(Preprint of Charness, N. (1985). Aging and problem solving performance. In N. Charness (Ed.) Aging and human performance (pp. 225-259). Chichester, U.K.: John Wiley and Sons.)

Aging and Problem-solving Performance

Neil Charness

Problem-solving is an activity engaged in routinely by everyone, yet one could argue that success at it is essential for older, less mobile people. It is not that farfetched to assert that the decision to institutionalize someone is usually made when the person can no longer solve essential problems such as feeding, cleaning, or dressing themselves well enough to preserve their social and biological integrity. Even when extreme dysfunctions are not present, the older individual is much more likely than his or her younger counterpart to be physically disabled. Thus, some ingenuity is required to make available facilities (recreation, shopping, visiting) truly accessible. Problem solving, by definition, is the activity that enables someone to attain a desired state from an initial one in which it is not immediately clear how to reach the desired state.

Unfortunately, the older person is also less likely than a younger one to have mental resources operating at peak efficiency. Memory ability declines with increasing age, as the previous chapters by Kausler and by Spilich indicated. Similarly, physical resources are likely to be on the wane as well, as Verrillo and Verrillo, and Stones and Kozma have shown, in their chapters.

Fortunately, expertise in problem-solving is related to the size of the domain-specific knowledge base of the problem solver. Also, the size of a knowledge base is roughly proportional to the time spent operating on domain problems. (See Simon and Chase, 1973, for a discussion of chess skill.) Thus, older, experienced people are not necessarily a disadvantaged segment of society for certain classes of problem-solving. As many investigators have pointed out (e.g., Demming and Pressey, 1957; Gardner and Monge, 1977), when tasks relate more strongly to the ecological niches that the older person inhabits, age-related deficits are less prominent. For instance, when the tasks involve scientific career activities (Cole, 1979), age-related declines are so slight as to be inconsequential.

As Giambra and Arenberg (1980) aptly observed in an earlier review: `The problem-solving literature reviewed represents a heterogeneous mixture of procedures and material highly resistant to organization and synthesis'. Since things have not improved, I am forced to act in Procrustean fashion, stretching the interpretation of some studies and chopping off others to fit a coherent theoretical framework. Even spatial performance, which seems to decline with age for unfamiliar tasks (see Plude and Hoyer, this volume) can be remarkably accurate in familiar settings (see Kirasic and Allen, this volume).

One goal of this chapter is to examine how problem-solving in novel domains relates to problem-solving in `semantically rich' ones, those where a large knowledge base is essential. Another goal is to provide a fine-grained analysis of the problem-solving process in order to evaluate the factors underlying changes in ability with age. We'll start with the latter.

THE PROBLEM-SOLVING PROCESS

You encounter a problem when you want something ­ call it the goal ­ and do not immediately know how to go about getting it. A more formal way of viewing problem-solving, following Newell and Simon (1972), is to see it as the set of transformations (usually mental operations) that enable the solver to reach the goal state from an initial state. Finding a job, a marital partner, a way to run a household within a fixed budget, and solving puzzles such as 'Tower of Hanoi', or choosing a good move in a chess game, are examples of problems. Understanding a psychologist's instructions for an experiment and finding an efficient way to carry out her task also constitutes a form of problem-solving.

We can carry this cognitive imperialism to great lengths, since almost any human endeavor can be seen to have a problem-solving component. Fortunately for reviewers of the aging and problem-solving literature, researchers have generally chosen a much narrower set of tasks to investigate ­ e.g., concept formation, logic problems, and the twenty questions game.

The problem space

It is assumed that when a problem is presented, the solver will create an internal representation that encodes critical aspects of the problem. To begin with, the solver must understand the problem instructions (see Hayes and Simon, 1977; Hayes, 1981), and evoke a representation that contains a description of the goal state, the initial state, and the methods for operating on these descriptions. This internal representation is called a problem space.

