square_25 442 Report post Posted May 2 (edited) I’m helping out at a math class at a coop, and the teacher said today that finger counting should be discouraged. This was news to me! I always encouraged any strategy that made sense to my daughter, while also introducing her to more efficient strategies. She hasn’t used her fingers in more than a year, but it was a lovely stepping stone. Having dug around, I found that math education has been anti-fingers for years, but I can’t tell if there’s good evidence for this. I also found this: https://www.ncbi.nlm.nih.gov/m/pubmed/18387567/ Does anyone know if there’s good evidence against finger counting?? Do you personally have experience with the pros and cons of this strategy? Edited May 2 by square_25 Share this post Link to post Share on other sites

HomeAgain 13,717 Report post Posted May 2 I don’t like it because I think it works against fluidity of numbers and breaking them into appropriate groups. I don’t discourage it until they’re past the counting stage and firmly in addition/subtraction, but I don’t encourage it either. And no, I have no data to back me up. 🙂 2 Share this post Link to post Share on other sites

square_25 442 Report post Posted May 2 22 minutes ago, HomeAgain said: I don’t like it because I think it works against fluidity of numbers and breaking them into appropriate groups. I don’t discourage it until they’re past the counting stage and firmly in addition/subtraction, but I don’t encourage it either. And no, I have no data to back me up. 🙂 I tend to encourage whatever strategy makes sense to kids, which is why this recommendation is counter to my intuition... It's interesting to think about it, though. 1 Share this post Link to post Share on other sites

ClemsonDana 920 Report post Posted May 2 My 2nd grade teacher encouraged finger counting as how we should do arithmetic...and I counted on my fingers until at least high school. Although I wouldn't have liked it at the time, I wish we'd been encouraged to do it differently because I wasn't as quick with adding and subtracting as I was with multiplication and division (which we were forced to learn for timed tests in 4th grade). My kids used singapore math and they learned to 'see' everything as groups of tens. So, they never counted from 8 to 14 to see that 14-8 is 6 - they would know that you needed 2 to get to 10 and then 4 more was 6. I had expected that a tens-based method would have more finger use, but because the kids only had to learn a tiny number of facts, they remembered them and never used fingers. I do use fingers with the kids that I help in my volunteer gig, but they seem to cling to counting without ever developing any number sense. 1 Share this post Link to post Share on other sites

square_25 442 Report post Posted May 2 4 minutes ago, ClemsonDana said: My 2nd grade teacher encouraged finger counting as how we should do arithmetic...and I counted on my fingers until at least high school. Although I wouldn't have liked it at the time, I wish we'd been encouraged to do it differently because I wasn't as quick with adding and subtracting as I was with multiplication and division (which we were forced to learn for timed tests in 4th grade). My kids used singapore math and they learned to 'see' everything as groups of tens. So, they never counted from 8 to 14 to see that 14-8 is 6 - they would know that you needed 2 to get to 10 and then 4 more was 6. I had expected that a tens-based method would have more finger use, but because the kids only had to learn a tiny number of facts, they remembered them and never used fingers. I do use fingers with the kids that I help in my volunteer gig, but they seem to cling to counting without ever developing any number sense. Hmmmm, interesting. Maybe the right progression is to use fingers as long as you need, but also do some drill along the way to make sure you get the facts down (plus other strategies)? How old are the kids you help when volunteering? Share this post Link to post Share on other sites

happysmileylady 16,915 Report post Posted May 2 12 minutes ago, square_25 said: Hmmmm, interesting. Maybe the right progression is to use fingers as long as you need, but also do some drill along the way to make sure you get the facts down (plus other strategies)? I think this is the way to go generally speaking. Like a previous poster, I was finger counting for an extended period of time. However, it never really bothered me. And I did eventually memorize the basic addition and subtraction facts just through use. I am finding with DD10's math that the need for speedy calculations has been pushed down in grades, so I am working to try to ensure that she has the facts of all 4 operations memorized...I am crossing my fingers we will get there by the end of the summer. DD8 already has probably half the addition facts and most of the related subtraction facts memorized. 1 Share this post Link to post Share on other sites

