*This is a guest post by Kudzayi Chakahwata, a freelance writer and epic mathematics enthusiast. She blogs at http:// mathematicalstateofmind.wordpress.com/*

photo credit: 4-6

At primary school, mathematics homework corrections were not most welcome with me. Don’t get me wrong, I have always loved mathematics itself, but the feelings that came with it…no thanks.

I would do the work, and then my dad would take my book and check it. If there were any wrong answers, I’d get an ear-full. He’d yell at me! At least that’s what it seemed like as a 7 year old. As a result, I believed that mistakes were bad… really bad, and as if they were not allowed. Whenever I made a little slip, I ended up feeling scared, stupid and somewhat worthless.

Having such negative feelings should be banned around a beautiful subject such as mathematics!

As you may have guessed, I had some issues with doing my maths corrections. It was a battle of wills! But it didn’t have to be that hard. Perhaps you’re going through similar things in your household. If so, I would like to share some things with you that worked with me as a child.

### 1. Stay calm, keep your voice soft and gentle

photo credit: khalid Alamos

This has been said many times I’m sure, but I cannot emphasise enough how important doing this will be. When I had made a mistake, I was more receptive to correcting it when encouraged patiently. After all, the learning brain works best in a relaxed state. It was in my nature to do well, as it is with most children I believe. But the way I was sometimes approached, resulted in the reluctant release of my rebellious side as opposed to corporation.

I remember when I was 7, the first good maths teacher I had in primary school was a strict, firm, well spoken old lady. When I did her class work and made a mistake, she’d smile at me and just point at it, patiently waiting with an encouraging nod. This made me really keen to correct the answer. When I did, she’d say something very uplifting like, “Well done! Excellent piece of work!” Of course she did the same for the whole class!

### 2. Treat mistakes as normal, not evil

Referring to the same wonderful teacher, she told our class that she “liked” mistakes. I used to think that this was a little sick, but I now truly understand her!

The point I’m sure she was trying to make, is that mistakes can be positive. Mistakes are good teachers. The concept will end up strengthened and understanding deepened when corrected.

Another by-product of not making mistakes punishable by metaphoric death, is that we’ll end up with young mathematicians who are not phased by mistakes in their work. They will see errors as a normal part of their mathematical development, and being human! Not something to feel frustrated, worthless and inferior about.

### 3. Find alternatives to the words “again” and “wrong”

Gosh, I really detested hearing,

“You got this one wrong” or

“You need to do this one again”

I would often flee from the dining room table at the hint of these phrases.

When there are a couple of errors in a generally well done piece of work, a more effective, somewhat sly approach which I used while tutoring younger pupils, would be to say,

“You did those questions really well. Lets try something else!”

While using a very excited, lively tone. Then I’d write down the previously incorrect questions on a separate piece of paper, and hand them over to the pupil.

He/she would then do these seemingly new questions without the little slips as before. I would then show them the original question with the wrong answer next to it, along with the new piece of paper with the same question corrected. We’d then laugh it off!

### 4. Use a hobby as an analogy

photo credit: Markus Bollingmo

If you face some resistance when the time comes for necessary corrections, you could try explaining the need for doing corrections out of context. For example, if your child has a hobby like dancing, you may want to explain,

*“Sometimes in your dance class, you may not do a move correctly or safely. The teacher will then correct you to make sure you don’t hurt yourself. You’ll then feel better doing the move and your dancing will start getting better. Maths is almost the same. Each time you correct your mistakes you are building your knowledge and making yourself get better and better.”*

### 5. Say encouraging things often

photo credit: david_a_lea

Sadly a lot of young children have very negative feelings around mathematics (I was one of them). Mistakes can be a knock on confidence. In order to keep confidence up, I liked to re-assure my students that mistakes are not an indication of ability, as even the most advanced mathematicians, such as professors make mistakes, and often!

My message to young mathematicians is to have confidence in your abilities. Mathematical confidence will come from sorting out problems and correcting mistakes as they arise. So see mistakes as an opportunity to build your mathematical strength and confidence, not to destroy it.

*Kudzayi graduated from King’s College, University of London with a Master’s degree in mathematics, January 2011. She currently feels sad that maths is feared and avoided by many adults. Part of her solution is to share her enjoyment for applying maths to life unconventionally, such as relating it to our emotional side.*

*She hopes that in the near future it will be just as strange to avoid doing maths, as it is to avoid reading and writing.*

*Kudzayi is known for unleashing the light-hearted, mischievous side of mathematics.*

The advice is great, but will it encourage a society which can do math only when egos are properly stroked?

Hello William, thank you for taking the time to comment.

I just have to politely ask: what exactly do you mean? Do you mean to ask whether my advice could result in the situation where people can only do mathematics when they are in an exaggeratedly pleasant atmosphere, with an excessively benevolent teacher?

If so, my answer is no! I do not think that the 5 points I have discussed above could be of such consequence. I say this because I am targeting only a very specific situation here, where mistakes, hence corrections could conjure up negative feelings, due to a young pupil’s potentially sensitive disposition.

At the early stages of mathematical development, it is essential that the foundations are strong. Sometimes a little more kindness than usual is necessary to make this happen! Only on a strong foundation can further knowledge be effectively built, hence providing an evident improvement in abilities, with the complementary increase in confidence to follow. This increase in confidence could then gradually diminish the need for some disproportionate pleasantry, of which you speak, around mathematics.

As you know, we all have our different learning styles and preferences. Those who need an abundance of encouragement in order to do maths may indeed only study maths if the conditions best suit them, and that’s fine. Many people I know would have taken mathematics to a higher level and enjoyed it more, if they were just given more encouragement.

If the approaches I discussed were to be used for every single student, in all contexts, throughout their “mathematical life,” without taking personality into account, and not adapting teaching methods to match changing confidence levels and needs of specific pupils…Then I think one may end up alienating the people who just like maths for what it is, i.e. those who don’t really welcome the “gently-gently” parameter around their equations.

If you’d like me to further elaborate on anything, I’d be happy to do so. I could talk about this all day!

Good post, made me think of additional ways I could encourage my son. Thanks! :)

You’re welcome! Thank you for saying so, I’m glad this gave you more ideas. :)