One view of the problem-solving process is that it involves 'growing' paths, both forwards and backwards, between the initial state and the goal state. It is analogous to working through a large maze. There are dead ends, backups to previous points, detours around obstacles, and hopefully, a completed path. The way that a solver finds the critical path is through search.

It is surprising how big the `tree' of possible paths is, even for relatively simple problems.

Suppose someone is planning a simple dinner (see Byrne, 1977, for an analysis of planning meals). There may be three categories for the main entree (fish, fowl, meat), three for the starch (rice, pasta, potatoes), and three for the vegetable (green, yellow, other). As Figure 6.1 makes clear, there are 27 types of meals (3 x 3 x 3) to be evaluated. When you consider that there may be at least 3 more instances for each class type (meat: beef, lamb, veal), and perhaps 3 additional styles of preparation within each of these sub-categories (beef: roast, pan fry, broil), you begin to appreciate the size of the problem space, as defined by possible paths (3⁵ = 243 `simple' meals).

Figure 6.1 Problem space for planning a meal. The node at the bottom on the extreme right represents a meal consisting of meat, potatioes, and a non-green, non-yellow vegetable.

(The size of this type of problem space is determined by the branching factor, b, and the depth, d, of the tree, such that paths = b^d.) By the time you add in a beverage and dessert, the problem space has expanded to thousands of alternatives. Picking a meal from this set that will please people with different preferences surpasses the complexity of many laboratory problems. (I wonder if this has anything to do with why Grandma is seen as 'rigid' or 'cautious' in her selection of Sunday dinners?). This particular example is illustrative of a reasonably well-structured problem. Most puzzles in the laboratory ­ for instance, concept identification with well-defined attribute classes ­ fit into this category. Most real-world problems are ill-structured. See Greeno (1976), Simon (1973), for a discussion of this distinction. How do you write a good chapter on aging and problem solving? What test can you apply to tell when the goal has been reached? When faced with such situations people 'satisfice' (Simon, 1981).That is, they accept something as a solution when it exceeds some predetermined criteria, rather than searching for an optimal solution. Hiring an employee or choosing a spouse falls into this category. People interview until an available candidate is found who exceeds their level of aspiration.

Search Process

Recognition

At the base of all mental operations is the act of recognition - accessing a symbol structure by matching a current event to a past event. What is 6x6? Most adults recognize the answer to this problem as soon as they encode the problem statement. In some sense there is no problem to be solved since stored in memory is a response for the index (6x6=?). This does not mean that the act of recognition is not itself decomposable into other processes. (See Stazyk et al., 1982, for a discussion of how memory may be organized to perform mental arithmetic.) It is convenient, however, to treat this process as elementary. One way to model how this problem can be solved is to adopt the convention of representing such information in `production systems' (Newell, 1973). A production is an 'if-then, statement that consists of a condition linked to an action. When the condition is true, the action is taken. Productions can be seen as operators, taking symbolic expressions as inputs and generating new symbolic expressions, or ultimately, actions in the world, as outputs. Thus the 6x6 problem could be solved by a system containing the production: 'If asked for the product of two sixes, then respond thirty-six'. Presumably, one of the purposes of all the arithmetic drills done in the primary grades is to fill a child's head with a large set of such productions.

For an adult it would hardly be fair to call this process problem-solving. Yet, in any problem-solving task, a person must be able to reduce a particular step to one for which she knows (recognizes) the answer. Thus, recognition lies at the heart of problem-solving. Any finding of a slowing with age in the time to carry out the recognition process has implications for problem solving speed.

Generate-and-test

With some problems, the only way to search a problem space is via a generate-and-test strategy. 'I'm thinking of an integer in the range one to ten. If you can only ask 'single integer' questions, the way to discover my number is obvious. Generate an element (candidate digit) from the potential solution set and test whether it is the goal element. As long as your generator can produce all the elements, and can keep track of which ones have been generated and tested, you will eventually succeed. Generate-and-test works well when the problem space is small, but becomes increasingly less effective as the space increases: e.g., 'I'm thinking of an integer between one and a million.'

