Ask the grumpies: Math practice and enrichment for different kinds of learners

Natasha asks:

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?

Posted in Uncategorized. Tags: , . 24 Comments »

24 Responses to “Ask the grumpies: Math practice and enrichment for different kinds of learners”

  1. Zenmoo Says:

    I was just about to send a similar question through – I’ve got a 3rd grader who thinks she’s “not good at math” because she is amazing at English and reading comprehension and so math is by comparison ‘hard’. She gets overwhelmed by pages of numbers but was perfectly happy to work through challenging problems and concepts in the context of a “choose your own adventure “ type story. Do you (or readers) have any good resources that might appeal to a very verbally oriented child?

    • nicoleandmaggie Says:

      I can have a longer answer to this that doesn’t really answer your specific question. My first thought is to ask the school district if you can get her tested for math learning disabilities. There are several dyslexia-like LD that only affect numbers and not letters. If that’s the case, there are techniques she can learn to compensate! If that is ruled out, then you have to work on the “not good at math”– I HATE this– it is, in fact, what I spend most of my first semester required class stamping out, (and a good part of why I request to teach this class instead of fun electives with fewer students and less grading). I probably have an old post on it, and if I don’t, then I will create one. She is NOT “not good at math”– she just thinks she is. Some teacher told her that at some point or some teacher was really terrible and passed math hatred along or she missed an important class day and never recovered. Whatever it is, she will continue to be “not good at math” until she realizes she’s actually good at math. Changing the attitude changes the outcomes. If it’s not a LD, then this is not her fault– she’s been misinformed or she’s missing something, and that can be rectified.

      • Jenny F. Scientist Says:

        I have a mild form of “number dyslexia” (think it’s called dyscalculia technically, as a condition) where I can’t see the difference between multi-digit numbers sometimes. It’s relatively common! (I check my work carefully; mostly arithmetic gets me, rather than symbolic math. I no longer balance the checkbook, it never comes out right.)

        The spouse’s students often insist they are bad at math (so do mine! drives me up the wall) and he asks them how much time they’ve spent practicing…

      • nicoleandmaggie Says:

        Dyscalculia is the most common, but there are a couple related types I’ve had come through my classes. Dyscalculia can be taught neat tricks (ex. Point counting). For one of the other (more severe) types, people who have it get very good at mental math.

      • Jenny F. Scientist Says:

        I never thought about it but I guess I *do* do most math in my head if possible.

    • nicoleandmaggie Says:

      p.s. MOST kids struggle with word problems even when they can get the sheets of regular problems, so the fact that she’s not having problems suggests that no, she’s not bad at math even if she thinks she is. She may have to just suck up the boring problem sheets or practice them enough that they go quickly. (Or again, she could have a learning disability and she will get very good at doing math differently than most kids do, which is fine too. It still doesn’t mean she’s bad at math.)

      • Zenmoo Says:

        I know! I don’t think the ‘not good at math’ feeling came from a teachers comment. I think it is just that it takes an effort compared to reading (which for her, is like breathing – just something she does). Also, she compares herself to other kids. I know I used to do the same thing. I used to see myself as “not that good at math” – even AFTER I made it through an engineering degree and a thesis that involved numerical modelling. I was ridiculous. I’m guessing she is probably fairly similar to me in learning style. I had to work at math – and practicing facts was boring. By university I realised writing equations out in words stopped my eyes skipping over numbers, which was very helpful. I am also very spatially oriented. If math made physical sense and I could imagine the problem in space, I was ok. Calculus was a revelation. I focus on bribery to address boredom with math facts and re-writing or drawing concepts a different way (eg re writing 100 + 50 + 2 as
        100
        + 50
        + 2

        Oh and sticking a plain piece of paper over the page so she can only see one problem at a time seems to help. (we also do this with her piano practice).

