Flexibility in partitioning strategies of fourth graders

This study combines the concepts of flexibility and partitioning, and aims to probe fourth grade students’ flexibility in partitioning strategies. Seven students participated in this descriptive case study. Students were given three partitioning tasks. Forty-eight answers produced by students were evaluated and classified based on the strategies defined in the taxonomy developed by Charles and Nason (2000). Results showed that students could easily change their strategies both within and across tasks. Namely, they displayed both inter- and intra-task strategy flexibility to a large extent even though they did not have any intervention on partitioning. Another point that findings have implicated was that the fourth graders’ flexibility in partitioning strategies may be utilized to introduce concepts of equivalent fractions and mixed numbers. Results are discussed in terms of their implications related to mathematics education, and some recommendations aimed at learning environments and future studies are presented.

Grade 9 learners’ understanding of fraction concepts: Equality of fractions, numerator and denominator

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners’ understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners’ transition from whole numbers to rational numbers enabled them to deal with the more complex concept of fractions. A qualitative case study approach was followed. A test was administered to 40 learners. Based on their written responses, eight learners were purposefully selected for an interview. The findings revealed that learners’ definitions of fraction were neither complete nor precise. Particularly pertinent were challenges related to the concept of equivalent fractions that include fraction elements, namely the numerator and denominator in the phase of rational number. These gaps in understanding may have originated in the early stages of schooling when learners first conceptualised fractions during the late concrete learning phase. For this reason, we suggest a developmental intervention using physical manipulatives to promote understanding of fractions before inductively guiding learners to construct algorithms and transition to the more abstract applications of fractions required in Grade 9.

Implementation of Online Learning During the Covid 19 Pandemic in Mathematics with a Scientific Approach in SD Daarul Qur'an Kalibata City

This study aims to (1) find out online learning planning in mathematics subjects with a scientific approach at SD Daarul Qur'an Kalibata City, (2) find out the implementation of online learning of equivalent fractions in grade 4 SD Daarul Qur'an Kalibata City, (3) find out the results of online learning in mathematics with a scientific approach at Daarul Qur'an Elementary School Kalibata City. This research uses a qualitative approach with the type of case study research (case study). The location of this research is the 4th-grade students of SD Daarul Qur'an Kalibata City. Sources of data in this study were the principal, waka curriculum, mathematics teacher, and eight students. Data collection techniques used are observation, interviews, and documentation. The sampling technique in this study used primary and secondary data, using data analysis techniques, namely reduction, categorization, data presentation, and conclusion drawing. While checking the validity of the data using the degree of trust, transferability, dependence, and triangulation of sources. The results of the study revealed that: (1) online learning planning during the covid 19 pandemics in mathematics subjects with a scientific approach using the application zoom. Then for the curriculum using the 2013 curriculum and adjusted when in the field, (2) the implementation of online learning of equivalent fractions in grade 4 uses a scientific approach. The reason is that students are active in learning. Because so far online learning has only focused on monitors, (3) the results of online learning in mathematics with a scientific approach show that online learning in mathematics subjects with a scientific approach is quite difficult to apply online, then not many students can follow the steps. step. So the scientific approach is not suitable if applied online.

Sulfur, lead, and mercury in South Africa coals: existential form of the elements, isotope, and emissions from the coal fired-power plants

Coal-fired power plants (CFPPs) are the dominant source of electricity in South Africa due to natural abundance of coal in the country. However, emission of SO2, Pb, and Hg has raised serious environmental and public health concerns. Hence, to reduce emissions and utilize coal efficiently, estimating emission trend, understanding the forms of elemental occurrence in coals, and affinities to minerals, organic matter, and pyrite, are essential. Therefore, this paper aimed to assess the forms of elemental occurrence of sulfur, and Pb and Hg affinities to ash and sulfur, in the coals via statistical correlation and their isotopic compositions. This study also estimated SO2, Pb, and Hg emissions from 1971 to 2018 from the CFPPs on levels of activity and emission factors. Based on the results, South Africa coals mostly comprise equivalent fractions of organic and pyritic sulfur. The Pb were correlated with ash (R2 = 0.393), which is an indication of the presence of bound clay mineral. However, the highest Pb208/Pb206 and the lowest Pb208/Pb206 in South Africa coals which contain high inertinite (organic matter) and low sulfur, reveal organically associated Pb. Similarly, clay minerals associated Hg appeared based on its relationship with ash (R2 = 0.450), and the remaining could be an organic matter related. As an organic matter associated element least cleanability and readily oxidizing nature, burning South Africa coals containing a substantial quantity of organic sulfur and organically bound Pb and Hg without washing will obviously result to higher emissions. The estimated for SO2, Pb, and Hg emissions were 355.84 Gg, 168.91 tons, and 4.84 tons in 1971, and increased to 1468.13 Gg, 696.89 tons, and 19.95 tons in 2018, respectively. The values approximately increased by a factor of 4.