Heuristic search

When searching large spaces, the only hope is to search selectively, by searching smaller subspaces where the answer is likely to be. For instance, having played many million digit guessing games, you may have discovered that people never choose even numbers and use only numbers in the range of 1-1000. If you use these constraints in generating candidate digits, you will need, on average, 250 questions rather than 500,000 to find my number. (On average, if there are n alternatives, generate and test will find the goal element in n/2 questions.) Selective search, though it always runs the risk of missing the crucial solution element, is the hallmark of human problem solving. Selective search is better known as 'heuristic search' (Newell and Simon, 1972).

To search heuristically is to make the generator dependent on the test, rather than independent as in the case of generate-and-test. Rather than discarding a new element if it is not the goal element, an evaluation is made whether to use it as a stepping stone to approach nearer to the goal element, or to abandon it and generate another element. If search is seen as movement through a tree-like structure, or network of arcs and nodes, then heuristic search represents the case where nodes are evaluated for their apparent distance to the goal, not just whether they represent the goal. An excellent example of heuristic search is provided by the means-end reasoning of a computer program called the General Problem Solver (GPS ­see Ernst and Newell, 1969). Means-ends reasoning involves knowing what operators or actions are relevant to reducing the difference between the present state and the goal state. It involves partitioning a problem into sub problems or sub-goals and tackling the series of sub-goals that lead to the goal.

The flavour of such means-ends reasoning is well conveyed by the example of `solving, the problem of being hungry and wanting a meal while working in your office. What is the difference between my current state and the goal state? A meal. Where do you find meals? In a restaurant or cafeteria. (Or at home, but home may be too far away.) What is the difference between my position and the restaurant? Distance. What reduces distance? Walking! Thus I can walk to a (nearby) restaurant, order a meal, and satisfy my hunger. This recursive process of putting off the main goal to tackle the necessary sub-goals exemplifies means-end reasoning. Rarely are problems as straightforward as this, since people usually try to satisfy multiple goals in any situation (e.g. in the previous problem you might want to take a car if it is raining to minimize the discomfort of getting wet). Putting up a good impression for the experimenter, or saving face when confronted with a difficult task may also be goals adopted by someone in a laboratory experiment, aside from the one set by the experimenter.

Problem representation

The nature of the problem representation is often critical to the probe ability of solution and the ease of searching. Take the nine dots problem. The task is to connect the dots with four or fewer straight lines drawn in a continuous sequence such that the pen or pencil does not lift from the page.

Figure 6.2 The nine dots problem: connect all points with four straight lines drawn without lifting the pencil from the paper.

This task is impossible to do if, as most people do, you adopt the assumption that the lines must stay within the boundaries of the square which the dots define. (If you are willing to suspend the assumption that the paper must be left intact, and you are skilled in paper folding, you can even find a solution with one straight line-see Adams, 1978.)

One need not go to extreme cases such as this to show how the nature of the initial representation is critical to problem solving. Work done by Hayes and Simon (1977), and D'andrade (cited in Rumelhart and Norman, 1981) on 'problem isomorphs', shows how formally equivalent problems yield very different searches and hence solution probabilities. A problem isomorph is a `twin' of a problem that has a one-to-one correspondence between the problem elements and rules.

Take the problems in Figure 6.3. Which cards must be turned over to verify the rule (for CARD PROBLEM): if there is a vowel on one side, there is an odd number on the opposite side? For the invoice problem the rule to be evaluated is: If the price is over $20, the manager's signature must be on the opposite side. Few people (13%) solve the cards version, yet most (70%) solve the invoice version, despite the complete correspondence of rules and examples.

Figure 6.3 Problem isomorphs for the card problem.

