Criteria for frame-and-pillar dwellings selection in Russian archeology

The work is devoted to the study of various types of post-frame structures based on archaeological and ethnographic data. The analysis of the structural features of dwellings of different eras and archaeological cultures is carried out. Ethnographic parallels are also drawn. The main attention was paid to the study of the bearing elements of the buildings the pillars that were dug in along the perimeter, and on which the roof rafters rested. This made it possible to single out the criteria by which Russian researchers ranked household and residential buildings as frame-and-pillar type. This study showed that initially archaeologists attributed the buildings to the pillar type. This trend continued for several decades. But with the beginning of the 21 century modern researchers were increasingly attributing such structures to the frame-pillar type. Sometimes an equals sign was put between the two types of buildings, which could lead to confusion in the scientific community. There are two options for identifying the types of buildings: on the basis of their own clear criteria, or the use of already established concepts in architecture and construction practice. The author is inclined to believe that the medieval buildings of the Perm Cis-Urals of the Lomovatovskaya and Rodanovskaya archaeological cultures should be classified as pillar structures.

Young students’ understanding of mathematical equivalence across different schools in South Africa

Background: Mathematical equivalence is a critical element of arithmetic understanding and a key component of algebraic thinking which is necessary for success in all levels of mathematics. Research studies continue to highlight misconceptions related to equivalence and reveal that many primary school students have a narrow and limiting view of the equals sign as an operation.Aim: This study aims to investigate young students’ understanding of mathematical equivalence in South Africa with a particular focus on their interpretations of the equals sign.Setting: Research data was obtained from students across six schools from different contexts within the Western Cape.Methods: We gave students an adapted standardised assessment containing 15 items related to equivalence.Results: Our analyses indicated that students focus more on the equals sign as an operation which involves calculating an answer. While some referred to equivalence as meaning the same as, most of them were inclined to accept the operational definition of the equals sign (i.e. the answer to the problem) as a better and preferred definition. In addition, student performance was poor on equation-solving problems and they rarely used comparative relational strategies in their solutions.Conclusion: The findings of this research confirmed that difficulties with equivalence reported by earlier research is widespread across this group of grade 4 students. This has implications for both curriculum, textbook and materials design and teacher professional development.

Eddington's mass-luminosity relation and the laws of thermodynamics

Ever since its formulation by A. S. Eddington, the mass-luminosity relation has been viewed as a triumph for theoretical astronomy and astrophysics. The idea that the luminosity of the stars could be controlled solely by their mass was indeed a revolutionary concept. The proof involved two central aspects: (1) the belief that stars could be treated as ideal gases in hydrostatic equilibrium, and (2) that the opacity of Capella could be used as a reference mark applicable to other stars. Yet, when the mass-luminosity relation was advanced, no thought was given to the need for thermodynamic balance. Within thermodynamic expressions, not only must the dimensions (hence units) be consistent on each side of the equals sign, but the extensive nature of the properties must also balance. Namely, thermodynamic expressions must be balanced by properties which are extensive to the same degree. In this regard, mass is an extensive thermodynamic property and can be represented by a homogenous function of degree 1. Conversely, the luminosity of a star is neither extensive nor intensive, but rather can be represented by a homogenous function of degree 2/3. Consequently, the mass-luminosity expression is thermodynamically unbalanced and stands in violation of the laws of thermodynamics.

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.

Early Understanding of Equality

One of the first math symbols introduced=the equals sign=underpins much of the algebraic reasoning a child will use in later years.