Informing Practice: Developing Symbol Sense for the Minus Sign

Lamb, Lisa; Bishop, Jessica Pierson; Philipp, Randolph A.; Schappelle, Bonnie P.; Whitacre, Ian; Lewis, Mindy

doi:10.5951/mathteacmiddscho.18.1.0005

Cited by 24 publications

(4 citation statements)

References 1 publication

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“…This level includes interpreting minus as a binary, symmetric, and unary function. Based on this, Lamb et al (2012) explained three meanings of minus sign (see Table 1).…”

Section: Context and Review Of Literaturementioning

confidence: 99%

Teaching and Learning Activities in Classroom and Their Impact on Student Misunderstanding: A Case Study on Negative Integers

Fuadiah¹,

Suryadi²,

Turmudi³

2019

INT J INSTRUCTION

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This study is a series of Didactical Design Research in prospective analysis stage to comprehensively identify some obstacles in learning negative integer in order to capture how the learning process used by teachers and how the impact on students in understanding the concept of negative numbers. This research is a case study administered to seventh-grade students in one of the classes in a junior secondary school in Indonesia to investigate how the teacher managed the learning process of integers and identify students' thinking construction. Involving a mathematics teacher and 37 students, this qualitative study collected data from field observations, interviews and document review. The data were analyzed by the perspectives of learning obstacles based on Theory of Didactical Situation. Findings show how teacher describes the negative integers and the arithmetic concepts to the students and its contribution in causing misunderstanding on the students. Within the framework of epistemological obstacles, the result of this study is used as a basis for designing a learning program which can overcome problems related to teaching and learning of negative integers.

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“…This level includes interpreting minus as a binary, symmetric, and unary function. Based on this, Lamb et al (2012) explained three meanings of minus sign (see Table 1).…”

Section: Context and Review Of Literaturementioning

confidence: 99%

Teaching and Learning Activities in Classroom and Their Impact on Student Misunderstanding: A Case Study on Negative Integers

Fuadiah¹,

Suryadi²,

Turmudi³

2019

INT J INSTRUCTION

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“…It can be seen that subject 1 (S1) already understands positive integers. According to Whitacre et al (2012), to understand the concept of positive and negative integers, it takes a very long time to equate the knowledge obtained with the experience previously obtained.…”

Section: Discussionmentioning

confidence: 99%

Transitional-Apprehending Mental Model for Junior High School Students in Understanding the Concept of Integers

Sukiyanto,

Nusantara,

Sudirman

et al. 2023

Acta Sci.

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Background: A concept that exists in students' minds and is used to describe and explain a phenomenon is called a mental model. Objective: This study aims to describe the transition-apprehending mental model of students in understanding the concept of integers. Design: This study used a qualitative approach and the type of research conducted was descriptive. Setting and participants: The subjects of this study were 35 students in grade VII Junior High School. Subjects were given a test to determine their understanding of the concept of integers. Data collection and analysis: data collection 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) analyze the process of forming mental models; and 6) verifying the findings. Results: showed that grade VII students were at the transition-Apprehending level, as evidenced by students being able to compare negative integers and positive integers with the same magnitude symbol. Conclusion: based on the results of research that has been found, students already understand positive integers and negative integers using a number line.

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“…−1 + 8 → (1 -1) + 8 = 0 + 8 Aqazade et al, 2016;Bofferding, 2010Bofferding, , 2014Bofferding, , 2019Hughes, 1986;Lamb et al, 2012;Murray, 1985 Use addition and binary meaning (Both signs)…”

Section: Interaction Of Knowledge-pieces and Knowledge-structurementioning

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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Informing Practice: Developing Symbol Sense for the Minus Sign

Cited by 24 publications

References 1 publication

Teaching and Learning Activities in Classroom and Their Impact on Student Misunderstanding: A Case Study on Negative Integers

Teaching and Learning Activities in Classroom and Their Impact on Student Misunderstanding: A Case Study on Negative Integers

Transitional-Apprehending Mental Model for Junior High School 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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