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Hurdle, Zach; Warshauer, Max; White, Alex – Mathematics Teacher, 2016

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

Descriptors: Mathematics Instruction, Mathematics Activities, Mathematical Formulas, Computation

Hallman-Thrasher, Allyson; Litchfield, Erin T.; Dael, Kevin E. – Mathematics Teacher, 2016

Matrices occupy an awkward spot in a typical algebra 2 textbook: sandwiched between solving linear systems and solving quadratics. Even teachers who do not base their course timeline and pacing on the class textbook may find a disconnect between how matrices are taught (procedurally) and how other topics are taught (conceptually or with real-world…

Descriptors: Multiplication, Algebra, Mathematics Instruction, Teaching Methods

Smith, Christopher E.; Paré, Jana N. – Mathematics Teacher, 2016

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…

Descriptors: Mathematics Instruction, Teaching Methods, Art Education, Interdisciplinary Approach

Vinogradova, Natalya – Mathematics Teacher, 2016

In fall 2013 the author taught a graduate course entitled Topics in Geometry for Middle and High School Teachers. The majority of the participants had extensive experience teaching mathematics in middle school or high school. The fact that participants were rather comfortable with the basic concepts of school geometry made it both possible and…

Descriptors: Geometric Concepts, Geometry, Mathematics, Mathematics Instruction

Rubel, Laurie H. – Mathematics Teacher, 2016

Diversity and equity are stated priority areas across the field of mathematics education, from the ivory towers of the academy, across teacher education programs, to school districts, schools, and individual classrooms. The talk surrounding diversity and equity is usually framed around categories of race, cultural background, language, disability…

Descriptors: Mathematics Instruction, Gender Issues, Controversial Issues (Course Content), Advocacy

Stephens, Greg – Mathematics Teacher, 2016

Most word processors, including Google Docs™ and Microsoft® Word, include an equation editor. These are great tools for the occasional homework problem or project assignment. Getting the mathematics to display correctly means making decisions about exactly which elements of an expression go where. The feedback is immediate: Students can see…

Descriptors: Mathematics Instruction, Equations (Mathematics), Technology Uses in Education, Educational Technology

Steketee, Scott; Scher, Daniel – Mathematics Teacher, 2016

One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

Descriptors: Geometry, Algebra, Mathematics Education, Mathematical Concepts

Gilbertson, Nicholas J. – Mathematics Teacher, 2016

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

Descriptors: Mathematics Instruction, Mathematical Formulas, Validity, Mathematical Logic

Corcoran, Mimi – Mathematics Teacher, 2016

Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…

Descriptors: Statistics, Mathematics Instruction, Mathematical Concepts, Learning Activities

Strayer, Jeremy; Matuszewski, Amber – Mathematics Teacher, 2016

In this article, Strayer and Matuszewski present a six-phase strategy that teachers can use to help students develop a conceptual understanding of inferential hypothesis testing through simulation. As Strayer and Matuszewski discuss the strategy, they describe each phase in general, explain how they implemented the phase while teaching their…

Descriptors: Mathematics Instruction, Teaching Methods, Hypothesis Testing, Simulation

Reed, Cameron – Mathematics Teacher, 2016

How can old-fashioned tables of logarithms be computed without technology? Today, of course, no practicing mathematician, scientist, or engineer would actually use logarithms to carry out a calculation, let alone worry about deriving them from scratch. But high school students may be curious about the process. This article develops a…

Descriptors: Mathematics Instruction, Computation, Numbers, Mathematical Concepts

Schloemer, Cathy G. – Mathematics Teacher, 2016

Whether students are beginning their study of probability or are well into it, distinctions between complementary sets and mutually exclusive sets can be confusing. Cathy Schloemer writes in this article that for years she used typical classroom examples but was not happy with the student engagement or the level of understanding they produced.…

Descriptors: Probability, Learner Engagement, Teaching Methods, Mathematics

Nirode, Wayne – Mathematics Teacher, 2016

A part of high school geometry is devoted to the study of parallelograms in the context of proving some of their properties using congruent triangles (CCSSI 2010). The typical high school geometry book's chapter on quadrilaterals focuses on parallelograms (e.g., their properties, proving that a given quadrilateral is a parallelogram, and special…

Descriptors: Geometry, Geometric Concepts, Mathematics, Mathematics Instruction

Stump, Sheryl L.; Bryan, Joel A.; McConnell, Tom J. – Mathematics Teacher, 2016

Integrated approaches to education in science, technology, engineering, and mathematics (STEM), especially those set in the context of real-world situations, can motivate and deepen students' learning of the STEM subjects (National Academy of Engineering and National Research Council 2014). This article describes two integrated investigations used…

Descriptors: Mathematics Teachers, Science Teachers, STEM Education, Elementary Secondary Education

Ko, Yi-Yin; Yee, Sean P.; Bleiler-Baxter, Sarah K.; Boyle, Justin D. – Mathematics Teacher, 2016

This article describes the authors' three-component instructional sequence--a before-class activity, a during-class activity, and an after-class activity--which supports students in becoming self-regulated proof learners by actively developing class-based criteria for proof. All four authors implemented this sequence in their classrooms, and the…

Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic