Subtraction involving negative numbers: Connecting to whole number reasoning

In this article, we explore how students attempt to bridge from their whole number reasoning to integer reasoning as they solve subtraction problems involving negative numbers. Based on interviews with students ranging from first graders to preservice teachers, we identify two overarching strategies: making connections to known problem types and leveraging conceptions of subtraction. Their initial connections suggest that rather than identifying the best instructional models to teach integer concepts, we should focus on identifying integer instructional models that build on the potentially productive connections that students’ already make; we propose an example of one such form of instruction

Leveraging Different Perspectives to Explore Student Thinking about Integer Addition and Subtraction

This is the third meeting of a working group on student thinking about integers. The main goal of this working group includes utilizing different theoretical perspectives and methodologies in small groups to design complementary studies, where student thinking about integer addition and subtraction will be explored. This working group aims to provide a space for participants to capitalize on their differences in theoretical perspectives and methodologies to promote productive scholarly discussion about the same research topic, student thinking about integer addition and subtraction. Participants will actively engage in work that progresses towards these studies, with the intent to develop a monograph that highlights this research

International Integer Curriculum Comparison

A discussion group met and discussed the current state of research in the domain of integers at the joint PME 38 and PME-NA 36 meetings (Bofferding, Wessman- Enzinger, Gallardo, Salinas, & Peled, 2014). During these meetings productive discussion revolved around what it meant to understand integers. Additionally, the organisers presented a literature review of the research on integers from all of the PME and PME-NA proceedings, which the group discussed. At the conclusion of this meeting, the group expressed interest in investigating integers further together by pursuing an international curriculum comparison study. This working group aims to begin this curriculum comparison study of integers

Negative Numbers: Bridging Contexts and Symbols

At the latest PME-NA (35), a working group met on the topic of negative numbers. Groups presented on their research within one or more categories related to negative integers: role of contexts, models, historical development, algebra, student understanding, and teacher knowledge (Lamb et al., 2013). We began a productive discussion on issues related to each of these categories and would like to broaden the discussion with the inclusion of members from the international community. Further we aim to develop research collaborations around mutual areas of interest

Where to Start and How to Judge? First and Third Graders\u27 Measurement Conceptions

We analyzed students’ responses to a series of broken ruler measurement tasks in the form of incorrect worked examples. The measurement tasks challenged students’ initial conceptions of where the measurement starts and how to determine the overall length

Take a Giant Step: A Blueprint for Teaching Young Children in a Digital Age

Calls for enhancing early childhood education and teacher preparation and development by incorporating digital learning and highlights best practices, policy and program trends, and innovative approaches. Outlines goals for 2020 and steps to achieve them

Jump as Far as You Can [Problem Solvers: Problem]

This month's problem examines the standing long jump, an Olympic event until 1912. Students will jump as far as they can from a standing position and measure the distance by using different units, such as cubes, feet, and inches. A good problem can capture students' curiosity and can serve many functions in the elementary school classroom: to introduce specific concepts the teacher can build on after students recognize the need for additional mathematics or to help students see where to apply already-learned concepts. We encourage teachers to use the monthly problem and suggested instructional notes in their classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.</jats:p

Second and Fifth Graders’ Use of Knowledge-Pieces and Knowledge-Structures When Solving Integer Addition Problems

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

Jump as far as You Can [Problem Solvers: Solutions]

This department showcases students' in-depth thinking and work on problems previously published in Teaching Children Mathematics. The problem scenario in the December 2013/January 2014 issue involves concepts of formal and informal measurement and encourages students to use different units to measure and compare.</jats:p

Early Elementary Students’ Use of Shape and Location Schemas When Embedding and Disembedding

Elementary students’ early development of embedding and disembedding is complex and paves the way for later STEM learning. The purpose of this study was to clarify the factors that support students’ embedding (i.e., overlapping shapes to form a new shape) and disembedding (i.e., identifying discrete shapes within another shape) through the use of filled shapes as opposed to shape frames. We recruited 26 Grade 1 students (~6–7 years old) and 23 Grade 3 students (~8–9 years old), asked them to work on two layered puzzle designs from the Color Code puzzle game, and interviewed them about their thinking processes. The first graders had higher success rates at fixing and embedding the tiles correctly, and students at both grade levels improved on the three-tile design when encountering it a second time about two months later. The four-tile design was more difficult, but students improved if they could identify a correct sub-structure of the design. Successful students used a combination of pictorial shape strategies and schematic location strategies, systematically testing tiles and checking how they could be embedded. The results suggest that helping students focus on sub-structures can promote their effective embedding