Helping Students With Mathematics Difficulties Understand Ratios and Proportions

Dougherty, Barbara; Bryant, Diane Pedrotty; Bryant, Brian R.; Shin, Mikyung

doi:10.1177/0040059916674897

Cited by 21 publications

(25 citation statements)

References 13 publications

(13 reference statements)

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“…Currently, fewer literature has been found related to reversible reasoning investigations in conceptual relationships for inverse function problems. The focus of previous researchers are more on the operational aspects, for example by identifying error reversals that students make for the problem of "students and professors" (González-Calero, Arnau, & Laserna-Belenguer, 2015;Soneira, González-Calero, & Arnau, 2018;Tunç-Pekkan, 2015), reversible multiplication relationships (Hackenberg, 2010), cognitive conflict and insufficient mental processes to reverse problem situations (Ramful, 2014), the type of task that causes reversible reasoning (B. Dougherty, Bryant, Bryant, & Shin, 2017;B. J. Dougherty, Bryant, Bryant, Darrough, & Pfannenstiel, 2015;Sangwin & Jones, 2017;Simon, Kara, et al, 2016;Vilkomir & O'Donoghue, 2009).…”

Section: Discussionmentioning

confidence: 99%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

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Researchers have argued that reversible reasoning is involved in all topics in mathematics. The study employed a qualitative research approach, consisted of three sessions (pre-assessment, thinking-aloud, and interview), and involved eight participants enrolled in Algebra class. The aim was to explore the potential role of reversible reasoning on students' inverse functions. The result of study indicated that there three categories of reversible reasoning that refer to the consistency of students in completing inverse function tasks, which are relational-harmonic, relationalvisual, and relational-identity. Mental activities performed by the students in constructing and reasoning inverse functions were also explained. In addition, potential aspects of the students' reversible reasoning created during the process of constructing meaning were highlighted. These findings provide perspectives on reversible reasoning, students' understanding of inverse functions, and areas of future research

show abstract

Section: Discussionmentioning

confidence: 99%

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Ikram¹,

Purwanto²,

Parta³

et al. 2020

Journal for the Education of Gifted Young Scientists

View full text Add to dashboard Cite

show abstract

“…to Allen (2007), mathematical misconceptions are faulty and incorrect ideas resulting from students' misunderstanding about a mathematical idea or concept. Misconceptions are often based on applications of inappropriate rules or generalizations [5]. Misconceptions and errors are related.…”

Section: Accordingmentioning

confidence: 99%

“…In term of ratio and proportional reasoning, Dougherty et al (2017) mentioned three types of a misconception that lead to students' difficulties in solving problems, including additive versus multiplicative comparisons, the incorrect conceptualization of fractions, and lack of covariational thinking. Misconception about additive and multiplicative comparisons is a popular problem of primary students.…”

Section: Accordingmentioning

confidence: 99%

“…Misconception about additive and multiplicative comparisons is a popular problem of primary students. Teachers can prevent misconceptions by using multiple representations, making a table in teaching ratio and proportional reasoning, especially equivalent ratio [5].…”

Section: Accordingmentioning

confidence: 99%

“…Therefore, ratio and proportion are two important options that must be taught in primary schools [1]. According to Dougherty et al, while teaching the concept of ratio in elementary school, teachers should pay attention to three features as follows [5]: (1) The relationship between the quantities in a ratio is multiplication in nature, not addition; (2) A unit rate of quantity is always found although one of the numbers in the ratio is not a factor (or multiple) of the other number; (3) Equivalent ratios are not necessary integral multiples of another ratio.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solving Word Problems Involving "Ratio" Concept of the Fifth - Grade Students: A Study in Vietnam

Phuong¹,

Loc²

2020

ujer

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The ratio is a mathematical concept that is useful in real life. In Vietnam, at an elementary level, students are acquainted with ratios in grade 4 through word problems and arithmetic operations. In grade 5, students continue to be familiar with proportional quantities and percentages which are related to ratios. In secondary schools, students will continue to study the slope of a straight line and trigonometric concepts which are essential applications of the ratio. Therefore, it is essential to help Vietnamese students understand the concept of a ratio and successfully solve word problems involving ratios. It should be an indispensable objective in teaching mathematics at primary levels in general and in grades 4-5 in particular. The paper presents the results of the analysis of mathematical content related to the ratio in primary mathematics textbooks of Vietnam and an experiment on solving word problems related to ratios of the fifth-grade students. It was found out that the misconceptions of ratio and lack of solving strategies cause primary school students' difficulties in solving word problems involving ratio. From that, the authors propose some solutions to improve students' abilities in solving these problems.

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Proportional Reasoning to Move Toward Linearity

Kastberg

Hord

Alyami

2022

Enabling Mathematics Learning of Struggling Students

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Helping Students With Mathematics Difficulties Understand Ratios and Proportions

Cited by 21 publications

References 13 publications

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics

Solving Word Problems Involving "Ratio" Concept of the Fifth - Grade Students: A Study in Vietnam

Proportional Reasoning to Move Toward Linearity

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