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Zhao, Manqian; Lapuk, Karen – Mathematics Teacher, 2019

According to the National Center for Education Statistics (2016), the number of public school students in the United States who were English learners (ELs) was estimated at 4.5 million. However, in 2005, the national standardized testing scores (Fry 2007) show that about 51 percent of eighth-grade EL students were behind other students in reading…

Descriptors: Mathematics Education, Mathematics Instruction, English Language Learners, Mathematics Teachers

Eichhorn, Melinda S.; DiMauro, Peter J.; Lacson, Courtney; Dennie, Barbara – Mathematics Teacher, 2019

One of the most important roles of a teacher is to create a safe space for learners, consistent with the Center for Applied Special Technology (CAST) Universal Design for Learning guidelines (CAST 2011). Universal Design for Learning (UDL) is a framework for teaching and learning, based on neuroscience research, that guides teachers to eliminate…

Descriptors: Educational Environment, Mathematics Education, Access to Education, Learner Engagement

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

Bowers, Adam – Mathematics Teacher, 2019

The fundamental theorem of calculus (FTC) plays a crucial role in mathematics, showing that the seemingly unconnected topics of differentiation and integration are intimately related. Indeed, it is the fundamental theorem that enables definite integrals to be evaluated exactly in many cases that would otherwise be intractable. Students commonly…

Descriptors: Calculus, Mathematics Instruction, Teaching Methods, Symbols (Mathematics)

Sole, Marla A. – Mathematics Teacher, 2019

The National Council of Teachers of Mathematics (NCTM) has called on teachers to create supportive and equitable classroom environments, to steadfastly advocate that all students can learn mathematics, to hold high expectations for all students and to adopt practices that offer students the opportunity to excel (NCTM 2014). The overarching aim of…

Descriptors: Mathematics Instruction, Classroom Environment, Mathematics Achievement, Teacher Expectations of Students

CadwalladerOlsker, Todd – Mathematics Teacher, 2019

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is…

Descriptors: Statistics, Mathematics Education, Misconceptions, Hypothesis Testing

Henderson, Christie – Mathematics Teacher, 2019

Embedding mathematics in a relatable context has changed the way Christie Henderson's elementary students view the subject. In this article, Henderson discusses how presenting mathematics through a relatable context enables students to visualize the math and make a pictorial representation to aid them in solving it. When relevant and relatable…

Descriptors: Mathematics Instruction, Elementary School Students, Elementary School Mathematics, Mathematics Teachers

Frank, Isaac – Mathematics Teacher, 2019

In this brief article, the author illustrates the flaws of FOIL (multiply the First, Outer, Inner, and Last terms of two binomials) and introduces the box method. Much like FOIL, the box method can become easy to use. Unlike FOIL, however, the box method is a more direct and visible link to using the distributive property to determine area, a…

Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematics Teachers, Multiplication

Suzuka, Kara; Venenciano, Linda – Mathematics Teacher, 2019

Fragile understanding is where new learning begins. Students' understanding of new concepts is often shaky at first, when they have only had limited experiences with or single viewpoints on an idea. This is not inherently bad. Despite teachers' best efforts, students' tenuous grasp of mathematics concepts often falters with time or when presented…

Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Misconceptions

Deshpande, Anjali; Guglielmo, Shannon – Mathematics Teacher, 2019

In recent years, increased attention has been given to the ideas of growth mindsets, brain science, and mathematical mindsets thanks to the important contributions by Dweck (2008), Boaler (2015), and their research teams. Many math teachers invest the time and energy into thinking about what motivates students to learn. The body of work on…

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

Weber, Christof – Mathematics Teacher, 2019

Students' difficulties understanding the meaning of logarithms could stem in part from differences between teachers' and students' views of them. The purpose of this article is to unpack some specialized content knowledge for teaching logarithms. The author discusses the history of logarithms to show why they can be understood as repeated…

Descriptors: Mathematics Instruction, Teaching Methods, Difficulty Level, Numbers

Ptak, Karine S. – Mathematics Teacher, 2019

During the 2013-2014 school year, the Maryland State High School Assessment in Algebra with Data Analysis (HSA) was a requirement for high school graduation in Maryland. At Frederick High School, only 27 percent of students who took the test that year passed. To respond to such an alarming failure rate, three teachers and the author developed and…

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

Purvinis, Elaine M.; Fagan, Joshua B. – Mathematics Teacher, 2019

In first- and second-year algebra classrooms, the all-too-familiar whine of "when are we ever going to use this in real life?" challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect…

Descriptors: Algebra, Mathematical Concepts, Equations (Mathematics), Mathematics Instruction

Mooney, Eileen B. – Mathematics Teacher, 2018

Top-down implementation of technology is one of the most pervasive phenomena of the last couple of decades in educational history. It is the subject of many books, articles, and blog posts on how to fix schools or why educational technology is not working in the classroom. The idea of providing teachers with technology so they can make students…

Descriptors: Educational Technology, Technology Uses in Education, Teaching Methods, Mathematics Instruction

Teuscher, Dawn; Palsky, Kylie; Palfreyman, Charlie Y. – Mathematics Teacher, 2018

The goal of this article is to raise questions that will promote discussions among secondary mathematics teachers about the concept of inverse functions and how to motivate a more conceptual understanding of them in their classrooms. The authors share data to answer the following questions: (1) What meanings of inverse functions do high school…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Mathematical Concepts, Teaching Methods