To promote and facilitate the teaching of math modeling throughout the K-16 setting, the Consortium for Mathematics and Its Applications and the Society for Industrial and Applied Mathematics recently published the GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) Report. This paper provides insight into how the…

We examine the challenges of teaching probability through the use of modelling. We argue how an integrated modelling approach might facilitate a coordinated understanding of distribution by marrying theoretical and data-oriented perspectives and present probability as more connected to the social lives of modern-day students. Research is, however,…

The Models and Modeling Working Group at PME-NA has provided a forum for discussing and collaborating on projects fundamental to research on mathematical modeling since the first PME-NA conference in 1978. We propose to convene this Working Group at PME-NA 41 with a dual purpose: (1) to build on a theme begun in Greenville, holding a focused…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

This study aims to obtain a description of the application of Realistic Mathematic Education (RME) that can improve students' mathematical communication ability. The type of research used is a classroom action research that refers to the design of Kemmis and Mc.Taggart research they are planning, action, observation, and reflection. The results…

The integration of innovative interdisciplinary approaches to the ?-12 Curriculum aims to deepen students' knowledge and help them develop transversal skills. Applying an interdisciplinary lens, with a focus on pandemics, can help shape attitudes by means of inculcating the values of responsible global citizenship, and a high sense of personal and…

The purpose of this study was to justify of the formation technique of representation of modeling methodology at computer science lessons. The necessity of studying computer modeling is that the current trends of strengthening of general education and worldview functions of computer science define the necessity of additional research of the…

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

Many science problems require students to convert units. While this skill may not get the attention that more central science concepts do, teachers in the middle school and early high school grades will be doing their students a great service by leaving them with a strong understanding of both the skill itself and the reasons behind it. When the…

Lesson Study is rapidly becoming one of the most adopted models of teacher professional development worldwide. In this paper, we examine the teachers' discussions that are an integral part of the Lesson Study research cycle. In particular, we investigate the "dialogic mechanisms" that enable teachers' pedagogical intentions to be…

Radical reform in science and mathematics education is needed to prepare citizens for challenges of the emerging knowledge-based global economy. We consider definite proposals to establish: (1) "Standards of science and math literacy" for all students. (2) "Integration of the science curriculum" with structure of matter,…

The association between the observable physical world and the mathematical models used in theoretical physics to describe this world is examined. Such models will frequently exhibit solutions that are "unexpected," in the sense that they describe physical situations which are different from that which the physicist may initially have had in mind…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

This theoretical paper explores the decision-making process involved in modelling and mathematizing situations during problem solving. Specifically, it focuses on the authority behind these choices (i.e., what or who determines the chosen mathematical models). We show that different types of situations involve different sources of authority,…