Tuesday, May 8, 2012

Stamp Game and a Request for Advice

Last week Kal-El began work on the stamp game.  I have a question or two about the sequencing of this (at the end of the post), so if you are an experienced Montessorian and want to put in your two cents they will be welcomed with open arms!

The first day I put together a version of the old golden beads demonstration tray and Kal-El learned to associate the stamps with the correct amount of beads.  That same day we moved on the formation of numbers with the stamps.

This is what my stamp game tray looks like right now.  I do have the skittles and discs (kibbles and bits?) that go with it, but they can be removed for early work with the game.

If you have a really, really long memory you might recall that my stamp game is a hand-me-down from a friend who made her own.  The stamps are made from uniformly cut pieces of cardboard that have been covered with printed out numbers against a colored background and taped.  My friend says the tray is from an office supply store.  I have seen videos of a store-bought stamp game in actions and I will say that the store-bought version has some distinct advantages over our DIY version, but it was nice to not have to buy something for once.

Here is an example from last week of Kal-El using the stamps simply to form numbers.  I prepared a stack of index cards ahead of time with numbers written on them in colored ink.  The stack I made had several examples of numbers of different sizes (2-, 3-, and 4-digit) and also with zeroes in various positions.  I told Kal-El that there was no hurry, but after he built all of the numbers on those cards he would be ready for the next step.  The first day he felt like building six, the second day he built 3, the third day he burned through the remaining ten in the stack.

In the above picture you might be able to spot the first problem with our DIY stamp game.  Our stamps are HUGE.  Kal-El loves his mat that I got him to go with the game, but as you can see above we would be hard-pressed to fit two addends on that mat with stamps this size.  The second problem is that the taped corners of the stamps catch on the felt mat so it will be difficult to "sweep" ten stamps into the palm of our hand to make one of the smooth exchanges that make the stamp game so attractive.

The third problem, while I'm on the topic, is that the stamps fit in their designated spot only when they are relatively organized.  It is nicer to be able to "sweep" ten stamps into your hand for an exchange and then "dump" them into their compartment.

Today he was super excited to receive his very own "stamp game book." All of the special things I make like this specifically for Kal-El are bright red because he is the "red ranger" at our house.  Me Too's will be blue because he's the "blue ranger."  They love vintage Power Rangers.  I bring it up only so you won't be wondering how the color of the cover fits into a Montessori color-coding scheme.  This is what you'll find inside:

I used the free stamp game paper that came with my Karen Tyler albums.  You can find it online here.  This one from The Montessori Print Shop would provide the color while using less ink and it is also free.  I guess I was feeling extra-colorful the day I chose.  I bound the book using my handy, dandy Comb Binding Machine that I barely used during primary and has become indispensable during our transition to elementary.

Most of the pages in the book are completely blank.  Last night I filled the first three pages with examples of static addition using a variety of 2-, 3-, and 4- digit numbers.  The photo above was taken before I showed it to Kal-El so it is still missing the "plus" and "equal" signs.  In the math sequence we are following the stamp game is the first time the child records his or her work and it is at this point that they are introduced to the operational signs and terminology of equations.  I wrote in the "plus" and "equal" signs as I explained to Kal-El what they meant.

And here he is recording his own work!  Today he learned the vocabulary "addend" and "sum."  He also learned how to write the "plus" and "equal" sign and added them to the equations in his book.  He started out by announcing that he thought he might complete the "WHOLE FIRST PAGE!" (He gets really excited.)  But, as it turns out, he finds the stamp game addictive and completed all nine problems.

So...this brings me to TWO questions.  In the AMI primary math album that I use, the collective exercises with the golden beads are taught as a group.  Within a handful of days, the child experiences all four operations (likely static).  Then, they move on to dynamic operations and practice them with all four operations as a group.  This is different than the way I see it most frequently online.  They didn't learn static addition, then dynamic addition with an exchange in the tens, then dynamic addition with and exchange in the hundreds, then static addition with exchange in the 10's and 100's...and so on...and then addition with a zero in particular places...and so on...And then finally, after all of that is completed, begin subtraction.  Then go through all different types of subtraction.  Then when that is completed, begin multiplication and all of it's variations.  Then finally, division and all of it's variations.  My album introduces all operations quickly and you progress through all of the variations using all four operations together.

