What I love about the internet is that you can have heated discussions with complete strangers!
“Musician Dad”, I’ve decided to make you famous (not DiCaprio famous, just Maths Insider famous!)
Not because of your musical skills.
Not because of your fathering skills;
But because you disagree with me (and your writing is better than mine)!
You are a finger counting fanatic!
I wrote the post No! No! No! No! Don’t let your child finger count! in response to the intense debate on the mothering.com education forum.
The original question from “Emilysmama” was:
How do I get my 6 y.o. to stop counting with her fingers?
If finger counting is an issue for your child, it’s worth reading the whole thread.
However, the most eloquent of the pro finger counters was “Musician Dad”.
I present a selection of his quotes below, in green, from the mothering.com forum, with my responses in black :
Regarding Finger counting as a visual starter
Using a different set of items is still using a visual representation of numbers, the only difference is you have your fingers with you at all times. You can’t misplace them, and taught properly, you can do larger number equations as well. You won’t need a whole bag of them to do 233 + 432.
If you have your fingers with you all the time, and use them all the time, there is no incentive to try to memorise and figuring out how to do more than basic arithmetic can be harder than using other visual or memory based techniques.
Regarding Finger counting disadvantages a child
Someone who can figure out a complex math problem using their fingers can still figure out a complex math problem. Failing them because they can’t do it fast enough is just plain dumb.
I finger count at times, I have friends that finger count at times. Many of us have excelled in math intensive studies in spite of (or maybe because of?) this.
I agree that lightening speed is not necessarily the main objective (but it’s cool!), especially if accuracy suffers. I’ve seen 10 year olds take 20 seconds to work out 13 + 9 because they’re counting out 13 fingers, then adding another 9. (very uncomfortable!)
Mathematics is actually a broad subject, so it’s true that you can excel at higher level maths without memorising basic facts as it’s often the deep understanding of mathematical concepts that elevates mathematicians who solve the worlds most complex mathematical problems.
Regarding Finger counting discouraging memorisation
There are people, the more times they count on their fingers to figure out the equation, it puts the equation into the “I did it myself, so I have an easier time remembering next time” category.
One day while out with his dad, who knew he was working on multiplication, a father asked his son a question.
“Son,” the dad said, “can you tell me what 2 x 6 is?”
Without even looking at his hands the boy announced “It’s twelve, right?”
“That’s right,” the dad replied. “You are very good at math, aren’t you.”
“I guess, but mostly I just figured it out on my fingers so many times that I had no trouble remembering it now.” The boy told him. And it’s true, he had counted by twos on his fingers so often that by that time he just knew what the answer was.
This can also be true if you ask a child to visualise counting their fingers or other objects in their head.
I ended with this quote:
“Musiciandad, your arguments are both reasoned and persuasive, but if we return to the OP’s(Original Poster’s) question, her child only recently started finger counting and was previously able to recall number facts to 10. What I want to draw attention to is the unspoken idea that not only is it ok not to be able to recall number facts with ease but that as a parent, the OP shouldn’t try to help her child memorise these facts.
Yes, I’m sure her child could still become a great mathematician even if she continued finger counting, but let me support the OP in her attempt to help her child”
The full debate continues on the mothering.com forum!
So who do you agree with?
Tell us in the comments!
I have had year/grade 7 and 8 below-average maths students who finger-count. I was initially surprised at how embarrassed some of them were to do so. There is a stigma attached to it and there are apparently teachers who discourage its use.
My take is this…. if finger-counting allows you to engage with me and the maths I teach now, by all means use it. It’s a tool and yes, there are more efficient ways and tools but for some, that’s all they have. There are bigger battles to fight, i.e. doing maths at all.
Following this train of thought, some will argue that the use of calculators dumb kids down. As a computer programmer in a previous lifetime, I believe that technology is there for such purposes. If, as a maths teacher, I can get a student to a point ready to punch calculator buttons (or count fingers) to solve a problem – and make sense of the resulting answer…it’s not all in vain.
