual and procedural knowledge can develop by mutual bootstrapping in a bidirectional and iterative fashion (e.g., Rittle-Johnson & Schneider, 2014). However, the very constructs of conceptual and procedural knowledge (especially procedural knowledge) have been critiqued for inconsistency in definition and lack of operationalization (Star, 2007). The analysis in this article addresses this critique by modeling the diverse forms of conceptual and procedural knowledge needed to implement a strategy as a complex knowledge system: a strategy system. Furthermore, the strategy system model is used to elaborate processes of mutual bootstrapping between conceptual and procedural knowledge at a moment-by-moment time scale. The strategy system model builds upon the Knowledge in Pieces epistemological perspective (diSessa, 1993), and coordination class theory in particular (diSessa & Wagner, 2005). Both the theoretical notion of a strategy system and the bidirectional model of mutual bootstrapping between conceptual and procedural knowledge are illustrated using data from a case study of a pre-algebra student who iteratively refined a procedure for solving algebra word problems. The strategy system model highlights the complexity of both strategies and concepts and offers a window into what can be learned by students during strategy construction processes.

Supplemental Material for Learning and Solving Algebra Word Problems: The Roles of Relational Skills, Arithmetic, and Executive Functioning

Supplemental Material for Learning and Solving Algebra Word Problems: The Roles of Relational Skills, Arithmetic, and Executive Functioning

Algebra word problem solving approaches in a chemistry context: Equation worked examples versus text editing

Text editing directs students’ attention to the problem structure as they classify whether the texts of word problems contain sufficient, missing or irrelevant information for working out a solution. Equation worked examples emphasize the formation of a coherent problem structure to generate a solution. Its focus is on the construction of three equation steps each of which comprises essential units of relevant information. In an experiment, students were randomly assigned to either text editing or equation worked examples condition in a regular classroom setting to learn how to solve algebra word problems in a chemistry context. The equation worked examples group outperformed the text editing group for molarity problems, which were more difficult than dilution problems. Empirical evidence supports the theoretical rationale in using equation worked examples to facilitate students’ construction of a coherent problem structure so as to develop problem skills and expertise to solve molarity problems.

Fostering analogical transfer: The multiple components approach to algebra word problem solving in a chemistry context

Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated multiple components (symbolic equations, symbols, categorization, hint) in the source, or target, or both, to address the four analogical tasks. Different combinations of the components were tested in a series of four experiments. Symbolic equations (main component) fostered a mental construction of the problem in its solution mode. Categorization enabled an identification of the problem category. A hint in the target directed the learners to the source problem. The interaction between these components facilitated the mapping of the symbolic equations in the source onto the target, resulting in the superiority of the MC approach in fostering analogical transfer. Neither the main component alone nor the main component plus one sub-component was sufficient for analogical transfer. Hence for analogical transfer to occur, at least the main component (symbolic equations) and two sub-components (categorization and hint) are required. However, symbols may not have additional effects for transfer to occur.

Inhibiting interference from prior knowledge: Arithmetic intrusions in algebra word problem solving

In Singapore, 6–12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13–17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is correlated with the ability to inhibit intrusions from the earlier arithmetic strategies. Similar to typical school practice in Singapore, we asked 14 year-old students ( N = 157) to use only letter-symbolic algebra to solve 9 algebra word problems. After having controlled for algebraic knowledge, working memory, and intelligence, better inhibitory ability still predicted fewer arithmetic intrusions and higher problem solving accuracy. Path analysis revealed 2 types of inhibition. Inhibition-of-reified-processes predicted accuracy through arithmetic intrusions. Inhibition-of-recently-learned-associations predicted accuracy through intelligence. Findings suggest establishing pedagogical links between arithmetic and algebraic methods may facilitate students' transition to letter-symbolic algebra.

Substituting one mystery for another: the role of self-explanations in solving algebra word-problems

Explanations students provide themselves (self-explanations) in the course of learning or problem-solving have been shown to be positively associated with performance. However, the role self-explanation plays in problem solving has not been fully elaborated. This study aims to analyze the role of self-explanation in solving algebra word problems. We argue that self-explanation may function as verbal mediation that supports the transformation between different external representations of the problem. Our analysis of the problem solving protocols aims to illustrate this point through a multiple case studies design. Specifically we illustrate the way a particular kind of self-explanation (categorical explanation) mediates students' transformation from the sentential representation of the problem to the tabular one.

Learning the Algebraic Method of Solving Problems

This study of students' attempts to formulate and solve algebra word problems shows that the logic underlying algebraic problem solving methods is little understood. Students' prior experiences with solving problems in arithmetic gives them a compulsion to calculate which is manifested in the meaning they give to “the unknown” and how they use letters, their interpretation of what an equation is, and the methods they choose to solve equations. At every stage of the process of solving problems by algebra, students were deflected from the algebraic path by reverting to thinking grounded in arithmetic problem solving methods.

Action to process: constructing functions from algebra word problems

Abstract The ability to build a mathematical model of a situation described in ordinary language has always been an important goal of school mathematics teaching. This paper gives one explanation for the difficulties many students experience with certain stylized modeling tasks (solving algebra word problems) and puts these difficulties in the context of a theory about the acquisition of the concept of mathematical function. It also describes a visual programming language that can act as a bridge, and in some sense an alternative, to formal algebraic notation as a language for describing situations. Tracing the author's classroom experiments and his reflections on those experiments, the paper suggests a method for helping students.

Selecting analogous problems: Similarity versus inclusiveness

Students were asked to select one of two analogous problems in order to solve algebra word problems. In Experiment 1, one problem was less inclusive and the other was more inclusive than a test problem. The students judged the complexity and similarity of problems, selected analogous problems, and used the solutions to solve test problems. They performed significantly better on the test problems when given the more inclusive solutions, but used perceived similarity rather than inclusiveness to select analogous problems. The same pattern of results occurred in Experiment 2, in which isomorphic problems replaced the more inclusive problems. The results show that students are deficient in selecting good analogies, both from the same category (Experiment 1) and from a different category (Experiment 2). Students who saw the analogous solutions (Experiment 3) or were majoring in mathematics (Experiment 4) were more likely to select an isomorphic problem over a less inclusive problem, but were not more likely to select a more inclusive over a less inclusive problem.

Usefulness of analogous solutions for solving algebra word problems.

Usefulness of analogous solutions for solving algebra word problems.

Usefulness of analogous solutions for solving algebra word problems.

Quatre experiences etudient, chez des eleves d'un cours d'algebre, la possibilite d'utiliser les solutions de differents problemes pour resoudre d'autres problemes appartenant a la meme categorie