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Edwards, Thomas G.; Chelst, Kenneth R. – Mathematics Teacher, 2019

While tutoring his granddaughter in second-year algebra recently, the second author lamented that every textbook he could find expresses the quadratic formula as probably the most common form of the formula. What troubled him is that this form hides the meaning of the various components of the equation. Indeed, the meaning was obscured by the…

Descriptors: Mathematics Instruction, Mathematical Formulas, Algebra, Teaching Methods

Stegall, Joanna B.; Malloy, Jacquelynn A. – Mathematics Teacher, 2019

The ties between literacy and numeracy exist in the development of vocabulary and language for understanding mathematical concepts. Research indicates that explicit instruction in mathematics vocabulary supports success with mathematics problem solving (Biemiller 2009; Pierce and Fontaine 2009; Rubenstein and Thompson 2002) for native…

Descriptors: Misconceptions, Mathematics Instruction, Algebra, Mathematics

Hubacz, Meghan – Mathematics Teacher, 2018

During the author's eighteen-year tenure as a high school mathematics teacher, there has been one question that she has yet to answer: "Why don't students do homework?" On the basis of research, many factors may lead to a student leaving homework undone. A student may lack the drive to complete work out of school. Or a student may choose…

Descriptors: Problem Solving, Mathematics Instruction, Homework, Student Motivation

Popelka, Susan R.; Langlois, Joshua – Mathematics Teacher, 2018

"Flatland: A Romance of Many Dimensions" is an 1884 novella written by English schoolmaster Edwin Abbott. He describes what it would be like to live in a two-dimensional (2D) world--Flatland. It is fascinating reading that underscores the challenge of teaching three-dimensional (3D) mathematics using 2D tools. Real-world applications of…

Descriptors: High School Students, Secondary School Mathematics, Calculus, Computer Uses in Education

Dibbs, Rebecca; Beach, Janessa; Rios, Daniel – Mathematics Teacher, 2018

Rich mathematical modeling activities are crucial to giving students agency and making mathematics meaningful. Proportional reasoning and transitional algebraic reasoning are the primary topics in the prealgebra curriculum, so a need exists for meaningful modeling activities using proportional reasoning in addition to geometric modeling. In…

Descriptors: High School Freshmen, Grade 9, Mathematics Education, Mathematics Activities

Dickman, Benjamin – Mathematics Teacher, 2018

What do nonroutine algebra problems look like for a second-year algebra course, and where can such problems be found? Starting from the belief that even challenging, nonroutine problems should be solvable with the resources that students possess, Benjamin Dickman proceeded to formulate a small collection of tasks to push students into integrating…

Descriptors: Mathematics Instruction, Algebra, Problem Solving, Mathematical Logic

Rebholz, Joachim A. – Mathematics Teacher, 2017

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…

Descriptors: Mathematics Instruction, High School Students, Secondary School Mathematics, Graphs

Nirode, Wayne – Mathematics Teacher, 2017

Since the 1970s, the Mathematical Association of America's (MAA) journals "Mathematics Magazine" and "College Mathematics Journal" have published "Proofs without Words" (PWWs) (Nelsen 1993). "PWWs are pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one…

Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Secondary School Mathematics

Kirwan, J. Vince – Mathematics Teacher, 2017

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

Descriptors: Visualization, Mathematics Instruction, Teaching Methods, Algebra

McCulloch, Allison W.; Whitehead, Ashley; Lovett, Jennifer N.; Whitley, Blake – Mathematics Teacher, 2017

Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

Descriptors: Mathematics Instruction, Audio Equipment, Textbooks, Word Problems (Mathematics)

Czocher, Jennifer A.; Moss, Diana L. – Mathematics Teacher, 2017

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Descriptors: Mathematical Models, Problem Solving, Mathematics Instruction, High School Students

Richardson, Janessa; Bachman, Rachel M. – Mathematics Teacher, 2017

This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…

Descriptors: Preservice Teachers, Mathematics Instruction, Mathematical Concepts, Mathematical Logic

Rhoads, Kathryn; Mendoza Epperson, James A. – Mathematics Teacher, 2017

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

Descriptors: Mathematical Models, Intervals, Mathematics Instruction, Algebra

Housen, Monica – Mathematics Teacher, 2017

In this article, Monica Housen describes how she uses Guess the Number of . . . , a game that develops estimation skills and persistence to provide a fun, to provide a meaningful experience for her high school students. Each week she displays objects in a clear plastic container, like those for pretzels sold in bulk. Students enter a…

Descriptors: High School Students, Mathematics Instruction, Educational Games, Teaching Methods

Leith, Chad; Rose, Elena; King, Tony – Mathematics Teacher, 2016

To create a classroom learning community in which all students are engaged and inspired, a mathematics teacher's mastery of the content must be matched by an awareness of the needs of individual students and an understanding of the instructional strategies that will enable all learners to develop their mathematical knowledge and skills. Yet when…

Descriptors: Mathematics Instruction, English Language Learners, English (Second Language), Immigrants