In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

How is the president of the United States elected? Why is this the method used? Is this the best and most efficient way of electing the president of the United States? Questions such as these are well suited for a mathematics discussion that promotes numeracy, because, "notwithstanding the immense value of numeracy for education and vocation,…

The social and educational status of black male youth in the United States has been receiving increasing attention. In February 2014, President Barack Obama announced a new national initiative--My Brother's Keeper--for helping black boys and male youth or, to speak more generally, boys and young men of color, to "stay on track; providing the…

The statistics about community college developmental math level and completion rates can seem disheartening, especially for those who work with these students day-to-day and know their life stories. When it comes to teaching her students, the author chooses not to focus on the statistics. Instead, she pays attention to their varied career goals…

While one author was reading "The Simpsons and Their Mathematical Secrets by Simon Singh" (2013) in preparation for a presentation, the second author asked what in the book would be interesting to discuss. The topic of Klein bottles was on the first author's mind at that moment, so he tried to describe and explain the form to her--a real…

The Gale-Shapley stable marriage theorem is a fascinating piece of twentieth-century mathematics that has many practical applications--from labor markets to school admissions--yet is accessible to secondary school mathematics students. David Gale and Lloyd Shapley were both mathematicians and economists who published their work on the Stable…

The National Council of Teachers of Mathematics (NCTM) launched the "standards-based" education movement in North America in 1989 with the release of "Curriculum and Evaluation Standards for School Mathematics," an unprecedented action to promote systemic improvement in mathematics education. Now, twenty-five years later, the…

What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…

Finding patterns and making conjectures are important thinking skills for students at all levels of mathematics education. Both the Common Core State Standards for Mathematics and the National Council of Teachers of Mathematics speak to the importance of these thought processes. NCTM suggests that students should be able to recognize reasoning and…

Mathematical ideas exist and develop in many different cultures. From this multicultural perspective, teachers can use a variety of approaches to acknowledge the role of culture in the teaching and learning of mathematics. Curricular materials that "emphasize both the mathematical and sociocultural aspects" not only help teachers achieve…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

Building coherence in the development of mathematical ideas across the grades is key to improving students' mathematical learning in the United States. Knowing the mathematical experiences, understanding, skills, and habits of mind that students bring to a grade level and what the expectations are for the following grades can help teachers bridge…

Technology use in mathematics often involves either exploratory or expressive modeling. When using exploratory models, students use technology to investigate a premade expert model of some phenomena. When creating expressive models, students have greater flexibility for constructing their own model for investigation using objects and mechanisms…

A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…

Constructivism has constituted a predominant philosophical trend in mathematics education, but its implementation in the classroom has proven to be "far more difficult than the reform community acknowledges". This difficulty may be due in part to administrative cultures that might insist on more procedural types of instruction aimed at testing, in…