How important is CRA? Here in Texas, it’s actually written into the standards–the Texas Essential Knowledge and Skills (TEKS). My point here is not only the importance of the CRA sequence of instruction, but also that the majority of our students are getting far too little concrete and pictorial experiences with key concepts, and that is a major cause of their lack of understanding. If, however, a child has had many experiences folding fraction strips, using fraction tiles, working with fractions on a number line, and cutting up brownies or cookies into equal parts, there is no earthly way they would say that 1/8 is larger than 1/4. Why? Because 8 is larger than 4, of course. Next, ask a student, 3rd through 5th grade, which fraction is larger, 1/8 or 1/4, and many will tell you that 1/8 is larger. If a child has not had concrete, hands-on, place value experiences he will not understand that the first number is larger because it has more ones. Sound a little far-fetched? Ask a child which number is larger, 3.5 or 1.389, and I guarantee you a high percentage will say 1.389. The child might say that a blueberry is bigger because it has more letters. Now ask the child to compare the two fruits. Assume a child has never seen, held, or tasted an apple or a blueberry. Can a person truly understand an apple at a deep conceptual level without holding and tasting one? I don’t think so. Think of the picture at the top of this post. There is no additional cost to you, and I only link to books and products that I personally use and recommend. This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. It says, quite simply, that students must experience and interact with a concept to develop a true understanding. Regardless of the letters used, this sequence of instruction is based on the research of Jerome Bruner. They call it CPA, with the P standing for pictorial.
What changed? They adopted a teaching philosophy that is built on the concrete, representational, abstract (CRA) sequence of instruction. Twenty years ago, Singapore occupied the space squarely at the bottom of the world rankings in math. You may have heard of a little country called Singapore and its successful math instruction. It has some curved lines and some straight lines, like the letters a, b, or p. Until a child knows that 5 means 5 fingers, or 5 dots, or 5 toy cars, or 5 years old, the symbol doesn’t look much different than a letter. Now I know it’s a number. Think about that for a minute. All he said was this: I used to think 5 was a letter. It was an adorable little boy facing the camera. What’s this got to do with math? I once saw a very short video clip, lasting no longer than about 10 seconds. How did you do? Did you see any distinguishing characteristics that helped you make your determination? I sure don’t. Symbols 1 and 4 are numbers, while symbols 2 and 3 are letters. Can you tell which are letters and which are numerals? For the rest of you, look at the symbols below. If you speak and write Hindi, you can skip this quiz.
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