In Taiwan elementary schools, Scratch programming has been taught for more than four years. Previous studies have shown that personal annotations is a useful learning method that improve learning performance. An annotation-based Scratch programming (ASP) system provides for the creation, share, and review of annotations and homework solutions in…

Anne Roche and Doug Clarke discuss the importance of developing students' persistence in relation to problem solving during the use of challenging tasks. They provide a useful list of strategies that teachers can use to encourage persistence amongst their students.

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

In the middle years of school, it is important that mathematics is challenging, engaging and focuses on worthwhile mathematics. In this article, Anne Roche describes a lesson that seemed to have all three of these characteristics, as students grappled with issues of scale to create a fun run, given a range of challenging mathematical constraints.…

This study examined the effects of a research-based intervention, schema-based instruction (SBI), implemented by experienced- (taught SBI in previous study; Jitendra et al., 2015) and novice-teacher implementers (taught SBI for the first time with professional development) on the mathematics outcomes of seventh-grade students. SBI is a…

This article reports on an analysis of episodes of invalid or controversial arguments that occurred while two different groups of students worked on similar fraction tasks and examine the role that these types of arguments played in the development of students' reasoning. One group consisted of suburban, middle-class, fourth graders who worked on…

Teachers working with students with reading difficulties must decide when and how to intervene. Wood (2002) suggested that teachers' shift their levels of support to match students' needs based on moment-by-moment observations--that is, teachers should scaffold their support. In this qualitative analysis, we investigated instructors' scaffolding…

The use of high-stakes assessment to measure students' mathematical performance has become commonplace in schools all over the world. Such assessment instruments provide national or international comparisons of student (and potentially teacher performance). Each form of assessment is specialised in nature and is characteristic of the culture and…

Three clinical interviews were conducted with each of 15 sixth grade students to test conjectures about the relationship between their level of multiplicative reasoning and their solution of combinatorics problems that could involve single and multi-digit multiplication. The problems that involved multi-digit multiplication were designed with the…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

The goals of this study were: 1) to study the situation, problems and needs for a learning model to enhance the social skills of sixth grade students; 2) to develop a learning model that would address those needs; 3) to study the effectiveness of that learning model; 4) to compare performance on pretests and posttests of social skills; and 5) to…

To challenge students' reasoning and to align with a physical fitness unit that students were studying, teachers and authors, Scott Frye and Signe Kastberg adapted a ratio comparison problem from Susan Lamon, "Ratio and Proportion: Connecting Content and Children's Thinking," (1994) to include athletes and doctors who share…

In the current educational climate of IDEA 2004 and No Child Left Behind, teachers are required to find methods to give all students, including students with mild intellectual disability, access to the general education curriculum. The purpose of this study was to investigate the effects of instruction integrating the…

Commercial video games undergo usability studies to determine the degree to which the player is able to learn, control, and understand the game. Usability studies allow game designers to improve their games before they are released to the public. If usability studies could be expanded to include information about the presentation of the…