The challenge posed by algebra story problems creates a significant hurdle for many students, transcending both the mathematical content of the problem and the specific instructional background received. This study offers a distinctive contribution to the existing literature by focusing on the cognitive conditions essential for comprehension in…

This study aims to evaluate cognitive conflict in constructing mathematical concepts, based on thinking errors. The data were collected through observations of words or sentences, leading to the derivation of qualitative outputs. Furthermore, the results showed that the two selected subjects experienced cognitive conflicts regarding thinking…

This study was designed to examine the use of mistakes to promote students' performance in undergraduate Algebra classes by developing a growth mindset. Participants were seventy-four students from three Algebra classes and received one of the three interventions along with regular instruction: (a) growth mindset feedback on mistakes…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…

Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

This is a descriptive research on the difficulties of Filipino high school students in translating algebraic word problems into mathematical equations. This research is composed of three parts: (1) development of an 11-page "Filipinized" questionnaire; (2) analysis of the mathematical thinking processes of the respondents based on the answers to…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

This paper focuses on the identification of some conceptual factors underlying the initial learning of algebra. It describes a study which uncovered three predominant notions existing in a sample of ten 12- and 13-year olds prior to formal instruction in algebra, and the ways in which a particular approach to the teaching of algebra affected both…

Data indicate that relatively advanced science-oriented college students can experience serious difficulties in symbolizing certain meaningful relationships with algebraic equations. Reversal errors in formulating equations were seen to stem from two main sources: (1) a syntactic word order matching process and (2) a semantic static comparison…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…

Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…

Results from a British study on Strategies and Errors in Secondary Mathematics are considered. Students' views of algebra and their difficulties are summarized, with some suggestions for teachers. (MNS)

Examined relations between algebraic word-problem attributes and students' strategies, errors, and problem difficulty. Found that constructed responses capture strategy formulation and high-level planning--as do traditional measures of quantitative reasoning--but are more sensitive to individual problem characteristics and procedural errors that…

The investigation reported is primarily a description of how college students solve or fail to solve algebra equations. Protocols were collected from two groups of college students; one group was expected to be good solvers, the other group contained many poor solvers. The investigators sought to identify and classify the difficulties students…