maths-screaming

[maths-screaming]

Numi-numi-numicon

I ordered a set of Numicon tiles sometime before Christmas. They finally arrived.

They're pretty neat, from a sensory perspective. Each set is a different color, and they're weighted so (for example) the 2 tile is exactly twice the weight of the 1 tile. My fingers fit perfectly in the holes. They make satisfying clicky noises.

At first, I had no idea what I was going to do with them. I ordered them back when I still trying to teach my brain basic numbers. Did I really still have a use for them now, two months later?

Then I started playing with them. And yes - these are perfect for some of my brain's particular hangups about basic numbers.

Putting anything on top of the 10 tile makes it immediately obvious what the relationship between that number and 10 is. 10-7 is 3. 17 is 3 away from 20. And so on. I don't have to remember arcane symbols for that or take someone's word for it - the Numicon tiles make a law of physics for me.

As I've mentioned in previous posts, my brain wants proof of things - especially when dealing with basic numbers, where my entire math education was "memorize these random things we tell you are facts, no it doesn't matter if you understand them."

I've known for a long time that 1+2+3+4=10. But the dopamine rush of getting to see that! Of having the Numicon prove me right! So good.

Being able to break numbers down is cool too. The set only came with one 5 tile, so here's 5+2+3.

1+2+6=9, visualized. Ugh. So satisfying. So memorable. So much more trustworthy than "here is a shape that could be a letter but isn't, memorize exactly how many Things it is, what do you mean how do we know that this many Things is this Shape, it just is that many stop asking so many questions."

[maths-screaming]

Division by 1 is tyranny

Sam gets the guillotine.

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In which I do some coloring

Discovering that numbers have patterns and relationships is absurdly exciting to me. If someone had told me this at any time in my childhood, I might not have feared and hated math so much.

So I printed this 1-100 number chart I found online and colored it. Numbers 2-9 are each assigned a color, in rainbow-esque order (pink, red, orange, yellow, green, cyan, indigo, violet). Each square has a stripe representing each color it is a multiple of/can be evenly divided by. When I ran out of stripes, I finished filling in the square with the final stripe to indicate "that's as far as this number goes."

Is it useful? idk. Was it fun? Very much so.

Numbers are friends. Friends have relationships. Now I know who not to seat next to each other at my (imaginary) wedding. Whee.

[maths-screaming]

All the observations I can make about this feel repetitive at this point

My elementary math teachers would have strenuously disagreed with the notion of using number discs to help here. (N.b. the "number discs" in question are labeled 1s, 10s, etc - nobody is counting out 798 individual poker chips.)

I'm very good at messing these up on paper. Even when I use graph paper to keep the columns straight. (N.b. I was not allowed to use graph paper to keep the columns straight in school; that was an innovation my dad hit on because his own fifth grade math teacher let him do it, but my fifth grade math teacher vetoed it on the grounds that "she needs to learn to do neater work." Which...was the point of the graph paper? To teach me to do columns properly?? ugh. anyway.)

I can actually do 104 divided by 8 in my head now, which feels like a MASSIVE and COMPLETELY UNEXPECTED BUT IN THE DELIGHTFUL WAY breakthrough, given where I was when I started this project.

I do it in my head by doing it left to right, aka the way we were taught not to but that actually works better for me (see a couple posts ago).

Doing DIVISION. In my BRAIN MEATS. WHO KNEW.

[maths-screaming]

These books are no match for ADHD

Bold of you to assume I have *any* sense of how time works, textbook editors.

[maths-screaming]

Variations on A Mathematician's Lament

(If you've not read "A Mathematician's Lament" by Paul Lockhart, please do so. I'll wait.)

A friend sent me this delightful long essay/short book several weeks ago. I've now read it twice. Though, to be honest, he had my (horrified] attention at "imagine we mandated 12 years of music theory classes before ever letting a child touch an instrument."

Lockhart explains beautifully the problems with current K-12 maths education, aka the Recipe for Mass Maths Anxiety in a General Population. He doesn't dig into solutions for this problem, but my takeaway is this:

Any mathematics education worth anything has got to involve play.

Incidentally, I also think play is the cure for math anxiety, too.