Skippy 342 Report post Posted May 2 16 minutes ago, square_25 said: Maybe the right progression is to use fingers as long as you need, but also do some drill along the way to make sure you get the facts down (plus other strategies)? Yes, I think this is a good compromise. Using fingers and other things like skip counting can be useful and are fine early on. But eventually drill will probably be necessary to ensure that the facts come quickly. 1 Share this post Link to post Share on other sites

square_25 442 Report post Posted May 2 3 minutes ago, Skippy said: Yes, I think this is a good compromise. Using fingers and other things like skip counting can be useful and are fine early on. But eventually drill will probably be necessary to ensure that the facts come quickly. That's certainly what I did with my daughter. But I never discouraged finger use when she needed it, I just made sure to include drill (usually verbal drill) and questions that exercised other strategies. We started adding when she was in the finger phase, and she had to do quite a lot of visual regrouping, so I think that encouraged her not to use fingers (since she was using pictures instead.) But I was always fine with her checking her calculations on fingers if she needed to... Would any of you discourage finger use as opposed to gently encouraging other things? I would really worry about teaching helplessness to kids... like "my teacher took away my favorite strategy, and I'm not good at others yet, so what do I do??" Share this post Link to post Share on other sites

Skippy 342 Report post Posted May 2 1 minute ago, square_25 said: That's certainly what I did with my daughter. But I never discouraged finger use when she needed it, I just made sure to include drill (usually verbal drill) and questions that exercised other strategies. We started adding when she was in the finger phase, and she had to do quite a lot of visual regrouping, so I think that encouraged her not to use fingers (since she was using pictures instead.) But I was always fine with her checking her calculations on fingers if she needed to... Would any of you discourage finger use as opposed to gently encouraging other things? I would really worry about teaching helplessness to kids... like "my teacher took away my favorite strategy, and I'm not good at others yet, so what do I do??" I agree with your thoughts. I wouldn't prohibit using fingers but would include other strategies to improve comprehension and speed. Share this post Link to post Share on other sites

happysmileylady 16,915 Report post Posted May 2 7 minutes ago, square_25 said: Would any of you discourage finger use as opposed to gently encouraging other things? I would really worry about teaching helplessness to kids... like "my teacher took away my favorite strategy, and I'm not good at others yet, so what do I do??" I personally wouldn't. I wouldn't worry about teaching helplessness or anything like that. But I see no reason to discourage it. Just encouraging other methods that help to increase speed. Share this post Link to post Share on other sites

RootAnn 10,408 Report post Posted May 2 (edited) If finger counting is discouraged, I would make sure other manipulatives are available for easy use. I needed that concrete item to move around until I could use my brain to visualize the groupings and relations. I had one kid that needed manipulatives a lot longer than most kids. We used fingers, counting dinosaurs (instead of the usually sold counting bears), an abacus, cuisinaire rods, base 10 blocks, etc. Then we moved on to visualizing concrete items like stacks of hay & number of horses or stalls in a barn. Or chickens & eggs. Or cookies & kids. Or pieces of pie & number of kids. [Obviously, she was well into division at this point. Using the abacus for long division was ... interesting.] Finally, she was able to just deal with the numbers without the items or the idea of the objects behind the numbers. I think fingers/manipulatives help some kids to eventually get to the visualization stage and then the straight number stage. Some kids can visualize right away. Others can go straight to the numbers. Edited May 2 by RootAnn 3 Share this post Link to post Share on other sites

