Weekend Mathematics Article and Personal Updates!

It’s that time of the week again. I will be writing on calculations and mental mathematics today, but first I need to get some personal stuff off my chest. If you want to skip me crying all over my keyboard, click here to go to the maths.

So, rounding off the week is a bout of delicious paranoia. Wonderful, I know, but we’re old friends; we’ve known each other for about 10 years now.

And you know what? I wish we didn’t. I wish paranoia would stop calling me up, contacting me on Skype, walking up to me in the street as if we’re best friends or peering over my shoulder whilst I work. It’s annoying. More than annoying. This time, paranoia is here to let me know two things:

1 – I’m utterly useless. So, apparently the January crowd on my course (it’s split so that the first wave join in January, then the second wave are added in March and finally the third wave are added in June) is for people who have not done an A-level in Mathematics. It feels like Paranoia (who we will capitalise now like a proper noun as he has, by now, taken on a human-like form. And yes, it’s a he, because I’m also obviously a man-hating feminist who believes that anyone bearing a Y chromosome should be enslaved. Obviously) is holding this sentence up to my face and laughing hysterically. Am I really so crap? As someone who did both an A-level in Mathematics -and- an A-level in Further Mathematics, this is really weighing on my thoughts. Heck, I more than just did an A-level in Mathematics; I managed to get an A grade whilst also managing crippling depression, insecurities and identity issues. It was a metaphorical cake-walk that only took up a relatively small percentage of my brain power to do, though Further Mathematics required more than I had available and I would be interested to see what I would get now that I am (mostly) over these hurdles. So why the hell am I in the “you haven’t done an A-level in Maths” group? Why am I not in the March group of people who have done an A-level in Maths? Am I so useless that the University feels that I need to be put in the group where I am, quite clearly, above the mathematical par? This isn’t just me being big headed, this is what I’ve observed. But am I? I feel like I’m trying to prove myself to myself in class, commenting on things that don’t necessarily need commenting on and asking questions that I already know the answer to in order to look intelligent. Like I’ve considered more than just what we’ve been shown.

2 – That leads me on to the other piece of paper that Paranoia is holding up to my face (he is a total bastard) which reads “everybody hates you. Even your instructor hates you. Because you’re an annoying little self-important ‘princess’.” I get the feeling that, because of my behavioural patterns derived from point number 1, my fellow trainee teachers hate me, as well as our instructor. I get the feeling that they think I’m aloof or self-important or that I am trying to prove that I am better than them (which is totally not me. I would never go out of my way to put other people down, having been bullied myself for the entirety of my days in primary school, and for two years afterwards as well). I’m really scared that my above feelings are making me do things that I would not normally do and that these are the first impressions that I’m making on what will be my peer group for the next 21 months. I feel as though I am going to alienate myself through no fault of my own, but because Paranoia is repeatedly punching me in the stomach and reminding me that I’m useless and everyone hates me.

This has me in a slight panic, so I’m going to go radio silent for the next week in class. I will speak when spoken to and no more. I can complete this work. I can complete this work with ease. I am learning from my time here and, as it is funded by the government, it is affordable (I get nothing from parents and couldn’t do a full time job alongside what is a pesudo-full time job) and preferable to spending another 3 months in Spain, going insane in a different way. It’s just… I have these thoughts in my brain that I really need to get rid of. Emotions: such a love hate relationship I have with them.

Anyway, that’s enough of that. Time to do some mathematics.

Picture courtesy of Wikipedia. The 4 basic numerical operations!

Picture courtesy of Wikipedia. The 4 basic numerical operations!

This is a maths article first and foremost, so let’s get down to the nitty gritty of calculations. I want you to ask yourself how many times every day, on average, you do mathematics. Got a number in your head? Good. Well, that was once at least, so we’re making progress. Here’s the part where I tell you the truth: it’s likely a larger number than what you just thought of.

