I have a kid who is […] having a tough time with math (3rd/4th grade): he grasps new concepts just fine, does well on tests… and then 2 weeks later he can’t remember any of it! His school math program seems to fly from topic to topic, and even though his teacher assures me that even if he missed something this year, all the same or similar topics will be revisited next year, I worry that he hasn’t had the chance to master the basic concepts. It’s more of an issue with retention of the material than understanding the concepts. I know you love math – do you have any suggestions as to what books or methods may be helpful to practice 3rd-4th grade math? I believe it is so important for kids to get solid foundation at the elementary-school stage.Teachers simply shrug and say it’s the student’s responsibility to practice old material (well, I do agree with that) and point to Khan academy. The school is using the Envision Math program. I am terrible at explaining but love doing math puzzles and fun problems together with kids – and that doesn’t seem to be enough.
On the flip side of the coin – I have a second grader who is doing really well in math and needs more challenge. The teacher gives her additional (optional) higher-level worksheets, but my daughter doesn’t seem to be thrilled about those and prefers to read or draw. We are doing some fun logic and puzzle games at home, but maybe you have additional advice on fun math activities (books, games, workbooks) that provide additional challenge without being too much like homework?
Let’s start with the older child. There are two potential things that could be going on.
The first is that your kid is a normal kid who is good at cramming for the test and then forgetting after. This habit is so normal that much of the US math curriculum just assumes it will happen– that repeating topics thing they’ll be doing next year even has an education jargon term. It’s called “spiraling”. The best math curriculum for this specific problem is called Saxon Math, which is not the most exciting math program (it can be enervating for gifted students), but does an excellent job of repeating and integrating concepts throughout the year and not doing the standard focus and forget. There’s a good research base behind Saxon Math working well for average to below-average math students (less well for high ability and gifted). If you’re attached to a university library, you could probably check out a textbook for 4th grade to see if it is helpful.
The second potential problem is one that I saw highlighted when I did a quick google of the Envision Math program (which I hadn’t heard of before this query). Apparently Envision Math is shallow (or at least that’s what people complain about along with it being repetitive) so it is natural not to remember the concepts– there’s not really anything to remember. If what people say online is true, it’s all surface with no roots. If you want to grow roots and approach math from a completely different angle, you can’t go wrong with Singapore Math. That’s exactly the opposite solution of what my initial thought was, but after having read a few of these links of people complaining, I’ve reconsidered. Another benefit to Singapore Math is that it ISN’T the same as what’s being taught at school. Being able to do the same math multiple ways is valuable both because it keeps you from getting bored, but also because it gives a much greater context and understanding to how this magical world of numbers and mathematical concepts actually works, how it’s put together. You start seeing the full 3-d math forest and not just the shadows of the math trees. Those Aha! moments have always been my favorite part of math tutoring and teaching. Singapore Math also has a strong research base, although most of this research is done on the full population of students, not any specific group.
Given my morning’s research, I take back my initial recommendation about Saxon and suggest starting with Singapore instead. They have placement tests he can take to see which books to start with. You will need two workbooks for each year (ex. 3a/3b) and the textbook is useful. We didn’t find the home instruction guide or teacher’s guide to be useful– it was essentially a lot more examples and activities for the teacher to demonstrate, but your son is already getting the concepts, so the textbook and workbook should be enough. It probably does not matter which of the three series (US/Core/CA) you use as long as you’re consistent. We use the US editions because the other two didn’t exist when DC1 started and we wanted to reuse the textbooks.
If he also needs to know his addition/multiplication facts, we don’t really know any solution for that other than practice. Flashcards aren’t much fun, but they do cement facts and make later math easier.
Turning to the younger daughter.
Second grade is the perfect year for Math for Smarty Pants. In another couple of years you can get used copies of Aha! and Gotcha! by Martin Gardner which are super fun. She may enjoy tessellations coloring books (and creating her own using graph paper!) or folding 3-d geometric shapes. I am having a really time finding anything on amazon, but somewhere out there, there should be workbooks that show you how to use a compass to create a triangle and then other 3-d geometric shapes from that. A quick google finds lots of the basics with “compass and straight-edge construction” (and some youtube videos where people put together the already made forms) but with cardstock, tape, and something to score with you can make really elaborate 3d designs. Origami is another fun math craft– DC1 has been watching youtube videos to make shapes, but there’s also a lot of great books out there. Tangrams are perfect for this age group. This classic set from Tangoes is my favorite (mine from childhood was black, my kids’ is blue), but DC1 also really enjoyed a magnetic set that comes with a book that is occasionally available from scholastic. I found the rubix cube super frustrating, but now there are online videos showing you how to solve it so it’s more fun. DC1 also really enjoyed maze puzzle balls (and saved up allowance money to buy a second)– but I also find these frustrating. I think it depends on your agility not just the thinking things through thing. (And, as we’ve mentioned before, DragonBox is fantastic.)
If your son is willing, there are a number of card games that secretly practice concepts that they might be able to play together. I tend to like the ones that Scholastic sells off and on– they have a really good one called money madness that was a money addition/subtraction game that we liked a lot. Our kids recently each won the raffle for the university’s math day and got math games. The one currently spread all over our dining room table is a simple memory game called rat-a-tat cat, and the one neatly stacked in a tin is 7 ate 9 which is a fast little addition and subtraction game. They’re probably too simple for your kids. :/
Our math tag has a bunch more suggestions for enrichment at various stages, including items our readers have recommended in the comments sections.
Best of luck!
What enrichment would the Grumpy Nation recommend for these ages?