When my oldest son was four, a friend loaned me the tapes of the speakers at the North Dakota homeschool convention. One speaker talked about Saxon Math and how it provided a spiral approach where the kids were constantly going back and practicing previously taught material. I was sold on the value of this approach. She mentioned that Saxon only had math programs starting at fourth grade. So, I set in my mind that when my child reached fourth grade we would start Saxon Math. Until then, I would just teach him basic daily math; counting, telling time, reading temperatures, days of the weeks, counting money, etc. I picked up some clearanced preschool and kindergarten practice books from Target and that was about it.
As the time grew closer, Saxon developed programs from the younger grades. They were very involved, fulling scripted and incuded lots of activities and manipulatives. I thought the whole program was overkill and prefered a more relaxed approached to our schooling but the Target books didn't provide enough for daily or a few times a week practice. So, I just bought the third grade student workbook. I would hand him the worksheet and if there were problems he didn't know how to do, I would explain them. I didn't have the answer key, but it was third grade, I didn't really need one.
About 1/4 into the book, Tony began to ask for workbook pages, too. Tyler was getting plenty of daily practice, so sharing a page with Tony wouldn't hurt his progress. I just tore out the next page and handed it to Tony. He knew how to do everything on the page. I couldn't believe it. When asked him how he knew how to do it, he said, "By looking at Tyler's." I had noticed him looking at Tyler's homework pages after Tyler finished, but didn't realize he was really studying them. And so began the fruitless persuit of trying to keep Tony working at his grade level. He is technically three grade levels behind Tyler according to his birthday. We managed to keep him working one level behind Tyler so at least there was no fighting over the books. We even gave that up shortly into last year because he was so bored with his program.
I have really liked Saxon Math. It is very thorough and rich in material. We didn't not buy a separate reading comprehension program or science program because Saxon covered many important topics and required that level of thinking and reasoning. It has been suggested that you don't need to have the kids do all of the problems, but since we didn't have tons of curriculum to get through in the day, I didn't feel that it was unreasonable for them to complete all the problems.
The boys have always done very well on their standardized tests in Math. The first year they took the PASS tests, Tony only got two wrong. We tested him a year above his school age and the test expect the students to get only 50 percent of the answers correct.
The last CAT standardized test Tony took he didn't get any wrong on the math portion.
As the kids got older and we added more structured subjects they began to complain about doing all 25-30 Saxon problems. They couldn't understand why school wasn't getting done at noon like it used. They didn't appreciate that this was the reality of life, as you get older you expected to do more work. So, last year Mike stepped in to help choose the curriculum. I presented him and the kids with various options and he choose Math U See for Tyler's Algebra course.
Math U See recommends starting at the basic even for older students. They want you to go back and lay good groundwork. I had seen the value in the Math U See approach but since our kids were doing very well in math, I didn't feel it was necessary to go back.
Math U See also says that once a kid gets a concept, you don't need to do all the practice pages, but each practice page gets a little more difficult. According to the placement test, putting Tyler in Algebra was going to be a stretch so he has done every practice page. It has gone very well and he is happy with the new program. Like I mentioned before, part way into the year, Tony was really bored working in his PreAlgebra or Algebra 1/2 (I can't remember what it was) and so he started working in the same Algebra book as Tyler.
What's the bottom line? I think it is really important for kids to have some time everyday where you say to them, "Do this exactly this way." I wanted a very free learning environment for my kids, but it was a little too free. When it came time to following important steps and directions, they were so used to doing things their own way, they resisted.
For this next batch of kids, the only formal curriculum we will use will be Math U See and the Madsen Method for English during the early years. Those subjects and chore time will provide structured, mom-lead learning and yet allow plenty of time for reading great books together, free exploration and creativity.