My wife and I homeschool our kids. My wife and I were also both homeschooled. We both did Saxon math through highschool. For me it was hard, boring and great. After about 9th grade I basically just opened up the textbook and worked through the thirty or so problems every day. They were repetitive lessons with a short paragraph about the concept and how to do an example problem or two. There was not much detail or explanation in the textbook. This forced me to work out the underlying concepts myself and I knew trigonometry, algebra and basic mental math better than most of my peers by the time I went to college.
My wife is more of a visual hands on learner and suffered through the same text books. In college she had a series of bad professors (like, cancelling class because the professor had a hangover bad) and this just cemented her view that she was bad at math.
All that long exposition is to say that people learn different ways and a "bad" method may result in a good outcome. Learning is a complex interplay of teacher, student, material and presentation that can be different for every person.
When I teach my kids I like to have them all in the same lesson even though they are different ages and doing different levels of work. The primary purpose of this is to just talk about math, make it normal to think and reason about it and show that it's not scary. Math concepts are often taught as a series of ever increasing obstacles to be jumped over. You jump over them until you reach a ten foot wall that you just can't summon the mental power to leap over. Then you are bad at math.
But math is more like a hike. you start out in the foothills where even your 5 year old can keep up with the rest of the family. Each footstep is a little closer to the peak. You are making progress and learning even if you only make it to the first mile marker. You get fitter and accumulate some equipment and technical skills for the mountaineering sections higher up as you go. It's challenging but fun and you have a sense of accomplishment no matter how high you are. As you get higher the vistas opened up to you show you the world in ways you could never see lower down and give you motivation to go forward towards higher peaks and better views.
Saxon was a great math program. I worked my way through the Algebra 2 book in 7th grade, and coasted on that until I reached college. For some reason (ahem-one of the teachers helped write it-ahem) my high school used a different, much shittier math program. Until the second half of my senior year AP calculus class, I didn't have to cover anything that I hadn't done in the Algebra 2 book.
Particularly for things like manipulating and simplifying systems of equations, the Saxon program was great, simply because it was built on repetition and practice - you would work through dozens of problems of a particular category over time. The other thing that was very nice about the Saxon program was that it would revisit older concepts - the problem sets would not just be on the current chapter concepts, you'd also have to work through material that had been covered over the previous 15-20 chapters. My mother is a special education teacher, and she's had success even with children that have serious memory deficits, because the repetition will pound the knowledge through into short, medium and long-term memory.
Yes the repetition can be really boring and some of the problems, even the easier ones from previous lessons can take a while to solve. But I still remember the concepts from algebra 1,2 and trig and can pull them out and apply them in real world situations. I had to build a gaga pit[0] for my towns school just this past weekend and some basic trig definitely came in handy there.
My wife is more of a visual hands on learner and suffered through the same text books. In college she had a series of bad professors (like, cancelling class because the professor had a hangover bad) and this just cemented her view that she was bad at math.
All that long exposition is to say that people learn different ways and a "bad" method may result in a good outcome. Learning is a complex interplay of teacher, student, material and presentation that can be different for every person.
When I teach my kids I like to have them all in the same lesson even though they are different ages and doing different levels of work. The primary purpose of this is to just talk about math, make it normal to think and reason about it and show that it's not scary. Math concepts are often taught as a series of ever increasing obstacles to be jumped over. You jump over them until you reach a ten foot wall that you just can't summon the mental power to leap over. Then you are bad at math.
But math is more like a hike. you start out in the foothills where even your 5 year old can keep up with the rest of the family. Each footstep is a little closer to the peak. You are making progress and learning even if you only make it to the first mile marker. You get fitter and accumulate some equipment and technical skills for the mountaineering sections higher up as you go. It's challenging but fun and you have a sense of accomplishment no matter how high you are. As you get higher the vistas opened up to you show you the world in ways you could never see lower down and give you motivation to go forward towards higher peaks and better views.