Assessment is essential for teaching and learning mathematical concepts. Teachers' and learners' understanding of how assessment is to be conducted in mathematics classrooms will guide what is to be taught and learnt and how teaching and learning will be conducted. The researchers' assertion is that circle geometry lessons require thinking-based…

The mode of assessment is one of the most important factors influencing learning. E-assessment usually includes only checking the final answer, thus limiting teacher's ability to check the complete solution, and it does not allow inclusion of math proofs problems that constitute an important part of math content. The e-assessment module of Halomda…

We developed an Authentic GeometryGo (AGG) app to help students application of geometry in authentic contexts through authentic measurements and peer assessments. The study included an experimental group (EG) using an AGG app and a control group (CG) using paper-based methods. The results showed that the EG outperformed the CG in terms of…

With the shift to next generation digital assessments, increased attention has focused on Technology-Enhanced Assessments and Items (TEIs). This study evaluated the feasibility of a high-fidelity digital assessment item response format, which allows students to solve mathematics questions on a tablet using a digital pen. This digital ink approach…

This article describes a carefully structured exploration of formative assessment, conducted in the form of a classroom research experiment. The authors are an instructor and a student in a graduate course that assigned teachers to research formative assessment strategies, implement one or more strategies for several weeks, collect data from…

Mathematical working space (MWS) is a model that is used in research in mathematics education, particularly in the field of geometry. Some MWS elements are independent of the field while other elements must be adapted to the field in question. In this paper, we develop the MWS model for the field of analysis with an identification of paradigms. We…

Latent variable models, such as the popular Knowledge Tracing method, are often used to enable adaptive tutoring systems to personalize education. However, finding optimal model parameters is usually a difficult non-convex optimization problem when considering latent variable models. Prior work has reported that latent variable models obtained…

While recent national and international assessments have shown mathematical progress being made by US students, little to no gains are evident in the areas of geometry and measurement. These reports also suggest that practicing teachers have traditionally had few opportunities to engage in content learning around topics in geometry and…

This article was inspired by a set of 12 cylindrical cups, which are volumetrically indexed; that is to say, the volume of cup "n" is equal to "n" times the volume of cup 1. Various sets of volumetrically indexed cylindrical cups are explored. I demonstrate how this children's toy is ripe for mathematical investigation, with connections to…

The article demonstrates that multiple solution tasks (MSTs) in the context of geometry can serve as a research instrument for evaluating geometry knowledge and creativity. Geometry knowledge is evaluated based on the correctness and connectedness of solutions, whereas creativity is evaluated based on a combination of fluency, flexibility, and…

The purpose of this article is to discuss specific techniques for the computation of the volume of a tetrahedron. A few of them are taught in the undergraduate multivariable calculus courses. Few of them are found in text books on coordinate geometry and synthetic solid geometry. This article gathers many of these techniques so as to constitute a…

We propose the development of a "population" of high-quality assessment tasks that cover the performance goals set out in the "Common Core State Standards for Mathematics." The population will be published. Tests are drawn from this population as a structured random sample guided by a "balancing algorithm."

In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual…

Now entering into its 20th year of data collection, Trends in International Mathematics and Science Study, (TIMSS) is an international assessment of mathematics and science at the fourth and eighth grades. TIMSS 2015 is the most recent in the TIMSS series, which began with the first assessments in 1995 and has continued every four years--1999,…

The wealth of assessment options that exists offers teachers and students a "menu" of selections. Just as matching appetite needs with appropriate food selection is fundamental to a successful dining experience, matching assessment options to targeted achievement needs is crucial to an effective assessment experience. The author uses a…