Our research programme, a part of which is presented in this paper, looked at four year old children's ability to use manipulatives in the construction of cube models. We looked at how pre-school children managed the creation of cube nets as a mathematical problem and whether graphical representations of solutions could become a useful tool in a…

In this paper, we frame mathematics classrooms as heterogeneous spaces wherein students draw on multiple storylines based on different notions of schooling and school mathematics to both communicate mathematical ideas and position themselves and one another. We focus on a fourth grade (age range 9.4-10.8 years) mathematics classroom discussion in…

New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

Feedback is generally considered a beneficial learning tool, and providing feedback is a recommended instructional practice. However, there are a variety of feedback types with little guidance on how to choose the most effective one. We examined individual differences in working memory capacity as a potential moderator of feedback type. Second-…

Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…

Cognitive interest is a vital learning motive for the successful learning process. Nowadays students' interest about science and mathematics are decreasing. The aim of the study is to explore the cognitive interest of Grade 9 students in science and mathematics. Students were surveyed and it helped to explore the respondents' cognitive activity…

Using two well known criteria for the diagonalizability of a square matrix plus an extended form of Sylvester's Rank Inequality, the author presents a new condition for the diagonalization of a real matrix from which one can obtain the eigenvectors by simply multiplying some associated matrices without solving a linear system of simultaneous…

One danger of integrating inquiry-based problem-solving activities into mathematics lessons is that different strategies could be accepted without in-depth discussions on the cogency and efficiency of the strategies. To overcome this issue, Japanese teachers typically go through a series of lesson-study-based teacher learning sessions and learn…

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9 th grade students and their mathematics teachers during…

Dr. Uri Treisman, professor of mathematics and public affairs at The University of Texas at Austin and the director of the Charles A. Dana Center, has deep and active roots in mathematics and mathematics education. Dr. Treisman is well known for his early work at the University of California at Berkeley, where he developed the Calculus Workshop…

The purpose of this paper is to analyze in detail the process in which a 5th grade student learned proportion and percent using double number lines and to obtain insights into how his use of those representations supported his learning. A series of lessons were designed and conducted in a class and the whole learning process of one student was…

Although learning from multiple representations has been shown to be effective in a variety of domains, little is known about the mechanisms by which it occurs. We analyzed log data on error-rate, hint-use, and time-spent obtained from two experiments with a Cognitive Tutor for fractions. The goal of the experiments was to compare learning from…

Teachers' ability to elicit and build on students' mathematical thinking during instruction is critical in order to support students' mathematical growth. An emerging hypothesis in the field is that the construct of a "learning trajectory" (LT) has the potential to support teachers in making sense of and using student…

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…