Norm-referenced error analysis is useful for understanding individual differences in students' academic skill development and for identifying areas of skill strength and weakness. The purpose of the present study was to identify underlying connections between error categories across five language and math subtests of the Kaufman Test of…

Research on teacher professional learning has shown that formative assessment can improve student learning more than most instructional practices. Empirical evidence indicates that thoughtfully implemented formative assessment practices improve students' learning, increase students' scores, and narrow achievement gaps between low-achieving…

This study is aimed at determining first-year university students' reflections when Fibonacci tiling, the ancient Chinese fang cheng procedures, and the ancient Indian meru prastara recursions were introduced as historical snippets in an adventure pedagogy for basic mathematics. Seventy-eight first-year students enrolled in a course in basic…

When the National Benchmark Tests (NBTs) were first considered, it was suggested that the results would assess entry-level students' academic and quantitative literacy, and mathematical competence, assess the relationships between higher education entry-level requirements and school-level exit outcomes, provide a service to higher education…

This study focused on how two algebraic concepts- equality and variable- predicted 8th grade students' equation solving performance. In this study, predictive design as a correlational research design was used. Randomly selected 407 eight-grade students who were from the central districts of a city in the central region of Turkey participated in…

This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct quantitative and qualitative analysis of students' mistakes to extract information regarding slope conceptualizations described in prior research. Results delineate procedural proficiencies and…

An argument is presented for including exponentiation as a "basic" of school mathematics. Key elements of the argument include the topic's increasing relevance in a rapidly changing world and its utility for supporting understandings of role of analogy in mathematical thought. The discussion is illustrated with an account of a…

In this paper I discuss the motivation behind using an introduction to Fourier series as a method to unify the topics of integration techniques and series calculations in a Calculus II course.

This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…

Overgeneralizing commonly accepted strategies, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students' math careers. In this article, the authors present thirteen pervasive mathematics rules that "expire." With the…

Student understanding of integration has become a topic of recent interest in calculus research. Studies have shown that certain interpretations of the definite integral, such as the area under a curve or the values of an anti-derivative, are less productive in making sense of contextualized integrals, while on the other hand understanding the…

This manuscript shares the implementation of an after-school literacy in STEM (science, technology, engineering, and mathematics) program designed for middle grades students to increase their interest in science and mathematics learning. This program was conducted at our local Boys and Girls Club facilities where students learned about four…

This article is concerned with the approaches to the root concept that lecturers in calculus, linear algebra and complex analysis employ in their instruction. Three highly experienced university lecturers participated in the study. In the individual interviews the participants referred to roots of real numbers, roots of complex numbers, roots as…

Values are the personal convictions which one finds important. Three different aspects which are associated with mathematics education differently are identified, namely, values through mathematics education, values of mathematics education, and values for mathematics. These are paired with Bishop's (1996) conceptions of general educational,…

In 2001, Kilpatrick, Swafford, and Findell proposed a new way to look at what it means for students to be mathematically proficient. They described mathematical proficiency as comprising five intertwined strands: procedural fluency, conceptual understanding, adaptive reasoning, strategic competence, and productive disposition. The vision is that…