In an effort to unravel my own crippling math anxiety, I have been approaching this entire process as play. I bought the colorful toys no one let me play with as a kid. I spent last night watching reruns of Star Trek: Voyager* and coloring a 1-100 number chart in rainbow stripes so I could see where all the multiples of 2-9 overlap. Last week I filled two entire pages in a notebook with addition/subtraction and multiplication/division "facts families" in various colors of felt-tip pen. Just because I could. Because it was fun.

When the anxiety creeps back, my go-to mantra is "Numbers are friends. We play games with friends." And then I play around until I figure out what I'm trying to do.

Humans are hardwired to learn through play - to follow our curiosity to a thing, then mess around with it until something happens.

Play is probably not a cure for dyscalculia (but what do I know, I'm not a neuroscienceperson), but it does seem to do wonders for my math anxiety.

---

*Seasons 5-7 are a meditation on what happens when no one will confront that one toxic family member for fear of what will happen to them if they're the first to step out of line. But I digress. This is not a blog for my crackpot Star Trek theories. Lmk if you want that blog.

[maths-screaming]

Doing Mental Math the Way I Was Always Told Not to Do Mental Math

(Maths - No Problem 4A)

Today I learned my brain has relatively little issue doing these problems if I do them left to right, as on a soroban.

In my head, 8x512 sounds like "40 hundreds, 80, 16, 4096."

I was taught not to do these left to right, since it risked not carrying tens or whatever. But it makes FAR more sense to me to do it that way than to try to hold these numbers in my head in both directions at once.

Curious to see how this goes when we start multiplying three-digit numbers by two-digit numbers.

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Another Thing I Was Not Allowed to Do In Arithmetic As a Kid for Absolutely No Good Reason

Suppose you have to divide 1143 by 27.

You put it in the little house-bracket thing. You figure out that 27 won't go into 11; you need to know how many 27s will fit entirely into 114. How do you do this?

No, seriously. Asking for a me.

This was never something I could guesstimate in school.* Instead, I'd fill the margin of my paper with "27x2, 27x3" and so on until I found the "Price is Right" answer - the number as close as I could get to 114 without going over.

I got marked down for this every single time. Even if all the math within the margins was correct.

I was never told what I was supposed to do instead, though. Just guess? Wi-fi that info into my skull (some 20 years before wi-fi existed)? What?

What was I supposed to do if I couldn't just estimate the answer?

I suspect I will never know.

--- *Today I can look at that and go "well, four 25s will fit in 100, and four 2s will fit in 14, so four." But I can only do that now because I've been taught how to do that. I wasn't taught that as a kid.

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Reading Books on Dyscalculia

Books on dyscalculia may have started this process, but they haven't been terribly helpful mid-journey.

Which isn't to say I don't recommend them! Especially if you are a parent or teacher of students with dyscalculia, or if you are trying to understand your own dyscalculia!

It's just that I expected them to offer more insight into the condition and more concrete ways to address it, and most of them...aren't. At least, they're not telling me anything I haven't figured out on my own from re-learning basic arithmetic with current best practices in teaching.

The facts are:

We don't actually know all that much about dyscalculia currently. The reams of research on dyslexia don't have a counterpart for dyscalculia. That research is currently being done - it's a very exciting time to be in the field - but it'll be 10-20 years before you and I can just go read works on dyscalculia that have the same depth and rigor as works on dyslexia do now.

We know even less about dyscalculia in adults. Less of everything. We know less about how it affects adult lives, how it affects adult cognition, how adults work around it, and how to teach adults.

Good luck finding resources on dyscalculia in teens and adults tackling advanced math classes. The overwhelming majority of resources are for teaching early number sense, counting, and basic arithmetic.

On point 3, I think of myself as an ad hoc test subject: I'm going to find out if I learn* algebra, trig, and stats more easily once I finally understand basic arithmetic. I'm going to see if the strategies and approaches I'm using for relearning basic arithmetic carry through, and if so, how far. I haven't yet found any books or resources that answer that question for me.