Two conceptions of fraction equivalence

In this study, we present a mathematical analysis distinguishing two conceptions of equivalence: proportional equivalence and unit equivalence. These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a) the distinction of equivalence gives a unified framework of equal fractions that has not previously been described in the literature; (b) a conceptual understanding of both fraction equivalences is integral to understanding rational numbers; and (c) knowledge of both conceptions of equivalence is important for developing a conceptual understanding of fraction arithmetic. Past research has largely overlooked the distinction between the two types of equivalence. However, this may provide an important foundation for central topics that build on equivalence, and a better understanding of these two types of equivalence may support a more flexible understanding of fractions. Last, we propose future directions for teaching equivalence in mathematics.

Desenvolvimento do Pensamento Teórico de Professores dos Anos Iniciais sobre FraçõesDevelopment of the theoretical thinking of early years teachers about fractions

ResumoO artigo analisa o desenvolvimento de aspectos do pensamento teórico do professor sobre frações, em particular: mediação de grandezas contínuas e a equivalência de frações. Apoiada teoricamente na perspectiva histórico-cultural e na Teoria da Atividade, a pesquisa adotou a Atividade Orientadora de Ensino (AOE) como referência para a organização de ações de uma formação continuada de professores. A análise dos dados produzidos junto aos professores revela a superação da ideia de fração como a quantificação discreta de partes já dadas de um inteiro, a criação de subunidade como estratégia para a quantificação de grandeza contínua e a apropriação do sentido de comparação de frações por meio de frações equivalentes. Concluímos que tais elementos revelam aspectos da superação do pensamento empírico pelo pensamento teórico.Palavras-chave: Teoria Histórico-Cultural; Fração; Formação de Professores. AbstractThe article analyzes the development of aspects of the teacher's theoretical thinking about fractions, in particular: the mediation of continuous quantities and the equivalence of fractions. Supported theoretically by the historical-cultural perspective and the Theory of the Activity, the research adopted the Teaching Guiding Activity (AOE) as a reference for the organization of continuous teacher education. The analysis of the data produced with teachers reveals the overcoming of the idea of the fraction as the discrete quantification of parts already given of a whole, the creation of a subunit as a strategy for the quantification of continuous magnitude and the appropriation of the sense of comparing fractions by means of equivalent fractions. We conclude that such elements reveal aspects of the overcoming of empirical thinking by theoretical thinking.Keywords: Cultural-Historical-Theory; Fraction; Teaching Guiding Activity. ResumenEl artículo analiza el desarrollo de aspectos del pensamiento teórico del profesor sobre fracciones, en particular: mediación de avances continuos y equivalencia de fracciones. Teóricamente apoyado en la perspectiva histórico-cultural y en la Teoría de la Actividad, una investigación adoptó la Actividad de Orientación Docente (AOE) como referencia para organizar acciones para la formación continua del profesorado. El análisis de los datos elegidos con los maestros revela una superación de la idea de fracción como una cuantificación de partes ya otorgadas un número entero, una creación de subunidad como estrategia para la cuantificación de magnitud continua y la apropiación del sentido de comparar fracciones por medio de fracciones equivalentes. Concluya que estos elementos revelan aspectos de superar el pensamiento empírico mediante el pensamiento teórico.Palabras clave: Teoría Histórico-Cultural; Fracción; Formación del profesorado