That said, I aspire for good number skills in all my students.
That’s a good point! I guess even as parents their children to finger count, there has to be a balance between encouraging memorization and pressuring then so much that they get turned off maths.
I have followed this with some interest as my daughter is a little behind in math. As a teacher (I teach HS English) I didn’t know it wasn’t advisable to finger count.
Here’s my question for you then – what about ADD/ADHD kiddos? They are known for having issues with memorizing math facts and unfortunately both of my kids fit this. My son almost aced the math portion of his state test last year, so he knows what is going on, he just still stumbles over his facts.
What are your thoughts on this?
I found this piece of research which amongst many things says that for children with ADHD, “(math) instruction should focus on math strategies rather then fact recall.”
Maths education (at least in the UK) has indeed moved towards teaching strategies (e.g. 5+7 is 5+5+2. I think all children can benefit from this combination of maths strategies leading to memorisation whether fingers, blocks, choc chips or counting rods are used!
Hope this helps!
Ooooo!!! This looks like an interesting discussion! I tend to think, let the kids use what works for them, as there are so many different learning styles. But when I know they can do it mentally, I would probably encourage them to do so. We used Singapore Math with our boys up through 6th grade, which really stresses mental math. After that, we loved Teaching Textbooks. Fabulous! Now my older two are in public school, and doing well there too.
Thanks for visiting my blog this morning.
P.S. I had never heard of the Kumon method before….I am learning the Orton Gillingham method for tutoring struggling readers/spellers…it is a multisensory approach…a big part of it is finger spelling and finger tracing (because muscle memory is huge)! But this is for remedial learning really, and not used if your child doesn’t need the extra help.
Yes, there is a fine line between what is seen is efficient and what can put a child off maths. My two older kids are both very different mathematicians from each other but both get it done in the end!
The Orton Gillingham method looks interesting. I’ll look into it further, maybe there’s a way it can be used for struggling mathematicians.
I don’t have strong feelings about finger-counting. I just want to warn you that you may get in trouble at mothering.com for “directing” people there, if they see that some people join specifically to get involved in this debate and especially if those people are on your side; they really don’t like that. And did you ask Musician Dad if it was okay with him for you to “reprint” what he wrote?
Hi ‘Becca!
I’d posted a link on mothering.com to my previous finger counting post a few weeks back and to this post just after I posted it. I was more worried that they would think I was pulling their readers away rather than me sending my gang to their doorstep, that’s an interesting point!
Yes, I messed up by not asking musiciandad prior to using his quotes; he pulled me up on that. I apologised on the forum and we’ve made peace! Valuable lesson learnt.
Interesting debate. My 7 year old started counting on her fingers in kindergarten and 1st grade. We gently tried to steer her away from it, afraid that she would be in trouble when it came to the higher numbers. Now, entering 3rd grade, she has improved at calculating answers in her head. So, without knowing about any debate, I was drawn to mental math rather than finger counting.
I wonder if it’s just us as parents wanting our children to be “just like us” so if we didn’t finger count then we don’t want our kids to either!
HI. I am a Math Intervention teacher (NOT Math Remediation teacher). I am glad to see you move into the natural progression of math from the to the mind. Great job! When a student is focused on basic math instead of what the teacher is teaching, a crack develops where more knowledge is lost! the purpose is to develop the mind not the fingers. m :-) what/whoever is doing the work is strengthened.
Mr. P
I’ve not had to deal with children finger counting to do arithmetic. At a very early age I taught my son to count in binary on his fingers, a skill I still find useful as an adult when I have to count things (particularly letters or numbers, which can be distracting for oral counting). Animated instructions are available as a
Scratch animation
My son was pretty much at grade level for memorizing number facts, though he got the algorithms and number sense much quicker than average. He did use counting-by-n for about a year as a crutch for multiplication, but doing a bunch of multiplication problems in school got him past that, since he prized being the first one done, and counting-by-n was slow.
