Conceptual models for integer addition and subtraction

Wessman-Enzinger, Nicole M.; Mooney, Edward S.

doi:10.1080/0020739x.2019.1685136

Cited by 6 publications

(6 citation statements)

References 28 publications

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“…In addition, elementary school students understand integers using productive means of their reasoning at the early stage rather than the school-based teaching they get (Lamb et al, 2016). Giving open number sentences in addition and subtraction operations of integers can be an insightful assessment tool to describe and understand students' thinking and learning (Wessman-Enzinger & Mooney, 2019).…”

Section: Introductionmentioning

confidence: 99%

“…In addition to providing information on the classification of drawing types, the open number sentences questions presented in several completion sessions can provide information on changing drawing types. This change has important information in the form of the development of cognitive ideas towards the addition and subtraction operations of integers in a better direction (Wessman-Enzinger & Mooney, 2019).…”

Section: Introductionmentioning

confidence: 99%

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Learner-generated drawings by students with mathematical learning difficulties in finishing open number sentences

Amir

2022

jel

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Although MLD students do not have good mathematical performance in completing addition and subtraction operations of integers, MLD students have suggestive ideas in the form of drawings produced in solving open number sentences questions. This study aims to classify the types and identify changes in the drawing produced by MLD students in solving open number sentences questions. This research method is qualitative with a micro generic study approach to understand students' thinking individually and explore drawing changes in solving open number sentences questions between sessions. The research subjects were 2 out of 20 MLD grade 5 elementary school students who produced the most varied drawings in solving open number sentences questions. Data collection techniques used are giving questions and interviews. The results showed that MLD students produced: discrete object drawings by focusing on the cardinality of the quantity of a number; transitions from objects to the number line by focusing on the magnitude of numbers; partitioning the number line using magnitude reasoning; number sentences; and others using verbal reasoning. Changes in the drawings produced by MLD students between sessions indicate the development of students' understanding towards a better direction in interpreting symbolic representations to visual representations. The results of this study contribute to the theory that although MLD students have low mathematical performance. However, MLD students can produce variations and changes in drawings with rich mathematical idea information representing integer operations.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Learner-generated drawings by students with mathematical learning difficulties in finishing open number sentences

Amir

2022

jel

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“…In Indonesia, this cloth is supplied at the standard faculty level, however this fabric is to aid the continuity of in addition getting to know at the junior to senior excessive college stage (Nicole, 2019). In Indonesia and numerous other nations, which include Singapore and Japan, the material for integers is in 7th grade.…”

Section: Introductionmentioning

confidence: 99%

“…in contrast to positive numbers, negative numbers do now not have an obvious reference. therefore, college students should try harder to recognize poor numbers (Blair et al, 2012;Nicole, 2019). This is regular with severa cases that severa researchers have located (Vlassis, 2008;Bofferding, 2010;Bofferding, 2014;and Van de Walle et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Model mental transition-attempting: The case of beginners students in understanding the concept of integers

2022

pegegog

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A mental model is a concept that exists in students' minds and is used to describe and explain a phenomenon. This study aims to describe the transition-attempting mental model of students in understanding the concept of integers. This study uses a qualitative approach and the type of research conducted is descriptive. The subjects of this study amounted to 58 students in class VII. Subjects were given a test to determine their understanding of the concept of integers. They were collecting data in this study using test questions and interviews. Data analysis used five steps, namely 1) data transcoding; 2) reviewing data; 3) data reduction; 4) presenting data; 5) analyzing the process of forming mental models; and 6) verifying the findings. This study indicates that students can compare negative integers and positive integers for symbols of different quantities. However, this finding cannot be categorized into the level of the mental model that already exists, so in this study, we solve the mental transition I model into a transition-attempting mental model. Based on the research results found, the mental transitionattempting model can be seen from the information held by students and stored in long-term memory before they are faced with certain concepts.

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“…There is general consensus on a bank of strategies that students use when solving integer addition and subtraction problems (e.g., Bishop, Lamb, Philipp, Whitacre, & Schappelle, 2018;Bofferding, 2019;Bofferding & Wessman-Enzinger, 2017;Wessman-Enzinger & Mooney, 2019). There are also some isolated accounts of how students use specific concep tions to justify strategy use; for example, Violet as described by Bishop, Lamb, Philipp, Whitacre, and Schappelle (2014), relied heavily on linear order to make sense of integer problems.…”

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confidence: 99%

Second and fifth graders’ use of knowledge-pieces and knowledge-structures when solving integer addition problems

Aqazade

Bofferding

2021

J. Numer. Cogn.

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In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. Fifty-one out of 102 second graders and 90 out of 102 fifth graders read or used negative signs at least once across the 11 problems. Among second graders, one of their most common strategies was subtracting numbers using their absolute values, which aligned with students’ whole number knowledge-pieces and knowledge-structure. They sometimes preserved the order of numbers and changed the placement of the negative sign (e.g., −9 + 2 as 9 – 2) and sometimes did the opposite (e.g., −1 + 8 as 8 – 1). Among fifth graders, one of the most common strategies reflected use of integer knowledge-pieces within a whole-number knowledge-structure, as they added numbers’ absolute values using whole number addition and appended the negative sign to their total. For both grade levels, the order of the numerals, the location of the negative signs, and also the numbers’ absolute values in the problems played a role in students’ strategies used. Fifth graders’ greater strategy variability often reflected strategic use of the meanings of the minus sign. Our findings provide insights into students’ problem interpretation and solution strategies for integer addition problems and supports a blended theory of conceptual change. Adding to prior findings, we found that entrenchment of previously learned patterns can be useful in unlikely ways, which should be taken up in instruction.

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Conceptual models for integer addition and subtraction

Cited by 6 publications

References 28 publications

Learner-generated drawings by students with mathematical learning difficulties in finishing open number sentences

Learner-generated drawings by students with mathematical learning difficulties in finishing open number sentences

Model mental transition-attempting: The case of beginners students in understanding the concept of integers

Second and fifth graders’ use of knowledge-pieces and knowledge-structures when solving integer addition problems

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