This book is not Euclid's "The Elements". The Elements, a compilation of many mathematicians' work, was written for mathematicians and their math-dedicated young disciples. Its opening proposition and complex figure reveals that the reader was expected to have a substantial degree of preexistent geometry knowledge.
To reach high school students who have only completed Algebra I, Jurgensen et al labels some theorems postulates to avoid getting bogged down, but so do the other high school geometry textbooks.
This book fulfills its mission to introduce students to a formal system of mathematically analyzing planar figures and objects. If it is carefully read and digested, every problem, including the most-challenging C and C-starred exercises, is solvable. Problems that require the student to write a half-dozen solution/proof statements, and remember (or refresh themselves by re-reading) material from prior sections, and even prior chapters, are commonly encountered (always for the C-level problems).
A small number of exercises require a dozen or so statements in which a student establishes one line of argument, then introduces another, and finally combines them, which is to say, students must be able to organize their thoughts into coherent streams, and then engage in translating visuo-spatial information into mathematical-language statements.
Is this hard? Yes. It takes not only intelligence, but serious effort to fully benefit from studying Jurgensen. Real math isn't something you breeze through. As a student encountering the material for the first time, you may frequently have to read a passage or statement several times, thinking, "I don't get this," then maybe even sleep on it, and then you'll have Eureka moments, "Oh yes! Why didn't I see this before? This is so obvious."
For anyone who wants to think about pursuing university studies in mathematics, engineering, and the sciences, acquiring diligent, persevering work habits is essential. Mathematics is not social studies. For some students the challenge is enjoyable, for others it is painful and a "waste of time". For teachers who find that their students can only consistently answer A-category problems, hit or miss on Bs, and can't even begin to tackle Cs, this book will probably not be satisfactory.
A larger question is when should Euclidean geometry be taught? Should it be taught at all?
I think it is disruptive, and counterproductive to teach algebra I, leave the subject for a full year to study geometry, then jump back to algebra. The trouble is that the "classical" curriculum of the 19th century only taught one course in algebra and then one course in geometry. But as mathematics education was extended, particularly during the Cold War, geometry held its place as the second course in the timetable, but was followed by additional algebra, pre-calculus and calculus, with insufficient thought given to the utility and efficiency of this particular sequence.
Measures such as focusing on analytical geometry (coordinate) exclusively, or nearly so, or teaching algebra II with trigonometry before Euclidean geometry, have been tried in some schools. I know of two schools that no longer even have a "Geometry" titled class. These and other alternatives seem to be working, according to people who are using them.
One thing I would point out is that most state high school graduation requirements today specify the completion of three mathematics units, and many universities require or recommend such. They DO NOT say "three mathematics courses, including geometry". So, for example, if a student is doing well in algebra, I'd say to him or her, stick with it. Go on to algebra II (preferably with trigonometry), precalculus and calculus. Learn about plane figures and solids from a modern perspective. (I can still remember generating the volume of a sphere using integration, and drawing a nicely shaded 3D sphere and discs thirty-something years ago in my second semester of calculus. I thought, "Wow, this is cool!")
So, I think schools should be flexible in their math curricula, and realize there is not a college or university in the country that will ever look at an applicant's transcript and say, "This student took AP Calculus, but there's no 'Geometry' here. Rejection."
If this book is to be used, I would recommend a couple stratagems. One is to for the student to try to prove its theorems before examining the authors' proofs. It's not hard to cover them up with a sheet of paper. This encourages students to acquire conceptual knowledge through active pursuit.
Secondly, students using Jurgensen or most other popular geometry books should subscribe to hotmath.com, where odd-numbered exercises solutions are presented in a thoughtful way, starting with a hint, then progressively revealing steps as the student feels the need to examine them for more help.
There was initially a mixed reception among educators to Hotmath, with some teachers enthusiastically signing up to provide solutions, while others were discomfited by an external knowledge resource that they felt undermined their ability to maintain traditional authority-control over what their students learned.
The disagreement was resolved. The American Mathematical Society invited Hotmath's president to give a lecture at one of its regional conferences several years ago, which was well received. All the leading textbook publishers got on board, which is to say, they recognized that the college-level promulgation of student solutions manuals starting two decades ago had proven to be heuristically sound, and the principle was applicable to college-preparatory mathematics.
For even-numbered exercise homework assignments, students can usually tackle the neighboring odd-numbered ones, check the Hotmath solutions, then apply the same principles to their homework problems. |
I have taught Honors and College Prep Geometry with this book (and its previous edition) for sixteen years.
This year I tried a different book with one of my classes. I am begging to go back to this book.
This book does not have all the 'bells and whistles' of new Geometry textbooks. It doesn't need them. My new textbook has powerpoint presentations, lesson planners, CD ROM testbanks, etc. Guess what? You can have them. They don't present lessons in any manner I would present them, and the test banks don't test the content of the chapter. In addition, I prefer to supplement lessons with my own real life examples and further explanations, not 'canned' material that is found in my current text and its technology.
A good teacher can take this book and raise the bar for academic excellence. No fluff, nothing watered down.
Newer is not better.
I know my students were given a mental workout-challenged themselves- and understood Geometry when I used this book. My classes will be going back to this book soon.
To the reviewers who say there aren't enough examples, that's the point! Geometry is about developing a skill. You can't build a skill if everything is given to you. Push yourself a little harder, don't be afraid to fail, and ask questions. That's how you learn.
The one con is that test questions are not available on a modern CD ROM, eliminating the need to cut and paste (and not giving the ability to change test versions with a click of a button).
Still, the test questions supplied are fantastic.
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