square_25 442 Report post Posted May 2 36 minutes ago, RootAnn said: If finger counting is discouraged, I would make sure other manipulatives are available for easy use. I needed that concrete item to move around until I could use my brain to visualize the groupings and relations. I had one kid that needed manipulatives a lot longer than most kids. We used fingers, counting dinosaurs (instead of the usually sold counting bears), an abacus, cuisinaire rods, base 10 blocks, etc. Then we moved on to visualizing concrete items like stacks of hay & number of horses or stalls in a barn. Or chickens & eggs. Or cookies & kids. Or pieces of pie & number of kids. [Obviously, she was well into division at this point. Using the abacus for long division was ... interesting.] Finally, she was able to just deal with the numbers without the items or the idea of the objects behind the numbers. I think fingers/manipulatives help some kids to eventually get to the visualization stage and then the straight number stage. Some kids can visualize right away. Others can go straight to the numbers. There were Cuisinaire rods available, to be fair. I think personally I would have shown using the rods along with using fingers instead of saying using fingers is bad, though... Share this post Link to post Share on other sites

mom2scouts 3,786 Report post Posted May 2 My high school algebra teacher had been some kind of mathematician in the military and he frequently used his fingers. After seeing how efficient he was with something you have available all the time, I decided I wouldn't forbid my children from using their fingers. I always thought it was interesting because we were shamed for counting on our fingers in elementary school. 2 Share this post Link to post Share on other sites

ClemsonDana 920 Report post Posted May 2 The kids that I volunteer with are elementary age, but some are older elementary. I have found myself doing long division with kids who have to figure out how many times 6 goes into 40 by counting by 6s...which would be fine if they could skip count, but they count each group of 6 on their fingers, leaving them no fingers to keep track of how many 6s they've counted. Painful does not begin to describe it. My own kids did use fingers when learning to count, but once they got into their school math they would sometimes use their hands to see the numbers but didn't seem to need to count them. I think once they got that there were 5 on one hand maybe they'd mentally count to get to 7, but they didn't really need to count them. Likewise, if they were thinking '10-3' they'd just put down 3 fingers and could 'see' 7. They may have counted at some point, but it was just a matter of days, maybe weeks, before they understood the numbers from 6-10 that would necessitate counting the second hand. The kids that I volunteer with don't really understand regrouping at all. By the end of K-1 I had coached them to start with 5 and just add the other fingers, but their curriculum the next year required them to draw sticks and count them, so they went from 'being able to hold the bigger number in their head' when adding 8+5 (start with the 8 and count up on 5 fingers) to having to draw 8 sticks and then 5 sticks and then start at 1 to count them all. I was ready to weep when, by spring of first grade, they had regressed and were no longer able to do what we were doing at the end of K. Constantly changing methods (and, for all I know, changing teachers), random worksheets with different requirements (much of it Eureka math), and the students' knowledge that everything would be marked wrong if they didn't draw...having done singapore math with my kids, I felt like they took random parts of it, made them as unwieldy as possible, and then stuck them back together in a nonsensical way such that the kids had neither the algorithms of traditional math teaching nor the concepts taught in singapore. It's worse than what I had in early elementary, which was 'traditional algorithm with no fact teaching so that you had to keep counting' - I remember a teacher saying that that's what those things on the end of our hands were for. 2 weeks of my kids using unit cube blocks to regroup into 10s and the mental math of all of us was better than what I had when I finished middle school. It's not the only way, obviously, but I remember watching them and thinking 'why did nobody do this with us...why did we keep counting?'. 1 Share this post Link to post Share on other sites

