How to Teach Your Child Math: Glenn Doman’s Dot Method

November 1, 2007 — Alenka | Posted in Math, Teach Your Child.

dots

Dot method?! What is it?

Out of all the methods by Glenn Doman, his approach to learning math is the most… surprising. We are used to recitals of sequence of numbers (1, 2, 3…), then simple counting, then long and difficult process of weaning off counting fingers and teaching kids to do it in their minds.

Glen Doman believes that there is no need for this long and difficult process. According to the research that was conducted in the Institutes of Achieving Human Potential, children are born with an ability to discern quantity of objects by sight. Remember Rainman? Looking at a hundreds of toothpicks and saying their exact number without counting. Apparently all the kids are able to do it and lose this amazing ability if we don’t help them develop it. In order to do it, Glen Doman suggests using large flash cards with dots (hence - Dot Method), increasing the number of random dots on the cards gradually, getting children accustomed first to quantities, then to equasions with those quantities, and finally even with algebraic sequences, sophisticated equations and even inequalities. Since children get used to doing equations with dots (quantities) instead of numbers (meaningless symbols!), they learn to UNDERSTAND problem solving in math, as opposed to memorizing the formulas to get to the correct answer of the problem. Once children go through this introductory concept of quantities, normal numbers are finally introduced and tiny children continue enjoying sophisticated equations in the more traditional for us way: 127+12-66*2=…dots

For the details and further proof, please read How to Teach Your Baby Math by Glen Doman. Once you are familiar with the method, you can find brief summary of steps to help you stay on track and further resources.

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Does it really work?

First of all, check this article at WordsBestEducation: The Math Mystery. In this article the bloger describes her own quest for understanding on how the math program works for the kids, how successful it is and what are the reasonable expectations. Elizabeth, the author of the article, cites a phone conversation with IAHP institutes where they answered many of her questions, and then shares her own suggestions on how to make this program successful.

My personal opinion is that, as with any learning system, it depends on a child. And a parent. The book dedicates an entire chapter for testimonials from parents who used this system. TeachYourBabyToRead group contains quite a number of parents who’ve used this system with a great success. There is also a great number of kids who went through the entire program without astonishing results. To each his own, but I am sure that the time they spent on trying to learn math this way was not waisted anyway: their visual pathway is definitely a lot more developed and they’ve spent a lot of quality (and fun!) time with their parents - what can be more rewarding? Besides, who knows, may be this knowledge will surface in a future, giving them boost in understanding of math in school and college.

Thanks to Laurie Tiemens for this important point: “I would like to add another important benefit. More brain pathways are being wired into your child’s brain thereby increasing their ease of learning anything.”

The greatest encouragement for me is my own husband. Even without any dot system, or Rainman’s disorders, he managed to retain this amazing ability: if you show him a card with 98 dots, he knows that there are 98 dots without counting! Number of grapes on a plate, or people in the room - he is never mistaken by more then 2. And, yes, he’s been taking special classes for kids gifted in math for years. So, why not help our kids to enjoy this amazing science?!

To read about other’s experiences with the program, or to share yours, scroll down to our Comments section! Looking forward to hear from you!

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Basic Rules of Teaching

  1. Begin as early as possible
  2. Be joyous at all times
  3. Respect your child
  4. Teach only when you and your child are happy.
  5. Stop before your child wants to stop.
  6. Show materials quickly.
  7. Introduce new materials often.
  8. Do your program consistently.
  9. Prepare your materials carefully and stay ahead.
  10. Remember the Fail-Safe- Law:
    If you aren’t having a wonderful time and your child isn’t having a wonderful time - stop. You are doing something wrong.

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FAQ

  • See more in Glenn Doman’s method’s FAQ and see Comments below for some personal experiences with math program by other parents.