(Each makes use of the logical argument that if 'a' implies 'b', then 'not b' implies 'not a'. Thus, the two top cards must be checked since the top left one relates to the first case, whereas the top right one relates to the second case.)

In the aging area there is a classic example in the work of Arenberg (1968). He attempted to present a logic problem (concept formation) to a group of older people. It was phrased abstractly as values of attributes that formed the concept. Virtually no one in the older group could understand the instructions. He re-phrased the problem as a 'poisoned-meals' problem where the 3-item courses led to the outcomes: lived or died. Although the young control group performed better, most of the members of the older group could work on these prob1ems. We can argue that some problem-solving methods are evoked when one representation is adopted, but not when another one is. For instance, in the invoice version of the logical reasoning task, people 'automatically' worry about errors of omission as well as commission and hence are more likely to make correct choices. That is, stored with a particular problem condition is a rule suggesting an action ­ perhaps something akin to the 'production rule, mentioned earlier. Few people are likely to have anything associated with as and bs in logic problems. Many people are likely to have a great deal of knowledge about the rules for checking invoices, and the rules for stomach upset. Thus we see that specific knowledge can be important for solving certain types of problems.

In fact, we can partition problems into two major classes. The first is novel situations for which the solver must rely on general ('weak') methods like generate-and-test and means-end reasoning. The second is familiar situations for which the solver may already have a handy set of tools or procedures ('powerful methods') that are attuned to the many specific situations that are likely to arise. Included under familiar situations are so-called novel problems that are analogous to familiar ones (assuming that the solver recognizes the analogy).

Now, one of the difficulties with using weak methods such as generate-and test and means-ends reasoning is that a heavy burden is placed on memory. That is, when there are many alternatives to be evaluated, you must remember which ones have occurred before in order to evaluate current states accurately, as well as to avoid redundancy in search-re-entering a previous state that has already been evaluated. As an example, use generate-and-test for the following variant on the meal problem. What is the most favoured 3-course meal for someone who values (lamb = 1, sole = 2) (potatoes = 2, rice = 1) (broccoli = 1, carrots = 2), where higher numbers indicate greater liking, and items are additive within a meal. Try to do this mentally, without using any heuristics, such as picking items with the highest numbers from each course. Thus, an initial generated meal might be lamb, potatoes, broccoli with a value of 4. There are only 8 unique meals that you can generate, but generating only unique meals and keeping track of which one has the highest value should be quite difficult.

As Kausler has shown in his chapter, older adults are less proficient at recalling previous activities, though this is less true for problem-solving activities. Since most problem-solving activity stretches over minutes, if not hours (years for scientific problem-solving), it is important to consolidate states and their values in long-term memory, if you hope to succeed.

Since, as seen in previous chapters, older people seem to take longer to consolidate new information, we can begin to understand why their problem solving behaviour is sometimes inefficient. A typical finding is that older groups ask redundant questions, or ask the identical question more than once. This redundancy in asking questions is a hallmark of novice problem solvers who work with very general procedures on a set of unrelated facts. See Anderson (1982) for the example of high school students learning to solve geometry problems. It becomes legitimate to ask whether old-young differences are nothing more than novice-expert differences.

PROBLEM-SOLVING IN UNFAMILIAR DOMAINS

Most work in problem-solving and aging has concentrated on unfamiliar problems, ones that would be met infrequently outside the laboratory. The most intensively researched ones involve concept formation (sometimes called concept identification), logic, anagrams, and the twenty-questions game.

Concept formation

Concept formation tasks usually require the person to discover (induce) a rule specifying a combination of attribute/dimension values that define the concept. The instances containing concept information are either provided by the experimenter (the reception paradigm) or are selected by the subject (the selection paradigm). Traditionally, the instances that are provided, or selected, consist of geometric shapes varying along dimensions such as size, color, number, and shape. An example might be the concept rule: 'If a card contains either a red object or a circle it is an instance'. Thus a display that contained 3 black squares and a black circle would be a positive instance, as well as one with 3 red squares. One with 3 black triangles would be a negative instance.

