Mathematics classroom interaction has often been described as an important context for involving all students. However, this article shows that teacher-student-interaction is still not really in the focus of teachers' attention. Based on classroom video studies, some authors hypothesize that the implicitness of establishing norms and practices is,…

This study explored the processes in which adult readers integrate text-figure information when reading geometric descriptions. Because geometry conveys rich spatial information, we investigated the reading scanpaths as text- or figure-directed and the given-new effects. Eye movement data from 65 college student participants showed that…

Practices such as making connections between topics, prioritizing content, and identifying broad themes are essential to learning mathematics. This paper describes a project designed to integrate these synthesizing activities into an abstract algebra class. Students used a classroom wall to record and organize their collective learning and…

When implemented correctly, feedback from assessments can result in students reflecting and rethinking their mathematics, while increasing their effort and motivation. This article explores a formative assessment technique for use in the first few minutes of each class. Readers will find out how they can use the QuickQuiz (QQ) to drive…

This paper aims to investigate the following question: How do students use mathematics in modeling activities? With this purpose, the paper reports on mathematization and use of mathematics, and deals with empirical data with focus on modeling activities performed by students in the first year and in the fourth year of a degree in mathematics.…

For students working on realistic complex modelling problems as autonomously as possible the support by a tutor is indispensable for the students. However, how this support can be realised is still a question that has not been sufficiently answered. Based on prior research, it turned out that teacher interventions based on heuristic strategies…

This article highlights four routines that use visual images and open questions to invite students to discuss, justify, make arguments, and question their own thinking as well as their classmates' thinking. The authors share specific classroom examples from each routine that highlight the meaningful discourse they can inspire. Teacher prompts and…

This study describes the way 14 pre-service teachers engaged in discourse about integers. The discourse being examined is framed by Sfard's view of a discourse as being composed of the four elements word use, visual mediators, routines, and narratives (Sfard, 2008). These elements combine to form a means for people to exchange and preserve ideas…

This research was carried out in order to establish a general opinion on the effect of the teaching technique, which is referred to as the Touch Math, on the academic achievement of special needs students in mathematics courses. To this end, graduate thesis, doctoral dissertation and articles, which were made between 1990-2017, and which have…

The purpose of this study was to determine if students scored significantly higher on the ACT after taking precalculus than they had scored on the ACT prior to taking precalculus. The researcher investigated whether there is an increase, not only in ACT composite scores, but also in ACT math subtest scores after high school students completed a…

The objective of Experiment I was to determine whether establishing conditioned reinforcement for engaging in math for pre-kindergarten students was possible using the three conditioning procedures outlined in previous research for conditioning book stimuli. The purpose of Experiment II was to determine whether this change in preference for…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

Mathematics educators advocate for the use of models as an instructional practice that can potentially aid in building students' understanding of difficult topics. Integers and integer operations are historically problematic for students and are critically important in both arithmetic and the future study of algebra. In this chapter, I explore one…

Teacher collaboration holds great promise for improving educational outcomes. Education policies commonly seek to foster teacher collaboration to bring about improvements in teacher learning, instructional quality, and improved student outcomes. Collaborative approaches including professional learning communities (PLCs), grade level teams,…

The traditional sequencing of the ninth- to twelfth-grade math curriculum in the United States has students taking Algebra 1 in the ninth grade, Geometry in the tenth grade, Algebra 2 in the eleventh grade and an optional advanced math course (e.g. pre-calculus, statistics) in the twelfth grade. In this traditional setup, talented math students…