Saxon Geometry is a new addition to the well-known Saxon math series. Until this point, geometry instruction in the Saxon textbooks had been integrated into Algebra 1 and 2 and Advanced Math. In the Singapore Math program, the approach is similar, there is no separate geometry course included in the four standard secondary level Singapore Math series of books. Like Saxon, Singapore Math does offer an optional separate course suitable for 9th or 10th grade students.
There are advantages to the integrated approach. Understanding the geometrical concepts as they fit into the “big picture” of algebra and other math may boost overall success in math. Asian and European countries that follow the integrated approach consistently rank higher than the US in international math test scores.
However, supporters of a separate geometry course point out that a thorough understanding of geometrical reasoning is more difficult to obtain when the concepts are broken up and interspersed with algebra. The logical training provided by working traditional two column proofs is also a valuable aspect of geometry that’s missing from the integrated programs.
Saxon’s publishers recognized this and have produced a text that focuses solely on geometry, and includes work with proofs. The book maintains the characteristic format of other Saxon books, with lesson and examples followed by practice set then problem set. The problem sets continue to provide a comprehensive review, with small margin numbers alerting students to the lesson in which each type of problem was first introduced. Algebra problems are frequently featured in the problem sets, to keep students fresh on the subject. The course typically would be taught in the tenth grade.
The geometry course from Singapore Math is a course in plane and solid geometry. It, too, is a dedicated geometry curriculum, which, if anything places more emphasis on proofs than Saxon does. The review is handled in typical Singapore style, which means the chapters are organized so that each one builds on and uses the previous material, so that there is natural review. A little more than halfway through the book, there is a set of review exercises which can be assigned as the teacher sees fit.
Overall, the whole Singapore Math program seems to be more logically organized and slightly accelerated in comparison to Saxon. The concepts in Saxon’s math series are broken down into small increments and taught in an order having little to do with the natural order of mathematics. John Saxon advocated teacher training in the use of his materials so that teachers could point out the connections among concepts and give students the sense of the “big picture” that was lacking in the ordering of their textbooks.
Some teachers and homeschoolers have complained that Saxon produces students who are competent at calculating, but have little understanding of mathematical thought. Due partly to the teaching and drilling of concepts in tiny incremental pieces, and partly to the fact that those pieces are mixed up together in seemingly no particular order, students tend to become highly skilled in mathematical methods, with little grasp of mathematical concept. Thus they score well on tests, while having missed an important result of the study of math. Singapore math is less vulnerable to this criticism, being carefully ordered according to a logical progression which is recognizable with far less teacher explanation needed.
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