But if you are a parent or teacher of kids with dyscalculia and/or you want to read up on what we do know, here's what's on my reading list currently:

Dyscalculia: Action Plans for Successful Learning in Mathematics, by Glynis Hannell. An overview of teaching/tutoring strategies for early learners. Most of these recommendations will work best in a one-on-one or small group setting, so I'd actually recommend this book for parents more than for teachers.

The Dyscalculia Resource Book: Games and Puzzles for Ages 7 to 14, by Ronit Bird. A collection of games and puzzles to teach number sense, arithmetic facts families, and so on. Pretty thin on the why and how behind dyscalculia, though.

The Trouble With Maths: A Practical Guide to Helping Learners With Numeracy Difficulties, Steve Chinn. Steve Chinn's name appears on several books on dyscalculia at this point (not all of which I could find through interlibrary loan). This book is a blend of theory and practice; it's not exactly recreational reading, but it's very insightful.

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*I'd say "re-learn," but I didn't really learn any of middle or high school math - at least not in a way that allowed me to retain any of it, with the notable exception of geometry.

[maths-screaming]

Division With Concrete Blocks

I have reached long division with remainders.

Division with remainders was a turning point in my math experience. I'd struggled with math lessons before, but division with remainders was the first time I really felt stupid. The first time I really believed I was just not good at math. The first time I believed that people who didn't struggle with it were objectively smarter than I was.

In hindsight, and with Maths - No Problem Textbook 4A open in front of me, I realize none of that was true. Once again, I was taught badly.

Specifically, I needed a concrete introduction to long division with remainders, and we didn't get it.

Maths - No Problem* introduces long division with remainders in an extremely concrete way. It literally begins with "this child has 11 balloons and wants to share them equally between her two friends. How many balloons does each friend get, and how many are left over?"

It does this with all kinds of things that would appeal to kids, complete with pictures: Cupcakes, candies, toys.

And, as I mentioned in my previous post, it doesn't get anyone hung up on the term "remainder." It's always presented as "how many does each person/box/plate get, and how many are left over?"

"Everyone gets the same number" and "leftovers" are concepts kids understand - often before they can count reliably. In hindsight, it boggles me that my own math education deliberately avoided discussing division in those terms!

The text even gets more abstract in the most concrete way possible: with money. How many $4 books can you buy with $30, and how much change will you have left over?

(These books were clearly not written in a country that adds sales tax at the till, haha. The book thinks the answer is "7, with $2 left over," but where I live the answer is "7, with $0.32 left over." In some states it's "6, with varying amounts of change left over.")

So far, the most frustrating part of this math relearning journey is discovering that my dyscalculia is maybe 20% of my problem; the rest is poor math education.

The best part is discovering that my dyscalculia is only maybe 20% of the problem. And I can fix the rest.

---

*I'm not trying to sell anyone on these books in particular - they're just what I have in front of me, and they're working for me. I absolutely am trying to sell people on the basic principles they use, however, including "make it concrete."

[maths-screaming]

Maths-Anxiety-Proofing Your Child (or Yourself): Some Suggestions

The Maths - No Problem textbooks have now introduced factoring.

I loathed factoring. Like, more than I disliked math classes generally. Factoring made no sense to me. I could parrot the explanation, but I did not see why I had to do it, what it was for, or when I'd messed it up. It was yet another bunch of mystifying crap that I memorized long enough to not-fail a test and then tried immediately to forget (to make room for the next bunch of mystifying crap I'd need to memorize long enough to not-fail the next test).

Since my on-ramp is better this time around, factoring makes more sense to me now. I also recognized it when it appeared despite the book never calling it "factoring," which excited me.

By comparing my current experience to how I originally learned about factoring, I've gleaned a few helpful tips on how to avoid developing math anxiety in kids or mitigating it in oneself, which are:

Don't try to pole vault from a standstill. Don't tackle or introduce topics without a solid understanding of the topics on which they're based. Back up to something you do understand and take a "running start" at the topic you don't. (I backed up all the way to "here's how to count to 20" - your/your kid's needs may vary.)

Build relationships. Factoring mystified and worried me as a kid because I didn't fully understand multiplication relationships. To me, multiplication was a bunch of random packets to be memorized (we weren't even allowed to use a table!). Having rediscovered multiplication as a series of relationships among numbers (and their family members, division) helped a lot when revisiting factors.

