scholarly journals Do adults treat equivalent fractions equally? Adults’ strategies and errors during fraction reasoning.

2020 ◽  
Vol 46 (11) ◽  
pp. 2049-2074
Author(s):  
Charles J. Fitzsimmons ◽  
Clarissa A. Thompson ◽  
Pooja G. Sidney
Keyword(s):  
2018 ◽  
Vol 16 (1) ◽  
pp. 67-76
Author(s):  
Disyacitta Neolia Firdana ◽  
Trimurtini Trimurtini

This research aimed to determine the properness and effectiveness of the big book media on learning equivalent fractions of fourth grade students. The method of research is Research and Development  (R&D). This study was conducted in fourth grade of SDN Karanganyar 02 Kota Semarang. Data sources from media validation, material validation, learning outcomes, and teacher and students responses on developed media. Pre-experimental research design with one group pretest-posttest design. Big book developed consist of equivalent fractions material, students learning activities sheets with rectangle and circle shape pictures, and questions about equivalent fractions. Big book was developed based on students and teacher needs. This big book fulfill the media validity of 3,75 with very good criteria and scored 3 by material experts with good criteria. In large-scale trial, the result of students posttest have learning outcomes completness 82,14%. The result of N-gain calculation with result 0,55 indicates the criterion “medium”. The t-test result 9,6320 > 2,0484 which means the average of posttest outcomes is better than the average of pretest outcomes. Based on that data, this study has produced big book media which proper and effective as a media of learning equivalent fractions of fourth grade elementary school.


Pythagoras ◽  
2021 ◽  
Vol 42 (1) ◽  
Author(s):  
Methuseli Moyo ◽  
France M. Machaba

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.


2021 ◽  
Author(s):  
Teklit Zerizghi Tekleab ◽  
Qingjun Guo ◽  
Changqiu Zhao ◽  
Chukwunonso Peter Okoli

Abstract 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.


1973 ◽  
Vol 20 (7) ◽  
pp. 591-599
Author(s):  
Edward C. Beardslee ◽  
Gerald E. Gau ◽  
Ralph T. Heimer
Keyword(s):  

One of the difficulties encountered when teaching the concept of equivalent fractions is that a student may be able to demonstrate equivalence with particular pairs of fractions, but all too often is unable to generalize the concept to other pairs of fractions. For example, a student may be able to establish the equivalence of 1/3 and 3/9 but encounter difficulty when confronted with the pair of fractions 5j 15 and 7/21. With this situation in mind, the authors conducted a series of investigations on how to effectively teach the concept and insure its generalization (Beardslee 1972, Gau 1972).


1971 ◽  
Vol 18 (4) ◽  
pp. 245-249
Author(s):  
Harry Bohan

Much emphasis has long been placed on the value of using concrete models and manipulative devices in the early stages of the development of mathematical ideas. As Johnson suggests, however, it is entirely possible for a teacher to use instructional aids and get little benefit from them. “Some use them but fail to take students from the concrete representation to the concept behind it. Others use an inadequate or inappropriate aid” (Johnson 1967, p. 20). Brownell emphasizes that the processes children use at the concrete and semiconcrete levels must be closely related to the processes they will use later in dealing with abstract symbols (Brownell 1928, p. 24).


1975 ◽  
Vol 22 (8) ◽  
pp. 636
Author(s):  
Richard Crouse

The rules for this game are similar to the rules for the television game. A “Concentration” board is needed. On a large piece of cardboard, rule off a number of squares (or rectangles)—the number will depend on the ability and grade level of the class the teacher is teaching. The examples used will depend on the kind of drill the teacher wants to provide. Suppose a teacher wants to drill students on equivalent fractions. Then the board might look like the one in figure 1.


1983 ◽  
Vol 30 (5) ◽  
pp. 38-41 ◽  
Author(s):  
Evelyn M. Silvia

Graph paper can be used for concrete representations of both fractions and operations with fractions. The combined use of graph paper and an overhead projector makes the presentation even more convincing. The paragraphs that follow are a description of how I have used graph paper to illustrate the algorithm for the division offractions. The activities on division were preceded by activ ities that covered equivalent fractions, as well as addition and multiplication of fractions.


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