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…

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…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

Based in part on our work in adapting existing paper textbooks for secondary schools for a digital format, this paper discusses paper form and the various electronic platforms with regard to the presentation of five aspects of mathematics that have roles in mathematics learning in all the grades kindergarten-12: symbolization, deduction, modeling,…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

While the study of geometry in some shape or form has existed for many millennia, it is within the past twenty years that a shift has occurred in how geometry may be learned through computer-based interactive geometric software. Software programs like The Geometer's Sketchpad[TM], Cabri[TM], and GeoGebra[TM] allow users to construct interactive…

The vision for science education set forth in "A Framework for K-12 Science Education" (NRC 2012) makes it clear that for today's students to become the scientifically literate citizens of tomorrow their educational experiences must help them become mathematically proficient. "The focus here is on important practices, such as modeling, developing…

The vision for science education set forth in "A Framework for K-12 Science Education" (NRC 2012) makes it clear that for today's students to become the scientifically literate citizens of tomorrow, their educational experiences must help them become mathematically proficient. "The focus here is on important practices, such as modeling, developing…

In June 2018 the Canadian Mathematics Education Study Group/Groupe Canadien d'étude en didactique des mathématiques (CMESG/GCEDM) held its 42nd meeting in the idyllic setting of Squamish, British Columbia. This meeting marked the first time CMESG/GCEDM had been in British Columbia since 2010 and the first time it had been held at Quest University.…

High academic standards are an important first step in ensuring that all Alaska's students have the tools they need for success. These standards reflect the collaborative work of Alaskan educators and national experts from the nonprofit National Center for the Improvement of Educational Assessment. Further, they are informed by public comments.…

Argues that a major difficulty in learning how to do mathematical modeling is in the first independent run through the modeling cycle. Reviews a case study (N=12) on mathematical modeling and presents the conclusions in three sections: (1) the choice of task; (2) the presentation of the task; and (3) tutor intervention and support. (ASK)

A game based on the group of permutations on four symbols is described. The game can be used in the study of many algebraic concepts. (SD)

Several examples of concrete mathematical models are discussed along with suggested criteria for good heuristic models. (MN)

Examines various processes of verbalizing in mathematics teaching. Describes several types of communication between school students and gives some examples for tasks. Interpretations for didactical concepts based on ideas about mathematical modeling, heuristic-experimental working, and also work with sequences of questions in mathematics teaching…

After considering the mathematical system common to various types of measure, the author argues that instruction needs to reflect the common aspects of measure systems as well as the distinctive attributes of different systems. (SD)