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    Steps

    1. Zero Step (for newborns - kids under 3 months old, all other kids should start at the First Step) - dot cards that are very-very large: 15″x15″, with black, very bold dots 1.5″ in diameter. Begin with one card, show it for 10-15 seconds and hold it absolutely still to give him a chance to focus on it. On a first day show “one” dot card 10 times, on second show “two” dot card 10 times; proceed for 7 days with different cards 10 times each day. Repeat for the following two weeks: so, for the first three weeks you show “one” dot on Mondays, “two” on Tuesdays… On week 4: chose dot cards 8-14 and cycle each of them 10 times a day for the following three weeks (card “eight” on Mondays, card “nine” on Tuesdays, etc.) Continue with this pattern until tiny infant is seeing detail consistently and easily (around twelve weeks or later). Chose the correct time of the day: when the baby is in a good mood. Once you realize your infant can see the detail clearly, proceed to step one.
    2. First Step - Quantity Recognition
      Teaching your child to to perceive actual numbers, which are true value of numerals - 5 dot cards 1-100. 2 sets of 5 cards each, three times a day each set.
    3. Second Step - Equations
      Start after you’ve showed first 20 cards for First Step.
      Don’t test, continue introducing new quantities, i.e. dot cards, (until you reach 100), and add sessions with simple equations: 2+2=4, 5+11=16. Avoid predictable equations: 1+2=3; 1+3=4; 1+4=5. After two weeks of different addition equations, do subtractions, followed by multiplication and division (at two week intervals of 3 sessions of equations per day).
    4. Third Step - Problem Solving
      You have completed First Step (showing dot cards), and First Step (simple Equations).
      Progress onto more sophisticated three step equations, e.g: 2×2x3=12.
      “You are still extraordinary giving and completely non-demanding” (GD, Math, p. 125)- you haven’t done any testing. “The Purpose of problem-solving opportunity is for a the child to be able to demonstrate what he knows if he wishes to do so. It is exactly the opposite of the test.” (GD, Math, p. 126). You can do it at the end of the session.

      • Hold two cards and ask where is 22 (always offer options!)
        “This is a good opportunity for a baby to look at or touch teh card if he wishes to do so.” If he does, make a big fuss. If he doesn’t, simply say, “This is 32″ and, “This is fifteen.” (GD, Math, p. 127).
      • Give a simple equation and then hold two dot cards for him to chose the result of the equation. Again, always offer options, and if your child doesn’t want to show a card, simply and upbeat say it yourself.

      After a few weeks of these equations, make them even more fun: combine addition and subtraction, multiplication and division, but don’t mix the pairs e.g. 40+15-30=25, not 4+2*7.
      After a few weeks, add another term to the equations: 56+20-4-4=68.
      You can further progress onto:

      1. Sequences
      2. Greater then and less then
      3. Equalities and inequalities
      4. Number personality
      5. Fractions
      6. Simple algebra
    5. Fourth Step - Numeral Recognition
      11×11 poster board with numerals written in large, red, felt-tipped marker: 6″ tall by 3″ wide.
      Combine numbers with dots: 12 greater then dot card of 7; dot card of 12=12 (number)
    6. Fifth Step - Equations with numerals
      Make 18″x4″ poster board cards for equations with numerals: 25+5=30; 115×3x2×5 not equals 2,500; 458 divided by 2 minus 229.

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    Resources

    • How to Teach your Baby Math Kit: collection of dot cards, that gets you through Steps 1-3. Cards for equals or not equals, or for numerals you have to do by yourself.
    • Perla Adams, the Classical Mommy, has a PowerPoint presentations with dots, dots and numbers and even some equations - you can print it on a card stock paper, or even show them on the computer: Teaching Quantity. Her presentations can help you cover the steps 1-4 and are absolutely FREE! Thanks, Perla, for another wonderful job!!
    • Your Smart Baby Newborn Program Kit: collection of initial cards for the infant, including 10 dot cards (though you probably need more then that - at least 21!), that gets you through Step 0.
    • FREE Matthew Hudson’s Doman plugin for Microsoft PowerPoint: terrific plugin that allows you to go through Step 1, 2, some of Step 3 (only two step equations: 15*2=30), step 4, and some of Step 5 (again, only two step equations and numbers are not that big). Plugin also contains a randomizer for your Encyclopedic knowledge words and even a word generator. I personally can’t imagine my son’s program without this wonderful plugin.
    • Prodigy Math/Reader for Infants and Toddlers by Geenogee: this is an inexpensive program that helps you through steps 1 and 3. It does get you a little further then Matt’s plugin - it allows 3 and 4 step equations (12/6×35=70), it allows student management, it remembers and reminders you to show the presentations certain number of times per day, tells you how many lessonettes are left for that day. Similarly to Doman, once you get to equations, it just throws a tiny pop up window with the equation, showing only the result dot card on the screen. Not bad, but I wish it could actually offer the entire program: inequalities, sequences, etc. It has numbers, but they are so small… and I haven’t discovered any ways to enlarge numbers, or how to make them red (if you have, please comment below or email me directly!) It’s a pity, that nobody does it! On the other side, same CD contains Prodigy Reader - similar software to teach your kid to read (see more about it at Teach Your Child with Multimedia).
    • Our Encyclopedic Knowledge Math section contains some presentations (even with sounds) in English, Russian and Spanish that can aid your math learning and make it more fun.

