We explore the various Mathematica functions for performing Gaussian elimination, specifically when the linear system contains input parameters. On the one hand, we want the solution, perhaps heuristically found, to be in terms of the input parameters, and as general as possible. On the other hand, we must adhere to all necessary conditions and…

We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…

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…

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…

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…

Investigators often rely on the proportion of correct responses in an assessment when describing the impact of early mathematics interventions on child outcomes. Here, we propose a shift in focus to the relative sophistication of problem-solving strategies and offer methodological guidance to researchers interested in working with strategies. We…

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 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…

The research aimed to analyze the students' abilities in solving realistic mathematics problems using "What-If"-Ethnomathematics Instruments with content focused on plane and space materials. The "What-If"-Ethnomathematics instruments are instruments that enable educators to analyze various errors and obstacles experienced by…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

Purpose: The aim of this paper is to study the use of FIS Response Analysis for Critical Thinking Assessment (FRACTA) method to assess critical thinking in STEM problem solving. The use of FIS (facts, ideas and solutions) chart as a tool to elicit student critical thinking responses and the method of scoring the responses are investigated. Method:…

Background: Base-ten thinking (BTT) -- children's ability to reason in tens and ones is a crucial measure of Foundation Phase learners' mathematical performance in South Africa. Aim: The study looks at the six learners using BTT to solve additive tasks through two different assessments. Setting: Six purposely selected Grade 3 learners in…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

Problem solving is at the heart of mathematics, and is known to support learning for a diverse range of children. However, challenges can be encountered when teaching mathematics through problem solving. This article provides insights from research literature into: (1) the nature of the challenges; and (2) some ways that problem solving can be…

The aim of this study is to determine the teaching activities of pre-service teachers in the course of mathematics teaching methods. All of the pre-service teachers have selected an attainment content from the primary (1-4) mathematics education curriculum at the beginning of the semester in the scope of mathematics teaching methods course. Data…