Redefining the Whole: Common Errors in Elementary Preservice Teachers’ Self-Authored Word Problems for Fraction Subtraction

Dixon, Juli K.; Andreasen, Janet B.; Avila, Cheryl L.; Bawatneh, Zyad; Deichert, Deana; Howse, Tashana D.; Turner, Mercedes Sotillo

doi:10.1080/24727466.2014.11790336

Cited by 11 publications

(12 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This word problem looks correct, but the two units (pizzas) may not being the same size and shape. A similar finding is also discussed by Dixon et al (2014) on subtracting of fractions: when PSTs are asked to pose a word problem, for instance − , they tend to write a problem to represent − × . They tend to use an incorrect redefinition of the whole, and the fractions involved in the tasks influence PSTs' performance on writing the word problems.…”

Section: Teachers' Knowledge Of Operations With Rational Numberssupporting

confidence: 68%

“…They tend to use this technique especially when the task involves two fractions with different denominators. A common method to investigate teachers' knowledge of adding and subtracting fractions is to ask them to write word problems (Austin, Carbone, & Web, 2011;Dixon et al, 2014;Kar & Isik, 2014). Austin et al (2011), focusing their study on adding fractions, found an issue related to PSTs' inability to recognise that uniform units have to be used.…”

Section: Teachers' Knowledge Of Operations With Rational Numbersmentioning

confidence: 99%

See 1 more Smart Citation

Danish Pre-service Teachers’ Mathematical and Didactical Knowledge of Operations with Rational Numbers

Putra

2019

Int Elect J Math Ed

View full text Add to dashboard Cite

The aim of this study is to investigate Danish pre-service teachers' (PSTs) mathematical and didactical knowledge of operations with rational numbers. This knowledge is studied through their collaborative activities to certain tasks related to the teaching of operations with rational numbers. An explicit model of the teachers' mathematical and didactical knowledge is designed based on the anthropological theory of the didactic (ATD) and used to analyse five-groups of PSTs' collaborative work. The findings show that the Danish PSTs prefer to use contextual or reallife situations in their teaching, but they encounter various challenges to realise general ideas in the context at hand.

show abstract

Section: Teachers' Knowledge Of Operations With Rational Numberssupporting

confidence: 68%

Section: Teachers' Knowledge Of Operations With Rational Numbersmentioning

confidence: 99%

Danish Pre-service Teachers’ Mathematical and Didactical Knowledge of Operations with Rational Numbers

Putra

2019

Int Elect J Math Ed

View full text Add to dashboard Cite

show abstract

“…However, many PTs struggle to write appropriate word problems to support fraction operations (Dixon et al, 2014). Thus, those PTs who plan to teach mathematics at any grade level need practice constructing well-written and meaningful fraction word problems to prepare them to convey the concept of a fraction and to create rich learning environments for their future students (McAllister & Beaver, 2012).…”

Section: Representing Symbolic Expression Using Wordsmentioning

confidence: 99%

“…PTs' ability to write story problems reflects their "mathematical content knowledge and literacy, which can be classified into a hierarchical system of performance levels and indeed the highest level of mathematical literacy should include a contextual application and an understanding of mathematics" (Luo, 2009, p. 85). However, Dixon et al (2014) found that many PTs in the United States were unable to provide contextual support for subtracting fractions and experienced significant difficulty writing sensible fraction story problems for given operations. In their research, Dixon et al (2014) (Luo, 2009; see also Ball 1990aBall , 1990b.…”

Section: Representing Symbolic Expression Using Wordsmentioning

confidence: 99%

“…However, Dixon et al (2014) found that many PTs in the United States were unable to provide contextual support for subtracting fractions and experienced significant difficulty writing sensible fraction story problems for given operations. In their research, Dixon et al (2014) (Luo, 2009; see also Ball 1990aBall , 1990b. In particular, in order to teach fraction subtraction PTs need to know why the subtraction algorithm works, so that they can links the algorithm to appropriate representations, can write word problems for fraction expressions, and can choose an appropriate word problem for a given symbolic expression (Dixon et al, 2014 to find the values of (1 × 4 and × ), and then to create corresponding word problems.…”

Section: Representing Symbolic Expression Using Wordsmentioning

confidence: 99%

See 1 more Smart Citation

Preservice Teachers Making Sense Of Fraction Concepts And Operations In A Mathematics Education Content Course

Desta¹

View full text Add to dashboard Cite

Effective mathematics learning is often the result of effective teaching with students learning mathematics through experiences that teachers provide for them (NTCM, 2000). Teachers need to have deep mathematics content knowledge in order to understand their students' thinking and so be able to select mathematics tasks which provide meaningful experiences to their students. There is overall agreement that teachers need to have well-formed content knowledge because this affects what they teach and how they teach it (Da Ponte & Chapman, 2016). It is, therefore, no surprise, that teachers' knowledge of mathematics continues to be an important theme in research on preservice mathematics teacher education (Da Ponte, & Chapman, 2016). It is reasonable to plan and conduct research which addresses elementary preservice teachers' (PTs') learning, with special attention given to their knowledge of fraction concepts and operations, issues related to this knowledge, and to how its development has been facilitated in mathematics education content courses. That is because preservice teachers are expected to teach important mathematical ideas at elementary level (McCormick, 2015; Behr, Wachsmuth, Post, & Lesh, 1984). In particular, studying PTs' knowledge for teaching fractions is important because it is widely recognized that the topic is difficult to learn and teach (Rosli, Gonzalez, & Capraro, 2011). Mathematical Understandings of Preservice Teachers Many research studies have shown that the mathematical understandings that preservice teachers gain from schooling and university mathematics courses do not adequately prepare them to teach primary school mathematics effectively (Ball, 1990a, 1990b; Even, 1993; Ma, 1999; Simon, 1993), particularly given the kind of teaching demanded by recent reforms of the

show abstract

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

Powell

Nelson

2020

Psychology in the Schools

View full text Add to dashboard Cite

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.

show abstract

Redefining the Whole: Common Errors in Elementary Preservice Teachers’ Self-Authored Word Problems for Fraction Subtraction

Cited by 11 publications

References 13 publications

Danish Pre-service Teachers’ Mathematical and Didactical Knowledge of Operations with Rational Numbers

Danish Pre-service Teachers’ Mathematical and Didactical Knowledge of Operations with Rational Numbers

Preservice Teachers Making Sense Of Fraction Concepts And Operations In A Mathematics Education Content Course

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

Contact Info

Product

Resources

About