Does D&D Help With Math?
Devora, priestess of Oghma, could also admire their mindless fury, the orc hordes throwing themselves at the city walls with abandoned fury. They were being thrown back time and time again, but occasionally one or two would make a foothold on the walls before the defenders swarmed to that location and the wall was reclaimed. She knew she should hate them for their destruction, for the hurt they caused to the outlying villages and farms, but analytically, she understood that this was the way they lived their lives. The life of an Orc consisted of little more than fighting, rutting, hunting, and sleeping. An ambitious warlord would occasionally gather enough power to make a foray into the lowlands, where the humans farmed the land.
A piercing whistle cut through the chaotic sounds of battle. It indicated that the orcs had filled the channels, almost undetectable but to the perceptive. Huge boulders dropped from large claws on the far right of the walls; soon gaining momentum, the juggernauts crushing bone and steel like paper. One of the boulders seemed to stall as it hit a particularly large orc - “Orog” was the name she recalled from her reading - this orc bellowing a challenge to boulder as he faced it full-on, but it was no match for the weight or momentum. Devora allowed herself a smile as she watched the Orc shamans who were starting their frantic gibbering prayers on the hilltops. They used the gaps in the treeline, the perfect vantage points to view and overlook the battlefield. The mortars rang out their explosive charges, precisely clearing the two concentric city walls in a perfect parabolic arc, raining down fire onto those perfectly placed gaps that the shaman was in.
The cheers went up from the allied forces of light as the orcs started fleeing. One keen soldier, of the guard who had been assigned to her guard, started to chant “Hail to Oghma! Praise be to Oghma!” and the cheers and chants were soon being echoed up and down the wall.
I see it time and time again, mainly because as the pretentiously self-nominated “Educational DM”, I keep an eye out for and make an effort to repost articles on the educational value of the game: “D&D is good for your child’s Maths skills”. But is it???
In a recent retort, I said, “It's basic arithmetic. It's not exactly maths.” when talking about THAC0 (“To Hit Armor Class Zero” from 2nd Edition AD&D for those who aren’t grizzled old-timers out there). I immediately got a reply with a screengrab of the dictionary definition of arithmetic.
IMAGE SOURCE: Google.
A fair riposte, but I wasn’t done.
My reply: “It's like saying that anything that involves reading is English. Technically, yes it improves your English, and highly recommended at a basic level, but you're hardly going to be taking a university degree off the back of it. In fact, I would say that the reading and vocabulary that D&D encourages does far more for your improvement in English than D&D improves your mathematics skills... and yet so many players still can't spell Rogue correctly…”
IMAGE SOURCE: https://www.reddit.com/r/StarWars/comments/5h7sm9/its_spelled_rogue_not_rouge_thats_something_else/
Having come from a home where English wasn’t my parents’ first language but made every effort to make sure that their three children’s English was good, I know first hand the benefits of reading. I attribute a lot of my fair grasp of English to my insatiable appetite for reading (not to mention a couple of great English teachers - thank you, Mr Tim Head, Mr. Hall, and Ms. Saner); much of that was fantasy and sci-fi my teenage years obviously.
Back to the question, however: Does D&D help with your mathematics? My simple answer: Well, yes... but probably not in the way that you think.
Starting D&D at an early age MAY help with their basic arithmetic. I have sixth form students (16-18-year-old) who have players who still struggle to add two dice rolls, but little children who make the effort to add those, not to mention working out how to optimize dice rolls, who compare spells and weapon damage, who calculate maximum, minimum and average damage per round, will improve those basic number skills and even gain a good grasp on basic probability. This can translate into very young D&D players gaining great confidence in the early stages of maths. Quick number skills and confidence, not to mention the positive attitude towards maths, can carry young students a long way.
You can see this in the prevalence of parents signing up children for that worldwide phenomenon that is Kumon and similar Maths courses. Let me make this clear, I DO NOT LIKE KUMON (bear with me, I do have a point in my disdain of Kumon).
