The Origami Algorithm And C3 (Common Core Confusion)

When my grandchildren are being tortured by Common Core math homework their mother tries to help them. Sometimes she throws up her hands in frustration and asks me if I can help. Thus began my training in the mysteries of Common Core Math. But before I could help, I first had to figure out one of the great Common Core math mysteries. What is an algorithm? But the answer to that mystery has to wait until you get to the end of this blog.

Working with the grandkids on their homework, I learned the first rule of Common Core math is sequence. You are not supposed to think. You are not supposed to imagine, estimate, or consider options. You are to follow instructions and solve problems in the right order.

This April the grandkids took the sixth grade math test so I decided to look at the questions released by New York State to see what I could learn. I discovered these things. It is a reading test with content specific vocabulary and the prompts contain extraneous information designed to confuse students.

Reading Test: Common Core math, for better or worse, is no longer about calculations; it is about reading. Most of the "released" questions were word problems, which means a student who has difficulty in reading is going to fail math, even if they know how to do the math. This will be especially unfair for English Language Learners.

Vocabulary: Passing the math test means memorizing specific the vocabulary. Word problems on the sixth grade released questions used the words or terms (listed in alphabetical order) approximate, calculate, centimeter, constant, coordinate, corresponding, determine, diagonal, discount, enclose, equation, equivalent, expression, grid, hourly, inequality, kilometer, opposite, percentage, plane, plot points, possibility, properties of operations, pyramid, quotient, rate, ration, rectangular, relationship, represents, trapezoid, units, and vertices. The term function, which I think is a synonym for equation, appears 172 times in the 83-page explanation of the New York State Math Learning Standards but not on the sixth grade math test. I have no idea why.

Extraneous information: The questions often have extraneous information that students must recognize and disregard. For example, according to one question, "The summit of a volcano is 10 kilometers (km) above the ocean floor, as shown below. If the ocean floor has an elevation of -5 kilometers, which statement describes the elevation of sea level and the summit?
A. The elevation of sea level is 0 km and the elevation of the summit is 5 km.
B. The elevation of sea level is 5 km and the elevation of the summit is 5 km.
C. The elevation of sea level is 0 km and the elevation of the summit is 10 km.
D. The elevation of sea level is 5 km and the elevation of the summit is 10 km.

The metric system has nothing to do with this question. Information could just as easily been provided in feet or yards. A student unfamiliar with or unsure about kilometers may be thrown by the question even if they understand the math. The information about the ocean floor is also extraneous and only confuses. The elevation at sea level is 0 km so the elevation of the volcano summit is 10 km.

Whenever you question a Common Core standard or a question on a Common Core test you are always told it was carefully chosen as appropriate using an algorithm, the mysterious Common Core algorithm.

Did you ever bake a cake, found the recipe confusing, or you were short an ingredient and had to jerry-rig a substitute? One way to think of an algorithm is like recipe. As with any recipe, with an algorithm, if the instructions are confusing or the ingredients are inappropriate, the outcome could be a disaster.

Now back to the origami algorithm. I originally developed this activity, creating an origami paper crane, as part of a unit for teaching elementary school students about the impact of nuclear war and the need for peace and middle-level students about Japanese culture. Now I use it to help teachers understand what an algorithm is. It remains a great activity for students and teachers of all ages.

Origami is the Japanese art of paper folding. In Japanese, oru means "to fold" and kami means "paper." Paper folding originally developed in China, probably soon after the invention of paper in the first century AD. In an example of cultural diffusion, paper and paper folding were brought to Japan in the sixth century AD by Buddhist monks. In Japan, paper and paper folding became important aspects of architecture and the Shinto religion. Kami (paper) is a homonym for spirit or god.

While leading a class in paper-folding, I stress four basic rules that are also applicable in Common Core math:

Sequence (steps must be done in order).
Symmetry (what you do to one side you must do to the others).
Concentration (the open side must always be down).
Precision (folds must done carefully and firmly).

Origami Paper Crane

The crane is usually not for beginners but I think it is worth a try. Everyone is not going to be able to create one the first time. It is easier if you work in pairs with one person reading the directions aloud. There are videos online that can help.

• Start with a square of paper. Usually it is brightly colored or patterned on one side. While you can use any size, I prefer a six-inch square. A larger piece can be awkward to work with and a smaller is just plain difficult for inexperienced or clumsy fingers. 'Top' means the corner or side pointing away from you. 'Bottom' means the corner or side pointing toward you.

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