Changes of Meanings in Multiplication across Different Contexts: The Case of Amy and Beth

Chin, Kin Eng; Jiew, Fui Fong

doi:10.29333/ejmste/108440

Cited by 3 publications

(7 citation statements)

References 22 publications

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“…Making sense of multiplication is a complex process (Chin & Jiew, 2019). A mathematics expert teacher in the study of Jiew and Chin (in press) reasoned inaccurately when he was required to explain the meaning of multiplication across different contexts.…”

Section: Research Studies Of Multiplicationmentioning

confidence: 99%

“…In fact, there are other researchers who also argued that solving multiplication problems solely based on repeated addition is not enough (Byers, 2007;Devlin, 2007). In the similar vein, Chin and Jiew (2019) argued that it is possible to have other meanings of multiplication thus they explored the conceptions of two mathematics teachers possessed about the multiplication symbol (×) in order to look for some possible alternative conceptions. The teachers were required to give real life examples based on the given mathematical expressions i.e.…”

Section: Research Studies Of Multiplicationmentioning

confidence: 99%

“…This study is different from Chin and Jiew (2019) where participants are required to create mathematical expressions based on the given real life problems i.e. from different real life contexts to symbolism.…”

Section: Research Studies Of Multiplicationmentioning

confidence: 99%

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Conceptions in Making Sense of Multiplication

Chin

Jiew

Taliban

2019

EURASIA J MATH SCI T

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This paper aims to explore how three secondary school teachers make sense of multiplication based on their conceptions of multiplication. The framework of supportive and problematic conceptions in making sense of mathematics proposed by Chin (2013) is exemplified in this study. Initially, data were collected through a survey assessment that consists of a set of mathematical tasks. Then follow-up interviews were conducted with these participants. Three secondary school teachers (Jessica, Sarah and Claire-pseudonyms) participated in this study. Findings revealed that the changes of meanings in multiplication have impacted the sense-making of Sarah and Claire. On the other hand, Jessica who sensed these mathematical changes could talk about multiplication sensibly.

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Section: Research Studies Of Multiplicationmentioning

confidence: 99%

Section: Research Studies Of Multiplicationmentioning

confidence: 99%

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Conceptions in Making Sense of Multiplication

Chin

Jiew

Taliban

2019

EURASIA J MATH SCI T

Self Cite

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“…Consequently, the learners were found limited in using commutative properties to be able to make meaning when multiplying decimals. Again, teachers are also implicated for their excessive use of repeated addition when trying to build multiplication concepts (Chin & Jiew, 2019). Earlier study by Seah (2004)has established learners' demonstration of restricted nature of their understanding in the concepts of multiplication.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, it has been declared that there is much emphasis on memorising facts of multiplication, and that this practice had led learners to only being able to express a limited view of the operation (Smith & Smith, 2006).This invariably makes learners unable to see beyond their limited scope, and they fall short of the wider application of the operation to different contexts. Chin and Jiew (2019) argue that since it is difficult for the learners to decide when the operation of multiplication could be used, they need foundational ideas of multiplication to be able to drive the meaning of the operation. They reasoned that multiplication is the only operation among the basic arithmetic operations that has been seen in use for different contexts and as such the understanding of teachers ought to be investigated to be able to aid the child learner's multiplicative thinking.…”

Section: Introductionmentioning

confidence: 99%

Pupils’ Understanding of Multiplication and Division in Multiple Contexts

Fletcher¹,

Baidoo²

2019

ijird

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The concepts of multiplication and division are building blocks for the learning of nearly all mathematics topics. Yet pupils, particularly those in lower primary and the starting point of the upper primary level find these concepts difficult to handle. This paper reports on a month-long study carried out in four primary schools in the Cape Coast Metropolis, which was a study of the impact on Teaching multiplication and division in multiple contexts on pupils' understanding of multiplication and division and their ability to solve problems in these areas. Multiplication has always been treated as repeated addition, whereas division has been seen by many teachers only as equal grouping of given quantities despite the different practical situations and contexts that make use of these operations. The quasi experimental design involving experimental and control groups was used. The study involved 137 pupils from primary four intact classes. The main instruments used in the study were a pre-test and a post-test. The results indicate a significant difference in the performance of pupils in the experimental and control groups in their: a) ability to distinguish between multiplication and division concepts; b) understanding of multiplication; and c) understanding of division.

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The Transition from Real Numbers to Complex Numbers

Taliban¹,

Chin²,

Jiew³

2020

ASMSJ

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Humans make sense of mathematics by relating it to personal conceptions and experiences. This might not be a smooth process as it may involve conceptions that work in an old context but do not work in a new context. The framework proposed by Chin and Tall (2012), Chin (2013) and Chin (2014) highlights how prior experiences shape humans' conceptions can be either supportive or problematic in making sense of extended contexts of mathematics. A supportive conception is a conception that supports learning and generalisation in a new context while a problematic conception is a conception that impedes learning and generalisation in a new context. By employing this framework, this study aims to explore how a group of respondents that consists of 30 mathematics undergraduate students from a public university in Malaysia make sense of complex numbers. The system of complex numbers is an extension of real numbers thus students will learn real numbers prior to learning complex numbers. How the respondents cope with the transition from real numbers context to complex numbers context is the focus of this study. Data were collected through a questionnaire and follow up interviews. Respondents participated in the follow up interviews voluntarily and data from three respondents were reported in this study. The result shows that these respondents have several supportive conceptions, such as the concept of addition and multiplication of real variable. The data also support the existence of problematic conceptions in making sense of complex numbers, namely the concept of positive-negative numbers and inequalities. These conceptions are originated from the context of real numbers.

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Changes of Meanings in Multiplication across Different Contexts: The Case of Amy and Beth

Cited by 3 publications

References 22 publications

Conceptions in Making Sense of Multiplication

Conceptions in Making Sense of Multiplication

Pupils’ Understanding of Multiplication and Division in Multiple Contexts

The Transition from Real Numbers to Complex Numbers

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