I recently purchased an
an old pre-algebra book by Mary Dolciani (I got my copy for much less than advertised at that link). I also bought a slightly
newer edition for peanuts.
I wanted to compare old pre-algebra books with the newer ones. IMO, today's math books are dog's dinners of mashed up concepts that fail to present material in a coherent way. Their shortcomings are exacerbated by problems that use ideas that haven't been taught yet. Yes, they really are that bad.
So I have this book from 1973 sitting in front of me and have gone through it. The difference between pre-algebra in the 21st century and the older books is astounding. Bottom line: they're completely different courses.
The new books dive into variables in chapter 1. By Chapter 3, students are solving thorny inequality problems (it takes 2 chapters to get to these problems in a good algebra 1 book). The sections on decimals are actually just messy variable equations that happen to have decimals as coefficients. And the fractions...oh dear, the fractions.
Etc.
The Dolciani books from 1973 and 1977 are from a different world. In looking at the 1973 book, it was clearly designed as a year-long review ensuring that students had a solid understanding of maths up to an 8th grade level. Kids who already had this understanding at the end of 8th grade were expected to take Algebra 1 in 9th grade --- thus, unlike today,
there was no expectation that pre-algebra was a requirement for algebra 1. Pre-algebra was simply a review for students who needed to hone their math skills. I'll write a separate message at lunctime with the details, but the basic idea is that students were given a solid foundation in elementary and junior high math concepts:
Let's practice arithmetic and learn mathematical properties. Let's learn about different counting systems and how to convert between (for example) base 5 and base 10. Let's learn about the number line, and fractions, and negative numbers, and basic geometry, and statistics. Etc..
In looking through this book, it's easy to see that the authors understood that some students needed an extra year of review before they were ready for algebra. The material is presented in an orderly way, and stuff in later chapters reinforces stuff from earlier chapters. In looking back, I'd say about half my 9th grade class fit into this category --- and the teachers were not "at fault." No one was. Some students just weren't ready for Algebra 1 in 9th grade, and
that was completely okay.
As I think about it, I wonder if these old books could be effective tools for parents here looking for a way to compact the late elementary and middle school curricula, while doing so in an orderly fashion.I honestly don't understand how a student can be led through the new books and understand any of it in a meaningful way (unless a parental unit or tutor is filling in all the gaps). I suppose that these books play a role in the proliferation of places like Kumon and the Mathnasium, which use mathematically correct proprietary curricula.
