Study Tip #25
SCIENCE: DEALING WITH VOCABULARY, SYMBOLS AND MATH

Some facts about new vocabulary, symbols and math
The most obvious difference about science courses, noticed by students at every lecture and textbook chapter, is the thick wall of words. Yet you’ve got to deal with words first because words are the legs that ideas walk on. This Study Tip deals with the challenge of vocabulary, symbols and math, and I warn you it won’t be pretty. The fundamentals are still the same: Get new knowledge accurately, make associations to the new chunks of knowledge, and make them firm.

Many science courses use a large amount of new vocabulary. A college biology course may introduce more vocabulary than a foreign language course does. One astronomy book’s chapter on the Sun used 40 new technical words, many of which would be unfamiliar to ordinary readers. In addition, many sciences often use symbols. They use them to stand for elements and chemicals, properties of objects and events, units of meas-urement, and parts of formulas. Science courses also include numbers, formulas, graphs, tables and charts be-cause the sciences use math to measure things and events and to summarize the relationships among them.

Words can be hard to learn. Keeping several new words from getting confused is also hard. Research on memory reveals that people learn highly meaningful material far more accurately and quickly than they learn material that is low in meaning to them. Since many technical terms, symbols and math are low in meaning to students, their memory will fade unless they take explicit steps to understand and memorize them.

Why it matters to deal with words, symbols and math
Nearly always, when a textbook introduces a new term or symbol, it defines it immediately. Normal readers who have the prequisite knowledge can understand it at that time. But complications happen. As students read on, the text teaches and the readers read more new words and symbols, and their memories fade for the earlier words. When they encounter an already introduced new word a few pages later, their fragile memory means they cannot recall the meaning of the new word or understand the sentence it is in.

Adding to the difficulty is that the new words refer often to things that students have not heard of. It would be easier if the new words simply named things they have already met. But students must learn both the new concept and attach a new label to it. And if the scientist also uses short symbols for the concepts, as chem-ists do with elements such as Na for sodium, students must learn the symbol, translate it into the word sodium, and recall its properties—three learnings.
The point is that you must deal with these difficulties. If you don’t treat words, symbols and numbers differently than you treat the interesting big ideas, you’ll have unnecessary difficulties in learning science.

Strategies for dealing with new words during your first reading
The first reading of a science chapter is special because it is all new to you. Your main task now is to under-stand the text on the direct obvious level. Later you can get deeper understanding, perceive many relationships among the parts of the new knowledge, relate it to your own knowledge, and commit important things to mem-ory. Since you will read for understanding at the beginning, you will use strategies for new words that do not conflict with getting good comprehension.

• As you read and encounter new words, do not try to memorize right then and there, because the interruption to your reading will damage understanding of the larger passages.
• The most important thing: When you encounter new concepts and new words, do pause and think enough about what the words mean that you understand them at the time. The idea is to have the mean-ing very clear so that all you are doing is attaching a word to an already understood meaning. Do not read so fast that you are trying to attach a fuzzy word to fuzzy, badly understood ideas.
• Notice the definition, examples, and any graphics that illustrate them. Make a visual image of a concrete example of the new concept if possible. Pause and look back and forth between words, examples and pictures.
• Realize that you may forget the word’s meaning later and need to take steps to help yourself.
  • Option #1: Mark the definition. Either write the letter D in the margin or take a felt tip pen and mark the word itself. (There’s no need to mark the whole definition because the short swipe over the word will clue you in later to the location.)
  • Option #2: Jot down each new word in a column on a separate piece of paper. Write a short clue to the definition. Put down the page where you found it. Use the list as you read on through the chapter to quickly find and review new words.
• When later you read a later passage and see a word that you have forgotten it, do look it up.
  • If you feel annoyed at using time to look it up, think of this: Won’t it annoy you even more later on a test if you cannot answer a question because you didn’t understand today the sentence that the word was in?

The above suggestions will help you during your first reading to get as much possible while maintaining your focus on the big picture. But you can do a lot more to learn words by studying and making more contacts with the text material. I will now suggest some useful methods for studying vocabulary, symbols and math.

Studying after your first reading: Collect six aspects of definitions of concepts
During later contacts with science material, your goal changes to finding more relationships and building memory. Whereas you’ll understand some of the ideas almost automatically, you will almost certainly need to make explicit efforts to firm up the vocabulary. Your first task is to collect and bring together up to 6 major aspects of new concepts and vocabulary; most writers will give only some of them.

A concept can be thought of as an idea in our minds. Writers will try to communicate concepts in several ways.

• The verbal definition is the string of words that say what it is. “A triangle is a 3-sided plane figure.” “A social norm is a rule that tells a group what they should do, ought to do, and are expected to do.”
• A visual image is often provided to display an example in a visual representation. Pictures and diagrams are common, even in some dictionaries.
• One or more positive examples of the concept are often provided. If we were learning the concept of a dog, a book might give the names of several breeds as positive examples—German shepherds, poodles, collies, and chihuahas. A good text will give a wide range of examples—both obvious examples and unusual ones. The purpose: to prevent students from mistakes that rule out perfectly good phenomena that fit the concept.
• One or more negative examples are also often given. Negative examples are confusing cases that learners might get confused with the real thing. When books name negative examples, they help readers pre-vent confusion before it gets entrenched. For example, young students might confuse bats and large in-sects with birds, so a book might name bats and dragonflies as negative examples of the concept of birds.
• A prototype example is an important kind of positive example. Prototypes are really good examples of the concept, so that if you need a concrete instance of a concept to remember you would do well to think of the prototype. People in North America often think of robins as a prototypical bird. And people remembering percentages make up an easy percentage problem in a standard format as prototype (20% times 50 = 10). Then when they get a new question framed differently, they can solve it by taking their prototype, rearranging it, and changing the numbers.
• A unit of measurement is a way of turning a scientific concept into something measurable. Thus temperature can be measured in kelvins which equal degrees Celsius + 273. Measurements need to be learned along with the other aspects of new concepts.

