Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment

Behr, Merlyn J.; Wachsmuth, Ipke; Post, Thomas R.; Lesh, Richard

doi:10.5951/jresematheduc.15.5.0323

Cited by 30 publications

(27 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A similar phenomenon occurs when comparing fractions without common components. Students tend to think that a fraction is larger if the numerator and denominator are larger (Behr et al 1984;Gelman et al 1989;Resnick et al 1989). Accordingly, they perform better on items where the largest fraction has the largest numerator and denominator (so-called congruent items, for example: 2/3 vs. 7/9) than on items where the largest fraction has the smallest numerator and denominator (incongruent items, for example: 3/4 vs. 5/9).…”

Section: Natural Number Bias In Numerical Rational Number Size Tasksmentioning

confidence: 99%

Various ways to determine rational number size: an exploration across primary and secondary education

et al. 2019

View full text Add to dashboard Cite

Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is students' tendency to apply the properties of natural numbers (inappropriately) when they are working with rational numbers (a phenomenon called natural number bias). Focusing on rational number comparison tasks, recent research has shown that other incorrect strategies such as gap thinking or reverse bias can also explain these difficulties. The present study aims to investigate students' different ways of thinking when working on fraction and decimal comparison tasks. The participants were 1,262 primary and secondary school students. A TwoStep Cluster Analysis revealed six different student profiles according to their way of thinking. Results showed that while students' reasoning based on the properties of natural numbers decreased along primary and secondary school, almost disappearing at the end of secondary school, students' reasoning based on gap thinking increased along these grades. This result seems to indicate that when students overcome their reliance on natural numbers, they enter a stage of qualitatively different errors before finally reaching the stage of correct understanding.

show abstract

Section: Natural Number Bias In Numerical Rational Number Size Tasksmentioning

confidence: 99%

Various ways to determine rational number size: an exploration across primary and secondary education

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Enright (1990), Behr, Wachsmuth, Post, and Lesh (1984), and Steffe and Olive (1991) proposed common errors and misconceptions in fraction-related items; but these studies were limited in which they did not speculate about error patterns across items. In addition, Brown and Quinn (2006) classified 25 fraction problems into six categories, analyzed errors, and provided the descriptions of common errors students made in each item category.…”

Section: Framework For This Studymentioning

confidence: 99%

A Descriptive Analysis of the Error Patterns Observed in the Fraction-Computation Solution Pathways of Students With and Without Learning Disabilities

Hwang

Riccomini

2019

Assessment for Effective Intervention

View full text Add to dashboard Cite

Developing an understanding of fractions is critical as a significant predictor for the learning progression of advanced domains; however, students face significant challenges in learning fractions because of their unique properties. To systematically approach remediation, this study examined the common error patterns committed by middle-school students with and without learning disabilities in mathematics when solving fraction computations involving addition. Based on the logic that errors reflect meaningful misconceptions, errors associated in each solution stage established in a solution algorithm were analyzed. Findings provide instruction implications to develop practical guidelines for researchers, insights into a starting point of instruction when teaching students in diverse achievement levels, and an awareness about specific problematic areas requiring more intensive instruction and intervention. Careful consideration of errors associated within a solution pathway can maximize the efficacy of instructions. Future research directions, educational implications, and limitations are discussed.

show abstract

“…The other is the very large literature on students' knowledge and learning of school mathematics concepts and procedures, particularly number concepts and operations. This work has produced detailed analyses of whole number concepts (Fuson, 1992;Resnick, 1983), additive relationships (Carpenter & Moser, 1984;Siegler & Jenkins, 1989), multiplicative relationships (Greer, 1992;Harel & Confrey, 1994), rational numbers (Behr, Wachsmuth, Post, & Lesh, 1984;Smith, 1995), and algebraic concepts and procedures (Kieran, 1992;Usiskin, 1988). Notably, far fewer studies have examined the development of students' spatial and geometric reasoning (Clements & Battista, 1992).…”

Section: Finding the Mathematics In Work Activitiesmentioning

confidence: 99%

Tracking the Mathematics of Automobile Production: Are Schools Failing to Prepare Students for Work?

Smith¹

1999

American Educational Research Journal

View full text Add to dashboard Cite

Global competition and technological innovation, it is" often argued, have fundamentally changed the nature of work, making it more technically demanding, while schools have not kept pace. But the mathematics used in workplaces, much less whole industries, is rarely examined carefully. Observations at 16 sites involved in automobile manufacturing indicate that the level and content of mathematics required by work practices vary substantially. High-volume assembly made minimal to modest demands on workers, primarily for measurement and nu-merical~quantitative reasoning. Machine tool operation and work in quality labs, however, required substantial spatial and geometric knowledge in two and three dimensions. Technology affected the mathematical demands of work, but the effect was shaped by management orientation and patterns of work organization. These results raise questions about how badly schools are failing to prepare students fi)r "the global competitive workplace." JOHN E SMrru, III, is an Associate Professor, Department of Counseling, Educational Psychology, and Special Education, Michigan State University, 442 Erickson Hall, East Lansing, MI 48824. He specializes in the nature of understanding and student learning in mathematics, the use of mathematics in the workplace, and the working practices of mathematicians.

show abstract

Order and Equivalence of Rational Numbers: A Clinical Teaching Experiment

Cited by 30 publications

References 0 publications

Various ways to determine rational number size: an exploration across primary and secondary education

Various ways to determine rational number size: an exploration across primary and secondary education

A Descriptive Analysis of the Error Patterns Observed in the Fraction-Computation Solution Pathways of Students With and Without Learning Disabilities

Tracking the Mathematics of Automobile Production: Are Schools Failing to Prepare Students for Work?

Contact Info

Product

Resources

About