In this digital ITEMS module, Dr. Jacqueline Leighton and Dr. Blair Lehman review differences between think-aloud interviews to measure problem-solving processes and cognitive labs to measure comprehension processes. Learners are introduced to historical, theoretical, and procedural differences between these methods and how to use and analyze…

Arguably the largest obstacle freshmen face in their mathematics courses is their unfamiliarity with the language of mathematics. Addressing this problem right at the start seems like a sensible strategy, as comprehension of mathematical communication helps students in all mathematics courses they will take. In this paper we discuss general…

Policy briefs written by academics--the kind typically published in "Education Finance and Policy"--should be a crucial source of information for policy makers. Yet too frequently these briefs fail to garner the consideration they deserve. Their authors are too focused on the potential objections of their fellow academics, who are…

Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students' learning in experimental classrooms. However, these sequences involve…

Educational measurement is generally thought of as empirical, quantitative, and large-scale, whose purpose is to monitor educational systems. Sociocognitive studies, on the other hand, are associated with small-scale, theoretical, and qualitative studies, the purpose of which is to conduct fine-grained analysis of learning or teaching, or to…

This paper describes methods for an alignment study and psychometric analyses of a formative assessment system, Diagnoser Tools for physics. Diagnoser Tools begin with facet clusters as the interpretive framework for designing questions and instructional activities. Thus each question in the diagnostic assessments includes distractors that…

When given opportunities to explore mathematics, make conjectures, and write about what they have discovered, students gain a deeper understanding of this fascinating subject. In this article, the author describes her successful Geometry Portfolio class. In addition to traditional student work, the author frequently added short essay questions or…

Procedural evaluations of limits of functions provide invariably better understanding of the limits than the approximations using a calculator. The purpose of this article is to demonstrate that better understanding can be promoted if mathematical understanding precedes the impulse to use calculators. The note clarifies the stages when the…

This work addresses the subject of mathematics education at secondary schools from a current and stimulating point of view intimately related to computational science. Cryptology is a captivating way of introducing into the classroom different mathematical subjects such as functions, matrices, modular arithmetic, combinatorics, equations,…

There is no common agreement on the meaning of the word "understand". However, there is agreement on what students should be able to do with material they understand. Bloom et al. discuss kinds of tasks a student should be able to do, provided that the student understands. In a similar way, Biggs and Collis provide a taxonomy intended to evaluate…

Web-based statistical instruction, like all statistical instruction, ought to focus on teaching the essence of the research endeavor: the exercise of reflective judgment. Using the framework of the recent report of the American Psychological Association (APA) Task Force on Statistical Inference (Wilkinson and the APA Task Force on Statistical…

History and the social sciences can be defined as recorded narratives or stories about the past or present that describe change and continuity over time and seek to explain this change and continuity through a series of cause and effect propositions based on evidence and shaped by the scholar's social frame of reference. In social studies there…