Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

Making meaningful connections between mathematics and other scientific disciplines has become a priority in education. In recent years, numerous national reports have called for more cross-disciplinary material in entry-level mathematics courses. (Cohen 1995 is one such example.) In this article, we consider an application of quadratic equations to a standard problem in chemistry. We show how quadratic equations arise naturally in solving the problem and then go on to consider a standard approximation using a simpler quadratic. This focus brings to light several important mathematical ideas. They include the sensitivity of the solutions on the equation coefficients and the use of inequalities to obtain upper bounds on the error

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Sharing Teaching Ideas: A Squeeze Play on Quadratic Equations

Mathematics Teacher ◽

10.5951/mt.75.2.0132 ◽

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.

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On the Frequency of Algebraic Brauer Classes on Certain Log K3 Surfaces

Canadian Mathematical Bulletin ◽

10.4153/s0008439518000590 ◽

2018 ◽

Vol 62 (3) ◽

pp. 551-563

Author(s):

Jörg Jahnel ◽

Damaris Schindler

Keyword(s):

K3 Surfaces ◽

Upper Bounds ◽

Hasse Principle ◽

Brauer Group ◽

Integral Points ◽

Quadratic Equations

AbstractGiven systems of two (inhomogeneous) quadratic equations in four variables, it is known that the Hasse principle for integral points may fail. Sometimes this failure can be explained by some integral Brauer–Manin obstruction. We study the existence of a non-trivial algebraic part of the Brauer group for a family of such systems and show that the failure of the integral Hasse principle due to an algebraic Brauer–Manin obstruction is rare, as for a generic choice of a system the algebraic part of the Brauer-group is trivial. We use resolvent constructions to give quantitative upper bounds on the number of exceptions.

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

Mathematics Teacher ◽

10.5951/mt.103.1.0069 ◽

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.

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Corequisite mathematics education at Missouri community colleges

10.32469/10355/81568 ◽

2020 ◽

Author(s):

◽

Trisha White

Keyword(s):

Community Colleges ◽

Workforce Development ◽

Research Question ◽

Underprepared Students ◽

Mixed Method Research ◽

Completion Rates ◽

Structured Interviews ◽

Mathematics Courses ◽

Entry Level ◽

Persistence Rates

In an effort to raise graduation rates, the Missouri Department of Higher Education and Workforce Development directed public institutions to establish policies and create corequisite support structures to allow some underprepared students to take entry-level mathematics courses without first completing non-credit remedial courses. The present study explored the variety and effectiveness of corequisite structures implemented at 12 independent public community colleges in Missouri. Using a pragmatic parallel mixed method research design, this study used highly structured interviews and data from the Enhanced Missouri Student Achievement Study to address the research question: Which corequisite structures and policies have produced significant increases in persistence rates and completion rates of entry-level mathematics courses at community colleges in Missouri? This study described the unique structures and policies implemented at the colleges and using a chi-square test for homogeneity, compared the statewide and college persistence rates and completion rates of entry-level mathematics courses for students beginning in Fall 2014 and Fall 2018. The findings indicated that the statewide persistence rates increased but the increase was neither widespread nor consistent amongst the 12 individual colleges in the study; however, the increase in completion rates of entry-level mathematics courses was widespread and consistent with 11 of the 12 colleges seeing statistically significant increases. The study identified four conceptualizations of corequisite supports and noted that colleges allowing underprepared students greater access to non-STEM pathway courses with corequisite support saw the highest completion rates of entry-level mathematics courses.

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The Pentagon Problem: Geometric Reasoning with Technology

Mathematics Teacher ◽

10.5951/mt.89.2.0086 ◽

1996 ◽

Vol 89 (2) ◽

pp. 86-90

Author(s):

Rose Mary Zbiek

Keyword(s):

Mathematics Learning ◽

Geometric Reasoning ◽

Geometer's Sketchpad ◽

Mathematics Courses ◽

Learning And Teaching ◽

Mathematical Ideas ◽

Geometric Figures ◽

Algebraic Expressions ◽

Use Of Technology

We value the use of technology in mathematics learning and teaching, and we want students to reason and to explore mathematical ideas in their mathematics courses. In recent years, such computing tools as The Geometer's Sketchpad (1991) and Cabri Geometry II (1994) allow us to devise and operate on geometric figures similarly as symbolic manipulators allow us to work with algebraic expressions. In this article, we call these tools figure manipulators. These tools make it possible for students to explore and connect geometric ideas from synthetic, analytic, and transformational perspectives. Yet we wonder how we can actually get this synthesis to happen in our classrooms. Our doubting colleagues, and we, question the effects of such experiences on our students' understanding of mathematics in general and of geometry in particular.

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A Geometric Approach to the Discriminant

Mathematics Teacher ◽

10.5951/mt.88.4.0323 ◽

1995 ◽

Vol 88 (4) ◽

pp. 323-325

Author(s):

R. Daniel Hurwitz

Keyword(s):

Geometric Approach ◽

School Mathematics ◽

Evaluation Standards ◽

Mathematical Ideas ◽

Quadratic Equations ◽

Algebraic Concepts ◽

Transformation Geometry ◽

Integrated Mathematics ◽

Coordinate Geometry

An important connection between mathematical ideas to which the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) repeatedly refers is using graphs to help understand algebraic concepts. For many students, the ability to “draw a picture,” either by hand or with the aid of a graphing utility, is valuable. For this reason, the second course of many integrated mathematics sequences places chapters on coordinate geometry, and perhaps even transformation geometry, before the chapter on quadratic equations (for example, see Keenan and Dressler [1981, ch. 12- 15] or Bumby and Klutch [1979, ch. 8-12].

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