Throughout November I will be going live on my Facebook page to quickly explain some of the most common misconceptions, or stumbling blocks, that the children I work with often display, and provide advice on overcoming them.
I’ll take a look at each of them further in this blog.
The Maths Blocks:
Firstly, a couple of maths issues that crop up again and again: multiplying and dividing by powers of 10 and the commutativity of multiplication.
Multiplying and dividing by powers of 10.
A power of 10 is 10, 100, 1000 etc. When I was at school, and I’m sure when you were too, we were taught to add zeros when we multiply by powers of 10 and to take zeros away when we divide by powers of 10. It was only when I was in teacher training college 20 years ago that I found out this is mathematically incorrect, and sets children up for problems further down the line (and probably helps explain one reason why I struggled with maths). It is important to teach this correctly from the start so children don’t get stuck later on. However, children are still being taught this “trick” and I’ve lost count of the times it has put a barrier in their way over the years.
So, if adding and taking away zeros is not correct, what is?
We need to understand that it is the digits moving and changing their place value. When multiplying, numbers get bigger, so the digits move up the place values. This leaves a space, or spaces, so we need to use a zero as a “place holder” to show there are no ones, for example.
When we divide numbers, they get smaller, so here the numbers move down the place values.
So far, however, the trick of adding or taking away a zero works and gets the right answer, so what’s the issue? Why does it matter whether we add or take off a zero or move the digits?
Let’s start with looking at dividing. When dividing, not all numbers have a zero on the end to “take away”. If you have been taught to take off a zero and then you are presented with 32÷10, you are now well and truly stuck. You have no idea how to solve this problem. You get despondent and frustrated. Maths becomes “difficult”. If you have, however, been taught that the digits move, then this barrier never appears. We just know what to do – move the digits. No problem was created and we can continue to access maths and understand number. The digits might need to “jump” over the decimal point to become tenths or hundredths. When I was at school, I was told to move the decimal point. Again, this is fundamentally incorrect. The decimal point is fixed to the spot. It doesn’t move. It is glued down. The digits move around it.
What about when we are multiplying? We are adding a zero so why is it a problem? The answer is because it leads to poor understanding of place value. This is understanding what each digit represents – hundreds, tens and ones (sometimes called units). If we just add a zero to 32 without moving any digits we still have 32. We don’t write 32.0 because the zero tenths is not telling me anything useful, because I don’t need to know I don’t have any tenths. Adding a zero on the end of 32 does not change the number in any way. We need to move the digits, then place a zero in the empty place value columns to show clearly what the number is and avoid confusion. A three in the tens column means 30, but 30 what? 31? 38? The zero place holder is saying “there are no ones”. This zero is vital. And it’s vital it is in the ones column, not the tenths column. Where it is means very different things.
Children enjoy practising these skills by moving numbers up and down a place value chart. Imagine the numbers sprouting feet, or wheels, or being pushed in a trolley – whatever works to remember they are MOVING.
To know how many places on the chart to move, look at the power of 10 you are multiplying or dividing by. 10 moves one place because there is one zero, 100 two places because there are two zeros, 1000 three places etc.
Times tables are commutative:
Commutative means that the calculation can be written either way around. 3X4=12 is the same as 4X3 =12. As I’ve explained in my blog “What Can I do to Help my Child with their Learning?”, it is best to learn all the related times table facts together as it creates less work in the long run. If you know 3X4 = 12 you therefore know 4X3 = 12 and therefore 12÷4 = 3 and 12÷3=4. That’s four facts for the price of one! Lots of children, when presented with 12X5 for example, will say they don’t know their 12 times table. When asked “do you know your 5 times table?” they say yes and know 5X12 = 60. Understanding that you can swap the numbers around is liberating. Children think the 12 times table is hard, or that they don’t know it. They will know more 12 times questions than they think. Turn the question around!
It also shows 12 eggs divided into rows of 2 = 6 eggs in each row and 12 eggs divided into rows of 6 = 2 eggs in each row.
The English Blocks:
Over sounding phonemes and resistance to editing writing.
Phonemes are the smallest unit of sound within a word. Children are taught phonics from the early years and there is a huge focus on it in school. Children will be familiar with the word “phonics” and “phoneme”. We use phonics to sound out words to help us read and write (this is only helpful to a point in English as lots of English words are not phonetic).
The children I work with who struggle with reading and spelling often are not sounding phonemes correctly. They say, for example, “c-hu – ah – t-hu”. We don’t say cat “cuhahtuh”, it’s “c-a-t”. The sounds are very small and quiet, with no “uh” on the end. The vowel sounds (a, e, i, o, u) are louder and may have a slight “uh” on the end, but the consonants are small, made by a little puff of air (b, p), or restricting the back of the throat (c, k, q) for example. Encourage your child to say the sounds as small and quietly as possible (but still being able to hear them!) This will help them hear the word they are sounding out – “c-a-t” sounds like “cat” -which helps with reading and spelling.
As a side note, I’ve noticed lots of children calling letters words – “how many words in the word?” It’s also important to know the difference between the name of the letter (A – ay) and the sound it makes (“a” as in apple).
Proofreading and Editing:
Children are generally great at writing. They have fantastic ideas which they write down eagerly. However, many think that once they’ve written the last word (not necessarily with a full stop after it) they are done and it’s time to move on to the next thing. When you explain that the next thing is to go over and edit the writing, they sometimes become frustrated and despondent, and issues around fear of mistakes and getting things wrong surface.
Children need to understand that writing is a process, and correcting their work is an integral part of that process. Proofreading (finding spelling, grammar and punctuation errors) and editing (changing the word choice, word order, sentence structure etc) are essential parts of being a writer. Every writer goes through this process and every piece of text that has been professionally published goes through this process, multiple times. Find your favourite book. The author didn’t write those words first time, and then it was printed and you bought it. Those words are there after a process of changing, correcting, adding in or taking out many, many times before it was printed and sent to the shop. Being a proofreader and/or editor is a career. People are paid to check writing and make it as good as it can be. It is not a criticism or telling off. It is an essential part of the writing process.
When children understand that the first draft of their writing is not the finished version and there is an expectation to proofread and edit, and that is done in an engaging, creative way, they are able to see this as part of the process and embrace the task of making their writing “as good as it can be”.
A first draft should be about getting ideas out of your head and on paper. Children shouldn’t be worrying about how to spell words or where to put full stops at this stage. What’s important is getting the ideas down. The next stage is to check the spelling, punctuation etc. Children should do this themselves first, before someone else checks it (it is good to have a fresh pair of eyes look at it which is why authors use professional proofreaders and editors.) Instead of looking for all the things that need changing at once, focus on one thing at a time. Are the capital letters correct? Now the full stops and other punctuation? Are there any words I know are spelt incorrectly, or I think might be? Check them (put a wiggly line under them first). Be a writing detective. Put yourself in the shoes of your reader. Have you made your writing as clear as possible for them? Will they understand and enjoy it?
Drafts of writing should be messy. There should be crossing out, insertion, asterisks to show where new sentences and paragraphs are that couldn’t be fitted in. Use different coloured pens if it helps, but it’s not necessary. This shows the child has gone back and thought about their writing, and corrected errors, embedding learning along the way.
Young children in Years 1 and 2 should be checking they have used capital letters and full stops correctly, and maybe checking 1 or 2 spelling words. Build up the amount of proofreading and editing done as the children become older and more skilled in their writing abilities.
Editing is often seen as a chore by children, but it is actually a really creative process. Is there a better word or phrase to use to really get across what I want the reader to know or imagine? What happens if I move the words around, take a word out, change a word, move a comma…? Editing is being playful with language. That is fun!
To see my short explanations of these misconceptions, please visit my Facebook page. Coming in the new year will be my Learning Support Membership where there will be short, engaging video lessons and supporting activities to address these misconceptions. Do get in touch if you are interested in discussing how I can help support your child’s learning.
I’m now off to proofread and edit this blog before publishing! What you are reading is not the first draft 😉.