A note: You will find that many test questions will bear on vocabulary and may include examples.

Studying: Major strategies
Here are some important ways to study vocabulary. Be aware that this list does not cover strategies needed for such other learning tasks as building problem-solving skills, learning factual knowledge, studying explanations of scientific phenomena and scientific arguments. The following methods work especially well with vocabulary; use them as needed.

• Use distributed study methods. Make multiple contacts with the vocabulary. It is often fairly practical to revisit your vocabulary list many times because the units you are looking at are short. The purpose is to make your memory and associations firm.
• Study a concept and its examples by making discriminations, i.e. noticing differences. In other words, take a concept and notice how examples of it are different from related concepts. Go beyond thinking abstractly how the verbal definition differs from a related concept. Think also of visual or kinesthetic imagery of an example and how the example looks and feels and then compare it to an example of a different concept.
• Study a concept by making generalizations, i.e. noticing how far it goes to many examples. Identify unusual phenomena that are examples of the concept. By the time you are done making discriminations and generalizations of a concept, that may be enough to make the concept firm. Your self-tests will tell you.
• Make row and column charts of related concepts. List their properties in the chart. The spatial layout taps very powerful potentials of your brain for making visual associations.
• Make hierarchical diagrams showing concept relationships. A famous example of a hierarchical chart comes from biology showing the relationships among species, geneuses, families, and so on. The spatial layout will make memory easier.
• Study and test yourself. Ask a question, give an answer, and check your answer. Repeat.
• Study by rearranging the parts of the definition in the same order that you expect will match the future order of questions and answers on tests or in real-life situations. For example, teachers may start a test question with the word, the verbal definition, a description of a concrete example, or a picture of the concept. Prepare yourself for any way the word starts.
• For your self-tests ask yourself verbal questions and give verbal answers. In other words, talk to your-self; avoid vague fuzzy thinking.
• Use look-away techniques. (Look at information, look away, ask a question, give answer, look back and check, correct and try again).
• Use cumulative-addition-to-a-set. (Study one item. Study a second item, then study both until perfect. Study a third, then study all three until perfect. And so on—up to fifteen or twenty items. Then start a new set.)
• Use mnemonic techniques that create images and artificial meanings. The Keyword method is very powerful.
• As your current degree of learning improves, adjust the time gap between looking at the word and looking away and giving the definition. As you know it better, increase the length of the delay you insert before you test yourself. When just starting, give the answer right after looking away. As you get better, pause 5-10 seconds. When still better, allow a filled 30-second pause (filled means that you think of something else during the time gap). Finally, give yourself overnight time gaps; in other words, test yourself the next morning without having looked at the material.
• Ask the question about words and definitions,“Why does this make sense?” and think of answers as a way to build memory. Sometimes a new word is built on roots that are familiar to you. For example, you may know that ultraviolet is high frequency because you know that ultra- means something way beyond. You may know that infrared is low frequency because infra- means something below. If you do not know the word’s roots, you may make up a silly answer to the make-sense question. For example, oxidation means that one molecule takes electrons from another molecule. Why does this make sense? Imagine the “ox” in oxidation moving his horns to hook a electron from a molecule.

Dealing with symbols
Symbols are either abbreviations of words (kg for kilograms, K for temperature kelvins) or more abstract as in Greek letters like mu, lambda and delta). Each symbol usually translates into a word. So your study tasks are to associate the new symbol to the word and then make it firm, so that when you see the symbol, you can recall the word, and vice versa. Use the methods described above for learning vocabulary and test yourself.

When scientists measure the properties of objects and events, they use measurement symbols. Then the symbols are used as part of formulas. Formulas involve equations: there are two sides separated by an equals (=) sign. At first you may not find an equation meaningful.

Make an equation meaningful in two ways: (1) Use the text explanation of the principles involved to un-derstand it in words and mental images. (2) Learn the meaning of the symbols; each symbol should match something in the words used by the text. (3) Pick a pair of units, one on the left and one on the right of the equation, and say to yourself their relationship. Pick an item on the left and an item on the right, and say to yourself something like, “As X gets bigger, Y gets smaller.” And you can be more detailed. If 2x = y, you can say, “As X goes up one unit, Y gets twice as big.” Notice that this procedure starts by taking two units at a time, no more. The purpose is to minimize the demand on your working memory. After you’ve got all the parts straight two by two, then look at the larger units in threes and fours until you have a feel for the entire equation. Later when you see the equation again, you will understand its meaning better.

Dealing with math
As with words and symbols, you need to know what your teacher’s goals are. A lot of numerical information does not need to be memorized. In certain science situations some specific numbers do need to be understood and memorized. Use some of the methods described above for words and definitions to learn numerical infor-mation.

If your task is to solve problems, you will use cognitive skills. Check the Study Tip on learning cognitive skills.
Some basic methods are to:

• Study the author’s worked-out examples of problems;
• When doing a problem of a new type have a worked-out example problem nearby and use it as a model;
• Practice solving a wide range of problems on the same topic;
• Break things down into steps and learn for each step its specific situation and its current subgoal that trigger you do a certain action, because you must associate three things for each step;
• When you have solved a problem correctly, pause and do two things to build memory:
  • Review mentally the steps you took that led to the solution;
  • Praise yourself for using the techniques correctly (do not just praise mere raw success).

(Dan Hodges. 7/07)

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