Thanks for joining the debate! Yes, the binary counting is cool. Great website! Mr Maths Insider showed that to my kids a few months ago! You’re right that peer pressure and sheer ambition probably have a great influence on how quickly children stop finger counting.
I’ve recently discovered your blog- congratulations!! Many of the topics/discussions you raise are exactly what i’ve been pondering over for the last few months!!
Here’s my question, do you ‘teach’ strategies to kids for working out maths equations in their head(I know in the UK they focus on,for example, ‘making 10’ and other strategies to help ‘work out’ other arithmetic questions )..or do you do short drills and then allow children to work out their own strategies?..
My husband is a mental maths whizz, his brain seems to do these quick strategies without thinking.I asked if he was taught these strategies, but he couldn’t remember:)
I’ve tried to teach simple strategies to my nearly 7yr old.She’s super fast when I remind her of the strategy to use..but I have to keep reminding her, so i’m thinking perhaps she just needs short drill for now and let HER brain do the rest- after all the brain is a brilliant,mind boggling machine!
Any advice? I await with anticipation..
Thanks for your question, I’m sure it’s one that lots of people have!
From my personal experience with my own children and with Kumon students when I ran a Kumon centre, it’s definitely helpful to introduce various mental maths strategies but it’s the actual repetition that will produce the speed. Some people, like your husband probably use mental maths more recreationally, for example working out how much the full tank of petrol will cost, or approximating the sale price in a shop, or the bill in a restaurant. The more he uses it, the more he’s comfortable with using it and the more he’ll use it etc.
For our children, some again will be working out house points they need to get a bronze certificate or their change in the school canteen, but until they get comfortable using mental maths regularly, then drills and strategies will help them built up their skill and confidence.
Do you repeat,asking them to use a strategy you’ve introduced or just repeat?…sorry hope it makes sense?
Thank you for your response
Try this:
1)Test them
2)Show them the strategy and practice with that strategy
3) Test them again to see if that strategy has improved their fluency
In all cases, if they work faster/more confidently without a strategy or with their own strategy then that’s fine!
Do pop back and let us know how it goes!
I am a member of Mensa and do well on tests, including math tests. I am also a teacher. I have always used my fingers (and little dots on the numbers on the paper…which I invented myself, not knowing someone else also invented it, packaged it and made money off of it….who’d a thunk?) on addition and subtraction problems.
I had actually heard that there were studies saying that those who use their fingers to work math problems had a better understanding of math concepts than those who don’t….i’m not sure this is factual, but I sure believe it. I was wondering if anyone had heard of such research?
It also seems to me that one can memorize ANYTHING, including incorrect math facts. One can also recall them incorrectly. One will not miraculously grow or lose a finger mid-math computation; they are always there and always accurate. As long as counting is very accurate (ie. not calling a five a four every now and then) fingers will always be correct.
1 second answer speed and 100% accuracy for addition and subtraction are SO foundational for long division, and many other math operations at higher levels. I do believe that carefully building toward that goal is the best way, not simply memorizing flash cards without reason. For example, all even numbers 10 or less start like this. 8 =4+4, 3+5, 2+6, 1+7, 0+8 Every even number has a matching pair that looks like backwards counting. Memorizing pairs of numbers greatly simplifies addition, and subtraction in the same way. Odd numbers just start out a little weird, 11 = 5+6, 4+7, 3+8, 2+9, 1+10, 0+11. Understanding pairs of numbers while physically sitting on their hands is the best and quickest way to say goodby to the slow, finger counting method.
Finger counting is basic as the child advances to do complex calculations quickly the child has to master other ways of solving arithmetic problems. It’s a trend today that children learn the beauty of numbers and lose fear of mathematics doing abacus activities. It is good to encourage children solve problems with useful maths techniques early on, so the child learns to do maths smartly. Let the child feel that maths is magic and has logic and structure to it, counting makes maths routine and tiresome. Basically there are lots of creative ways to solve sums, so kids should be introduced to them.