Stretching student teachers’ understanding of fractions

Harvey, Roger

doi:10.1007/s13394-012-0050-7

Cited by 11 publications

(8 citation statements)

References 32 publications

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“…Conceptually, fractions present a hurdle as students attempt to transfer their understanding of whole numbers to a new but related class of numbers. Several researchers (Mack 2001;Lamon 2007) and, more recently, Harvey (2012) showed us that fractions are a problematic area of learning for both students and their teachers. Investigations conducted by Tirosh (2000) showed that pre-service teachers tended to have a mechanical understanding of fractions and this knowledge is less likely to help them support their students develop conceptual knowledge that girds fraction problems that involve division.…”

Section: Pre-service Understanding Of Fractions and Misconceptionsmentioning

confidence: 99%

Generating procedural and conceptual knowledge of fractions by pre-service teachers

Chinnappan

Forrester

2014

Math Ed Res J

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Knowledge that teachers bring to the teaching context is of interest to key stakeholders in improving levels of numeracy attained by learners. In this regard, the centrality of, and the need to investigate, the quality of teachers' mathematical knowledge for teaching mathematics has been gaining momentum in recent years. There is a general consensus that teachers need a robust body of content and pedagogical knowledge related to mathematics and that one impacts on the other. However, in current debates about this interconnection between content knowledge and pedagogical content knowledge, there is limited analysis about the procedural-conceptual nature of content knowledge that, we argue, has significant impact on the development of pedagogical content knowledge. In this report, this issue is investigated by examining the state of procedural and conceptual knowledge of two cohorts of pre-service teachers and analyzing the impact of a representational reasoning teaching and learning (RRTL) approach aimed at supporting a balanced development of these two dimensions of Content Knowledge. Abstract Knowledge that teachers bring to the teaching context is of interest to key stakeholders in improving levels of numeracy attained by learners. In this regard, the centrality of, and the need to investigate, the quality of teachers' mathematical knowledge for teaching mathematics has been gaining momentum in recent years. There is a general consensus that teachers need a robust body of content and pedagogical knowledge related to mathematics and that one impacts on the other. However, in current debates about this interconnection between content knowledge and pedagogical content knowledge, there is limited analysis about the procedural-conceptual nature of content knowledge that, we argue, has significant impact on the development of pedagogical content knowledge. In this report, this issue is investigated by examining the state of procedural and conceptual knowledge of two cohorts of pre-service teachers and analyzing the impact of a representational reasoning teaching and learning (RRTL) approach aimed at supporting a balanced development of these two dimensions of Content Knowledge.

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Section: Pre-service Understanding Of Fractions and Misconceptionsmentioning

confidence: 99%

Generating procedural and conceptual knowledge of fractions by pre-service teachers

Chinnappan

Forrester

2014

Math Ed Res J

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“…Research supports the idea that teaching and learning fraction concepts is a difficult and complex undertaking (Ball, ; Harvey, ; Lamon, ; Ma, ; Newton, ). Charalambous and Pitta‐Pantazi () and Harvey () assert that the teaching and learning of fractions has traditionally been problematic while Newstead and Murray () suggest that it is well documented that fractions are among the most complex mathematical concepts that elementary students encounter. Further research reveals that there are several factors that contribute to students' challenges with developing deep conceptual understanding of and procedural fluency with fractions.…”

mentioning

confidence: 62%

“…According to the literature, either the challenge of learning fractions with deep understanding lies in the inherent nature of fractions and the multifaceted construct of fractions or it is due to the instructional approaches for teaching fractions that are employed by teachers (e.g., Behr, Harel, Post, & Lesh, ; Brousseau, Brousseau, & Warfield, ; Cramer & Whitney, ; Kieren, ; Lamon, ; McNamara & Shaughnessy, ). Many purport that the problem is the confluence of these factors and that the problem is further complicated by the fact that many prospective and in‐service teachers have a limited and incomplete understanding of fractions themselves (Ball, ; Becker & Lin, ; Chinnappan & Forrester, ; Cramer, Post, & del Mas, ; Harvey, ; Ma, ; Wu, ).…”

mentioning

confidence: 99%

What Is a Fraction? Developing Fraction Understanding in Prospective Elementary Teachers

Reeder

Utley

2017

School Sci & Mathematics

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Classroom teachers need a well‐developed deep understanding of fractions and pedagogic practices so they can provide meaningful experiences for students to explore and construct ideas about fractions. This study sought to examine prospective elementary teachers' understandings of fraction by focusing specifically on their use of fractions meanings and interpretations. Results indicated that prospective elementary teachers bring with them to their final methods course a limited understanding of fractions and that experiences in methods courses resulted only in minor improvement of those limited understandings. The limited part‐whole understanding of fractions that prospective elementary teachers entered the course with was resilient. The implications of this study suggest a need for prospective elementary teachers to continue to develop their conceptual understanding of fractions and for changes to the content and instructional strategies of mathematics content courses designed for prospective elementary teachers.

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“…That is, students determined a fraction was lesser if the difference between the numerator and denominator was less (e.g.,

\frac{3}{5}

is less than

\frac{1}{10}

because 2 [i.e., difference of 3 and 5] is less than 9 [i.e., difference of 1 and 10]). Harvey (2012) also noted this same thinking with a university‐level preservice educator. As Nelson and Powell (2018) explained with fraction computation, elementary students separately added all of the digits in an addition problem to reach the solution (e.g., the student answer

\frac{1}{3}

\frac{1}{4}

= 9, as the student added 1 + 1 + 3 + 4), which provides another example of students applying natural number knowledge to fractions.…”

Section: Rational Number Error Patternsmentioning

confidence: 73%

University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

Powell

Nelson

2020

Psychology in the Schools

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To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's response and identified error patterns for items answered incorrectly. Students attempted foundational understanding and calculations problems more often than word problems, and students made fewer errors with foundational understanding and calculation items. Students demonstrated the most unique errors with calculations and word problems items. Given all items on the rational numbers assessment required elementary or middle school knowledge of rational numbers, the number and diversity of errors with a sample of university students demonstrates the persistent difficulties with rational numbers that students carry into adulthood. Elementary, secondary, and developmental mathematics educators should be aware of such errors and provide specific instruction on avoiding such errors.

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Stretching student teachers’ understanding of fractions

Cited by 11 publications

References 32 publications

Generating procedural and conceptual knowledge of fractions by pre-service teachers

Generating procedural and conceptual knowledge of fractions by pre-service teachers

What Is a Fraction? Developing Fraction Understanding in Prospective Elementary Teachers

University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

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