Applied Algebra: The Modeling Technique of Least Squares

2008 ◽  
Vol 102 (1) ◽  
pp. 46-51
Author(s):  
Jeremy Zelkowski ◽  
Robert Mayes
Keyword(s):  
Mathematical Modeling ◽  
High School ◽  
Community College ◽  
Least Squares ◽  
Real World ◽  
School Community ◽  
Modeling Technique ◽  
Algebra Students ◽  
Static View ◽  
Real World Problems

Algebra on the high school, community college, and college levels is often viewed by students as an abstract game—as skills to be mastered and algorithms to be memorized. To move students from this static view, algebra on all levels should be grounded in applications so that students see it as a useful tool in solving real-world problems. Early in their study of algebra, students should be exposed to mathematical modeling, which can link to their interdisciplinary interests as well as illuminate the need for algebra as a tool for making decisions in a democratic society.

Maximizing Area and Perimeter Problems

2021 ◽  
Vol 114 (1) ◽  
pp. 41-46
Author(s):  
Samuel L. Eskelson ◽  
Brian E. Townsend ◽  
Elizabeth K. Hughes
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Mathematical Concepts ◽  
Area And Perimeter ◽  
Technological Tool ◽  
Real World Problems

Use this context and technological tool to assist students in embracing the mathematical and pragmatic nuances of “real-world” problems so they become fertile opportunities to explore mathematical concepts, express reasoning, and engage in mathematical modeling.

scholarly journals Mathematical modeling of tech-related real-world problems for secondary school-level mathematics

2021 ◽  
Author(s):  
Zehavit Kohen ◽  
Doron Orenstein
Keyword(s):  
Mathematical Modeling ◽  
Secondary School ◽  
Real World ◽  
Mathematics Curriculum ◽  
Secondary Mathematics ◽  
School Mathematics ◽  
School Level ◽  
Workplace Mathematics ◽  
Secondary School Level ◽  
Real World Problems

AbstractThe use of authentic real-world problems that reflect the applied nature of mathematics is not prevalent in formal secondary school settings. In this study, we explore the interface between workplace mathematics, particularly tech-related real-world (TRW) problems, and school mathematics, through the explication of mathematical modeling. The research questions are (1) in which tech domains can real-world problems be identified that can be addressed using mathematical modeling for the secondary school level? (2) Which methods do engineers use to simplify tech-related problems for non-experts in their field? (3) In which areas in the secondary mathematics curriculum can TRW problems be mapped? We present a three-phase model which yielded the creation of a pool of 169 TRW problems. The first two phases of the model included extracting authentic problems from the work of tech engineers and simplifying them to be meaningful or perceivable to students. These were explored by conducting task-oriented interviews with senior tech engineers and scientists from leading companies and universities. The third phase was accomplished by interviewing mathematics education experts, and included verifying the compatibility of the problems with the formal, secondary-level mathematics curriculum. The study has methodological, theoretical, and practical contributions. These include methodology that enables identifying TRW problems that are compliant with the secondary mathematics curriculum; adding to the literature about mathematical modeling by demonstrating the interface between workplace mathematics and school mathematics; and creating a large pool of TRW problems that can be used in secondary school math lessons.

A-Maize-ing Mathematics

2018 ◽  
Vol 111 (7) ◽  
pp. 540-544
Author(s):  
Liza Bondurant
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Mississippi Delta ◽  
Sub Saharan Africa ◽  
Actual Data ◽  
Percentage Change ◽  
Food Scarcity ◽  
Sub Saharan ◽  
Real World Problems ◽  
Algebra Class

In the set of percentage change activities described in this article, students learn about food scarcity in sub-Saharan Africa, how two specific viruses are spreading through maize in the region, and how scientists are using mathematical modeling to solve the problem. This context was particularly relevant to my students who live in the Mississippi Delta, an area where agriculture is the dominant industry. In this activity, students use spreadsheets to perform calculations on a set of data. The goals of this activity, designed for a prealgebra or algebra class, are to encourage students to examine how percentage change is computed in real-world problems, to look for and analyze patterns, and to create their own functions on the basis of actual data.

Tracking Trout: Engaging Students in Modeling

2018 ◽  
Vol 111 (6) ◽  
pp. 416-423 ◽  
Author(s):  
Ahmad M. Alhammouri ◽  
Gregory D. Foley ◽  
Kevin Dael
Keyword(s):  
High School ◽  
High School Students ◽  
Real World ◽  
School Students ◽  
Real World Problems ◽  
Teachers And Technology

After months of solving real-world problems, high school students enact the full modeling cycle supported by peers, teachers, and technology.

Number Theory and Public-Key Cryptography

1991 ◽  
Vol 84 (1) ◽  
pp. 54-63
Author(s):  
Phyllis Lefton
Keyword(s):  
High School ◽  
Number Theory ◽  
High School Students ◽  
Real World ◽  
Mathematics Teacher ◽  
Public Key Cryptography ◽  
Public Key ◽  
School Students ◽  
Pure Mathematics ◽  
Real World Problems

Secret ciphers fascinate students and are an ideal subject with which to motivate them to study mathematics. Recent articles in the Mathematics Teacher, for example, have described how various types of ciphers can be taught to high school students to enhance their learning of statistics (Feltman 1979), matrices (Camp 1985), functions and their inverses (Reagan 1986), and remainder arithmetic (Meneeley 1981). Ciphering also offers interesting examples of how so-called “pure” mathematics can be applied to real-world problems (Hilton 1984).

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