square_25 442 Report post Posted May 2 (edited) 14 minutes ago, ClemsonDana said: The kids that I volunteer with are elementary age, but some are older elementary. I have found myself doing long division with kids who have to figure out how many times 6 goes into 40 by counting by 6s...which would be fine if they could skip count, but they count each group of 6 on their fingers, leaving them no fingers to keep track of how many 6s they've counted. Painful does not begin to describe it. My own kids did use fingers when learning to count, but once they got into their school math they would sometimes use their hands to see the numbers but didn't seem to need to count them. I think once they got that there were 5 on one hand maybe they'd mentally count to get to 7, but they didn't really need to count them. Likewise, if they were thinking '10-3' they'd just put down 3 fingers and could 'see' 7. They may have counted at some point, but it was just a matter of days, maybe weeks, before they understood the numbers from 6-10 that would necessitate counting the second hand. The kids that I volunteer with don't really understand regrouping at all. By the end of K-1 I had coached them to start with 5 and just add the other fingers, but their curriculum the next year required them to draw sticks and count them, so they went from 'being able to hold the bigger number in their head' when adding 8+5 (start with the 8 and count up on 5 fingers) to having to draw 8 sticks and then 5 sticks and then start at 1 to count them all. I was ready to weep when, by spring of first grade, they had regressed and were no longer able to do what we were doing at the end of K. Constantly changing methods (and, for all I know, changing teachers), random worksheets with different requirements (much of it Eureka math), and the students' knowledge that everything would be marked wrong if they didn't draw...having done singapore math with my kids, I felt like they took random parts of it, made them as unwieldy as possible, and then stuck them back together in a nonsensical way such that the kids had neither the algorithms of traditional math teaching nor the concepts taught in singapore. It's worse than what I had in early elementary, which was 'traditional algorithm with no fact teaching so that you had to keep counting' - I remember a teacher saying that that's what those things on the end of our hands were for. 2 weeks of my kids using unit cube blocks to regroup into 10s and the mental math of all of us was better than what I had when I finished middle school. It's not the only way, obviously, but I remember watching them and thinking 'why did nobody do this with us...why did we keep counting?'. Oof, forcing kids to draw sticks and count them! That reminds me of my daughter's kindergarten class: her teacher insisted that she draw her "strategy" of how she did additions like 3+4, which flummoxed her, because she had already memorized this addition fact for a year, and she didn't know what to draw. Eventually, we convinced her and her teacher that she could just draw a picture of her hands showing her fingers for her "strategy" (even though I'm not sure she was really using her fingers at this point most of the time.) I now can't quite remember what we did with my daughter! There was definitely progress, though. First she showed everything on her fingers, then she'd just show the smaller number on her fingers and count up from 1 plus whatever number she was adding to, then we got into drawing groups of 10s and 1s for adding (if need be) and I think she'd just use her fingers as a reminder, and for a year now she doesn't use her fingers at all. I would definitely be worried if kids didn't move on from finger counting! For us, the useful tools were definitely fingers and visual representations of the base 10 system. Plus visual representations of equations that made the part-whole relationship clear. I think my daughter figured out the pairs that make 10 as a natural part of exploring how to add two digit numbers using place value... we didn't focus on it particularly. We did drill her facts somewhat, though, although I remember feeling like there was an age at which drilling didn't take and an age at which it did. Edited May 2 by square_25 Share this post Link to post Share on other sites

sweet2ndchance 821 Report post Posted May 2 I remember being discouraged and even reprimanded for using my fingers when I was a child. It just made me better at hiding the fact that I was using my fingers. I am firmly of the belief kids will only use their fingers for as long as they need that concrete stage and while there is a general age range that is considered normal for the concrete stage, a child that lingers longer in the concrete stage should not be discouraged, or worse shamed, for doing so. They will stop using their fingers when they make the conceptual leap into the abstract stage. Not every child will make that leap at the same time. It is one of the many reasons I am glad to homeschool my children, so they can learn at their pace without being made to feel awkward for learning faster or slower than anyone else. 3 Share this post Link to post Share on other sites

square_25 442 Report post Posted May 2 25 minutes ago, sweet2ndchance said: I remember being discouraged and even reprimanded for using my fingers when I was a child. It just made me better at hiding the fact that I was using my fingers. I am firmly of the belief kids will only use their fingers for as long as they need that concrete stage and while there is a general age range that is considered normal for the concrete stage, a child that lingers longer in the concrete stage should not be discouraged, or worse shamed, for doing so. They will stop using their fingers when they make the conceptual leap into the abstract stage. Not every child will make that leap at the same time. It is one of the many reasons I am glad to homeschool my children, so they can learn at their pace without being made to feel awkward for learning faster or slower than anyone else. That's certainly my strong belief as well. I'd need very strong evidence before I abandoned that belief, and I'm not finding it when I try to look up the literature (although it's possible it's out there and I haven't found it yet.) @ClemsonDana, I looked up the Eureka Math worksheets, and they don't seem obviously evil, but of course I've never used them. Do you think they do something wrong? Share this post Link to post Share on other sites

