Explaining appears to dominate primary teachers' understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop…

With recent increased attention to engaging students in written mathematical communication, the Elementary Mathematical Writing Task Force has recommended specific types of and purposes for mathematical writing with the ultimate goals of communicating and reasoning: Exploratory, Informative/Explanatory, Argumentative, and Mathematically Creative.…

The social studies curriculum travels through time and space and is bigger on the inside than it is on the outside. To an outsider, the social studies curriculum is a single line on a program of studies, 45 minutes of a student's school day. Those on the inside, however, know that the field covers history, geography, civics, economics, and much…

The purpose of this study is to describe, critically analyse and discuss the Swedish system of assessing ethics education in compulsory school through national tests. The publicly available tests from 2013 for grades six and nine have been studied as have the assessment instructions for teachers. Staff responsible for the test construction have…

Even though a school in Southern Virginia had been utilizing a variety of manipulatives, calculators, and computers to transition students through the concrete-representational-abstract (CRA) sequence; students did not meet the state proficiency requirement on the standardized math assessment. A qualitative descriptive case study design, grounded…

Central to ambitious teaching is a constellation of practices we have come to call "leveraging student thinking." In leveraging, teachers position students' understanding and reasoning as a central means to drive learning forward. While leveraging typically is described as a feature of mature practice, in this article we examine…

This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic…

In this paper, we present a third-grade ecology learning environment that integrates two forms of modeling--embodied modeling and agent-based modeling (ABMs)--through the generation of mathematical representations that are common to both forms of modeling. The term "agent" in the context of ABMs indicates individual computational objects…

Students' explanations of their mathematical thinking and conclusions have become a greater part of the assessment landscape in recent years. With a sample of 71 fourth-grade students at risk for mathematics learning disabilities, we investigated the relation between student accuracy in comparing the magnitude of fractions and the quality of…

Knowledge of technology is an educational goal of science education. A primary way of increasing technology literacy in a society is to develop students' conception of technology starting from their elementary school years. However, there is a lack of research on student recognition of and reasoning about technology and technological artifacts. In…

Recent research shows that teachers' level of Mathematical Knowledge for Teaching (MKT) and their beliefs about teaching and learning effect teaching practices and student achievement. Higher levels of MKT typically lead to more effective teaching abilities in terms of helping students make meaning of mathematical concepts, but beliefs seem to be…

Systems and system models are recognized as a crosscutting concept in the newly released framework for K-12 science education (NRC [National Research Council], 2012). In previous work, I developed a learning progression for systemic reasoning in ecology at the elementary level. The learning progression captured five levels of students' reasoning…

This research study explored robotics as the catalyst for computational thinking (CT) by sixth-grade students as they are engaged in a science lesson. The interactions, understandings, and applications are discussed, along with the participants' connections and implementations of CT concepts (decomposition, abstraction, pattern recognition, and…

Detecting a pattern within a sequence of ordered units, defined as patterning, is a cognitive ability that is important in learning mathematics and influential in learning to read. The present study was designed to examine relations between first-grade children's executive functions, patterning, and reading abilities, and to examine whether these…

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…