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    Related posts:
  • Teach Your Child Music: Doman method
  • How to teach your child… Foreign Language with Doman Method
  • Doman math - does it work?

    • 37 Responses to “How to Teach Your Child Math: Glenn Doman’s Dot Method”

    1. ANMB Says:
      March 11, 2009 at 4:17 pm

      Dear Alenka,

      Is there a downloadable daily schedule for the math program to use with the cards?

      Thanks.
      ANMB

    2. Alenka Says:
      March 15, 2009 at 9:06 pm

      Sure, just look at the steps above. If your baby is older then 3 months old, start with step one: pick first 10 dot cards, divide them into two sets - 5 cards in each set, and show each set 3 times a day (a total of 6 times). Again, after 10 days, retire one card in each set and add one new card.

      If your baby is younger then 3 months old, then it is better to go by the rules outlined in “How Smart Is Your Baby?” - they have a different schedule for everything.

    3. Shailendra Says:
      March 22, 2009 at 6:28 am

      I have baby 5 months old. I consistently use to flash math cards to him. Every time when I use to flash card, I observe that my baby becomes happy. He may identify the difference in quantity of dots. I am now moving towards equation now. lets see how he responds.

    4. Alenka Says:
      March 23, 2009 at 8:14 pm

      Wow, this is so remarkable! Congratulations to both of you!!!

    5. Charmon Says:
      May 25, 2009 at 4:53 am

      I’d like to start with this program. When you show the dots do you verbalise the number or do you also show the number in print

    6. Alenka Says:
      May 25, 2009 at 6:35 pm

      You hold the card outside baby’s reach and say it happily and enthusiastically: “This is one.” Show the card just for one second (as long as it takes to say it). The faster, the better - babies get bored easily. No need for more descriptions. Just take the next card and repeat the process for the first five cards. No need to show the back. Don’t ask the baby to repeat it back to you, hug and kiss the baby in the end, tell him how terrific she is and how much you love teaching her! Repeat it twice in the first day, each session at least half an hour apart from previous. After the first few weeks, the sessions can be fifteen minutes apart. On a second day add a second set. Eventually you’ll no longer need to say “This is one” or “this is 32″, you’ll just say “one, thirteen,…”
      Good luck! Share how it goes!

    7. Brooke Says:
      May 29, 2009 at 11:47 am

      Hi, just a question about the math dot cards. I started with my 16 month old and we are up to card 20. I started to retire the 2 lowest cards on day 6. Then day 7 another 2 and so on, until now where we are using cards 11 through 20 in 2 batches. My question is, do I continue to retire 2 cards each day until I reach 100 or is there a break of a few days before starting to retire more?
      I am finding it quite difficult for my daughter to focus on the cards and enjoy it. She seems more interested in my face or anything else really. Any tips?
      Thanks

    8. Alenka Says:
      May 31, 2009 at 7:03 pm

      After you show the first 20 cards, you just continue retiring cards the same way: two old cards go away, two new cards show up. Once your baby has seen the first 20 cards, she is ready for step 2. So now you’ll be showing dot cards AND equations. You’ll be having 9 sessions each day: 2 sets of bits and one set of equations.

      My friend’s daughter was never itnerested in words cards, but was fascinated with dot cards! My son was completely disinterested in them. So I played peekaboo with him, hiding behind the card, so that he momentarily looks at it, and then praising him for it a second later.

      They also say that the faster you show, the more interested the kids are. There are plenty other ideas that different parents came up with for word cards, that you might find useful:
      Runaway Baby: The Alternative Ways of Showing Cards to An Active Child

    9. Miyer Says:
      August 3, 2009 at 1:42 pm

      Can I use 81/2 X 11 inch cardstock instead of 11 X 11?
      Thanks!

