Last week I talked about the importance of providing short practice sessions spread out over time (distributed practice and spaced repetition) and making sure that practice sessions involve a variety of the skills (interleaving practice). Today I want to touch on a couple of other points to keep in mind when setting up practice.
When the content allows, it is extremely useful to present practice activities that reveal the underlying structure of what they are investigating. For example, a difficult part of learning how to spell the word “president,” is to know that the vowel in the second syllable is written with an “i.” This is difficult to remember because the sound we say in the word in the second syllable is a little “uh," a vowel sound called a schwa that is common in the pronunciation of unaccented syllables. Unfortunately, this sound can be spelled with any of the one-letter vowels. It so happens, however, that there is a form of the word in which the second syllable is accented, namely, “preside,” in which we say the so-called “long sound” of “i.” If the student’s practice routine involves connecting the word “president” to the word “preside,” he will be able to recover the underlying sound of the vowel and thus find it much easier to remember the spelling. Moreover, the practice will have reinforced some of the structural ways that words are related in English. This same relationships can be used to help remember the spelling of hundreds of words.
Practicing letter/sound relationships as students do in phonics programs likewise helps them connect the reading and spelling of particular words with other words and reinforces a central part of the structure of our writing system.
The study of elementary math provides many opportunities for enhancing practice by highlighting critical structural relationships, although most curriculum materials do not take advantage of these opportunities. When learning how to do calculations with decimals, for instance, it is extremely useful to investigate the same calculation when using common fractions. Even something like memorizing the multiplication facts can be made much easier by practice that stresses relationships. For instance, when I am reviewing multiplication facts with students and they have difficulty recalling a fact, I ask them to connect it to something that they know. If a student forgets the product of 6 x 6 but knows the product of 5 x 6, he can talk himself through the problem by adding 6 to the product of 5 x 6. Another option is to draw an array on a grid board that corresponds to the multiplication problem. When trying to figure out 6 x 6, for example, this means drawing a 6 by 6 rectangle. The student can then divide that shape into 2 or 3 parts and then calculate the product by adding the parts. Of course, the ultimate goal of this practice is for the student to have rapid and accurate recall of the facts. But by emphasizing the way every fact is part of a broad network of relationships, you will accelerate how quickly your students achieve fluency and, at the same time, help them develop a sense that the various things they are learning in math aren’t random and isolated but tightly interconnected.
Of course, not everything we want to learn has the kind of structure we find in our writing system or in mathematics. Some things, such as learning the order of the colors of the rainbow, the order of the planets in the solar system, or the capitals of the states, are associated in arbitrary ways. Many of us have learned such things with brute-force memorization, simply repeating the order of the items and their connections over and over. This technique often works eventually, but in most cases, there is a faster and easier method.
Since antiquity there have been people interested in developing systems to help with memorization. What these memory system have in common is that they provide ways to impose a structure on abstract, random information by associating it with something you already know. As Harry Lorayne and Jerry Lucas write in their classic, The Memory Book, “In order to remember any new piece of information, it must be associated to something you already know."
This is the idea behind mnemonics such as the sentence “Every good boy deserves fudge,” to learn the order of notes represented by the lines on a scale. This mnemonic works because it is much easier to remember common, familiar words organized in a simple sentence than to remember the order egbdf. Memory trainers such as Lorayne and Lucas have developed flexible systems that utilize the same underlying principle and that can be applied to memorizing any content. The key to most of these successful memory systems involves developing ridiculous and wild images that connect objects. In the Lorayne and Lucas book, they offer the example of trying to learn a random lists of 10 objects. If the first 2 objects were airplane and tree, the person should make a crazy image in which the two are together, such as a tree that has small airplanes for leaves, or an airplane that has a variety of trees as passengers. There are a variety of elaborations or extensions of this basic technique, but all successful memory systems rest on this fundamental strategy.
A number of years ago I had the opportunity to travel to China and wanted to try to study the language a little bit before the trip. As you may know, it is quite a challenge to learn to read Chinese characters, because it is necessary to memorize thousands of them in order to attain even the most basic level of literacy. In the course of my studies I found a really interesting book to learn the 800 most basic characters. The technique used in each book was to break each complex character into parts, and have each part represented by a visual image. They then constructed a little story that connected these images with additional clues about the words meaning, its pronunciation, and its tone. Thus, for each character, one had an easy to visualize story that connected all the essential elements needed to read the word. I found this approach very useful and much easier than the brute-force approach I had tried previously.
The Chinese book gave me the idea to try to adopt this technique to prepare an English spelling book, and thus I developed the ABeCeDarian Spelling Book B-1. This book addresses first grade words such as “boat” and “rain.” The first skill a person needs to spell well is an ability to break a word into individual speech sounds. To spell a word such as “mop,” requires a person to break the word into its three sounds and then remember how each of those sounds is spelled. This a a relatively easy task because there is not much ambiguity about how to spell each of these sounds. But a word like “rain” offers an additional challenge because there are several common ways to spell its vowel sound. Is it “rain,” or “rane,” or perhaps “ran” or “rayn”? To overcome this confusion, the ABeCeDarian spelling book presents all new words within sentences that have silly clues about the correct spelling of any ambiguous part. Students learn, for instance, that the word “ape” is used to signal the letter “a,” and the the word “I” to signal the letter “i.” When learning to spell “rain,” they then read, analyze and copy the sentence, “The ape and I sit in the rain.” When they practice initially, they don’t write the word in isolation but the entire sentence with the clue words to associate the spelling "ai" (the ape and I) with the word "rain."
I'll try to make some short videos demonstrating some of these techniques. It's much easier (and more compelling) to demonstrate them than to write about them. And in a future blog post, I'll show you a technique for memorizing the first 20 digits of pi.
So, here are the key points for today. When the content you are investigating with your student has structure, make sure that the practice activities of your students help them organize new information within a web of central relationships and connections. And when the content that your students are trying to master has a more arbitrary relationship, help your students use the techniques of memory experts and impose a structure on the material with silly, and thus vivid, associations.