Even Steven and Odd Todd Gingerbread Cut Outs

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We have been enjoying the Christmas season here at our house. We have also been doing a lot of learning. We read the book, Even Steven and Odd Todd by Kathryn Cristaldi which teaches children about odd and even numbers. We decided to make a Christmas themed craft about Even Steven and Odd Todd to reinforce the odd even pattern. We cut out a ginger bead chain out of paper. The original intent was to use brown paper, but we were out of brown construction paper and we did not have a paper bag so we improvised and used yellow paper instead. Even Steven all looks the same with a white button on his right arm, black button on his left arm, and a blue heart in the middle. Every Odd Todd looks different although Little BBQ did not want him to look too different because he wanted Odd Todd to have friends and dress nice. I think my little boy is already very socially conscious.

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How I Taught My Preschooler How to Multiply

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Little BBQ has been asking to learn multiplication, so I decided to give it a shot. Little BBQ already has a good grasp of addition and subtraction so multiplication seemed like a logical next step for him. Little BBQ seems to have a way with numbers; he can quickly pick up a new concept if I teach it to him visually and hands on.

Little BBQ in some ways is your typical child. He wiggles all the time and his attention span is short, but when he focuses his attention he can learn a lot in a short period of time. I taught him to multiply by using what I call the bucket system. I told Little BBQ that he has a choice: (a) the first number can be a bucket and the second number can be the number of beans or (b) the first number can be the number of beans and the second number can be the number of buckets.

He told me that he preferred option ‘b,’ so from here my example  will use the second number in a problem as a “bucket” and the first number represents the number of beans needed.

For this simple method a child sets up buckets that need to filled with a certain number of beans. For example, 4 x 5 would require 5 “buckets” filled with 4 beans.

Little BBQ used a tablespoon to fill up his buckets because he is a very hands on learner.  After working several different problems he quickly began to pick up a pattern. Within 20 minutes he was able to deduce all of the twos times tables and recite them.  We have used this method with numbers up to 13 successfully.



Addition with a Soroban Abacus

Soroban Abacus; Shown is the number 123456789 (zero is represented with all the beads pushed toward the sides)

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Early on I decided that I wanted to teach Little BBQ how to add using an abacus, so I always assumed that I was going to either buy or make an abacus with 10 beads per column since we use a base ten system in our society. However, when I started reading, Here's Looking at Euclid by Alex Bellos, I started to change my mind. He made some sound arguments that our brains can quickly differentiate between 1, 2, and 3 items but as we go higher in the number scale it becomes harder and harder for your brain to process more than three (p 14).

It seems that many ancient cultures understood this phenominon. You can see from the diagram below that the Chinese, Romans, and Idians all used dash marks for numbers 1, 2, and 3, but once you got past 3 they changed the symbol to another unqiue symbol in order to quickly distinguish the higher number (p 14).

Armed with this new found perspective I decided that an abacus with 10 beads did not make sense because Little BBQ would not be able to quickly distinguish the difference between 6 beads or 7 beads. I wanted the abacus to be an efficient tool for learning, and not a source of frustration. Many modern abacuses designed for children use brightly colored beads to distinguish the different numbers, but I still think that fewer beads will allow for faster processing.

I decided that a soroban abacus made the most sense. The soroban abacus uses five beads per column. By adding an extra horizontal line bisecting the columns you can quickly represnt the numbers 0-9 on one column. The soroban abacus was used between the seventh and nineth centuries in Japan to accomidate a new merchant class of people who needed to be able to quickly add numbers (p 40). To ease the transition between the abacus and the electronic world an abacus attached to an electronic calculator was sold in Japan for many years (p 41). Interestingly, addition is still quicker with an abacus than an electronic calculator since the answer to an addition problem is in front of you as soon as you  input the values while the calculator still needs to be told to process the information to come up with an answer (p 40). The efficiency of the abacus is probably why it is still a popular tool studied in Japan today by school children who form after school clubs to compete in adding a long series of numbers as quickly as possible using a soroban abacus (pp 40-41).

