Mathematics assessments should allow all students opportunities to demonstrate their knowledge and skills as problem solvers. Looking at textbook word problems, the authors share a process for revising them using Universal Design for Learning (UDL). Outlined in detail here are problems for kindergarten, grades 5 and 7, and high school (algebra).

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the…

We offer an analysis of calculus assessment items that highlights ways to evaluate students' application of important meanings and support their engagement in generative ways of reasoning. Our central aim is to identify characteristics of items that require students to apply their understanding of key ideas. We coordinate this analysis of…

Assessment plays a crucial role in the learning process and significantly impacts students' understanding of tasks and their engagement. With the increasing popularity of e-learning, cognitive assessment methods are becoming more prevalent, and they can help develop students' high-order thinking skills (HOTS). Thinking-Aloud Peer Assessment (TAPA)…

In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course…

Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…

There is a large body of research on how to improve student learning through active learning and metacognition. However, without well-structured guidelines, students do not tend to actively engage with the taught material, peers, and the instructor at a desirable metacognitive level (Deslauriers et al., 2019). To address this problem, a…

Simulations provide a unique opportunity to practice newly acquired skills in a low risk environment. For this reason, simulations have historically been used in preservice teacher education programs to enable student teachers to apply generalized pedagogical practices. This pilot study examined how simulations could be integrated with inservice…

Peer assessment is an underutilized tool in mathematics classrooms. We examined how peer assessment could be used in a mathematics course to improve mathematical communication and mathematical proficiency. To describe in what ways peer reviews compared to teacher reviews, we analyzed ratings and feedback of 32 6th graders and their mathematics…

It remains a challenge for teachers to integrate modeling tasks in everyday mathematics classes. Many studies have been conducted that show the difficulties faced by teachers. One of the challenging aspects in this regard is that of assessment. In the present study, a connection between structures of learners' solution strategies and cognitive…

This paper provides evidence that a short, fully online, well-constructed diagnostic test based on research literature can give teachers information about their students' thinking and strategies that is sufficiently accurate to use for formative assessment purposes. The example is a test for students beginning to learn to solve equations. The main…

This article illustrates and differentiates the unique role cognitive interviews and think-aloud interviews play in developing and validating assessments. Specifically, we describe the use of (a) cognitive interviews to gather empirical evidence to support claims about the intended construct being measured and (b) think-aloud interviews to gather…

First-year elementary pre-service teachers usually conduct field observations but are barely offered opportunities to engage in well-structured teaching situations. In the current study, we implemented mixed-reality simulations (MRS) in a mathematics methods course to improve elementary pre-service teacher's abilities to elicit, question, and…

In this article, the authors introduce the "Pre-K-12 Guidelines for Assessment and Instruction in Statistics Education II (GAISE II): A Framework for Statistics and Data Science Education" report. This report, which was published by the American Statistical Association (ASA) and endorsed by the National Council of Teachers of Mathematics…

This study used a pretest-posttest design to explore the scoring by female preservice teachers (n=25) of student responses to a pattern problem. The treatment consisted of a cooperative activity that required the preservice teachers to assign scores to a rubric intended to enhance careful attention to student reasoning expressed in written…