Sharing Teaching Ideas: A Squeeze Play on Quadratic Equations

1982 ◽  
Vol 75 (2) ◽  
pp. 132-136
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
Quadratic Equation ◽  
Senior Year ◽  
Quadratic Formula ◽  
Mathematics Courses ◽  
Quadratic Equations ◽  
Teaching Ideas

As a mathematics teacher whose present assignment is to teach science, I was somewhat dismayed when my physics class wa unable to solve a nontrivial quadratic equation. These students are all enrolled in senior-year mathematics and had taken all lower level mathematics courses available in our small Western Kansas high school. They charged this inability to having forgotten the quadratic formula. To the e students the quadratic formula is a magic passkey to solving “unfactorable” quadratic equations. On further di scussion, l discovered that they vaguely remembered having heard of the method of completing the square, but they saw no connection between the quadratic formula and that method of solving a quadratic equation. They could solve simple quadratics by hit-and-miss factoring, but that was their only tool with which to attack this problem.

The Influence on Mathematics Test Scores, by Ethnicity and Sex, of Prior Achievement and High School Mathematics Courses

1987 ◽  
Vol 18 (3) ◽  
pp. 180-186
Author(s):  
Lyle V. Jones
Keyword(s):  
High School ◽  
Test Scores ◽  
National Sample ◽  
Expected Improvement ◽  
White Female ◽  
Advanced Mathematics ◽  
Senior Year ◽  
Mathematics Courses ◽  
Mathematics Test ◽  
Student Socioeconomic Status

Data from a national sample of high school sophomores in 1980 from the High School and Beyond project show that senior-year mathematics test scores are highly dependent on the number of courses taken in mathematics, Algebra I or above. Within each level of course taking, senior test scores are predicted reasonably well from student socioeconomic status, sophomore-year verbal test scores, and sophomore-year mathematics test scores. The results support the theses that (a) whether black or white, female or male, sophomore students with similar levels of mathematics achievement may be expected to experience similar levels of improvement by taking additional mathematics courses and (b) the expected improvement is elevated for students with four or more credits of advanced mathematics or with three credits that include calculus.

Approaching quadratic equations from a right angle

2017 ◽  
Vol 101 (552) ◽  
pp. 424-438
Author(s):  
King-Shun Leung
Keyword(s):  
Secondary School ◽  
Mathematics Curriculum ◽  
Quadratic Equation ◽  
Bisection Method ◽  
Quadratic Formula ◽  
Secondary School Mathematics ◽  
Quadratic Equations ◽  
Newton Raphson ◽  
Raphson Method ◽  
Comprehensive Discussion

The theory of quadratic equations (with real coefficients) is an important topic in the secondary school mathematics curriculum. Usually students are taught to solve a quadratic equation ax2 + bx + c = 0 (a ≠ 0) algebraically (by factorisation, completing the square, quadratic formula), graphically (by plotting the graph of the quadratic polynomial y = ax2 + bx + c to find the x-intercepts, if any), and numerically (by the bisection method or Newton-Raphson method). Less well-known is that we can indeed solve a quadratic equation geometrically (by geometric construction tools such as a ruler and compasses, R&C for short). In this article we describe this approach. A more comprehensive discussion on geometric approaches to quadratic equations can be found in [1]. We have also gained much insight from [2] to develop our methods. The tool we use is a set square rather than the more common R&C. But the methods to be presented here can also be carried out with R&C. We choose a set square because it is more convenient (one tool is used instead of two).

4. Quadratic equations

2015 ◽  
pp. 40-52
Author(s):  
Peter M. Higgins
Keyword(s):  
General Equation ◽  
Solution Process ◽  
Quadratic Equation ◽  
Quadratic Formula ◽  
Quadratic Equations ◽  
Quadratic Approximations

A quadratic equation is one involving a squared term and takes on the form ax2 + bx + c = 0. Quadratic expressions are central to mathematics, and quadratic approximations are extremely useful in describing processes that are changing in direction from moment to moment. ‘Quadratic equations’ outlines the three-stage solution process. Firstly, the quadratic expression is factorized into two linear factors, allowing two solutions to be written down. Next is completing the square, which allows solution of any particular quadratic. Finally, completing the square is applied to the general equation to derive the quadratic formula that allows the three coefficients to be put into the associated expression, which then provides the solutions.

Call for Manuscripts: Entry-Level High School Mathematics Courses: Maximizing Learning for ALL

2009 ◽  
Vol 103 (1) ◽  
pp. 69
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
Entry Level ◽  
Learning Mathematics

The Mathematics Teacher is eager to publish articles about teaching mathematics at the entry level. These courses are critical to fostering students' pursuit of and love for learning mathematics through the high school years and beyond.

