This article describes research results based on multiple years of experimentation and real-world experience with an adaptive tutoring system named Wayang Outpost. The system represents a novel adaptive learning technology that has shown successful outcomes with thousands of students, and provided teachers with valuable information about students'…

A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

This article specifies how the setup, or introduction, of cognitively demanding tasks is a crucial phase of middle-grades mathematics instruction. The authors report on an empirical study of 165 middle-grades mathematics teachers' instruction that focused on how they introduced tasks and the relationship between how they introduced tasks and the…

Background/Context: Teachers in urban schools are sometimes seen as a large part of the problem with such schools; they are often spoken of as not knowing the content they need to know to teach, are not seen as committed to excellence or to reform-minded teaching, and therefore are not seen as a resource for school improvement. The case of Madison…

Adaptive learning technologies are emerging in educational settings as a means to customize instruction to learners' background, experiences, and prior knowledge. Here, a technology-based personalization intervention within an intelligent tutoring system (ITS) for secondary mathematics was used to adapt instruction to students' personal interests.…

The purpose of this research is to develop a multidimensional computerized adaptive test for diagnosing the cognitive process of grade 7 students in learning algebra by applying multidimensional item response theory. The research is divided into 4 steps: 1) the development of item bank of algebra, 2) the development of the multidimensional…

The aim of this study was to develop a tool to measure levels of mathematical knowledge gained in high school, as perceived by incoming engineering students. The study included 657 engineering students in the 2011-2012 academic year. Factor analysis was used to obtain a scale consisting of 47 items (Cronbach Alpha coefficient, 0.975). The…

To be most effective, teacher professional development needs to be designed and based on teachers' needs. This study provides information on topics that 53 middle- and secondary-level mathematics teachers believed would be beneficial in future training programs. The teachers had participated in a 2-year Teacher Quality Grant focused on content…

This paper reports on a mixed-methods study of 111 Advanced Placement calculus students' self-reports of their graphing calculator use, comfort, and rationale for trusting a solution produced with or without a graphing calculator when checking written work. It was found that there was no association between gender, teacher-reported mathematical…

The "urban" mathematics classroom has become an increasingly polarized site, one where many middle-class White teachers attempt to bridge the divide between themselves and their relatively economically disadvantaged, non-White students. With its mania for high-stakes testing, current education policy has intensified the importance of…

This paper reports part of a study of secondary mathematics teachers in "Technology-Rich Teaching and Learning Environment" (TRTLE's). Three TRTLE's, two year 11 and one year nine class and their teachers were the focus of the study. Seven "Teaching Roles" were identified as teachers acted to allow students to perceive and…

The study's goal was to examine the metacognitive practices and problem solving by preservice secondary mathematics teachers within secondary core content areas. The effort to analyze and describe the processes led to qualitative methods, a multiple case study. Transcripts of problem solving sessions and interviews were coded for the presence of…

This article makes two simple observations about high-stakes assessments. The first is that, because mathematics is a very technical subject, an assessment item can be mathematically flawed regardless of how elementary it is. For this reason, every assessment project needs the active participation of high level mathematicians. A second point is…

We address issues related to gender and cultural equity in a history of mathematics course. We first look at the preponderance of male European mathematicians represented in textbooks of mathematics and history or mathematics. Then we discuss ways to highlight the presence of female and non-European mathematicians in the history of mathematics.…

This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…