This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or minimum…

The concept of multiple representations of functions and the ability to make translations among representations are important topics in secondary school mathematics curricula (Moschkovich, Schoenfeld, & Arcavi, 1993; NCTM, 2000). Research related to students in this domain is fruitful, while research related to teachers is underdeveloped. This…

This article discusses assessments that can be used to help encourage a collaborative classroom community, in which students help one another learn mathematics. The authors describe participation quizzes and explanation quizzes as assessment tools that encourage students to work together, share specific questions on challenging mathematics…

Within the framework of the Testing Algorithmic and Application Skills project we tested first year students of Informatics at the beginning of their tertiary education. We were focusing on the students' level of understanding in different programming environments. In the present paper we provide the results from the University of Debrecen, the…

Statistical tasks that can be solved in a variety of ways provide rich sites for classroom discourse. Orchestrating such discourse requires careful planning and execution. Five specific practices can help teachers do so. The five practices can be used to structure conversations so that coherent classroom narratives about solutions to tasks may be…

We used event-related potentials (ERPs) to determine the time course of mechanisms underlying strategy selection. Participants had to select the better strategy on multiplication problems (i.e., 51 × 27) to find approximate products. They could choose between rounding up and rounding down both operands to their nearest decades. Two types of…

This article describes the development of a problem-solving instrument intended for classroom use that addresses the Common Core State Standards for Mathematics. In this study, 137 students completed the assessment, and their responses were analyzed. Evidence for validity was collected and examined using the current standards for educational and…

The purpose of this study was to determine the effectiveness of a point-of-view video modeling intervention to teach mathematics problem-solving when working on word problems involving subtracting mixed fractions with uncommon denominators. Using a multiple-probe across students design of single-case methodology, three high school students with…

Learners who lack knowledge often also lack the ability to assess their limited competence correctly. Due to the incorrect self-assessment, they are unlikely to apply strategies that would help them to acquire relevant knowledge. This effect is known as the double curse of incompetence. When students solve problems prior to being taught the…

The purpose of this study was to examine the mathematics instructional practices of 75 second-year elementary teachers (K-5) in terms of the learning opportunities provided to their students. On average, each teacher completed instructional logs for 43 days across the school year. Select items were analyzed in order to better understand the…

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

The aim of this study was to examine prospective mathematics teachers' proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews…

The purpose of this study was to identify cognitive and linguistic predictors of word problems with versus without irrelevant information. The sample was 701 2nd-grade students who received no specialized intervention on word problems. In the fall, they were assessed on initial arithmetic and word-problem skill as well as language ability, working…

The PIC Math program works with mathematical sciences faculty at US institutions to help them prepare students for careers in today's workforce. PIC Math faculty engage their students to solve data science and other research problems that come directly from industry. To accomplish the program's objectives, the authors conduct a three-day summer…