ClemsonDana 920 Report post Posted May 3 Part of the Eureka math complaint may just be how they're used - there seems to be no plan that builds math skills with the kids that I work with, so the homework pages are just random. There is also the insane amount of drawing - drawing once they know how to do it, drawing 20+ items (they take forever to draw, the kids don't want to draw sticks or dots for every problem so you're waiting for them to draw 13 + 12 stars, cars, etc) and the pages being set up in such a formulaic way that once you help the kids through the first problem they can often do additional problems without understanding. For instance, it will want the kids to add 12 + 13 by drawing, so they draw, and then they count and write 25, and then they fill in blanks so that it's 2 tens and 5 ones which is supposed to help them learn place value. But, they don't really get that they added the ones and got that there were 5 and then the tens and there were 2 because they never added them...they counted 25 stars and then just bring down the numbers 2 and 5 and put them in the boxes next to tens and ones, which are right under where they wrote 25. This approach seems sensible at first, but they don't move beyond it for ages. It led to the regression that I mentioned in my first post - once the kids can add, why would they continue to be required to draw for addition for another whole school year? And, did the writers give thought to how long it takes kids to draw 20+ objects for each of 5-10 problems? I saw kids fly through the math and then dejectedly go back to draw, and I saw others skip learning arithmetic because if they had to draw anyway, why not just count? And, although it might just be specific to this school, there seems to be no practice of facts and frequent moving on before early skills are mastered. It always feels like they add for 3 years and then multiply for 2 weeks before moving on to division. I'm sure it's not that bad, but trying to work through division problems with kids who don't grasp multiplication is painful. Then, when we got to the topic where I thought lots of drawing might help - fractions - there wasn't much. And, again, equivalent fractions before mastery of multiplication/division is painful. I think that what makes this so hard is that my younger kiddo is the same age as the younger of these kids - I started volunteering when both were in K (there was also a group of 1st graders that I helped with). At this point, several years later, my kid is years ahead of these kids. We started with 1st grade work, but we've moved through one year's book for each year of school, so we are finishing the 5th grade book now. The kids that I work with are 4th and 5th grade. They are doing math work that we did years ago. My kiddo is large for the age, and since my kid confidently helps with their math, they just assume that kiddo is older, but I remember when they were all learning how to add at the same time. I know that there are a lot of factors influencing the education of these kids, but for years I've been looking that their work and comparing it with what we're doing and I just can't process how it seems to be designed to frustrate those who understand while not being set up in a way that helps the confused. 2 1 Share this post Link to post Share on other sites