When a student becomes an soroban abacus master, he can move on to azan. Azan is a technique for visualizing a soroban abacus to quickly add numbers. Proficient pupils in azan can add a series of 15 numbers quicker than a person can use an abacus, pen and paper, or calculator. The catch is that each number is only shown for 0.2 seconds (p 42). That is hardly long enough to process the number on the screen. Azan students keep a visual soroban abacus in their head and when a new number is flashed the student visually moves the beads on the soroban abacus around in his head keeping a running tally of the sumation (p 42).

Interestingly, nueral imaging studies have shown that adding with soroban abacus stimulates areas of the brain that are associated with visuospatial processing while pen and paper addition stimulates areas of the brain that are associated with linguisting processing. In other words, the abacus uses the right side of the brain while the pen and paper method uses the left side of the brain. The soroban abacus is an excellent learning tool for visual students.

Want to really stimulate your brain? Some Japanses students can play shiritori while practicing azan (p 43). Shiritori is a word game where the first person says a word then the next person says a word that starts with the last syllable of the original word and then the first person makes a new word using the last syllable of the second word. The game continues on in this pattern. Bellos gives this demonstration of a young Japanese girl who is a soroban prodigy while she plays shiritori. In the demonstartion the girl is shown 30 three digit numbers during a 20 second time period while playing shiritori (p 43). Her shiritori dialogue with another student is shown in the text below

Ringo
Gorira (gorilla)
Rappa (trumpet)
Panda (panda bear)
Dachou (ostrich)
Ushi (cow)
Shika (deer)
Karasu (crow)
Suzume (sparrow)
Medaka (killifish)
Kame (turtle)
Medama yaki (fried egg)

At the end of the 20 seconds the girl states that the summation of the 20 numbers is 17,602 (p 43).

Given the sucess of soroban abacus training, I have decided to teach Little BBQ addition using a soroban abacus. To make the experience more person for him, we made our own soroban abacus out of a card board box.

Materials

card board box, lid removed
paint
ruler
knife or scissors
string
breads
tape

Procedure

1. Have the student paint the card board box.
2. Decide how many columns you want the abacus to contain. Cut notches into the top and bottom flaps of the cardboard box equal distance apart for the set number of columns that you chose (we  made our abacus with nine colums all 3.2 cm apart).
3. Cut the string to stretch across each the box from one notch to the other. Place 5 beads on each string. Insert the string in the notches and tape the string to the box. Continue in this pattern until all the columns are finished.
4. Make two notches on the sides perpendicular to the columns. These notches should be close to the top of the box but far enough away from the edge so one bead can comfortably fit abvoe the string line. We decided to use a red string to distinguish this line from the columns in our soroban.
5. Insert the string in the notches perpendicular to the columns. Tape the string.

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All references are from the book:

Box Assemblage

This week for math Little BBQ has been working on the concept of enclosure. For a young learner, “enclosure is when objects are grouped together and fenced or held together as a unit” such as a dozen eggs in an egg cart (Math Arts p151.) To explore this concept creatively Little BBQ made a box assemblage. We took box from my canning jars and went outside. Little BBQ was allowed to collect outside objects to place inside of his assemblage (a 3-D collage.) As we were gluing the objects inside of his box we discussed the fact that all the items inside the box are now together as a unit instead of a single leaf or rock they are a unit composed of lots of leaves, rocks, sticks, and grass. We also brainstormed other things that come as unit like eggs, bags of apples, and berries inside of boxes. Overall, the project was a lot of fun. I think this is a fun way to creatively learn about enclosure.

Materials (modified from Math Arts p 163)

A cardboard box
Small objects to put inside the box (we used items from nature)
Glue

Process

1. Choose the small objects to be placed inside the enclosure.

2. Place the objects inside the box.

3. Rearrange the items until the young artist is satisfied with arrangement.

4. Glue the objects inside the box.

5. Display the assemblage in a special place.

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Books that we read this week: