mental math addition strategies for preschoolers

H's school is participating in the World Education Games this coming March and being a kiasu school, the teacher told us parents to let our kids practise at home in the weeks leading up to the games. I always thought that H is good in maths, well he does know how to perform addition and subtraction but I guess he doesn't have the speed. So being a kiasu mom, I guess I'd need to teach him some basic mental math strategies to boost his speed in doing sums.

I came across this post by Shelly Gray and thought the strategies to be most apt for a preschooler like H. Here's a summary of the 6 strategies:

1. Counting On - Counting on means that you start with the biggest number in an equation, and then count up. For example, in the equation 5+3, you want students to start with the "5" in their heads, and then count up, "6, 7, 8." This is to discourage students from counting like, "1, 2, 3, 4, 5.....6, 7, 8." Students also need to be taught that if an equation looks like this: "2+6," they still should start with the bigger number in this case "6" and count up "7, 8." I know Math Monkey teaches this. Kids are taught to have a mental picture of the numbers 1-9 (made up of dots) so that they can use the 'counting on' strategy without having to count with fingers.

2. Doubles - Doubles are all around us; think of fingers and toes - 5+5, wheels on a car - 2+2, or the eggs in a carton - 6+6. When students know their doubles well, they should no longer have to think about the equation to solve it. Rather, the answer becomes automatic. This means that the student has developed automaticity. For example, when a student sees the equation 8+8, he should know that it equals 16 without even stopping to think. Building a strong foundation of doubles will help students with the next strategy, Doubles Plus One.

3. Doubles Plus One - This strategy is a natural progression from the doubles. It includes using a known fact and building on it. For example, in the equation 5+6, a student could think, "I know that 5+5 makes 10, and one more makes 11." This strategy will likely require a bit more teaching than the previous two, but it will be well worth it; when students know their doubles and doubles plus one facts, they know 25% of the addition table!!

 

4. Making Ten - The making ten strategy involves memorizing the number combinations that add to ten. This includes 7 and 3, 8 and 2, & 5 and 5. Again, it is important that students develop automaticity with regards to these facts so that when they see a combination, they quickly know that it is a making ten combination. Once students begin to use this strategy, "counting on" becomes unnecessary in some circumstances. Again I know Math Monkey teaches this. Kids are taught to draw a 'ten point circle'. The  numbers opposite each other are friends, i.e. number pair that sums up to 10.

 

5. Making Multiples of Ten - This strategy is a natural follow-up to making ten, as it uses the same number combinations in a different way. When teaching this strategy, students will learn to use the making ten facts in equations such as 27+3. In this case, students will see the ones digits and realize that 7 and 3 make 10, so 27 and 3 makes 30.

 

6. Front End Addition - This is perhaps one of the most powerful mental math strategies out there. Front end addition involves adding numbers from left to right, eliminating the need for carrying. For example, 54+19. You would do 50+10=60, then 4+9=13 and finally add up the 2 numbers, i.e. 60+13=73

Math Monkey

I took H to a trial class at Math Monkey today. Despite my reluctance to put him in any academic-type enrichment programme (see my previous post on mental maths), I thought I should just check it out anyway. My sister did some research on the various math programmes available out there (so that saved me some trouble) before enrolling my niece who's now in standard 1 in Eye Level (previosuly known as Enopi). But she suggested I check out Math Monkey cos they incorporate games in their curriculum, hence more fun. The reason why my niece isn't going to Math Monkey is that you need to start young (i.e. from 4) else you'd not be able to catch up on the techniques.  

So as usual, I had to prep H about going to the class. I was quite surprised he did not reject the idea when I told him we'll be going for a math class at Math Monkey (I also made a light joke out of it about monkeys doing math, etc. so that he wouldn't feel intimidated). The first thing the teacher did was to give him an assessment (4-year old paper) to test his level. Of course he wouldn't go into class alone, so Po-Po went in and sat with him. After the test, Po-Po was told to leave the room so that he can continue with the trial lesson but he wouldn't hear of that, so Po-Po left the room and I went in instead.

The trial lesson was at the Green Monkey Troop level with about 6 other kids all around H's age (4+ years old). Today's lesson was about Bigger and Smaller. The teacher drew a staircase and wrote 0 to 10 in ascending order up the stairs. The kids were told that the numbers become bigger as you go up the stairs and smaller as you come down the stairs. They were then told to count 0 to 10 as the teacher pointed up the stairs and 10 to 0 as the teacher pointed down the stairs. Then the teacher wrote pairs of numbers on the board and asked the children which number in each pair was bigger or smaller. This was way too simple for H since he's already mastered his numbers.

Next it was game time. The kids were divided into 2 groups. The teacher will flash a question and whichever group gave the answer first will win 2 points. H actually participated in the game and he was happily beaming away cos his team was leading all the way. The game was to fill in the missing number. E.g. 5, _, 7. Again this was way to easy for H.

After the game, the kids were asked to do a worksheet from their folder. Since H did not have a folder (he's not a student yet), the teacher asked him to go to the board in front and tested him. She asked him to count backwards from 10 to 0 and write the numbers on the board, she gave him more number pairs and asked him to circle the smaller number in each pair, she gave him more fill in the missing number questions - all he did with ease. The teacher then asked him to sit for the 5-year old assessment paper. Again he did it with ease and got all the answers correct.

In the same room, at the back of the class, there were 2 other boys being taught by another teacher. They were learning about division (lesson was on halving). And the teacher had written on the board a list of numbers, something like that (I think they read half of xx = yy):
H20 -> 10
H40 -> 20
.
.
.

H was actually more interested in what the big boys were learning. H asked "mommy what are the kor kor learning?" I told him they're learning halving, e.g. half of 20 is 10. H then said "if you have 40 candies and share, each one will get 20?"

What's my take on Math Monkey?
If you've read my previous post you'd have read that my concern is that these math centres teach techniques to perform calculations but not math concepts. It's good for kids who already have the fundamentals, since all you want out of the programme is to equip them with the techniques to perform mental calculations with speed and accuracy. But for kids who don't have the fundamentals, then we're just training robots to churn out answers without really understanding the meaning of the numbers. I cannot really conclude whether concepts are actually taught in Math Monkey since I've only attended one lesson (and a simple lesson at that - perhaps at the higher levels the lessons are taught differently).

For example, in today's lesson when the kids were taught about bigger and smaller, the teacher asked, "Why is 8 bigger than 4?". I was expecting her to show quantities, something concrete, so that the kids can witness for themselves that 8 is bigger or more than 4. Instead she said, "because it's higher up the stairs", pointing to the stairs she drew on the board. I didn't think that was right. It's perhaps a good way to make the kids remember, but it certainly isn't the right way to teach quantities.

Would I send H to Math Monkey?
If H does not have the strong math concepts that he has, NO! Since he loves numbers and loves doing maths, MAYBE. I'd certainly not send him if he's at the Green Monkey Troop level. For H, he's placed at the Lemur Troop level in which mental math techniques will be introduced. It'll definitely be something new and interesting to him. Besides, participating in the games will help him come out of his 'shy' self.

At the end of the lesson, I asked H whether he enjoyed himself and whether he wanted to go again, he nodded yes. So maybe we'll give it a try :-) 

mental maths - yes or no?

Following my previous post about H's keen interest in maths, I have done some desktop research on the various maths programmes available around KL. I won't be reviewing any of them since I've not personally paid them a visit to find out about their programmes (hence it won't be fair to offer my opinion) but I'll share my perspectives on mental maths / maths enrichment.

There are essentially 2 types of programmes out there - those that teach kids fancy techniques to solve math equations quickly (e.g. abacus, finger counting, vedic), and those that adopt the principle that ‘practice makes perfect’ (e.g. kids are given worksheets during lessons and homework to practise on). Reading off their websites, they all have their own so call unique selling proposition and it’s really quite tempting to enrol H into one of the programmes just to make sure he doesn’t lose out. But taking a step back and my kiasu hat off (I really hate to think of myself as being a kiasu mom), I asked myself “is being able to calculate with lightning speed really necessary?”

I am for one hopeless in mental calculation but that has never hindered my ability to deliver my work efficiently. My brain is just too lazy whenever required to calculate, e.g. after meals with friends when we have to split the bill, I’ll wait for someone to tell me how much to pay or simply whip out my phone calculator. So what I’m trying to say is that it’s a nice-to-have skill but not necessarily critical. Unless of course you want to land yourself that highly coveted investment banking job. That is the only time that lightning speed calculation is required (you’re not allowed to use the calculator) to pass those quantitative tests during the interviews. But then again, normally you are still given paper and pen, so as long as you’re not a math retard you should still be able to pass. 

What is more important I feel is comprehension, critical thinking and reasoning skills. After all, we want our kids to be able to solve problems not equations. There’s really no point in knowing how to recognise symbols and solve equations quickly, but not fully understanding the concepts of addition, subtraction, multiplication and division.  In the real working world, maths is not about doing sums, it’s about understanding the problem statement and knowing how to apply the right math concepts to solve the problem. Kids can be easily trained to solve equations such as 6+2=8 quickly using abacus, finger counting or other techniques, or simply through practice, practice and more practice! However, solving problems require comprehension and thinking skills. You need to know how to construct the right equations in order to calculate. If you can’t do so, there’s no point in knowing how to calculate quickly. An example of a problem statement is: Jane takes 3 hours to travel and starts off her journey at 5pm. If Jake takes an hour less to travel compared to Jane and starts off an hour later than Jane, what time will Jake arrive? By understanding the problem and applying the right math concept, you can then construct the right equation to solve for the answer 6 (o’clock) +2 (hours) =8 (o’clock).

Anyway, I’m not saying that mental maths / maths enrichment programmes are a waste of time and money. What I’m saying is that you need to know what the programmes are offering and decide whether they suit your kids and their circumstances. For us (or me at least), H does not have problems doing simple maths. He knows the basic math concepts. He loves doing maths – sometimes his workbook, sometimes by writing and solving his own equations – and always on his own initiative. So at 4 years old, I think it’s not necessary that he goes through the stress of formal maths lessons and homework. I will continue teaching him at home whenever a teaching moment arises and he should be no worse off for not attending math classes. But just to satisfy Hubs, I will still go visit some of those more well-known centres in December when I’m less busy. Who knows, maybe my perspective will change after that? We shall see…

Skip counting

H has a knack for numbers. He knows the concept of skip counting (which is in fact multiplication but he doesn't know that). For him, it's just a game. I'm not sure how he picked this up. It could be imprints from the tweedlewink classes he attended when he was a toddler, or from the "I Can't Sleep" bedtime storybook I read him in which the boy started counting animals to fall asleep - 1 by 1, then 2 by 2, then 3 by 3, then 4 by 4.

Last night, H said he wanted to show me a new game. He drew grids on his magnadoodle board and wrote 1-8 in the first column. The game was to skip count and write the correct numbers in the squares.


Not sure how this can be a game since he's essentially playing on his own. Halfway through it struck him that what he has is in fact a matrix, i.e. the 6th row is in fact the same as the 6th column. Daddy was rather impressed and thinks that we should send him for maths classes since he likes maths. Maybe mental maths? I'm not sure if that will kill his love for maths, last thing we want is to make it seem like work rather than fun. But I guess there's no harm finding out more about how some of these maths programmes are run, then we can decide.