The four basic mathematical operations are addition, subtraction, multiplication and division. I’m hoping that everyone reading this knows the basic premise of what these do. This isn’t calculus, this is simple mathematics. The first things that we learn and the cornerstone of everything to come. Basic arithmetic is incredibly important, and I can’t stress that enough. Arithmetic is used when we go shopping (fun!), when we order lunch, when we tell the time, when we cook, when we withdraw money from the cash machine, when we pay rent, when we gamble (well, those who do it), when we play any board game involving dice. I think you get the point I am trying to put across. We use arithmetic in our day to day lives and don’t even consider the fact that every time we do so we are doing maths. We take for granted how easily we can add two numbers, or multiply basic values (or at the very least estimate, another important mathematical skill), but over the past week I’ve had to look in detail into how we do it, and thus how to teach it to primary school children who have not learned how to do so yet. We start with counting. Addition is simply counting. Subtraction is reverse counting. Multiplication is repeated addition and division is repeated subtraction. It’s all linked.

I know that mathematics is not for everyone. Some people find numbers difficult, but may weave the most wonderful poems or create spectacular sculptures and paintings, so I’ve come up with 3 basic strategies to improve basic numerical skills that I have used through my life, considering that this is the cornerstone of mathematics, the foundations of the mathematical manor (and we all know what happens when you build a manor on shoddy foundations. It involves lots of costs and crumbling). You don’t even have to pay for this, it’s like witchcraft!

1 – Number games. Looking at the clock. It’s 23:05. What can I do with 2, 3, 0 and 5? Well, I can make 10 (2 + 3 + 5 + 0); I can make 0 (2 * 3 * 5 * 0 or 0 / (2 * 3 + 5) or 2 + 3 – 5 – 0). You can also introduce more complex operators into this number games if you’re bored of the basic 4, such as factorial or indices. I’ve done this myself since I could tell the time (which I believe I learned at about the age of 4(?)) and it really helped me grasp and manipulate numbers, even from a young age.

2 – Find a hobby that uses lots of arithmetic. For me, this is Warhammer 40k. Those of you who know me will know that I tend to theorycraft a lot. What happens if a unit of x fires at a unit of y? How many Guardsmen can I swamp the board with in 1500pts whilst maintaining tactical viability? What’s the average MEQ kill rate of Warp Spiders? The best part about this one is that it can be enjoyable. I love crunching the numbers to work out how streamlined I can make lists and how much I can expect a unit to do on the tabletop; it’s an extension of a hobby that I have loved for years. This has really helped me work out more complex multiplications (17 times table? That’s a unit of Striking Scorpions! 19? That’s Warp Spiders) and even juggle fractions in my head (1 boltgun shot from a Battle Sister will kill 1/9 Space Marines (2/3 to hit * 1/2 to wound * 1/3 to get through the armour save), so you need 9 to kill 1. This is probably the one that has helped me the most, because where the first was an idle action that I did when I looked at the clock, this one was an activity that I sought out in my own time. A suggestion for if you want a hobby with slightly more advanced mathematics would be AD&D dungeon creation. GCSE level circle theorems used to be a necessity for DMs!

3 – Practice. The most boring of the three. There are plenty of resources out there (don’t feel like an idiot for doing Primary level activities. I’m doing them as part of my teacher training and I don’t feel like an idiot for doing so!) to help with number skills. Use them. However, headbutting a wall until it falls over will leave a headache. The two above methods are akin to bringing a climbing rope and a rocket launcher to the wall first.

I’m just throwing ideas out there for this. Basic arithmetic is everywhere in our lives and is, in my opinion, an essential skill; an undervalued skill. As always, you can choose to try it or not. I was notoriously lazy as a child and lacked motivation for anything academic, so this was merely my way of getting around the fact that I never wanted to do anything. A shorter mathematical article today, but I am not madly in love with the idea of basic arithmetic. I may be a sub-par mathematician, but I’m slightly above basic arithmetic. Mainly because I’m a Warhammer 40k and tabletop RPG player. Got to have the best stats and everything has to be perfect!

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