PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…

In Spring 2020, the need for redesigning online assessments to preserve integrity became a priority to many educators. Many of us found methods to proctor examinations using Zoom and proctoring software. Such examinations pose their own issues. To reduce the technical difficulties and cost, many Zoom proctored examination sessions were shortened;…

The paper argues that there is a need for new approaches to teaching proof with newly-available technology. It contributes to filling this need by opening a discussion on digital proof assistants, programs that allow one to do mathematics with the aid of a computer, construct proofs, and check their correctness. The paper starts by exploring such…

This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…

This study focuses on computer-based formative assessment for supporting problem solving and reasoning in mathematics. To be able to assist students who find themselves in difficulties, the software suggested descriptions - diagnoses - of the encountered difficulty the students could choose from. Thereafter, the software provided metacognitive and…

Automated scoring of student responses to open-ended questions, including short-answer questions, has great potential to scale to a large number of responses. Recent approaches for automated scoring rely on supervised learning, i.e., training classifiers or fine-tuning language models on a small number of responses with human-provided score…

As educational systems move from onsite to online due to the COVID-19 pandemic, teachers face the difficulty of designing online examination formats which minimize opportunities for dishonesty. In this paper, we expose our design of such a format: a protected Microsoft Excel spreadsheet containing short-answer questions, which was implemented in a…

STACK is an online testing system that can automatically assess mathematical formulae. When working with STACK on a smartphone, inputting mathematical formulae is time-consuming; therefore, to solve this problem a mathematical formula input interface for smartphones has been developed based on the flick operation. However, since the time of…

Teachers often rely on the use of a range of open-ended problems to assess students' understanding of mathematical concepts. Beyond traditional conceptions of student open-ended work, commonly in the form of textual short-answer or essay responses, the use of figures, tables, number lines, graphs, and pictographs are other examples of open-ended…

Recently, institutions have increased their online course offerings as well as their online degrees. With this significant growth in online offerings, assessment integrity becomes a concern. In response to this concern, many institutions have adopted the use of online proctoring services. The aim of using these online proctoring services is to…

This paper reports on a design-based implementation study of the use of a diagnostic classroom assessment tool framed on learning trajectories (LTs) for middle grades mathematics, where teachers and students are provided immediate data on students' progress along LTs. The study answers the question: "How can one characterize the challenges…

Instructors of postsecondary classes in statistics rely heavily on visuals in their teaching, both within the classroom and in resources like textbooks, handouts, and software, but this information is often inaccessible to students who are blind or visually impaired (BVI). The unique challenges involved in adapting both pedagogy and course…

The purpose of this research study was to examine the effectiveness of culturally appropriate problem-solving instruction (CAPSI) incorporating elements from schema instruction, video modeling, and vocabulary instruction. Culturally relevant information and the students' native language were explicitly incorporated into math problem-solving…

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

Recently, there is an explosive growth of smartphone availability. In this work, we studied how mobile and Internet-based Student Response System improves the learning process. We used a free software application (Socrative©) to create a set of questions that can be deployed during the class. It was used in four different courses in three…