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Clinch, Adam – Mathematics Teacher, 2018
One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…
Descriptors: Mathematics Instruction, Algebra, Teaching Methods, Problem Solving
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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
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McDowell, Eric L. – Mathematics Teacher, 2016
By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…
Descriptors: Fractions, Number Systems, Number Concepts, Numbers
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Garofalo, Joe; Trinter, Christine P.; Swartz, Barbara A. – Mathematics Teacher, 2015
One method of proof is to provide a logical argument that demonstrates the existence of a mathematical object (e.g., a number) that can be used to prove or disprove a conjecture or statement. Some such proofs result in the actual identification of such an object, whereas others just demonstrate that such an object exists. These types of proofs are…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Secondary School Mathematics
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Conner, Kimberly – Mathematics Teacher, 2015
This article is based on the author's experiences as a second-year teacher at a small private school teaching all sections of Geometry and Algebra 2. Working with the same students in both courses, the author was aware of each one's levels of retention and execution of Algebra 1 concepts before the beginning of the year. The author often noticed…
Descriptors: Algebra, Private Schools, Geometry, Mathematics Skills
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Wendt, Ted; Murphy, Kevin – Mathematics Teacher, 2015
According to a 2012 study from the Program for International Student Assessment, twenty-nine out of sixty-five participating nations and other jurisdictions outperformed the United States in mathematics by a statistically significant margin (up from twenty-three in 2009) (Heitin 2013). To improve students' mathematical understanding, the authors…
Descriptors: Mathematics Instruction, Mathematics Achievement, Common Core State Standards, Mathematics Skills
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Trocki, Aaron – Mathematics Teacher, 2014
The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI…
Descriptors: Secondary School Mathematics, High School Students, Geometry, Technology Uses in Education
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Paoletti, Teo J. – Mathematics Teacher, 2013
To engage students, many teachers wish to connect the mathematics they are teaching to other branches of mathematics or to real-world applications. The lesson presented in this article, which uses the algebraic skill of finding the equation of a line between two points and the geometric axiom that any two points define a line, does both. A…
Descriptors: Mathematics Instruction, Relevance (Education), Algebra, Mathematics Skills
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Allen, Kasi C. – Mathematics Teacher, 2013
Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…
Descriptors: Algebra, Mathematics Instruction, High School Students, Secondary School Mathematics