square_25 442 Report post Posted May 3 8 minutes ago, ClemsonDana said: Part of the Eureka math complaint may just be how they're used - there seems to be no plan that builds math skills with the kids that I work with, so the homework pages are just random. There is also the insane amount of drawing - drawing once they know how to do it, drawing 20+ items (they take forever to draw, the kids don't want to draw sticks or dots for every problem so you're waiting for them to draw 13 + 12 stars, cars, etc) and the pages being set up in such a formulaic way that once you help the kids through the first problem they can often do additional problems without understanding. For instance, it will want the kids to add 12 + 13 by drawing, so they draw, and then they count and write 25, and then they fill in blanks so that it's 2 tens and 5 ones which is supposed to help them learn place value. But, they don't really get that they added the ones and got that there were 5 and then the tens and there were 2 because they never added them...they counted 25 stars and then just bring down the numbers 2 and 5 and put them in the boxes next to tens and ones, which are right under where they wrote 25. This approach seems sensible at first, but they don't move beyond it for ages. It led to the regression that I mentioned in my first post - once the kids can add, why would they continue to be required to draw for addition for another whole school year? And, did the writers give thought to how long it takes kids to draw 20+ objects for each of 5-10 problems? I saw kids fly through the math and then dejectedly go back to draw, and I saw others skip learning arithmetic because if they had to draw anyway, why not just count? And, although it might just be specific to this school, there seems to be no practice of facts and frequent moving on before early skills are mastered. It always feels like they add for 3 years and then multiply for 2 weeks before moving on to division. I'm sure it's not that bad, but trying to work through division problems with kids who don't grasp multiplication is painful. Then, when we got to the topic where I thought lots of drawing might help - fractions - there wasn't much. And, again, equivalent fractions before mastery of multiplication/division is painful. I think that what makes this so hard is that my younger kiddo is the same age as the younger of these kids - I started volunteering when both were in K (there was also a group of 1st graders that I helped with). At this point, several years later, my kid is years ahead of these kids. We started with 1st grade work, but we've moved through one year's book for each year of school, so we are finishing the 5th grade book now. The kids that I work with are 4th and 5th grade. They are doing math work that we did years ago. My kiddo is large for the age, and since my kid confidently helps with their math, they just assume that kiddo is older, but I remember when they were all learning how to add at the same time. I know that there are a lot of factors influencing the education of these kids, but for years I've been looking that their work and comparing it with what we're doing and I just can't process how it seems to be designed to frustrate those who understand while not being set up in a way that helps the confused. Ugh. That sounds super irritating. Drawing large pictures is a recipe for frustration. Once we were adding multidigit numbers, we always drew things in 10s and 1s: we'd draw boxes with 10 objects (which we wrote a 10 on) and then single dots only for the units. We're partially homeschooling to avoid the mathematics teaching at the elementary school level, which depressed me. So I'm not surprised by what you described, but it's so unfortunate for those kids :-(. I actually always wonder why there's SO MUCH addition and subtraction before you get to multiplication. I think we started on multiplication before we even had our addition facts memorized, just so we could get used to the idea of multiplying numbers. We worked on addition facts as we worked through multiplication and division... it worked out well for us, because she didn't get as bored since she had a new concept to work through. Share this post Link to post Share on other sites

Farrar 53,740 Report post Posted May 3 I read something recently about why math teachers should stop discouraging it, though I can't remember where. I understand some of the arguments for trying to stop it. A lot of big C-rod proponents are against finger counting. I do think taking the representation away from fingers to the greater versatility of the rods is nice for a lot of kids and encourages a deeper understanding of things like number bonds, not to mention fractions. But overall, I agree with you, Square. Whatever works. Share this post Link to post Share on other sites

Sarah0000 514 Report post Posted May 3 I tend to gently discourage my kids from counting at all but I do encourage them to use their fingers, just not for direct counting. So even for multiplication the fingers will be, for example 8s, so if it's 7x8 we'll use the fingers to show you could do five 8s plus the rest or whatever configuration makes sense to kiddo. Or today ODS used fingers to reduce four tenths to two fifths (it had been a long time since he reviewed fractions). Share this post Link to post Share on other sites

geodob 1,328 Report post Posted May 3 Perhaps I could introduce you to a method of finger-counting? To start with, form a fist with your left hand. Palm up. To start counting, extend your 'little finger for 1. Then extend the next finger, alongside it. To form 2. An important part of this, is that they form a 'group of 2'. The next finger is extended, for a group of 3. Followed by the last finger, and a group of 4. We then, contract all of the fingers, and extend the thumb. Where the thumb represents a group of 5. With the thumb extended as 5. We can then extend the fingers, to reach a total of 9. To count 10, ten is carried over to the right hand. Using the same method, except that the fingers represent 10's and the thumb 50. So that both hands, can be used to count up to 99. When this method is practiced? It develops a 'motor memory' of where the fingers are, to represent a number. So that one can then 'feel the number', without having to use their fingers/hands. 2 Share this post Link to post Share on other sites

mumto2 28,809 Report post Posted May 3 I would never discourage finger counting simply because fingers are always with you. 😀 One of our curriculums had some simple games that used fingers for drills with addition and subtraction. Ds played the games and fingers were never used again but he didn’t use any manipulatives unless forced either..... My Dd started using her fingers with that curriculum and developed her own crazy fast finger math system that she continued using until I allowed calculators all the time which was pretty late in the game.......I think pre calc for her. It became discrete over time, in terms of her hands would occasionally sort of flick while doing math, completely unconscious and for all I know she might still do it since I no longer get to watch her do math.......it didn’t hurt her, math degree.😉 1 Share this post Link to post Share on other sites