Play games, draw pictures, make it fun. The Maths - No Problem textbooks do this, literally. As in, one activity has students play in pairs; one chooses a number card and the other has to write down all the ways you can multiply two numbers to get the number on the card. Doing this led me to discover I can make "number lines" to check that I've got all the available factors. Play games, move beans around, whatever it takes. Numbers are friends! We play games with friends!

Don't get hung up on the vocab. Part of my problem in middle school was that the word "factors" was a field in my personal database that never populated with content. It returned a mental "file not found" error every time. I don't know why, but it did. The Maths - No Problem text doesn't use the term "factors" at all; it always presents factoring as "what numbers can you multiply to get [result]?"

As I often say when explaining my decision to genrefy the high school library I run: "Kids don't need to know that Dewey shelves poetry under 811. They do need to know that we have poetry and they are capable of finding and reading it."

Build the poetry collection and lead kids to it first. They can find out it's called "factoring" later.

[maths-screaming]

I Got Distracted by Internet Security and So Should You

Taking a scream break to fix my messy digital footprint, per this extremely useful and usable guide:

HIGHLY recommend.

[maths-screaming]

Known and Unknown

A couple days ago, I wrote:

My math education thought I could manage strings of confusing symbols in my head in two directions at once, but that I couldn't do any problem that required me to identify the unknown in relationship to the known. ?????????

Because of my Quest to Be Friendlier With Numbers, my take on my K-12 math education changes almost daily. The bottom-line take, "My K-12 math education was bad," stays the same. But every day, I learn more about why and how it was bad.

If you asked me today, I'd say the primary failing with my K-12 math education was not that it utterly missed my dyscalculia or how poorly it prepared anyone to understand numbers. Instead, I'd say its primary failing was its failure to allow us to experience ourselves as people who could confront an unknown, consider the tools available to us, and move the unknown into a known.

Here's an illustration:

In 2024, I took over a high school library that had been in storage for seven years.

The upside to unpacking an entire library is that the unpacker gets to decide how the books will be shelved. If you want to move from Dewey Decimal to, say, a genre-based system, there is no better time to do it.

After wrestling with that choice for three weeks (the time it took to unpack 12,000 books), I decided we would abandon Dewey in favor of a topic heading-based call number system. When I presented this to my principal, I said:

"Do the kids need to know poetry is shelved under 811? No. Do they need to experience themselves as people who can walk into a library and find the poetry? Yes."

As a teacher, I see my job less as "impart knowledge" than as "create the conditions under which you can experience yourself as a builder and user of knowledge."

Sometimes that does require me to impart some basic knowledge. More often, and especially at the high school level, it means I need to set up situations in which students can use their knowledge. Where they see an unknown and navigate to it using their available knowns.

I'm finally getting the hang of long division. But I'm still doing problems on the tens unit blocks, even though I can also do them on paper. The blocks give me that sense of "see an unknown, use your tools and strategies to navigate to it, turn it into a known" that I firmly believe is the foundation of all real learning.

I did not experience math education that way. And that is a big reason math lost my attention very early in school. That would have cost me even without dyscalculia gumming up the works.

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ACCURATE

If I were writing a math textbook I’d have a section in the beginning called “A Note on Notation” where I introduce all the notation Im using. And everyone would want to fuck me sooooo bad

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Soroban

A friend sent me a soroban for Christmas.

(Pictured: a soroban, reading "5" all the way across because I forgot to reset it before taking the picture.)

The soroban, or "Japanese abacus," is used in several countries (not just Japan) for rapid, accurate calculations. While a lot of schools have abandoned the abacus except in early childhood education, Japan still teaches entire classes on using it.

Watching people speed-math on this thing is truly impressive. Here's a seven year old girl adding 12-digit numbers as fast as they can be read to her. Poke around YouTube, and you'll find other videos of people mathing even faster.

When I told my friend about being obsessed with the abacus (but not allowed to touch it) in first grade, I expected to get a primary school abacus. Instead, I got this. And I'm not sorry, because this is much cooler.