      • nicoleandmaggie Says:

        Definitely talk to the school to see if you can get a label for her– the science of how to teach for the different types of numerical difficulties is very good (and has a lengthy and proven track record), but it differs by what’s going on. Maybe something with the word “sensory” or “processing” in the title? There’s no need to reinvent the wheel of learning strategies! (Which 2e children often do, which means the learning difference doesn’t get diagnosed.) If you have the label, you’ll be able to add to your tool-kit. (Also she’ll be able to get accommodations in exams at university if she needs more time or needs the exam set up in a certain way.)

  2. Zenmoo Says:

    Oh and the book series she liked was call Maths Quest by David Glover.

    • Zenmoo Says:

      I lied – the series is called Maths Quest but there are several different authors. I’ve also just seen another series on Amazon called Math Inspectors which looks similar- all about solving mysteries or police cases using math.

  3. Leah Says:

    For the second grader who likes drawing, have you checked out the Vi Hart videos on YouTube? She talks a lot about drawing and math relationships. Her videos go fast, but this might be a good thing to do together.

  4. Mary Says:

    One of my kids absolutely loves one of the books you recommended a while back: Hard Math for Elementary School. Loves it sooo hard that he keeps it in his bed and reads it until lights out time.

    I have never actually looked at the book myself (I know I should) but it has been an enormous hit. Hard Math for Elementary School

    • nicoleandmaggie Says:

      Yay!!! Glenn Ellison is the best! (After Martin Gardner.)

      We’re trying to figure out what to do this summer for math after DC1 finishes Hard Math for Middle Schoolers. I have a couple of geometry textbooks, but zie is taking geometry next year and they’re doing some proofs and some constructions, so it isn’t obvious that that’s the right approach. If they weren’t doing proofs I would 100% use Geometry for Enjoyment and Challenge. Alternatively, math circle made hir buy The Art of Problem Solving: Geometry, which starts with constructions and the gives a pretty comprehensive geometry program (including hard problems) and comes with a solution manual. I’m leaning towards that. OR we could just not do geometry at all. Like, it would be nice if we could teach programming, but as is readily apparent from a previous ask the grumpies, we don’t know how to go about that. Or we could do the first course in EE. Or statistics (but the AP statistics class taught in high school looks more comprehensive than the one I teach). We’re kind of at a loss for how to keep DC1 from bouncing off walls (which zie does without mental stimulation). (Alternatively, there are a number of summer camps we could send hir to at ~1K/week, but that doesn’t help for weekends, and most of them are overnight.) I should probably just write a post on this instead of blathering.

  5. gasstationwithoutpumps Says:

    Definitely Singapore Math as a core, not Saxon! Saxon is for people who want to drill, drill, drill, until the blood comes out their ears. Singapore math introduces multi-step problems early and continues to use math throughout, not doing the “we’re sin Section 7, so it must be subtraction” that so many American series use.

    A new series that is not quite finished yet is Beast Academy (from Art of Problem Solving), which is getting rave reviews from home-schoolers who have tried it. Art of Problem Solving has long had the best books for gifted math students for pre-algebra through calculus—Beast Academy extends their reach to lower grades.

    • nicoleandmaggie Says:

      Saxon has a proven track record with low to mid-ability students. It also continues to use math throughout, which is one of the benefits– students aren’t allowed to forget things they learned in previous sections.

      I suspect Singapore is good for everybody, BUT I don’t know of any tests in the low-mid range ability groups. Most of the research I’ve seen on it has been looking at entire populations. And I will say that Singapore definitely has some “we’re in section 7 so this must be subtraction”, having used it with 2 kids (we’re at the end of 1B right now with DC2). Right now we’re doing double digit addition. That’s the section. Not really different from Brainquest in that respect except in how they teach it (they’re doing it with mental math breaking things up rather than with borrowing and carrying).

    • Zenmoo Says:

      Beast Academy looks really good – I think the comic book style “guide” looks very appealing and the practice books don’t seem to have too many problems per page. Thanks for the recommendation!