My album was not specific about how to handle the stamp game.  I don't know if I should go through all of the addition exercises before beginning subtraction or, if like during the collective exercises, I should get him doing the other operations right away and perhaps introduce static subtraction tomorrow.

Theoretically, it makes sense to me to use the same pattern I used with the collective exercises.  However, this stage is a little different in that he is learning the vocabulary and symbols for equations.  I'm concerned that if I start him on subtraction tomorrow he won't have had enough practice with the vocabulary and symbols for addition and get confused.

Those of you who have been through this many times...what worked best for you?

Second question:  After completing the very first problem (4122 + 2615=6737) Kal-El noticed the columnar addition.  He said "Look!  In the thousands I had 4 and 2!.  4+ 2 equal six and that's what I put in my answer box for the thousands!"  Then he proceded to check the columnar addition for the other positions in his number against the answer.  (edited to add:  he noticed this in a different order than he did the problem.  When he did the problem he started with units.) So, on the next problem:


He counted the stamps for the thousands, then the hundreds.  Then he said "I don't need to count the stamps for the tens because I know it is going to be 8 because 7 and 1 equals 8."  I told him that he was right, and that he will have to do some extra steps when we get to problems that exchange.  (Edited to add:  This is backwards.  He should have started with units...as he did with the golden beads.  Me Too was crawling all over me to try to see what Kal-El was doing and I didn't catch him in time.  He did do the rest of the problems units first.  He said that he "didn't know the stamp game was the same.")

So, is there anything special I need to do?  Do I need to make him physically count the stamps whenever his skips that step and does the math without counting the stamps? I don't want to discourage him from doing the mental math when that is, after all, the end goal.

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  1. I'm no expert, as you well know, but for Bunny, I moved pretty quickly becuase she already knew how to do the work. Its not a new math, just a new material. For Bunny, I showed her addition one day and the next day or two we did exchange. After that, I showed her subraction and so on. She got it pretty well. I have seen Bunny do the math problems without all the beads too! I usually let her if it is right since abstraction is what we are working for anyway! Good Luck! Kal-El is doing a GREAT job!!!!!

  2. I answered over on the Playschool6 group, but thought I'd share here too for those who might have the same question but aren't part of our group (they should join!). :)

    The stamp game proceeds quickly - so I tend to present all addition, then all subtraction, etc; but it goes over a couple of days. As each new operation is added, there are still practice problems with the other operations. I let the children make up most of their own after the first 2-3 sample problems from me; this way I can teach responsibility when I say "keep the thousands low" (ie in addition) - yet they are still challenging themselves.

    And if they want to do the operations "out of order" I let it happen because by this point they are familiar with all 4 main operations and are just learning terminology and using smaller materials.

    For the counting (or not counting), as long as you have shown him how to do the counting, pointed out that there will be times he WILL need it, and point out when those times come that he now needs to count up the groups of 10 and exchange them, he is totally fine discovering and implementing those patterns he knows :)

    I love that mat you are using and I've seen others with similar mats, but I've never used them myself or seen them in action, face to face. The children just have to learn to keep them organized (typically the children will, at first, line up the categories underneath their category within the box itself, situating the box so the tiles are closest to the child with the skittles and disks away from the child). The homemade tiles might slide smoother just on the table surface - even the nice wood ones don't slide very well on a mat.

    What an exciting time!

  3. I would say for question one, make very sure that you think he understands what is going on and I would stick to one operation for a while. Don't forget, the maths is designed to have more than one subject being studied at once, so geometry, and bead chains and everything else travels in parallel. Beware of covering a lot of one small part of the curriculum and make sure you "go sideways" and cover other subjects too.

    In answer to your second question, make sure that he always, ALWAYS works from units. If you allow him to get into the habit of working from thousands now, even though it makes not difference, working with the dynamic version will be terribly hard to explain that he has to change direction. In fact, simply because of that, I would make him repeat the work, or some of it but reiterating time and again that you must start with the units.

  4. Re-reading my own comment - I meant to say "it goes over a couple of days for each operation" - so static, then dynamic addition; then go into subtraction on day 3 (or later if they are really into addition; sometimes on day 2, if they flew through the addition on day 1 and are that excited about it).