Reasons my dyscalculic brain likes the soroban:

I don't actually have to do mental math.

"Not doing mental math" includes never having to read a number one way but math it the other way. All numbers are inserted and read on the soroban from left to right.

If the beads are moved correctly, the answer is correct.

It's easy to move beads correctly because I can both feel and see whether they are right or not.

Moving beads correctly requires one to have memorized number bonds from 1-5 and 1-10 - especially in subtraction. But even here, I don't have to deal with the symbols for numbers as long as I know what the beads are supposed to look like.

For instance, my brain doesn't have to deal with "10 = 6 - 4." To add 4, I can just see that I don't have enough beads in my ones column, move a 10, and subtract 6 from the ones. I know I'm right without counting if I move the top bead and one bottom bead. Done.

For me, the soroban solves the problem I have with calculators. Calculators still require number symbols (like "4") to make sense - which they do not always do. Sometimes my brain just rejects that input. ("Ensign 9 is not on the Enterprise." "Where did he go?" "Please restate the question.")

The soroban doesn't. I have to know what the beads look and feel like, not what arcane picture humanity's ancestors drew to represent it. That helps me calculate. It helps a lot.

I have no plans to become a speed math wizard on this thing. But it'd be cool if I could reliably do my own taxes with it.

Further Reading:

Math With Soroban: A Japanese Abacus by the SAI Speed Math Academy. While there are several other resources online for learning soroban, Math With Soroban is my favorite so far for the clarity of its examples and the pages' worth of example problems available.

Soroban: The Japanese Abacus. Intro lessons from the Japan Society in the UK. (See also the League for Soroban Education in America.)

Soroban Abacus Handbook by David Bernazzani

"Japan's Ancient Secret to Better Cognitive Memory," BBC Reel - video on Japanese soroban classes.

[maths-screaming]

she screm

Starting to feel like my elementary math classes both over- and under-estimated our abilities, fam.

Still in Maths - No Problem Textbook 3A, about halfway through. If I'm reading the book intros correctly, this is what they have you doing about halfway through what we in the US call "third grade" (age 8-9ish):

This is pre-algebra.

To me, this is sixth grade (age 11-12ish). This is "you grew up so much we moved you to a whole new building" math.

I screamed at this one because my brain sees this as algebra, so it tries to do it as algebra. With variables and so on.

But this textbook hasn't introduced the concept of variables! This textbook thinks eight year olds can do this with basic arithmetic!

My math education thought I could manage strings of confusing symbols in my head in two directions at once, but that I couldn't do any problem that required me to identify the unknown in relationship to the known. ?????????

Anyway, I tried to do these as algebra problems, failed, and made myself go back several pages to re-practice basic multiplication and division. And then I did them with basic arithmetic, even though now my brain is jumbly because a bunch of half-remembered crap is shoved into the same slot as new arithmetic skills now.

I am confuse.

[maths-screaming]

Things That Are and Are Not Changing as a Result of Re-Teaching Myself Basic Math

Things That Are Changing

I am less anxious about basic math.

I have more tools for doing basic arithmetic problems.

I'm better at identifying which will be the fastest or easiest tool for any given problem.

I can more quickly and easily ID when an exact answer is needed or when an estimate will suffice.

I'm marginally better at noticing when an answer can't be correct.

Things That Are Not Changing

I still transpose numbers frequently.

I still transpose operations frequently (adding when I should subtract, dividing when I should multiply, etc.)

I still have initial anxiety when looking at a math problem, before the "oh yeah, I have more tools for addressing this now" kicks in.

I still frequently mix up my right and my left.

My sense of direction is still bad.

I cracked Maths - No Problem! Textbook 4A today, putting me halfway through the series. I'm making this list for future reference, because I suspect the things that aren't changing will continue to not change.

Better math education won't change the fact that I have dyscalculia. I didn't expect it to, but I also didn't know what it would or wouldn't change. When I started this, I didn't know where my dyscalculia ended and my poor math education or math anxiety began.

Still, if we can fix "poor math education" and "math anxiety," I'll be much further ahead than when I started - and more willing to live with the dyscalculia.