Kal-El working the subtraction snake game with an incredibly long snake
I wrote this post maybe two months ago when Kal-El was just finishing the addition memorization sequence and Me Too was just beginning it. It was never posted and got lost in the shuffle because I was unable to use the video I intended to for one of the demonstrations of the snake game. I finally drummed up the courage to MAKE a video to go with that section. So, I can finally post this information but the timing of the post would have made more sense two months ago. Here it goes:
(From two months ago) You may have noticed recently that we reached an interesting moment in time between the two boys in which Me Too is at the very beginning of the memorization of addition sequence and Kal-El was at the very end of the memorization of addition sequence. What may have seemed odd is that Me Too began the sequence with the addition snake game and Kal-El ended the sequence with the addition snake game. Kal-El has now begun the memorization of subtraction sequence with the subtraction snake game and in our home that sequence will also conclude with the subtraction snake game. How is it that the snake game came to be at both the beginning and the end?
If you have access to multiple albums as I do, you will find the snake game in different places. I have found that there is a distinct difference in the style of use when it is used at the beginning rather than the end. If you only were familiar with one style of use it would be very difficult to imagine using the game at the opposite end of the sequence. In other words, the way you use it has an awful lot to do with with where it should go. The primary album I use for math is Meg's Montessori by Hand album (an AMI album). She places the snake games at the beginning of the addition and subtractions sequences. I LOVE her eloquent explanation of how it fits into the sequence:
Memorization is introduced at a time when the child is incredibly comfortable with the four operations and numbers. We have not brought attention to memorization before--it is introduced gently now. There is a pattern to the way the child will memorize the facts. First there is a Sensorial experience--The Addition Snake Game--without any recording. The purpose of the Sensorial experience is to be able to explore a bit and to initially encounter the facts. Secondly, the child works with an orderly experience fo the facts (tables) while using Sensorial materials--The Addition Strip Board--to find the answer, yet now she records. Finally, the child works with charts--The Addition Charts--; she encounters facts in a random way and writes the whole equation, the problem and the answer. There is no material representing quantity here...When the child reaches the third step, she has basically memorized the facts already through working with the first two steps. The material for Subtraction is very similar to that of addition, there is a Subtraction Snake Game, a Subtraction Strip Board with a pre-printed orderly way to record facts, and one Practice chart (one blank, and one for the control).
-Meg Montessori by Hand Math album
I love the idea of using the snake games at the beginning of the addition and subtraction memorization sequences to provide a Sensorial experience without any recording. When a snake game is used at the beginning of the memorization sequence the child counts each individual bead using a notched tag that they leave in place each time they reach 10. The beads tend to stay in-line with the snake until they are collected for safekeeping. So if presented with 7 and 9 as the first two bead bars in his snake, this child will count 1...2...3...4...5...6...7...8...9..10 and leave his notched tab in place between the third and fourth beads of nine bar. They will place a golden bead bar above the beads they just counted. Then, they will count the previously uncounted beads on the opposite side of the notched tab 1...2..3...4...5...6 and place a bar from the black/white bead stair above those beads. Here is a video example of this style of snake game from Oak Haven Montessori School (you can see the portion of the game in question around 2:17):
When a snake game is used at the end of the memorization sequence the child will not be counting individual beads as described above. Rather, they will look at the each bead bar as a number (having the number memorized according to color really helps at this point) and will use the addition facts they have just memorized through the sequence of addition boards to complete the game. I love the idea of using the snake game at the end of the addition and subtraction memorization sequences so that the child can USE the facts they just memorized to play the game. In this style the child will often start at the beginning of the snake and pull a pair of bead bars forward to isolate the addition equation at hand. So, if presented with 7 and 9 as the first two bead bars in his snake the child might pull those two bead bars and say silently or aloud "7 plus 9 equals 16." They will then get a golden ten bar and think of how to make the sum of 16 with 10 as one of the addends. Then they will grab the six bar from the black/white bead stair. I am bummed :( I thought that the addition snake game was one of the free samples Montessori Live had up on YouTube and that I could link to it to show you the other style. Unfortunately, that video is by subscription only. If you have math albums from either Karen Tyler (AMS) or Montessori R&D (AMS) the addition snake presentation given at the end of the memorization sequence presents the snake game in this way. For those of you who get all turned around when trying to turn the steps in the albums into a real-life presentation I MADE A VIDEO. My heart rate jumped up to dangerous levels while making this video. I was super nervous. It's not perfect, but it is a quick look at the addition snake game at the end of the addition memorization sequence.
Like I said, I like both ideas. Both the Karen Tyler and Montessori R&D albums like both ideas as well. The first version of the snake game is included, not in the memorization section, but in the linear counting section of these albums. The second version is included at the end of the memorization sequence. What I think can get lost here is that the "linear counting" version is an important part of the start of the memorization sequence. It is likely that an experienced Montessori guide knows this and if you could lay out all of the different sequences of the math album across one another so you could see "periods" as in the Gettman book you would find that the child reaches the "snake game search for 10" in linear counting just before beginning the memorization sequence so that it IS the beginning of the memorization sequence. I really like how strongly the AMI albums position the early snake game in the sequence. They don't, however, seem to have it again at the end. Not only do I like that Kal-El was able to play the game using his newly acquired addition facts, but frankly before we could BEGIN the subtraction sequence with the subtraction snake game we needed to revisit snake game procedures anyway and it was easiest to do so with the addition snake game. So, perhaps this happens naturally. He had to be taught NOT to count the beads of the snake individually. With all of the work he is still doing with the long bead chains, t was neat to see him appreciate how much less cumbersome it was to just"know" the answer rather than count every individual bead. Also, as he nears completion with the long and short bead chains he is much more familiar with which color equals which number with the bead bars. I know they supposedly pick this up when they use the teen bead bars with the sequin boards. My kids didn't. They most definitely worked out which color was which number through working with the long bead chains. There is a REASON the colors of these things stay consistent across all of the Montessori materials.