This is a good point. It is different from what many people seem to mean when they talk about critical thinking today. I think they usually equate it with criticism in some way. I tend to have negative feelings about the term critical thinking myself because I usually see it used in a way that means kids are being taught to pick apart something they don’t understand. Or they’re being asked to give opinions about complex topics before they have a mature understanding of them. I think I liked the term “reverential thinking” in the article because it seemed to me that it was acknowledging the human need to feel wonder and awe for something outside of ourselves, whether we find it in music, math, art, nature, etc., rather than focusing on the child’s judgement of those things. I realize this isn’t the same thing as the definition of critical thinking that you gave though; it’s just a pushback against the way “critical thinking” is currently being interpreted.

Is there a software for creating your own math worksheets? When I search, all I find is generators that will give a whole page of problems that are all performing the same operation. This isn’t what I’m looking for. I don’t want something that creates the questions for me. I want a software that makes it easier to make number lines and bar graphs and add them to a page. I want to be able to have several types of problems on the page along with applicable images. Does anything like this exist?

If you’re planning a composer study, have you looked into Opal Wheeler’s biographies of composers? We’ve used a couple of those and enjoyed them. Another book we’ve used is A Child’s Introduction to the Orchestra. It might be young for the 14 year old, but it gives an overview of musical periods and composers as well as information about all the instruments in the orchestra.

While I don’t agree with everything in the article, I think he makes some good points about teaching tradition and reverence. Something he doesn’t address that I think is connected to this is humility. Having a reverence for what has come before you generates humbleness, which is necessary for true learning to take place. Similarly, teaching students to be critical of something before they really understand it will produce arrogance, which makes learning more difficult. If students think they know enough about a particular field to criticize it, they aren’t going to be as receptive to foundational instruction about it.

I agree that the book by Liping Ma is really good. Another one I liked is The Teaching Gap by James Stigler and James Hiebert. They studied classrooms in the US, Germany, and Japan and discussed the differences among them. The part I remember best was that American teachers felt like they needed to make math fun by adding funny word problems or silly songs, while Japanese teachers thought that math was inherently enjoyable and that students would like math for itself. In response to your question about memorization versus conceptual understanding, it seems like most books I’ve read talk about the importance of both. I’m not an expert by any means, but I have read a lot about math since we started homeschooling. I’ve read several times about how you can’t proceed to upper level math without memorizing math facts because people only have so much working memory. If you’re using all of it to figure out 9x8 because you don’t have it memorized, then you may struggle with the mental load of more difficult problems. But it’s also hard to proceed to upper level math if you have only memorized algorithms and don’t have a flexible understanding of numbers and why the algorithms work, which comes from conceptual knowledge. I’m actually reading a book right now that talks about this. Elementary Mathematics for Teachers by Thomas H. Parker and Scott J. Baldridge. Here’s a quote: “Ironically, the ability to recall these ‘basic facts’ is essential for the conceptual understanding of multiplication. It enables children to regard one-digit multiplication as trivial, which it is. That frees up short-term memory, allowing them to turn their attention to the overall structure of the problem. Conversely, children who have not memorized the basic facts will continue to think of multiplication as a procedure requiring time and attention. This can exhaust limited short-term memory. Children who do not know the basic facts are not merely slower at calculating, they have conceptual difficulties solving multi-step problems.” p. 29

Purple House Press is republishing some old Landmark books that might be of interest. Combat Nurses of World War II is available now, and Medical Corps Heroes of World War II is coming soon.

No, not really. Just an enjoyable story and preferably a range of difficulty, so all the kids could get something out of it.

I haven’t used Rightstart, so I can’t speak to that. I have used Miquon as a supplement and I have liked it quite well. Miquon guides kids into seeing patterns in math and allows them to play around with numbers in a way that most standard math curricula aren’t set up to do. I think it gives kids a deep sense of numbers, and many of the worksheets give kids the chance to create their own math problems. You have to use Cuisenaire rods with it, at least to get started, but both of my kids have stopped using them now unless they have to for a particular problem. You have some choices with the workbooks. You can work straight through them, going through multiple concepts, or you can focus on a particular concept, like addition, and do all of those problems in all of the books. We’ve mostly just worked straight through them. There is a Facebook group called Homeschool Math with Base Ten Blocks that I’ve found helpful. Their focus is more on the Gattegno books, but they do talk about Miquon too. Also, since Miquon is based on Gattegno’s methods, reading at least one of his books might be helpful to you too. “Now Johnny Can Do Arithmetic “ is a good introduction to his methods.

I try to do a group math time with my kids once a week for fun. We play a game or read a book together. What are some read aloud books for math that would be good for elementary ages?

I understand. Especially with skill-based subjects, even though I enjoy teaching them, it can get tiresome to always be doing the next thing in the book. Changing it up one day a week has been helpful for us during rough patches. So for math, one day a week we might play a game or use a supplemental curriculum. For phonics, we might have a day where we read a book together instead of doing the next thing in the curriculum. Some people do “Christmas-schooling” this time of year, where they focus more on Christmas books and activities and take a break from some or all of their regular curriculum. For our family, I try to keep the skill-based subjects (math, reading, handwriting) going, but I change up some of our content subjects. I also try to schedule regular breaks. When we start back from a break, we usually start something that’s new…a new song, new artist, new science topic, new historical period, new read aloud book, etc. (usually we aren’t changing all of these at once, but at least some of them). They are often small changes, but it gives me (and the kids) something to look forward to. The last thing I’ll add is some wise advice I received that has gotten me through rough homeschooling patches…make sure at least some of the books you’re reading your kids are books YOU really enjoy.

Following. I’ve been trying to decide the same thing.

If you look on their website, I believe they have placement tests for each level. That’s how I decided to put my kid in AAR2 instead of AAR1. This kid was able to read some level 1 readers before we started AAR2. My 5-year-old is learning letters and sounds this year but has not started putting sounds together into words. I’m planning for this one to do AAR1 next fall. I hope this is helpful. Do look at the placement tests though if you haven’t yet. I found those to be a good guide.

I think they are different enough that it would be challenging to teach phonics just from AAS. I agree with the others that reading tends to come before spelling. I would also say that AAR is just more fun than AAS, so my kid is much more compliant for AAR than AAS (although the tile app has helped tremendously with making AAS more enjoyable). With AAR there are activities for each lesson, and the readers are well done. Although both programs are good, if I had to choose between AAR and AAS, I’d choose AAR. I would agree with doing AAR1 first, and then AAR2 and AAS1 together. There is an All About Reading/All About Spelling Facebook group that may help answer your questions too.

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