    There is so much time for follow-up, practice problems; as long as he has the concepts and WANTS to move on, let him.

  5. I was wondering where your stamp game was made as I had never seen one with such large stamps. I was thinking that they would be very dramatic in the dumping. Nicely made - not withstanding the issues you mentioned.

    Question 1/2: In my training and readings (AMI and AMS with a smattering of PanAmerican), I have always understood stamp game to be a method (among several) to teach the various operations. It gets a lot of play because as the child becomes older it is easier and faster than golden beads. The goal is not the stamp game the goal is abstraction. It sounds like the ACTION OF ADDING is something that is abstracted to some large degree by your son. VALUE is a whole different piece of the puzzle and needs to be watched carefully.

    I've never rushed a child through the lessons. (I guess what I hear you describing seems like rushing to me - but maybe not if the child had a great understanding of the golden beads.) Although I often go through a different order set in my AMI albums - Addition, Multiplication, Subtraction, Division. This order requires an understanding of dynamic addition to do multiplication problems.

    Another thought is that I often teach subtraction as a way of checking the addition problems. "I wonder....."

    It looks very challenging for him and is keeping him engaged.

    I know your instincts will guide you well.

  6. Oh and: "Units, units, always units unless we shall divide."

    Really important for a child who is comfortable with seeing the 6+3 addition parts - she will often go through these doing the easiest or more obvious first and that is out of order and will really screw up carrying.

  7. Just commenting because I want to subscribe to the comments and learn from them:) I agree with the advice you were given. It just seems logical.

  8. Not an expert! But I totally agree with units first comment based on experience. DJ and Ken were already knowing how to do the static problems before showing them the stamp game. The stamp game is a material that definetly prepares for the Long Division with Racks and Tubes, because you don't want to turn him off to this work stay with units first. Otherwise it gets a bit too complicated and montessori moms(myself included) don't like to correct our children too much on their mistakes. Practicing the right way now will help to prevent too much verbal correction that may lead to a child not wanting to do the work. The goal is abstraction so we want to stay as concrete as possible for now. I am impressed with Kae-El's go get em attitude, It is great he is loving the stamp game. It is the absolute best montessori material I have ever invested in. If your not happy with the homemade version, I strongly suggest you purchase one. I got my from Kidadvance with shipping I think for under thirty dollars. You will get your monies
    worth. By the way I am a Pink Power Ranger fan and I will secretly share with you that every Halloween I try to bribe one of my girls to wear the costume. I have even offered them $20.00:)

  9. I love reading your blogs. I am able to get the best ideas that I can use for my two boys as well. I have also written an abstract of your post on our website.

  10. I love your stamp game book!

    Before I introduce the stamp game I make sure the children have had plenty of practice with all the operations using the golden beads and can complete sums without help. My children will also know the operation signs by now by working through the addition and subtraction strip boards and cards. This means that when my children start working on the stamp game the focus isn't so much on learning the signs or processes for each operation, but instead the child is working towards abstraction. My first presentation starts off by telling the child that I can show him a quicker way to work out the sums instead of using the golden beads. If a child is able to work out the answer without the stamps I use that skill as a challenge and get the child to work out the sums and then check the answers with the stamp game. The child then has the opportunity to work out the problem and also gets plenty of practice with the stamp game.
    I emphasis starting with the units while working on the golden beads. If the child is starting from the thousands when working on the stamp game I do not immediately correct it so the child can discover that he can not get the correct answers unless he start from the units. All my sum cards have the answers on the back so that the children can check their work. I love it when I hear a child whisper to himself 'It's wrong...oh I started from the thousands instead of units'. That discovery of the child is so powerful. However If the child continues starting from the thousands, I represent the operation and emphasis that we start from units. Good luck!

  11. VERY cool post! Your son is certainly in his sensitive period for math. Nice comments, too. My two cents: Do addition and subtraction back & forth until he seems solid then move to multiplication & division when he's ready. If he does operations mentally correctly, he's the man! just have him check his work as a control of error. If he's making mistakes, he'll figure out why. Great work!

  12. Thank you, everyone, for commenting. I used all of that good advice and things are continuing well. I'll update soon!