Concept rules typically used by experimenters involve single attributes (e.g. triangles are instances of the concept), conjunctions of attributes (instances are red and triangles), disjunctions of attributes (red or triangle), and compound versions of these rules (e.g. conditional, biconditional ­ see Kausler, 1982, Chapter 10).

Other variants involve defining relations between concepts across trials. For instance, the first concept may involve the critical dimension of color and ignore the shape dimension, and the next concept may involve a switch to the shape dimension, ignoring color ­ a so-called 'reversal' procedure. The idea here is to assess how flexible rule generation can be. Given the number of values that each dimension can vary on, and the number of dimensions, the type of rule determines the size of the problem space. Take as an example the poisoned food problems that Arenberg (1982) has investigated in a longitudinal study. There are 4 courses (dimensions) to a meal (A, B, C, D) and 2 food types (values) for each course (1, 2). For the single attribute rule there are thus only 8 solutions. (A1, B1, C1, D1, A2, B2, C2, D2). Arenberg requires his subjects to select complete meals. Although there are 16 possible unique meal selections, an optimal search path requires no more than 3 selections to identify the poisoned food, as seen in Figure 6.4

Figure 6.4 Problem space showing the optimal paths to solve the poisoned food problem.

When 2-attribute conjunctive or disjunctive concepts are given, the number of possible solutions expands to 24. (In a conjunctive poisoned-food concept task, a person dies only when 2 tainted foods, e.g. both Al and B1, are eaten in the same meal.) If the person is unaware of whether a l-attribute or 2-attribute rule is necessary, the size of the rule problem space expands again.

Usually the investigator is interested in both whether the rule is identified and how efficiently it is identified. Information theory measures (see Arenberg, 1970) are often used to determine selection efficiency.In cross-sectional investigations the findings have been consistent. Older people are less likely to solve these problems than younger ones, and they are less efficient in searching the rule space (see, for example, Arenberg, 1968; Wetherick, 1964; Wiersma and Klausmeier, 1965; Young, 1966). The old sometimes do disproportionately worse with more difficult problems, when difficulty is manipulated by increasing the number of irrelevant dimensions (Hoyer et al., 1979; Rebok, 1981), or by providing low initial information (Arenberg, 1982). The statement that the old perform worse must be qualified. In some of these studies samples consisted of young, middle-aged, and old people. Middle-aged people usually are not very different from young ones (e.g. Hartley, 1981; Hoyer et al., 1979).

In the sole longitudinal investigation (Arenberg, 1982) where age changes were measured, concept problem-solving performance did not decline until the 60s and 70s were reached, though the degree of improvement (or decline) from the first session to the second was age-related. The magnitude of the relation between change and age was quite small (correlations hovering around the 0.1 mark) but quite reliable. Nonetheless, it is worth noting that 99% of the variability in change is attributable to factors other than aging.

As Arenberg (1982) points out, because this is a highly select sample of participants, age changes are undoubtedly underestimated. On the other hand, the cross-sectional (cohort/age) trends in the data also point out the degree of overestimation of age-related change that exists in all other studies. It is fair to conclude that age is not the most important factor when accounting for individual differences in concept formation performance.

What aspect of age might be responsible for declines in performance? On the software side, whether or not someone already has a procedure for searching rule spaces efficiently would seem critical. Educational differences could be important here - particularly whether courses in logic or mathematics related to this search problem have been taken. If, as seems likely, the task is not familiar to most people, then the ability to construct and execute a search strategy would determine performance.

