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"Geometry, Analytic Study and teaching."
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Practical linear algebra : a geometry toolbox
\"Practical Linear Algebra covers all the concepts in a traditional undergraduate-level linear algebra course, but with a focus on practical applications. The book develops these fundamental concepts in 2D and 3D with a strong emphasis on geometric understanding before presenting the general (n-dimensional) concept. The book does not employ a theorem/proof structure, and it spends very little time on tedious, by-hand calculations (e.g., reduction to row-echelon form), which in most job applications are performed by products such as Mathematica. Instead the book presents concepts through examples and applications. \"-- Provided by publisher.
Book
A graphical user interface tool to teach plane curves in pandemic situations through a flipped classroom
During the pandemic and lockdown situations of the last few years, we transitioned to online, physical, and hybrid education approaches at various times. We had difficulty teaching multiple calculus and analytical geometry units online. In light of the current situation, a graphical user interface (GUI) teaching tool has been developed to teach university students many plane curve modules through a flipped classroom. With a few inputs and a single click as output, these executable spreadsheets can assist physics and mathematics students in practising several principles of analytical geometry. Spreadsheets can readily draw planes in three-dimensional geometry due to their widespread use. Some online vector GUIs present the results; however, this GUI conveniently illustrates the plot. The well-designed user interface also helps create new questions with answer keys and gives access to the teachers of physics and mathematics, which can make online teaching very easy. The effectiveness of this GUI was checked through Kolmogorov-Smirnov and Shapiro-Wilk tests, and a good agreement has been found in the results. Contribution: This article contributes to Mathematics teaching through GUIs.
Journal Article
Geometry essentials for dummies
Geometry Essentials For Dummies (9781119590446) was previously published as Geometry Essentials For Dummies (9781118068755).While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.
eBook
Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics
Have you ever daydreamed about digging a hole to the other side of the world? Robert Banks not only entertains such ideas but, better yet, he supplies the mathematical know-how to turn fantasies into problem-solving adventures. In this sequel to the popularTowing Icebergs, Falling Dominoes(Princeton, 1998), Banks presents another collection of puzzles for readers interested in sharpening their thinking and mathematical skills. The problems range from the wondrous to the eminently practical. In one chapter, the author helps us determine the total number of people who have lived on earth; in another, he shows how an understanding of mathematical curves can help a thrifty lover, armed with construction paper and scissors, keep expenses down on Valentine's Day.
In twenty-six chapters, Banks chooses topics that are fairly easy to analyze using relatively simple mathematics. The phenomena he describes are ones that we encounter in our daily lives or can visualize without much trouble. For example, how do you get the most pizza slices with the least number of cuts? To go from point A to point B in a downpour of rain, should you walk slowly, jog moderately, or run as fast as possible to get least wet? What is the length of the seam on a baseball? If all the ice in the world melted, what would happen to Florida, the Mississippi River, and Niagara Falls? Why do snowflakes have six sides?
Covering a broad range of fields, from geography and environmental studies to map- and flag-making, Banks uses basic algebra and geometry to solve problems. If famous scientists have also pondered these questions, the author shares the historical details with the reader. Designed to entertain and to stimulate thinking, this book can be read for sheer personal enjoyment.
eBook
On the teaching of linear algebra
Presenting research on the teaching and learning of linear algebra in the first year of university, this text aims to give university teachers in charge of linear algebra courses a wide range of information from works including theoretical and experimental issues. These works try to better understand the meaning of linear algebra in an epistemological approach, as well as the constraints and the difficulties in its teaching and learning. They also present teaching designs with the analysis of their experimentation. Elements of reflection are given to the reader with keys for his or her own experimentation. Through the variety of the works presented, this book also discusses theoretical issues which are consistent for all research in maths education at tertiary level.
eBook
\The Square Thing\ as a Context for Understanding, Reasoning and Ways of Knowing Mathematics
This paper introduces The Square Thing, a lesson that engages and invites student development of problem solving and reasoning skills, understanding through connections within the content, and mathematics voice. A background for the lesson, an enrichment topic that allows the teacher to set the stage for the problem, is described first. Next, The Square Thing is introduced, along with a discussion of student solutions and pedagogical notes grouped in sections as Estimation Approaches, Coordinate Geometry Approaches, and Parallel Line Approaches. A pedagogical discussion ends the paper, in which components for successful pedagogy and benefits for students experiencing this and similar mathematics pedagogies are described.
Journal Article
Stitching Quilts into Coordinate Geometry
Presents an activity using quilts for many mathematical investigations. Benefits arising from the use of quilts include being useful, visually appealing, steeped in history, and an integral part of many cultures. (ASK)
Journal Article
TIPS FOR TEACHING CARTESIAN GRAPHING: LINKING CONCEPTS AND PROCEDURES
Discusses activities to teach Cartesian graphing to young children in a conceptual way. Activities are organized around the concepts of finding one's way around in a plane and using the plane to represent variables in two dimensions by graphing equations in the usual way. (25 references) (MKR)
Journal Article