    10. Steph Says:
      August 10, 2009 at 10:38 am

      Hi Alenka,
      As I am waiting for my book to arrive, can you please please explain step 1 of math program in more detail?? My baby is 6 months old. Are we suppose to show numeral 1 and then 1 dot? I see that there are several presentations on other website. I am just unclear on how to start even after reading it above.

      And we can again use the our computer to show them? From experience is using the computer just as successful.

      Thanks soo much.

    11. Alenka Says:
      August 12, 2009 at 5:12 pm

      8×11 cardstock is exactly what I prefer to use too! Other parents use even smaller sizes. It’s more important to find something that works for you, then to follow the instructions to the letter.

    12. LWilliams Says:
      October 21, 2009 at 11:02 pm

      Is this work effective after a child passes out of the absorbtion stage around 7.

    13. Alenka Says:
      October 22, 2009 at 7:42 pm

      At that age, I’d rather go with rightstartmath. My son and I absolutely love it, we got it after tons of recommendations from other parents.

      I am not the author of the dot technique, Glenn Doman is, so I can’t say for sure. I guess the chances are slim.

    14. Diane Says:
      November 13, 2009 at 12:29 am

      I started the Doman Dot Method a couple of weeks ago. My daughter is 26 months and was successful already with YBCR. Anyways, I really want her to perceive quantity, but have no idea if it is working. And I feel like the pressure is on!!

      We are on 9 sessions a day having introduced equations; but for most of the time I hadnt known the sessions should be 15 mins apart, so I have been doing them 3 sessions back to back, 3 times per day.

      I have spread them all out now (much more difficult, as i have to find 9x per day to get her undivided attention instead of 3); ….. SO is this the right thing to do, or should I have started over?

      Also is there anyway to know if she is perceving the quantities before 8 weeks or more are invested?

    15. Alenka Says:
      November 19, 2009 at 7:46 pm

      I strongly believe, that if your baby is enjoying it - it means she is learning! 5 cards, 15 sessions - are arbitrary, sample numbers. Each baby is different. Some can do a lot more. My son never liked the dot cards, and the concept of quantities comes hard for him. I continued until he was three, and then started looking for another approach. We are doing rightstartmath and having a lot more success with it.

      My little one seems a lot more interested in math cards, that my older one. So I hope it works for him!

      There is a fabulous, fabulous article about Doman math here: Math Mystery.

    16. robert_plant137 Says:
      November 29, 2009 at 4:12 am

      what do you think from what start math or reading?we’ve figured out, that we will have no time for both( at least for now)
      many thanks

    17. Ida Says:
      December 2, 2009 at 2:01 am

      Hi Alenka,

      this is a wonderful and very very helpful webiste! I just want to thank you for doing this. =)

      I’m from Indonesia, and currently reading “How to teach your baby math” and “How to teach your baby how to read”, and I have some questions and hoping that you and other friends here may help?

      I speak 3 languages at home. Indonesian, English, and Chinese/ Mandarin. I read in the book that babies are genius and they can learn 5-8 languages without problems. So, I was planning to teach my baby these 3 languages.

      But I’m confused about HOW to do it. For instance, when I teach my baby math about 1 dot: Do I say it in Indonesian first, then continue with English, then Mandarin? Or is it English for today, Indonesian for tomorrow, Mandarin next?

      Help?

      Thank you so much before! And once again, your website has been a great help for a beginner such as myself!

    18. Alenka Says:
      December 2, 2009 at 11:25 pm

      In Doman books they insist it should be reading. Reading is a staple of knowledge. I’d second this: your kid needs reading regardless of the system you choose. Doman’s system allows you to start at the youngest age out of all other system that I’ve found, and it seems to be the least painful to both parents and kids. So, I’d go with reading and add math if you have time. Doman’s reading has an astonishing percentage of success. Doman’s math numbers are not so great - it works for some kids, doesn’t work for many others. You can still give it a try without investing too much money or time into it with some computer programs, like Matt Hudson’s randomizer that is free, or just the ppt presentations. Let me know if you already found these materials at this site or if you’d like a link.

    19. Alenka Says:
      December 3, 2009 at 9:38 pm

      I don’t think there is just one answer to this question: my personal guess is that either way is fine! When we are doing math at home, I am usually using Russian language, but indicate how it is called in English. When I show dot cards to my baby, I use only Russian. When we are doing math, I think it is important to concentrate on math, I don’t want to be distracted with other languages. The only reason I even mention English names for my older one is because he is going to learn math in English in school, so getting to know the terms in English would make the transition easier! The only reason we currently learn math in Russian, is because it is easier to me. Once we get to more advanced terminology, more advanced concepts - I’ll just use English names. I would like to avoid the confusion once he goes to school.

