Discourse Actions to Promote Student Access

We discuss how discourse actions can provide students greater access to high quality mathematics. We define discourse actions as what teachers or students say or do to elicit student contributions about a mathematical idea and generate ongoing discussion around student contributions. We provide rubrics and checklists for readers to use.

Computational Modeling Methods for Deployable Structure Based on Alternatively Asymmetric Triangulation

Asymmetric triangulation is an interesting method combined with concentric pleating to obtain a 3D shape without stretching or tearing. There exists some geometric properties in the process of folding to help realize extension and contraction, which can be used in parametric modeling of different regular polygons. To facilitate design and modeling, adequate computational modeling methods are indispensable. This paper proposes a new mathematical idea and presents a feasible way to build the parameterized models in the digital environment of Rhinoceros, utilizing the Kangaroo plugin in Grasshopper. Designers can directly observe the models’ kinematic deployment and calculate the folding efficiency. It is concluded that the tendencies of folding efficiency in different regular polygons are not the same. To realize rigid folding, each polygon has a limited folding angle.

Ethnomathematics and Modern Globalized Currriculum

The mathematical knowledge consumed in schools can and does influence culture and communities. There is a close connection between development of culture and idea of mathematics. Cultural thinking, practices, and products are mathematically intertwined. Cultural practices show mathematical thinking and operations and culture are better communicated through them. This goes on to confirm the practical fact that mathematics can be understood in cultural game, analysis of local arts, daily work procedures, and skills. Mathematical idea as a science of logical reasoning is better presented from natural/familiar base of culture of the people or else it will not be understood ultimately. Hence, development and human progress cannot be based on it. Mathematics will be useless to humanity. Thus, students need to develop abilities, such as creativity and a sound set of research habits, as they learn the required mathematics. This study focused on ethnomathematics and modern globalized curriculum.

But What if the Goal is to Model with Mathematics?

odeling mathematics has a longstanding tradition in the mathematics classroom, as teachers often engage students in representing mathematical ideas. For example, students can be seen using base-ten blocks to model a number or drawing an array to represent a multiplication fact. Modeling a mathematical idea in this way, however, does not necessarily meet the expectations described in the fourth of the Common Core's Standards for Mathematical Practice (SMP 4): Model with mathematics, which states that students should “apply the mathematics they know to solve problems arising in everyday life, society, and the workplace” (CCSSI 2010, p. 7). Although the SMP provide a detailed description of modeling with mathematics, Bleiler-Baxter et al. (2017) found it useful to consider three decision-making processes embedded within the modeling process.

Shoelace Formula: Connecting the Area of a Polygon and the Vector Cross Product

Understanding how one representation connects to another and how the essential ideas in that relationship are generalized can result in a mathematical theorem or a formula. In this article, we demonstrate this process by connecting a vector cross product in algebraic form to a geometric representation and applying a key mathematical idea from the relationship to prove the Shoelace theorem.

Representasi (Eksternal-Internal) pada Penyelesaian Masalah Matematika

This study aimed to describe the pictorial and schematic representations of student understanding. The subjects were 31 students of grade VIII. The results of this study is two pictorial representations (right and wrong) and two schematic representation (right and wrong). Representation understanding of student described as follows: translational stage, students read the word problem to identify relational statements and quantity, then he transforms the mathematical idea into another form that is more easily understood. Integration stage, students identifying relational relationships between mathematical ideas to be organized into a scheme or image. Solution stage, students devise a solution based on the scheme or image that was created, and then perform calculations and check the answer.

Using Mathematics to Elect the U.S. President

The often misunderstood Electoral College is based on the simple, yet powerful, mathematical idea of proportional reasoning.