Strategies depend heavily on memory capacity. If you cannot keep track of all the problem instances and the hypotheses you generate you may have to search very selectively and inefficiently, (Bruner et al., 1956, long ago noted that different strategies created different amounts of 'cognitive strain'.) Unfortunately, most of the research in this area does not provide enough detail to determine specific strategies and how they vary with age. Giambra (1982) has investigated this issue by observing three individuals across many problems and has found that the strategies of a 63-year-old and a 96-year-old are adapted to increasingly severe memory limitations.

Several studies have shown that older groups either fail to recognize that there are redundant displays in reception paradigms (Arenberg, 1968) or that they select redundant displays in a selection paradigm. Both situations exemplify inefficiencies in search that can be attributed to forgetting prior instances or hypothesized rules. This forgetting of instances/rules would seem to fall within the purview of both incidental and prospective memory (Kausler, this volume). Older people are either less efficient in retrieving the results of previous actions, or in instructing themselves to remember such actions.Logic

Although there have not been many investigations of logical reasoning (see Arenberg, 1974; Jerome, 1962; Young, 1966), results in general support the same conclusions that are obtained from concept tasks. Most of the work has been done with a problem which consists of a circuit that controls the lighting of a target. The solver is permitted to provide inputs (by pressing buttons) to the circuit and is told the possible properties of the input buttons. Then the solver attempts to find the combination of inputs that will light the target light, using the minimum number of button presses.These problems can be quite difficult to explain. Arenberg (1974) reported that between 45 minutes and 2 hours were necessary to provide instructions with a sample problem and then to do a practice problem.

As expected, young adults outperform older adults, as indicated by cross sectional studies. Arenberg (1974) has shown that this is attributable to a greater number of uninformative inputs for older solvers despite the fact that they were permitted to use `external memory', notes on paper, to record previous choices. About 10% fewer people solved the problems with each passing decade.

Further, since Arenberg's (1974) study was longitudinal, he could examine age changes over a 6-year span. He found that across problems completed on two sessions, people through the age of 60 improved over sessions, whereas those in their 70s declined. This was true despite sample attrition that meant that those who returned for a second session were better problem-solvers initially than those who failed to return.

There are exceptions to the age decline finding with symbolic logic problems. When young and older, highly educated physicians were given logical reasoning problems (Cjifer, 1966), no age differences were found. In fact, older physicians were nominally better at the task. Medical diagnosis involves logical reasoning not unlike that used in symbolic logic. With unskilled reasoners, however, age declines are consistently observed (e.g. Friend and Zubek, 1958; Nehrke, 1972).Anagrams

Unscramble the following letters to form a word: ULDAT. After a while you will probably come up with the answer. (If you still have not solved the anagram the letters go to the following positions: U to 3, L to 4, D to 2, A to 1.) How did you go about this task? One thing you probably did not do was to generate all orders for all the letters and check whether they formed a word. Given that there are 119 (5 x 4 x 3 x 2 x 1 - 1 ) possible permutations for these letters, this would be a very inefficient way to search if you wanted the solution quickly. More likely you searched heuristically, using your knowledge of the probable relations between letters in English words to help you generate good candidates. (For instance, you can rule out whole groups of permutations by recognizing that no word starts with TO, DT, TL, LT, LO, or DL.) In effect, you can cut the problem space down from about 100 candidates to a few dozen, by forming sub-problems such as finding likely pairs or triplets of letters with which to start the word, then generating words and verifying whether the remaining letters fit. (For more detailed views of possible anagram solution processes see Solso et al., 1973; Hayslip, 1977).

At any rate, success in this task clearly depends on vocabulary size, knowledge of the constraints of letter sequences in words, and the ability to form a program to do the task (strategy selection).

Vocabulary size, as indicated by performance on word definition tests (e.g. Gardner and Monge, 1977) tends to increase in young adulthood and then shows moderate decline in the 60s. It also seems likely that knowledge of bigram (2 letter sequence) frequency would increase with age, assuming that people continue to read and accumulate this knowledge incidentally. Fluency in generating items with specific cues seems relatively stable (e.g. Eysenck, 1975), but program construction ability might be expected to decline with age. Thus it is not too surprising that the few studies of problem-solving for anagrams show little or no age-related decline in solving (e.g. Hayslip and Sterns, 1979).

