The natural exponential and logarithm are typically introduced to undergraduate engineering students in a calculus course using the notion of limits. We here present an approach to introduce the natural exponential/logarithm through a novel interpretation of derivatives. This approach does not rely on limits, allowing an early and intuitive…

Even before the pandemic slowed learning for many, only 39 percent of California students demonstrated proficiency on the state math assessment. During the pandemic, the proportion of math-proficient students fell to one-third. At the same time, the STEM workforce faces shortages and a lack of diversity, which call into question the longstanding…

For integrals consisting of rational functions of sine and cosine a set of little known rules known as the Bioche rules are considered. The rules, which consist of testing the differential form of the integral for invariance under one of three simple substitutions x [right arrow] -- x, [pi] -- x, and [pi] + x, allow one to decide which of the…

Based on an enactivist perspective on learning mathematics, we articulate three key processes of designing mathematics-grounding activities (MGAs) where students' mathematical thinking can be motivated and shaped with the interactions between their enactments and the evolving tasks in the activities. Then, evaluation criteria and design steps will…

While mathematics and reading instruction share an emphasis on vocabulary, strategies may seem in conflict. Use the strategies presented here for connecting new learning to previous knowledge and experiences and providing meaningful paths for students' vocabulary development in the mathematics classroom.

Every application of integration by parts can be done with a tabular method. The trick is to identify and consider each new integral in the table before deciding how to proceed. This paper supplements a classic introduction to integration by parts with a particular tabular method called Row Integration by Parts (RIP). Approaches to tabular methods…

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we…

The concept of scaffolding in the learning process refers to teacher assistance to all students in the class when they are unable to solve math problems correctly, which is identified by errors in solving the issues. The assistance in question is temporary. The diversity of students' academic abilities in the class influences the teacher's…

Multilingual learners (MLs) encounter key language features that influence their mathematical word problem-solving processes. Much of the readily available literature surrounding MLs' experiences in the mathematics classroom explores either their content knowledge or how language affects their mathematics achievement. Far less literature has…

Although research highlights the importance of analyzing the geometric work of teachers, there are few validated instruments in this line. This study presents the processes of design and validation of a forced-choice questionnaire that allows the characterization, from a theoretical basis, of how geometry teachers organize their teaching practice.…

Research on teacher questioning often provides snapshots of questioning practices or study how interventions can lead to development of questioning, but few studies have investigated if and how teacher questioning evolves naturally over time. This study explored such natural variation by analysing the questioning practice of a Norwegian elementary…

This research examined the impact of the Cognitive-Communicative (C-C) model as a pedagogical strategy for teaching algebraic word problems (AWPs). The C-C model integrates structured dialogue, concept clarification, and systematic problem-solving steps to enhance students' comprehension and reasoning. Employing a mixed-methods framework, the…

This study investigates the pedagogical content knowledge identified in six prospective elementary teachers' written teacher practicum reports. Focusing on the three categories of pedagogical content knowledge included in the Mathematical Knowledge for Teaching framework, the study analyzes the prospective teachers' descriptions and combines their…

The introduction of large language models (LLMs) may change future pedagogical practices. Current research mainly focuses on the use of LLMs to tutor students, while the exploration of LLMs' potential to assist teachers is limited. Taking high school mathematics as an example, we propose a method that utilizes LLMs to enhance the quality of…

Describing and analyzing teaching practice has been a focus of researchers interested in the interaction and connections between teachers' content knowledge and their pedagogical knowledge. This study described the role of a teacher's mathematical content and pedagogical content knowledge in involving students in learning and solving Science,…