As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

Background/purpose: Investigation into the misconceptions of preschool students in mathematics and their differences between the ages of 4-5 and 5-6 years old helps form appropriate developmental mathematics teaching programs. However, although several studies have been conducted examining preschoolers' previous knowledge and misconceptions about…

This paper reports on the design, implementation, and evaluation processes of an activity that focused on the comparison meaning of the subtraction of integers and included the number line model as the primary representation. Finding the answer and determining the sign of the answer in the subtraction questions were targeted as the learning…

This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

Urban and rural children have different levels of performance in arithmetic processing. This study investigated whether such a residence difference can be explained by phonological processing. A total of 1,501 Chinese primary school students from urban and rural areas were recruited to complete nine cognitive tasks: two in arithmetic performance…

Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the "opposite model", which is a quantitative model,…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

In this article, we report the findings of a study conducted with 6 Grade 8 students in the United States. The students posed stories for open number sentences involving addition and subtraction of integers. We analysed the stories posed by the students to build models that describe the conceptual structures behind these posed stories -- the…

Students thrive when presented with tasks that are approachable, challenging, and interesting. Remembering to challenge all students is essential, not just those who excel in mathematics; teachers need to open the door to meaningful mathematics for every learner. In this exploration into subtraction patterns, teachers will see how curious young…

The number line and the neutralization model have been used very extensively in teaching integer additions and subtractions for decades. Despite their advantages, issues concerning subtractions on these models are still debatable. Therefore, the neutralization on an empty number line (NNL) model is proposed in this research to help students better…

This chapter identifies the ways in which 15 prospective teachers engage the strands of mathematical proficiency as they solve word problems involving integer addition and subtraction. The prospective teachers, through think-aloud interviews, demonstrated a strong focus on solving problems using procedures, which some did not explain and others…

Background: The concept of rational numbers is one of the learner's first experiences with a Mathematics concept beyond the basic skills operations on whole numbers. The personal knowledge of fractions that teachers bring to the teaching context is important because teachers mediate the conceptions that their learners construct. Aim: This study…

This research investigated students' sources and causes of errors and misconception in solving routine problems involving addition, subtraction, multiplication, and division of integers. This qualitative study involved observation of eight Year 7 classes and interviews with the respective classroom teachers. Sixteen Year 7 students who exhibit…

The "Reasoning Algebraically about Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the…

This study aims to develop a learning trajectory to help students understand concept of subtraction of integers using multimedia in the fourth grade. This study is thematic integrative learning in Curriculum 2013 PMRI based. The method used is design research consists of three stages; preparing for the experiment, design experiment, retrospective…