Michael12 103 Report post Posted May 8 What geodob describes is what our family calls the "secret soroban" - it's exactly how the Japanese soroban abacus is set up (and you always have it with you for when you've mislaid the actual soroban). The thumbs are the "heavenly beads" and the fingers are the "earthly beads". This helps with the idea of place value because ones are all on the right hand and tens are all on the left hand. There's also a way to count to 1023 on your two hands (thumb is 1, index is 2, middle is 4, ring is 8, pinky is 16) - but this seems a bit much for the preschool set. 1 Share this post Link to post Share on other sites

deBij 28 Report post Posted May 10 (edited) On 5/3/2019 at 7:15 AM, geodob said: Perhaps I could introduce you to a method of finger-counting? To start with, form a fist with your left hand. Palm up. To start counting, extend your 'little finger for 1. Then extend the next finger, alongside it. To form 2. I taught my oldest to do finger-counting. It worked really well and it is a fantastic way to get to 99. Edited May 10 by deBij spelling... Share this post Link to post Share on other sites

square_25 442 Report post Posted May 10 On 5/8/2019 at 1:22 PM, Michael12 said: What geodob describes is what our family calls the "secret soroban" - it's exactly how the Japanese soroban abacus is set up (and you always have it with you for when you've mislaid the actual soroban). The thumbs are the "heavenly beads" and the fingers are the "earthly beads". This helps with the idea of place value because ones are all on the right hand and tens are all on the left hand. There's also a way to count to 1023 on your two hands (thumb is 1, index is 2, middle is 4, ring is 8, pinky is 16) - but this seems a bit much for the preschool set. We've done binary with my daughter, actually! She knows how to show it on her fingers as well. But that's not what she does when she counts on her fingers ;-). Share this post Link to post Share on other sites

geodob 1,328 Report post Posted May 10 Yes, the method I described. Is based on the Japanese Soroban. But their is something important about the method? Which is that it based on 'forming groups'. For example, if you extend your 'little finger', and your finger alongside it. You have formed a 'group of 2'. This is very different from counting each finger: 1, 2, 3, etc. Which rather names each finger, and doesn't provide a sense of 3 representing a group of 3. 1 Share this post Link to post Share on other sites

Mainer 1,145 Report post Posted May 12 I love finger counting! There is research to support finger counting: https://www.theatlantic.com/education/archive/2016/04/why-kids-should-use-their-fingers-in-math-class/478053/ 1 Share this post Link to post Share on other sites

kiwik 4,448 Report post Posted May 14 (edited) My kids were at school. They did counting from one on their fingers then with their hands behind their back then just visualising. Then counting on. It was good except ds12 was at the counting on and back before he started school (the day after he turned 5 here) so it took him a year to get back to where he started. But fingers never fall behind the couch or get thrown or hidden by the kitten. Edited May 14 by kiwik Share this post Link to post Share on other sites

Cake and Pi 567 Report post Posted May 15 I don't know of any research against it. I did read in How the Brain Learns Mathematics (IIRC?) something about quantities being processed in the same region of the brain as our hands or fingers, or something along those lines. I would never discourage using fingers, but I always discouraged counting except where strategically preferable, like when measuring cups of water added to a pot, marking time while washing hands, that kind of thing. I taught my boys to subitize and segment using fingers (and lots of other things), but not to count and never to "count on." As my DS#2 loudly announced to his kindergarten teacher when she tried to coax him into counting aloud, "Counting is slow and inefficient and often inaccurate!" Personally, I was taught in school to "count on" and it was crippling for my number sense and fluidity with numbers. I taught myself to count to 110 on my fingers (using left hand for tens and right hand for ones and the ASL one-handed signs for 0-10). I still have to stop myself sometimes and remember to use more efficient strategies. Share this post Link to post Share on other sites