I don’t like Kumon... for maths at least. I am not intimately acquainted with Kumon, but I have had enough students go through the Kumon system to know how they operate. What they do is give their students a whole sheet of problems, starting off very simply and getting gradually harder and harder. The philosophy behind this is that the students learn how to solve problems organically. The benefits of Kumon are that the students learn to do maths very quickly. That’s a good thing, right? So why don’t I like it? The philosophy is sound, but in practice, rather than learning how to solve problems, students learn how to “do” problems. That is that they learn the method of getting the right answer quickly and without guidance (because that is the nature of Kumon), they don’t care how they get there. Mathematics without understanding will mean that you will eventually hit a ceiling. Kumon students come into my classes with a great deal of confidence (which is great), but when presented with a problem that requires a deeper understanding of how the mathematics holds together, all but the brightest, start to fall apart. Unfortunately, mathematics is far too often taught by “method” rather than “understanding”, especially by teachers who do not come from a mathematical background, and this situation is exacerbated by the pressure to get examination results (teachers work to make sure the students can get to the answer, not the why or how it works). I have seen many online mathematics tuition videos, worksheets and explanation websites are guilty of this, not least some of the well-known Khan Academy videos.
A few years ago, I spent a lot of time with an incredibly bright top mathematics class giving them “thinking problems”. Rather than concentrating on the answer, which they could often find by pattern spotting, we spent my time about the “WHY” of the answer. Take a simple problem: if I have a chocolate bar with 100 segments, how many breaks must I make to break it into those 100 segments? A well-drilled students may start with a bar with 2 segments, move onto 3, 4, before starting to see the pattern. The answer is 99. Beyond the reason that it fits the pattern, one way (and the students usually come up with many ways) to explain why it is 99 is that with each break adds one more piece to your pile. Since we want 100 pieces, and we started with one, we need 99 breaks. Let’s put a pin in that thought, and come back to it.
But... as I said, having that confidence and speed in their basic arithmetic can carry young D&D players a long way in maths. Both of those are great foundations to build on. I would say that probably 50% of my job as a maths teacher is building up their confidence in their mathematical ability. Most people think that teaching a bottom set mathematics class would be painful as a maths teacher. Actually only teaching the top students in the top year groups does the mathematics itself become anywhere near challenging and therefore interesting to me, so teaching mathematics is repetitive and it is more about the relationship with the students than the actually interest in maths that motivates me. Of course, I love to show all my students interesting areas of mathematics and love to have those Kodak moments of enlightenment, but usually, it’s more about the conversations and to have students eager to learn is a joy. So you might think that teaching the weakest students in a school would be trying to draw blood from a stone. In fact, it’s quite the opposite. Very few of those students are actually negative about maths itself, more often they are negative about their own perceived lack of ability at the subject. Present them simple mathematics and slowly show them that they can progress onto harder and harder mathematics and that they have some ability in the subject and most will be eating out of your hands. To a teacher, one of the most meaningful gifts that you can receive is a grateful heartfelt thank you note. About half of those that I have received in my twenty-odd years as a teacher have come from bottom set students. I have seen students who I have shown that they have some ability in mathematics rise to much higher sets and even go on to get top grades in the next few years. That’s the power of confidence in one’s own ability.
Devora felt a stab of jealousy and spite as she remembered the long days of supervising the construction of their war machines, not to mention the nights of planning and calculations since she and her fellow priests had arrived a scant three days before the first attack. She quickly quashed those feeling, acknowledging with a quick prayer of thanks to her god: Oghma, who had blessed her with the education and the intelligence to make those calculations, the temple of Oghma where she had been brought up once she was found to be blessed with the intelligence, and the authority and respect that being a priestess of Oghma afforded her
She looking on puffing-up with pride as saw her careful calculations come to fruition, and just as quickly she quashed that ungrateful thought too; her hand raised to the holy symbol on her chest and bowed to the troops. Oghma had provided and Ogham would go the glory.
“Praise be to Oghma!” she exclaimed. and the soldiers around her replied with hearty cheers. A stream of knights, resplendent in their noble house colors, charged out of the gates to mop up the fleeing orcs. The back of the hordes had been broken...
So how can D&D help with higher-level mathematics (16+ years old)?
I have used Anydice.com to demonstrate the Central Limit Theorem with multiple dice when teaching stacking probability distributions (see diagram below), but generally, my love of D&D and my love teaching mathematics does not have a great deal of cross-over. Those who delve into game design and looking at system mechanics may start to dabble in probabilities, but certainly, it’s not a requirement. A good grasp of how the probabilities work is helpful, especially as a DM, but it is mostly quite intuitive (says the maths teacher… lol). However, I certainly wouldn’t want to discourage anyone who wants to try, especially since mathematical ability and creativity have no real correlation (in fact many people who are good at maths and sciences, have low confidence in their own creative skills - something I hope to talk about in the future). Even DMs who don’t go into game design generally will gain a much better understanding, even if it’s intuitive, of probabilities, but that doesn’t really help much with their mathematics beyond the most basics of probability taught in high schools. During the course of preparation for a session, or during play, there is no algebraic manipulation, only possibly the lightest encounter with fractions. Personally, I have never seen calculus being used. Your games may be very different.