  6. Lisa Says:

    These are great suggestions! I’ve been wondering what to do with my kids for the summer – I have a rising middle schooler in a gifted program who will test at the beginning of the school year to see if she should be in the “regular” gifted math or the “advanced” gifted math program. She’s like the other kid mentioned above – LOVES reading and writing and thinks she’s “not great at math”. I don’t particularly care whether she tests into the advanced class, but I want her to be in the class that will be best for her – she does like math when she “gets” it and I could imagine her being more engaged in the advanced class. I wonder if the Hard Math for Middle Schoolers would be a good thing to work on over the summer? It seems pretty focused on the IMLEM (which is connected with MathCounts? I’m not on the east coast so I’m not familiar with this), but she has done MathCounts this year and not felt up to it – maybe practice would be good? My rising 4th grader is at the neighborhood school and will be testing for their pull-out GATE program in the fall. I think he could use the extra stimulation and want to help him prepare. The Hard Math for Elementary School looks like a good bet for him. I checked out “Gotcha” from our library last summer and didn’t really “get” it – maybe I didn’t read far enough but I didn’t see anything we could really work through together.

    • nicoleandmaggie Says:

      Start with Hard Math for Elementary Schoolers for both of them– it is beautiful and fun. Mods and bases are amazing. There’s also a section in it with marshmallows and toothpicks that teaches intro to graph theory. The one for Middle Schoolers still has a lot of errata in the solutions and it doesn’t come with hints. [ETA: You can get one textbook, one solutions manual, and two workbooks.]

      DC1 isn’t crazy about Math Counts– zie just really isn’t into competition. But fun math problems don’t have to be about competing.

      Aha! and Gotcha! are for kids reading on their own. Generally they can start around 4th or 5th grade just reading the comics strips. Then they come up to you and tell you about paradoxes (This sentence is false, Who cuts the barber’s hair?) and how cool they are and different levels of infinity, and so on. Aha! also has fun puzzles. As they get older, they can start reading the dense text and if they want do some of the mathematical proofs. It’s not really a family thing, other than listening to their minds expanding. (In graduate school over dinner I once temporarily stumped the then actuarial head of social security with one of the logic puzzles from Aha!– he emailed me from the airport after he figured it out!)

    • Rosa Says:

      My now-7th grader really liked an online math program we did a couple years ago that I would have sworn was called something generic like Elements of Mathematics and had lots of non-word logic puzzle style things, and awards and magical houses like Harry Potter. I’m trying to find something similar for this summer – getting to do math is his reward for suffering through writing essays and playing piano and studying Spanish – and not having a lot of luck. I really hope someone in the readership here has an idea! I’m going to ask his math teacher too – he’ll be in “9th grade math” next year and if I could get him to do stuff this summer they won’t cover in that so he’s not bored next year. So I’m looking for something at a high school level with bells and whistles a 12 year old will like.

      He’s basically on his own for math at home, since it’s me with the summer off and I’m the one who failed calculus twice.

      • nicoleandmaggie Says:

        What is 9th grade math? At that point it usually gets broken into Algebra/Geometry/Algebra II. If he qualified for TIP or its EC/WC/Midwestern talent search equivalents he can take a 3 week course that is supposed to cram all of Algebra in, then he could skip 9th grade math and do geometry. Though I guess that would probably involve parental transportation. Hm… I don’t know of any fun sideways apps, just books. And in terms of books, since DC1 is going to finish hard math for middle schoolers soonish and we don’t want to go through it again right away (as zie suggested), I’m not really sure what we should be doing for him this summer either. I think I talked about that in a comment above and should turn it into a new post some time.

  7. sarah Says:

    Ugh, Envision math is the worst. My child’s school uses it and I have been actively trying to get them to switch for years. The math teachers agree with me, but it is difficult to convince the administration.

  8. Natasha Says:

    Math for Smarty Pants is a big hit with both kids! It reminds me of books I had growing up…. Have you ever tried Moscow Puzzles by Kordemsky?


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