A freshman taking geometry without algebra first usually encounters a book that assumes a first year of algebra. All the texts for high school geometry that I have seen require a background in algebra. In fact, the more recent the text the more the book is filled with problems that require basic algebra to solve.

I have found however that at least in the introductory chapters of the current geometry, texts demand only a rudimentary knowledge of algebra which is mainly solving simple equations. After dealing with some of the non-algebraic material in the geometry book, I determined that spending about a week introducing students to the rudiments of algebra such as solving equations in one unknown and some basic work on signed numbers and like terms is sufficient to get them ready to solve the problems in the text. I try to do two concepts a period such as using the addition property and using the subtraction property of equations and with a week’s work capability of the students can be achieved.

The problems with algebra also enter into the lessons on the Pythagorean Theorem. For students with no algebra background, we must spend time learning to solve equations, squaring numbers, taking square roots, and reviewing the addition and subtraction properties of equations. Usually, the elementary math background covers some of these topics, but without the algebra course, most students would have difficulty. Therefore, the time taken on the Pythagorean Theorem is about three or four days including the algebra basics.

One of the most difficult problems encountered in a first year high school geometry course is the newness the deductive method and qualitative method of proof of the theorems, postulates and corollaries. I have found that freshmen are not used to this type of thinking at all.

For most of their lives, high school freshmen have been used to calculating, as have most adults, and when they encounter a course that is mainly composed of words and deductions, it takes them some time to learn the methodology involved in reasoning in proofs, for example. In this respect, I have to provide simple proofs as drills on ditto paper to get the students into the mental framework for dealing with harder proofs which involve more complex reasoning. Because the newer texts have many more problems involving algebra and calculating, the problems the students have with the verbal-deductions are a little lessened at present, although some of the proofs involve algebra.

My impression is that a first mathematics course in high school such as a Euclidian Geometry course with deductive proofs must be watered down because of its difficulty for new high school students. When a student has a year of algebra behind him, it seems to make a difference in the student’s performance. Although our first year requirement of geometry puts all freshmen in the course, we received transfers from other schools, and other students who for one reason or another have had at least one year of algebra and sometimes even algebra-trigonometry.

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