      Spanish numbers we learned just by counting. It is not important to me that my kids know how to correctly name “derivative” or “geometrical progression” in Spanish, so I don’t bother!

      What information do you want your baby to learn?

    20. Kayla Says:
      December 12, 2009 at 11:18 am

      Hi ALenka,

      Thank you so much for sharing this wonderful knowledge with us! I have a question though:

      “Sure, just look at the steps above. If your baby is older then 3 months old, start with step one: pick first 10 dot cards, divide them into two sets - 5 cards in each set, and show each set 3 times a day (a total of 6 times). Again, after 10 days, retire one card in each set and add one new card.”

      When I first teach my son, I pick 1-5 dot cards and put them into set-1. Then 6-10 dot cards and put them into set-2. According to the book, I should teach my baby 1-10 dots without trying to mix the cards. After a while, I mix the cards. So in set-1 I can have 1,5,7,9,10 dot cards, and the rest in set-2.

      Then after a while, you retire the 2 smallest cards, right? In this case it should be 1 and 2 dot cards, and replace them with 11 and 12 dot cards. I was told to separate these 2 new cards into each set. So set-1 should have 1 new card, and set-2 also. Let say I put card number 11 in set-1 and number 12 in set-2.

      My question is, if I do this, then card number 3-12 will not be in order then?

      Is that okay for the baby? Will he/ she know what number comes after what if we do this?

      Thank you!

    21. Alenka Says:
      December 13, 2009 at 11:46 pm

      I shuffle my cards after every showing session. I believe, that the book indicates, that the cards shouldn’t be in order, we strive for randomness. Otherwise the baby may learn what comes next like we learn poems: itsy-bitsy-spider-climbed-up-the-water… spout! 1,2,3,4…5! Reshuffling the cards, mixing the sets helps us to achieve this randomness as much as possible.

    22. kayla Says:
      December 17, 2009 at 2:55 am

      I see. So reshuffling the cards are not only okay, but it IS necessary. We only show the cards in order the first time, which include card number 1-10, then afterwards (when the time comes to add new dot cards), we must shuffle them.

      Am I getting it correctly? =P

      Thank you so much!

    23. Alenka Says:
      December 18, 2009 at 10:48 am

      Precisely! We reshuffle the math cards every time that we show them, to make sure that the babies (who are just waay too smart for us sometimes), don’t memorize them as a poem - as a sequence of numbers. And, of course, get bored with predictability.

    24. Ida Says:
      December 25, 2009 at 8:39 am

      Guys, need help here….

      According to the Glenn Doman’s book, the flash card (for math) should be in 11′x11′ size. But that way I can’t use my printer because it’s too big.

      Any idea how?

    25. kayla Says:
      December 27, 2009 at 10:51 pm

      Hi Ida,

      I just encountered the same problem. You’re right, 11×11″ (or 28 x 28 cm in my country) is just too big (to print). A friend of mind suggested to just use smaller size, the most important thing is the dots are all there. OR you can draw the dots =P but personally for me, it’s just won’t happen!

      I’m open for other suggestions from friends here. Alenka, how do you do it? Thank you!

    26. Alenka Says:
      December 28, 2009 at 8:49 pm

      Regular 8 1/2 by 11 cardstock paper is my personal favorite. 11 x 11 cards that we have, are a pain in the neck to store and, often, even use: they don’t fit into anything - folders, file storage, shelves…

      As for drawing the dots (it’s a very interesting idea - I haven’t thought of it), I guess it could work too. Or, may be, getting a really thick marker and making quick dots that way?

      In a book they recommend to get dot stickers (sold in office supply stores like Staples quite inexpensively) and create the cards that way.

    27. kayla Says:
      December 29, 2009 at 7:02 pm

      Hi Alenka! Just curious. Do you print or use dot stickers? =P

    28. Alenka Says:
      December 29, 2009 at 8:14 pm

      Neither: I purchased the number set someplace on ebay for my first one when he was a baby. Only afterwards I found the files, the programs, etc. If I’d find all those things before, I’d rather print - stickers are not for me - I would lose count…

    29. Ida Says:
      December 31, 2009 at 12:38 am

      Hahaha… you’re right. I’d lose count too! It’s just that somehow I like that 11×11″ size. A bit OCD I am. =P

      Guess I better start buying those stickers if I want to use the 11×11″ size then.

