We have used three different math programs so far with our kids. Singapore was our absolute favorite for a long time, but we're now using ALEKS. Let me tell you a little about each so you can decide if they might meet your needs.
1. Miquon Math. We started Ga'hoole Girl with Miquon Math when she was 4 or 5 years old. Miquon is a program that is intended for classroom use in which children discover math concepts on their own. Frankly, the whole "discovery" thing just didn't work for Ga'hoole Girl. She got very frustrated when she hit an obstacle in her thinking and she wasn't in a group to work through the problem. She might have done well with this in a classroom, but she got very frustrated on her own. The final straw came when they introduced negative numbers. They had her do subtraction until she got to 5-6 (or something like that). Ga'hoole Girl just started crying. She couldn't handle it. So, Miquon got shelved.
2. Singapore Math. You will probably hear all kinds of great things about Singapore Math because their students test so much better than US students in math. There are lots of things that go in to test results, but I will say that this curriculum is quite good. Ga'hoole Girl used it up through level 6 (about Grade 7 in the US) and Wild Man used it through level 3 (about grade 4).
The Good: Singapore Math is very strong in mental math. They want the kids to understand how to use numbers in their heads and on paper. They don't teach shortcuts until the concept behind the shortcut is well-developed. There is plenty of review, but not so much that it is overwhelming (and you can purchase extra books for kids who need more review). They are also very strong on word problems. And, not just word problems for the sake of word problems. The curriculum is big on being able to use math, so the word problems are to help kids really understand how to use math. The books are also quite inexpensive.
The Not-so-good: Singapore uses a different order of introducing concepts, so kids may have a hard time transitioning to public school math. I had to put both kids in lower levels of ALEKS than I expected because of this. The original books all use metrics and Singapore money, but there are now US versions that use American money and metric and English measurements - so check what you are ordering. The elementary books don't have answers, so you might want to get Sonlight's parent guides for the upper levels (after about level 4) to help grade the work and understand the problems yourself.
Why did we switch? Ga'hoole Girl was in Singapore level 6 and was getting to where she needed more explanation than she had previously. The textbook explanations are really pretty good, but Ga'hoole Girl was impatient. They also had her doing things in ways that I hadn't learned, so for me to explain them required that I go back to the text and relearn it. I was also having trouble keeping up with getting everything corrected, so the kids might misunderstand a concept and not get feedback for a week. I felt like we needed something with more immediate feedback and explanations that didn't always require my input.
3. ALEKS Math. ALEKS is an online subscription math program that can be used as a stand-alone math curriculum or to help kids struggling in school. It can also be used to help tutors (as Mr. Math Tutor is learning). Basically, you choose a level for your child and they take a pretest to see what they know. They get a pie chart with each pie slice representing a set of math concepts that they need to master (number theory, geometry, etc.). Each time they log on, they can choose which pie piece they want to work on (although there are times that they can't go any further on one section of pie until they finish a concept in another part of the pie). For each concept, they are given a problem. If they can do the problem, they are given several more until they show that they understand it and that section of the pie is filled in (actually, they get the same concept a few more times in review before the program considers that they have completely mastered it). If they can't do the problem, they click for the program to explain it. The program then explains how to do the problem step by step. Then, they are given another problem to try. If they miss the problem, ALEKS explains it. There is also a QuickTables feature that helps kids learn their math facts.
The Good: My kids love doing ALEKS. Wild Man's math (level 3) has a little dog called Aleks who does the explanations. Wild Man is a little past the character thing, but I can see how this could be helpful for younger kids. Both my kids love seeing how their pie is filling up. The explanations are very understandable and the kids rarely require much help from me. I love that they get immediate feedback. They are both moving very quickly through the program. ALEKS sends me reminders to check their progress monthly. It's very easy for me to check how they're doing and make any changes to the program. I can request retesting or move them to a different level as needed.
The Not-so-good: This is a subscription program, so if your kids don't use it real frequently, you may pay more than if you used something like Teaching Textbooks. Wild Man still needs me to read to him sometimes, but that's not unexpected. So far, I haven't seen lots of downsides.
4. Key To . . . This is a set of workbooks designed for middle/high school age kids that cover a particular concept. We used Key to Fractions with Ga'hoole Girl. She loved the four workbooks and learned fractions inside and out. Since then, she has done lots of review with Singapore and ALEKS and really knows her fractions. We haven't used any of the other books because she seems to be learning well with ALEKS. But, if Ga'hoole Girl were to need extra work on a concept, I wouldn't hesitate to use this series.
This has been our math journey so far. I'm really liking how easy ALEKS is for me and how much the kids like it. They are also learning quite a bit. Hope this helps you in your homeschooling journey.
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