I posted the question in a FaceBook “DMs and GMs” group recently. For the most part, most DMs admitted what I have said here that there is very little beyond the most basic arithmetic being used and practiced in games. Some commented that it helped their mental maths (see earlier) and spreadsheet skills, but otherwise no maths beyond what is learned in High/ Secondary School. There were a few exceptions: ThinkDM (https://thinkdm.org) does a lot of analysis, breaking down best damage, etc.. but again that’s mostly spreadsheet work (although I know that the maths behind the spreadsheets isn’t that simple), and you don’t need that high a level of maths to understand his breakdowns. I have seen the SUVAT equations (equations of motion) being used to work out projectile flights (that’s learned in A-Level mechanics and physics by 17 years olds); and I have heard of some DMs have tinkered in complex patterns and sequences to present something seemingly random events for their players. On the whole, however, there is not not much maths going on.
So does D&D help with higher-level mathematics? I return to this idea of having a brain for problem-solving. Just recently, in the English testing system, the GCSE syllabus introduced a whole load more questions that required a lot more thinking. The step up from GCSE to sixth form level maths (at age 16 - move to A-levels or IB) has always been about the level of ability to apply the maths and problem solve. These can only be improved with practice, not just mathematical problems, but problem-solving and critical thinking in lots of different areas. Here, I will just refer you to my other article on Critical Thinking (https://dumpstatadventures.com/guest-writers/real-world-problems-fantastical-solutions-critical-thinking-through-dampd ). I am sure that anybody who has worked at mathematics at the university level or above will tell you that at the highest levels the skills of critical thinking and problem solving are more important than having an encyclopedic knowledge of mathematical theory.
To summarise: Yes, playing D&D does help you with maths. It practices basic arithmetic skills, which in young players (5-10-year-olds) will help with their basic number work, confidence and speed of calculations. This gives them an important firm foundation and a leg up at the start of their schooling which can carry them a long way. At a higher level, it teaches students problem-solving and critical thinking skills, which are incredibly important, especially when applying the tools of mathematics in the real world.
Finally, a fun meme as evidence to the contrary:
IMAGE SOURCE: https://i.pinimg.com/originals/4f/8b/21/4f8b21f35140e4cc12050b7a4ee7b433.jpg
The city was quiet, even for the sun almost reaching its full height; the people had spent most of the night in revelry, celebrating their victory. Devora, being one of the honored guests had to attend the royal banquet but had slipped away once the speeches started to become slurred. Even then, exhaustion from the many days preparing the war machines had meant that she had slept later than her well-disciplined normal dawn rise. After her morning devotions to Oghma, she was enjoying a leisurely breakfast. At least, that was one of the perks of working for the rich and powerful.
Lost in her thoughts considering the improvements she could have made on the war machines, a well-buttered slice stuck half-way towards her mouth, her revery was interrupted by the clatter of hooves in the courtyard outside.
“I need to see High Song Devora”, came a young male voice.
She heard the booted feet make their way through the mansion before a knock at her door, and a young liveried man was shown in. One of the noble houses from Waterdeep, she registered, but at this time, she couldn’t quite remember which one.
“Your Grace, I beg your pardon for interrupting your repast, but I was sent by Lady Bryndraeth with an urgent message to be delivered to your eyes only”. A beautifully embroidered envelope followed.
A swift slice by the handy butter knife revealed an elegantly hand-written note entailing cracks in the tower of Lady Bryndaeth’s late husband. A Lord of Waterdeep, an influential political figure and a powerful magic-user in her own right, Devora sighed as she read the letter: this was not a request that she could reject.
Already the calculations for the requirements of the materials needed for such a project were whirling through her head as she strode towards her chambers to change into her riding clothes….
As a mathematician, I am well aware that my opinions and even observations are from a very small sample group. This is why this is an opinion piece. I would love to hear of your experiences and opinions (play nice… and so will I).
Many thanks,
Sam, The Educational DM
Twitter: @DMEducational
Instagram: @DMEducate
Facebook: Educational DM (@DmEducational)
Header Art - Illustration by Gloria Pizzilli