Sharing Teaching Ideas: Very Special People, Mathematically

1992 ◽  
Vol 85 (1) ◽  
pp. 32-33
Author(s):  
Benita H. Albert
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
School Environment ◽  
Oak Ridge ◽  
School Population ◽  
Teachers And Students ◽  
Special Person ◽  
Valentine's Day ◽  
Teaching Ideas ◽  
Special People

For several years the Oak Ridge Schools have observed “Very Special Person (VSP) Week” during Valentine's Day week in February. This five-day period is specifically intended to remind administrators, teachers, and students that acts of kindness toward each other enhance the school environment. As a mathematics teacher, I think that the most special thing I can do for my own students is to offer continual challenges and excitement in mathematics. It occurred to me, however, that I meet less than 10 percent of the high school population in any year and that many other students and teachers may not share my enthusiasm for mathematics. Thus I was determined that my Very Special Person project for 1990 would reach every classroom — in fact, every teacher and administrator — in the school.

scholarly journals REPRESENTASI MATEMATIS SISWA DALAM PEMECAHAN MASALAH PERBANDINGAN TRIGONOMETRI PADA SEGITIGA SIKU-SIKU DITINJAU DARI KECERDASAN LOGIS MATEMATIS, LINGUISTIK DAN VISUAL SPASIAL

2020 ◽  
Vol 2 (1) ◽  
pp. 1-15
Author(s):  
Merlin Hitalessy ◽  
Wilmintjie Mataheru ◽  
Carolina Selfisina Ayal
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Quadratic Equation ◽  
Mathematical Representation ◽  
Vocational High School ◽  
School Students ◽  
Mathematical Representations ◽  
Quadratic Equations ◽  
Visual Spatial

One of the skills needed in learning mathematics is the ability to solve mathematical problems. In solving problems in mathematics learning, mathematical representation is needed by students in the problem solving process. Students tend to use mathematical representations, but sometimes they don't understand what they are doing. In general, mathematical representations also play an important role in improving mathematical competence. Beside the ability of representation, students also have intelligence, including mathematical logical intelligence, linguistics and visual spatial. This research is descriptive with qualitative approach that aimed to describe the complete mathematical representation of vocational high school students in solving a quadratic equation in terms. The research phase begins with the selection of research subjects were determined by gender and math skills test results were similar. Having chosen the subject and the continuation of the problem solving quadratic equations and interviews. The validity of the data using a triangulation of time that is giving the task of solving a quadratic equation are equal at different times. The results of this study as the mathematic description shows that vocational high school students in solving quadratic equations problem according to Polya step problem solving

Sharing Teaching Ideas: Seven Wonders of the Ancient and Modern Quadratic World

2001 ◽  
Vol 94 (5) ◽  
pp. 349-361
Author(s):  
Sharon E. Taylor ◽  
Kathleen Cage Mittag
Keyword(s):  
High School ◽  
Fundamental Theorem ◽  
Multiple Representations ◽  
Classroom Activity ◽  
Quadratic Equations ◽  
Teaching Algebra ◽  
Fundamental Theorem Of Algebra ◽  
Teaching Ideas

After teaching algebra for many years in both high school and college, we noticed that our students were still having trouble understanding the concepts derived from the fundamental theorem of algebra. With the increased emphasis on multiple representations—graphical, numerical, and algebraic, we decided to design a classroom activity that examined solving quadratic equations by using a variety of methods.

Call for Manuscripts: Entry Level High School Mathematics Courses: Maximizing Learning for ALL

2009 ◽  
Vol 103 (3) ◽  
pp. 227
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
School Mathematics ◽  
Teaching Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
Entry Level ◽  
Learning Mathematics

The Mathematics Teacher is eager to publish articles about teaching mathematics at the entry level. These courses are critical to fostering students' pursuit of and love for learning mathematics through the high school years and beyond.

Sharing Teaching Ideas: Correspondence from Mathematicians

2000 ◽  
Vol 93 (8) ◽  
pp. 688-691
Keyword(s):  
Quadratic Equation ◽  
Quadratic Formula ◽  
The Past ◽  
Mathematics Problems ◽  
Intermediate Algebra ◽  
Teaching Ideas ◽  
Algebra Class

When struggling with mathematics problems in today's classroom, students occasionally experience a flash of discovery that is inspired by the past. An example happened in an intermediate algebra class at the end of a lesson on completing the square. In an attempt to pique students' interest and to connect completing the square with other mathematics, one of the authors, Jennifer Horn, challenged the students to complete the square on the standard quadratic equation, ax2 + bx + c = 0. Obviously, she intended for them to “derive” the quadratic formula that they had used in previous lessons.

College Bound: Advice for Academically Talented Students From Recent Graduates

2019 ◽  
Vol 31 (2) ◽  
pp. 87-110
Author(s):  
Melanie S. Meyer ◽  
Jeff Cranmore
Keyword(s):  
High School ◽  
High School Graduates ◽  
School Personnel ◽  
Application Process ◽  
Senior Year ◽  
Social And Emotional ◽  
Academic Courses ◽  
Recent Graduates ◽  
Talented Students ◽  
Academically Talented Students

For students who decide to enroll in college after high school graduation, there are numerous factors to consider when searching for potential matches and choosing from the available options. Ten recent high school graduates who participated in self-selected, ability-grouped, advanced academic courses in high school were interviewed at the end of senior year. These students shared valuable lessons they learned about the college decision-making process to offer guidance to students beginning the college search, and the adults, in and out of school, who help them make those choices. Participants offered advice about preparing to apply to college, the application process, and related social and emotional considerations. Nine key themes were identified in which participants encouraged early exploration of career-related interests, a focus on person-environment fit, and managing expectations. Implications for students, parents, and school personnel are also discussed.

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