This article presents the results of our analysis of a sample of 254 Calculus I final exams (collectively containing 4,167 individual items) administered at U.S. colleges and universities. We characterize the specific meanings of foundational concepts the exams assessed, identify features of exam items that assess productive meanings, distinguish…

We developed the Physics Inventory of Quantitative Literacy (PIQL) to assess students' quantitative reasoning in introductory physics contexts. The PIQL includes several "multiple-choice-multipleresponse" (MCMR) items (i.e., multiple-choice questions for which more than one response may be selected) as well as traditional single-response…

In an online asynchronous vector calculus course, we observed exam answers solved with a formula from online homework instead of the formula from lecture. Our exploratory study investigated (1) why students learned from homework instead of lecture for this topic and (2) their epistemological frames (e-frames) for lecture and homework. Per (1),…

In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within…

In this article we present the results of an investigation into semiotic aspects of an introductory differential equations class from two countries. In order to perform a comparative analysis, students in the USA and Tunisia were given common questions on their midterm exams that examined analytical and graphical competencies. Our results indicate…

The University Entrance Exam (UEE) has an important impact on how math instructors teach mathematics to prepare students for this exam as well as how their students learn mathematics. Since the UEE is like a bridge between high school and university, its importance becomes twofold. However, research regarding this issue is very limited in…

In this article, we discuss the development and the administration of a multiple-choice test, which we named "Test of Calculus and Vectors in Mathematics and Physics" (TCV-MP), aimed at comparing students' ability to answer questions on derivatives, integrals, and vectors in a purely mathematical context and in the context of physics.…

This study focuses on how students in different postsecondary mathematics courses perform on domain and range tasks regarding graphs of functions. Students often seem to focus on notable aspects of a graph and fail to see the graph in its entirety. Many students struggled with piecewise functions, especially those involving horizontal segments.…

We describe the development and initial validity assessment of the 20-item BioCalculus Assessment (BCA), with the objective of comparing undergraduate life science students' understanding of calculus concepts in different courses with alternative emphases (with and without focus on biological applications). The development process of the BCA…

Research on the test structure of the Force Concept Inventory (FCI) has largely ignored gender, and research on FCI gender effects (often reported as "gender gaps") has seldom interrogated the structure of the test. These rarely crossed streams of research leave open the possibility that the FCI may not be structurally valid across…

We report on a study investigating the influence of context, direction of translation, and function type on undergraduate students' ability to translate between graphical and symbolic representations of mathematical relations. Students from an algebra-based and a calculus-based physics course were asked to solve multiple-choice items in which they…

Using the capabilities of expert knowledge structures, the researcher prepared test questions on the university calculus topic of "finding the area by integration." The quiz is divided into two types of multiple choice items (one out of four and one out of many). After the calculus course was taught and tested, the results revealed that…

In this study, we developed a three-dimensional framework to characterize post-secondary Calculus I final exams. Our "Exam Characterization Framework" (ECF) classifies individual exam items according to the cognitive demand required to answer the item, the representation of both the task statement and the solution, and the item's format.…

Spatial skills have been shown in various longitudinal studies to be related to multiple science, technology, engineering, and math (STEM) achievement and retention. The specific nature of this relation has been probed in only a few domains, and has rarely been investigated for calculus, a critical topic in preparing students for and in STEM…

The purpose of this study was to investigate the effect of a calculus system that was designed using an adaptive dynamic assessment (DA) framework on performance in the "finding an area using an integral". In this study, adaptive testing and dynamic assessment were combined to provide different test items depending on students'…