The authors describe their approach to teaching a course on finite fields and combinatorial applications, including block designs and error-correcting codes, using a hybrid of lectures and active learning. Under the discussed classroom model, there are two lecture days and two discovery-based discussion days each week. Discussions center around…

The School of Engineering of the Polytechnic of Porto (ISEP) has embraced the DrIVE-MATH project, since September 2017. Active-learning (AL) techniques were implemented in several Math courses, namely Linear Algebra and Analytic Geometry, Probability and Statistics, Statistical Models, Computational Mathematics, and Differential and Integral…

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in and for teaching (MKT). We argue that Rowland's (2013) Knowledge Quartet for MKT, in particular, the…

In the first chaotic days of the crisis, schools across the United States organized to assemble and distribute instructional materials and to make a rapid transformation from school-based to home-based learning. the impact of this crisis on all students is significant. As districts resume instruction in the upcoming school year, they will not only…

The educational laws establish an organization and a grouping of the contents of the educational system they rule. As far as we know, the set of experts who design it neither follow precise objective criteria nor use computer tools. That is why they are not usually rotund. We consider that defining precise objective criteria is the key to develop…

This article examines the bodies of knowledge that influence and inform the teaching of mathematics methods courses for preservice early childhood teachers, focusing on the U.S. context. In particular, the article reports on an analysis of scholarship published over the last 20 years in four journals (two focused on early childhood education and…

The developing synergy of legislation and research throughout recent history points to the current momentum behind college and career readiness for every student. Researchers have found that embedding academic content into career education improves student learning. Integrated learning can vary in approach and style and can be adjusted to fit into…

In this article, by way of an analysis of a case of mathematics teacher training, I explore the general idea of pedagogic expectation of an alignment of pedagogic identities and specific realisations of mathematics in pedagogic contexts. The particular case analysed has a constructivist orientation, but the analytic resources brought to bear in…

This study investigated the learning process of preservice elementary teachers (PSTs) through lesson study in a mathematics teaching methods course. Lesson study meeting data of kindergarten PSTs were analyzed to examine the shifting focus on (1) student collaboration in classroom (vision), (2) teaching practices (making content accessible), and…

Group work has been a main activity recommended by mathematics education reform. We aim at describing the patterns of interaction between teachers and students during group work. We ask: How do teachers scaffold group work during a problem-based lesson? We use data from a problem-based lesson taught in six geometry class periods by two teachers…

Graduate teaching assistants serve as instructors of record for numerous undergraduate courses every semester, including serving as teachers for mathematics content courses for elementary preservice teachers. In this study, we examine 6 teaching assistants' teaching practices in the context of a geometry content course for preservice teachers by…

This exploratory research project investigated graduate students' satisfaction levels with online learning associated with human (professor/instructor and instructional associate) and design factors (course structure and technical aspects) using a survey study. A total of 81 graduate students (master's students who majored in math and science…

Curriculum standards provide classroom teachers with frameworks to guide instruction during the academic year and throughout a student's schooling. Unfortunately, standards are misconstrued as all-encompassing--as a compendium of all mathematics content that can and should be taught to students. Such a view is unfortunate. Mathematics teachers…

Using an apparently simple problem, ''Design a cylindrical can that will hold a liter of milk,'' this paper demonstrates how engineering design may facilitate the teaching of the following ideas to secondary students: linear and non-linear relationships; basic geometry of circles, rectangles, and cylinders; unit measures of area and volume;…

The purpose of this study is to determine whether educators believe mathematics should be taught to liberal arts students, what topics are taught in liberal arts mathematics courses, and what the motivation is for teaching such topics. The study consists of two parts, a review of the opinions of educators regarding liberal arts mathematics, and a…