    30. Alenka Says:
      January 1, 2010 at 8:30 pm

      The beauty of 11×11 is that the cards don’t have “top” - the dots are even more random, since you can rotate the card and show it from a completely different side up every time. If your printer takes paper that has width of 11″, then you can try feeding it through the printer and avoid the stickers by printing the dots. Or, you could print the dots on a regular 8.5×11 paper and just paste (or laminate) the paper on 11×11 card. If you use scotch tape to paste it, you probably can even reuse the 11×11 cards for something once you are done with the dots.

      The sky is the limit! Have fun!

    31. Neira Says:
      January 9, 2010 at 3:23 pm

      Hi,
      I started making the flashcards myself too, it was a hard job… Then I found the babybit DVDs and bougth them.
      All the flashcards are made!!. You don’t need to print anything. Just put the DVD on the DVD player and that’s all… :). It saved me a lot of time.

      You could find it on http://www.babybit.com

    32. Owen Says:
      January 21, 2010 at 9:10 pm

      Why don’t you have some examples of the math dots for people to see what it is your talking about. Random dots would not be as good as a fixed set to help remember numbers. If you have a real example I would like you to send me a visual sample of how the dot cards look.

    33. Alenka Says:
      January 30, 2010 at 8:21 pm

      I updated the post with some pictures.

      I also found a video of a 1 year old baby pointing to different quantities:
      http://grhomeschooling.blogspot.com/2007/12/math-program-anthony-first.html

      Since we are trying to teach our kids to understand what numbers are, not just memorize a pattern of dots on the page, the more randomly the dots are distributed on the page, the better it is. We show every card ~15 times (three times a day for five days and retire it at the end), so the child slowly progresses from smaller numbers to bigger ones. We don’t need to do anything special for making sure that the cards are at a different angle every time - just place the card in a set differently, and the pattern will look different from a new angle tomorrow! That’s the beauty of square cards.

    34. mariama Says:
      February 28, 2010 at 10:15 am

      Hi I have two children 18 months and 4 years old I read the books I am learning glenn doman Alire was my baby but I could not get the math book here in Morocco can help me exactly what scire I have to do to start the program math aus two children and how the material itself makes even seen that Morocco bookstores have not lived up these books nor his kit and time is short I do not want to waste more time and is Should I start a long learning two at the same time I am a little confused repondez s’ilvous me quickly please

      Proposer une meilleure traduction
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      Hi I have two children 18 months and 4 years old I read the books I am learning glenn doman Alire was my baby but I could not get the math book here in Morocco can help me exactly what scire I have to do to start the program math aus two children and how the material itself makes even seen that Morocco bookstores have not lived up these books nor his kit and time is short I do not want to waste more time and is Should I start a long learning two at the same time I am a little confused repondez s’ilvous me quickly please

    35. Alenka Says:
      February 28, 2010 at 8:42 pm

      Doman math works until certain age… kids lose the ability to perceive quantity after certain age. I’d try showing cards to the little one and see if the older one responds to that too. You can try Matt Huddson’s power point plug in (it’s free) or if you don’t want to do it on the computer, then just print out the files available at the Classical Mommy site - thanks to Perla for sharing it! - Teaching Quantity - and use it as Doman’s flash cards.

      For my own four year old - RightStartMath works the best. I can’t praise it enough.

      Good luck!

    36. mariama Says:
      March 1, 2010 at 5:20 pm

      thank you for responding so quickly in fact I think I’ll make myself at home and I thought before I had to write the chifre the same time that the point you think it will not work for my son 4 years is already too late?

    37. ari-free Says:
      March 7, 2010 at 6:13 pm

      Some points:
      When I want to teach the concept of 2, I may show 2 dots but then I’d also show 2 apples, 2 bunnies, 2 birds etc so the child gets the idea that you’re talking about a quantity. Otherwise, if you just show the 2 dots in the same place then that may be seen as just a symbol that has nothing to do with quantity. He might think 2 is something to do with dots and nothing else. You may also want several random dot arrangements for each number so that he actually has to count each time instead of seeing the ’shape’ of the 7 dot card and guessing 7.

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