The purpose of this study was to compare students' performances in a freshmen level quantitative reasoning course (QR) under three different instructional models. A cohort of 155 freshmen students was placed in one of the three models: needing a prerequisite course, corequisite (students enroll simultaneously in QR course and a course that…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

Young children naturally engage in mathematics as they play and explore. Although many early childhood educators are aware that children are frequently interacting with mathematical ideas, a certain level of knowledge and awareness is required to identify and highlight the mathematics that children are engaging in and to create opportunities for…

Equity is an important element of educational discourses pertaining to mathematics and science education. Creativity is an aspect of the classroom that is often ignored due to curricular constraints and the burden of testing. However mathematics offers avenues to infuse the regular curricula with activities that are thought provoking and require…

Prior to the recycling process, raising awareness of plastic waste impact, e.g., polluting oceans worldwide, is undoubtedly a first attempt to tackle this pandemic environmental issue. With this in mind, the presented practical session is an effort to entice an interdisciplinary audience of science undergraduates toward a sustainable future. The…

In some math classrooms, students are taught to follow and memorize procedures to arrive at the correct solution to problems. In this article, author Mike Flynn suggests a way to move beyond answer-getting to true problem solving. He describes an instructional approach called three-act tasks in which students solve an engaging math problem in…

Digital games have demonstrated great potential for supporting students' learning across disciplines. But integrating games into instruction is challenging and requires teachers to shift instructional practices. One factor that contributes to the successful use of games in a classroom is teachers' experience implementing the technologies. But how…

We recently developed the "Framework of Achievement Bests" to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as "optimal achievement best," which stipulates the idea that individuals may, in general, strive to achieve personal…

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

This ethnographical study aims to interpret how an intelligent tutorial system, geogebraTUTOR, mediates to the student's argumentative processes. Data consisted of four geometrical problems proposed to a group of four students aged 16-17. Qualitative analysis of two selected cases led to the identification of the development of argumentative…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

In our contribution we focus on the possibility to use an educational tool called Concept Cartoons in future primary school teachers' education, as an instrument for observing how future primary school teachers reason about fractions. In the introduction section we present Concept Cartoons, and also the primary school level of the fractions topic.…

The research presented in chapters 2, 3, and 4 in this dissertation uses a sociocultural and sociohistorical lens, particularly around power, authority of knowledge and identity formation, to investigate the complexity of engaging in, supporting, and evaluating high-quality argumentation within a college biochemistry inquiry-oriented classroom.…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

The purpose of this study was to replicate and extend the study of the schema-based intervention (SBI) conducted by Jitendra et al. (2015) that demonstrated impact in proportional problem solving for a homogeneous sample of Upper Midwest students and teachers who were predominantly White and middle class. This study was replicated in two…