HeighHo 2,138 Report post Posted May 15 Its not finger counting that is the issue, the issue is not moving on from count by ones; most likely because they do not have 1:1 correspondence, but sometimes because they haven't had the experience with the names of the numbers and the sequence. This may be helpful: https://nzmaths.co.nz/number-early-learning-progression When I was a parent helper for K, 1, and 2, my dc's classroom teacher had a number of activities for the students that help give them experience and move them forward thru the stages of addition as they develop their number skills. Keep in mind that because public school is full inclusion, the classroom will have students at all stages...even in grade 3 some included students will be taught to use their fingers for multiplication via memorized sequences like the nines finger trick so they can participate in the whole class activities, although the reg ed students are expected to use what is appropriate to their stage of development. https://www.k-5mathteachingresources.com is helpful, you might call someone there are get some recommendations for professional development material. Share this post Link to post Share on other sites

HeighHo 2,138 Report post Posted May 15 8 hours ago, Cake and Pi said: I don't know of any research against it. I did read in How the Brain Learns Mathematics (IIRC?) something about quantities being processed in the same region of the brain as our hands or fingers, or something along those lines. I would never discourage using fingers, but I always discouraged counting except where strategically preferable, like when measuring cups of water added to a pot, marking time while washing hands, that kind of thing. I taught my boys to subitize and segment using fingers (and lots of other things), but not to count and never to "count on." As my DS#2 loudly announced to his kindergarten teacher when she tried to coax him into counting aloud, "Counting is slow and inefficient and often inaccurate!" Personally, I was taught in school to "count on" and it was crippling for my number sense and fluidity with numbers. I taught myself to count to 110 on my fingers (using left hand for tens and right hand for ones and the ASL one-handed signs for 0-10). I still have to stop myself sometimes and remember to use more efficient strategies. I found count on and count back to be good methods to know when doing the coding units and Algebra. Very easy to teach the shifts, especially if the child had the number line or the x-y graph in his mind's eye. Agree, I would move on from count by 1s if they have 1:1 correspondence down as well as developed the ability to count backward and know their small sets by sight (can look at a domino and tell you how many dots on each side for example). Share this post Link to post Share on other sites

square_25 442 Report post Posted May 17 We went through a counting and then a counting on stage and it didn’t seem to hurt her understanding. I think the issue is not moving on from it, not doing it at first. Share this post Link to post Share on other sites

Mainer 1,145 Report post Posted May 18 One of my students was stuck in the "counting ALL the things" stage, like if she had 4 buttons and 3 buttons, how many in all? She would NEVER start at 4 and count on 3 more... she always started at 1. When she counted on her fingers, for something like 7+9, she started at ONE and then counted seven, and then tried to count 9... it was a mess! Doing it that way, she'd do 7+9 and get 6. Arg! I finally eased her into counting on by having her add one die with the dots on it, and the other die with just the number on it. I also had to prompt her to start with the larger number. It took a long time but now she always does it. I think it's just a developmental stage, just as moving on from it is a developmental stage... I'm all for some gentle encouragement to move on, but if it's too soon, there's not much to do except wait and practice! Share this post Link to post Share on other sites

ClemsonDana 920 Report post Posted May 20 The further chronicles of my after-school homework help kids...last week I was helping a 1st grader with math. She had problems like 'If you have 3 pencils and 9 pens, how may writing utensils do you have?' and 'If you have 14 pencils and give 6 to your friend, how many do you have left?'. They were supposed to set them up, Singapore bar graph style...and then draw the correct number of dots in each part of the bar. So, I did the expected work of helping the kiddo see whether they were looking for the total or if they had the total and needed to subtract, and then they'd draw the bars and put the numbers in the right place. For addition, they would then draw the dots and count, starting at 1. For subtraction, they would draw the dots in one part, then recount the dots and add dots to the other part until they got to the correct total, and then go back and count how many dots they drew in the 2nd box (for instance, drawing 6 dots, then counting 1-6, then continuing on with 7-14 while drawing dots, then counting the 8 dots). Share this post Link to post Share on other sites