Fraction Operations: An Examination of Prospective Teachers’ Errors, Confidence, and Bias

Young, Elaine; Zientek, Linda Reichwein

doi:10.1080/24727466.2011.11790307

Cited by 13 publications

(18 citation statements)

References 19 publications

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“…For example, Brown and Quinn (2006) asked high school students to simplify

\frac{24}{36}

to its simplest form and many students miscalculated the division. Extending into postsecondary education, Young and Zientek (2011) asked preservice educators to solve fraction computation problems across all four operations. Even though all participants had taken and passed a university‐level algebra course, a common error included miscalculating natural numbers.…”

Section: Rational Number Error Patternsmentioning

confidence: 99%

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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“…For example, Brown and Quinn (2006) asked high school students to simplify

\frac{24}{36}

Section: Rational Number Error Patternsmentioning

confidence: 99%

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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“…(p. 629) Research has shown that teachers' content knowledge for teaching mathematics is important to student success (Hill, Rowan, & Ball, 2005). Prospective teachers have been more capable adding and subtracting fractions than dividing fractions (Li & Kulm, 2008;Marchionda, 2006;Newton, 2008;Young & Zientek, 2011). Research also indicates that when errors with fractions are made, prospective and in-service teachers often display errors that are similar to the students they will teach (Silver, 1983(Silver, , 1986Tirosh, Fischbein, Graeber, & Wilson, 1998).…”

Section: Introductionmentioning

confidence: 99%

“…In addition to competence, prospective teachers need to be confident and accurate in assessing their abilities related to topics they will teach. Young and Zientek (2011) reported that teachers were more confident in their ability to add fractions with like denominator than adding or multiplying with relatively prime denominators and dividing fractions. Li and Kulm's (2008) results suggest an incongruence in teachers' beliefs that they were ready to teach fraction computations and the teachers' abilities to do so.…”

Section: Introductionmentioning

confidence: 99%

Solving equations with fractions: An analysis of prospective teachers’ solution pathways and errors

Jones

Zientek

Sharon³

et al. 2020

School Sci & Mathematics

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We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the written solutions, determined which solution pathways led to the correct solution, and identified common errors in the solution pathways of respondents who incorrectly solved the equation. Respondents initially attempted different methods. The most common method was solving by using fractions, but the majority of respondents who solved by using mixed numbers were able to correctly solve the problem. Common errors related to fraction arithmetic and the distributive property.Nearly all of the abandoned pathways contained no errors, but ended with a step that likely would precede an operation with fractions. Our findings suggest that the ability to solve an arithmetic equation with no fractions was necessary, but not sufficient, to solve an arithmetic equation involving fractions, and that the problem of solving equations with fractions was more closely tied to one's difficulties with rational number arithmetic and less with one's understanding of algebra. K E Y W O R D S algebra, fractions, prospective teachers, solving equations | 233 JONES Et al.

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“…Particularly, pre-service and novice primary teachers have difficulties with dividing fractions (Tirosh, 2000). Research suggests that novice teachers lack of deep understanding of fraction division and have weak knowledge of students' misunderstanding (Young & Zientek, 2011) Traditionally, teachers hide and ignore students' mathematical mistakes and make students afraid to make mistakes (Durkin & Rittle-Johnson, 2015). If a teacher ignores students' errors (SE) or does not correct student's error, the error may be repeated or accumulated or cause other related errors.…”

mentioning

confidence: 99%

Fostering Novice Teachers’ Knowledge of Students’ Errors on Fraction Division by Using Researched-Based Cases

2017

JME

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There are increasing studies on knowledge of students' learning, but limited study focuses on detecting students' errors gathered in authentic classrooms and repairing them. Novice primary teachers, as well as students, have difficulties with dividing fractions and have weak knowledge of students' understanding and misunderstanding. Thus, this study was designed to foster novice primary teachers' knowledge of anticipating, identifying, and correcting students' errors on dividing fractions through using research-based cases. The data were collected from a case-based discussion group including four novice teachers and a facilitator. Five case-based discussions were tape-and videorecorded. A pre-and post-test consisting of four items with 16 sub-items were carried out. The result shows that the novice teachers became more versatile in anticipating students' errors and shifted from algorithms based errors toward conceptually based errors. The pedagogical strategies of repairing students' errors to be used included to help students revisit their prior knowledge, understand semantics structure of fraction division word problems, and realize the nature of fraction division. They were able to offer various pedagogical strategies corresponding to specific errors to repair students' errors.

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Fraction Operations: An Examination of Prospective Teachers’ Errors, Confidence, and Bias

Cited by 13 publications

References 19 publications

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

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

Solving equations with fractions: An analysis of prospective teachers’ solution pathways and errors

Fostering Novice Teachers’ Knowledge of Students’ Errors on Fraction Division by Using Researched-Based Cases

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