The conception of substitution of the equals sign plays a unique role in students' algebra performance

Students’ conceptions of the equals sign are related to algebraic success. Research has identified two common conceptions held by children: operational and relational. The latter has been widely operationalised in terms of the sameness of the values on each side of the equals sign, but Jones, Inglis, Gilmore and Dowens (2012) argued that the substitution component of relational equivalence should also be operationalised. In this study, we investigated whether students’ endorsement of the substitution definition of the equals sign is a unique predictor of their algebra performance independent of the other two definitions (operational and sameness). Secondary school students were asked to rate the ‘cleverness’ of operational, sameness, and substitution definitions of the equals sign and completed an algebra test. Our findings demonstrate that endorsement of substitution plays a unique role in explaining secondary school students’ algebra performance above and beyond school year and the other definitions. These findings contribute new insights into how students’ algebra learning relates to their conceptions of the equals sign

Developing and Reporting Psychometric Evidence of Prerequisite Algebra Skills Instrument

Background: Assessing prerequisite algebra skills among secondary school students is an essential part of learning to achieve success in formal algebraic classes. Objectives: Therefore, this research aims to develop prerequisite algebra skills (PAS) instrument in the context of early algebra for seventh grade. Design: It was conducted in quantitative descriptive and cross-sectional design. The PAS instrument developed was in the form of a multiple-choice questions. Participants: Three experts were selected and 85 Grades 7 students in West java Indonesia were participated to check the psychometric evidence. Data Collection and analysis: 3 experts filled an assessment sheet to assess content validity and inter-rater reliability, which was analyzed using a content validity index (CVI) and Kappa coefficient (κ). The construct validity and reliability were examined using the Point-Biserial correlation and Kuder-Richardson's 20. Results: The result of content validity revealed that overall instrument evaluation based on the dimensions substance and construction were valid and reliable. The construct of 23 items indicated valid with various difficulty levels and acceptable discrimination value. The developed instrument was considered reliable based on Kuder-Richardson's 20 value of 0.73. These results indicate that it is recommended to be used, as it is relevant, fast and easy to manage. Conclusions: The recommendation for improvement is emphasized in the language clarity aspect. The future study is also widely open about the provision of the test in an online-based format

Simple pictorial mathematics problems for children: locating sources of cognitive load and how to reduce it

Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems essentially attempt to depict a dynamic situation (e.g., One bird flies away while there are three birds still sitting on the fence). Previous research suggested that such pictorial decrease problems impose higher cognitive load on children than the corresponding increase problems, even though both are solved with addition. However, the source of this cognitive load is unclear. It could be the direction of the depicted change or the position of the unknown (start vs. end set). To address this question and disentangle the sources of the load, we presented the problems in two different formats: 1) The conventional static one-picture problems and, 2) An adapted threepicture problem-format, which depicted the dynamic change in sequential steps. We also examined whether the three-picture problem-format makes the decrease problems easier. Seventy-nine first-graders participated in this study. Results showed that, overall, problems with the position of the unknown at the end were easier to solve than the ones in which the unknown was at the start. Furthermore, three-picture decrease problems with the unknown in the last position were easier than the one-picture decrease problems, and therefore appear to be a meaningful way to make such problems easier for children to understand.</div

Developing the concept of task substitution and transformation by defining own equivalences

The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to the results of several researches, these changes do not occur automatically, and the neglect of their development leads to students' insufficient adoption of substitution. The submitted contribution presents a new way of teaching substitution, the stages of which support the gradual development of the necessary competences of students, so that substitution becomes part of their computing apparatus. The effectiveness of the mentioned method of teaching substitution was also verified experimentally. By conducting a pedagogical experiment, it was confirmed that the application of the substitution teaching method developed by us led to more frequent use of substitution by students from the experimental group (47 students) compared to students from the control group (82 students) who learned substitution in the usual way. It emerged from the interview with experimental group students that they considered the proposed method suitable and that it encouraged them to learn substitution in depth.Ministry of Education, Science, Research and Sport; Agentúra na Podporu Výskumu a Vývoja, APVV, (APVV-14-0446

The Conception of Substitution of the Equals Sign Plays a Unique Role in Students' Algebra Performance

Students’ conceptions of the equals sign are related to algebraic success. Research has identified two common conceptions held by children: operational and relational. The latter has been widely operationalised in terms of the sameness of the values on each side of the equals sign, but it has been recently argued that the substitution component of relational equivalence should also be operationalised (Jones, Inglis, Gilmore, & Dowens, 2012, https://doi.org/10.1016/j.jecp.2012.05.003). In this study, we investigated whether students’ endorsement of the substitution definition of the equals sign is a unique predictor of their algebra performance independent of the other two definitions (operational and sameness). Secondary school students were asked to rate the ‘cleverness’ of operational, sameness, and substitution definitions of the equals sign and completed an algebra test. Our findings demonstrate that endorsement of substitution plays a unique role in explaining secondary school students’ algebra performance above and beyond school year and the other definitions. These findings contribute new insights into how students’ algebra learning relates to their conceptions of the equals sign