Twenty questions

Perhaps the most popular problem-solving task in the recent literature is the twenty questions game and its variants. The usual version involves presenting people with an array of 42 pictures and asking them to identify the target picture by asking questions that can be answered by `yes, or `no. Further, people are required to identify the picture with as few questions as possible.

Efficiency in this game has proven to be quite age-sensitive, as numerous investigations by Denney and her colleagues (e.g. see Denney, 1979, for a review, and also Denney, 1980; Denney and Palmer, 1981; Denney and Denney, 1982; Denney et al,, 1982) and others (e.g., Hartley and Anderson, 1983a, Hybertson et al., 1982) have shown.

The trick to doing well in this task is to discover how to partition the problem space with effective questions. The optimal solution involves using questions that divide the alternatives in half. If you number the items as 1-42, then one optimal initial question is: `Is the target above (below) the 21st position? A `yes, or `no, reply eliminates half of the targets. Further questions should also eliminate half the remaining alternatives until you are left with 3 alternatives (2 if the initial number of alternatives is a power of 2) when single target questions become efficient.

Many older people never catch on to this strategy and either immediately start to ask single target questions (e.g., `is it the cow,) or ask constraining questions that are less than optimal (e.g. `is it in the first row', when there are 7 rows).

Figure 6.5 Problem space showing the optimal paths to solve the sixteen-item version of the twenty questions game. The notation, n > 8, represents the question: Is the target number greater than 8?

As Figure 6.5 indicates, there is a close kinship between concept formation optimal strategies and twenty questions optimal strategies. In fact, the two problems can be isomorphic (for instance, I attribute poisoned food problems with 4 items/meal and an 8-item twenty questions game). It would be interesting to examine both problems in the same study. If the young adult problem solving literature is any guide, we would not expect similar solution rates across isomorphs presented with different cover stories (Hayes and Simon, 1977). As expected, different solution efficiencies are obtained when twenty questions is played with pictures vs. playing cards (Denney, 1980), but only for elderly subjects (those 60-90 years old). Playing cards seem to induce more effective question strategies ­ perhaps because the suits form more obvious categories than an abstract dimension of pictured objects such as animate vs. inanimate. On the other hand, when Hartley and Anderson (1983b) used imagined vs. real arrays of asterisks in an `identify the target, asterisk task, they found no differences in solution efficiency.

As Hartley and Anderson (1983a) speculate, twenty questions may tap whether there are age-related differences in the way such a problem is represented internally. Just as experts `see, a different problem than do novices, so older people may see (or represent) displays of objects differently. Denney and Denney (1982) provide evidence that classification differences may mediate age differences in efficiency in the twenty questions game. Following the game the participants were asked to choose pairs of pictures that were alike. Those who classify on a similarity basis (e.g. both objects fly) were more efficient than those who classified on a complementary basis (e.g. a cow goes into a barn).

Twenty questions, however, is really quite a trivial problem. There is little doubt that it would be relatively easy to teach old people (or children) the strategy of dividing the alternatives in half. Denney et al. (1979) approximated this with training by giving examples of constraint-seeking questions and by providing rules for formulating questions. The possession of this question-generating `operator' is almost all that divides efficient from inefficient solvers. (People also have to keep track of the answers and what alternatives remain.)

Some support for this notion is provided by Kesler et al, (1976) who showed that when education level was controlled (statistically), age relations disappeared. (This did not occur for Hartley and Anderson, 1983a.) The strategy of dividing alternatives in half is explicitly taught in some university courses, and the general principle of attacking a problem by partitioning it into sub-problems is a tenet of all courses on problem solving (Hayes, 1981; Polya, 1957; Wickelgren, 1974).

PROBLEM-SOLVING IN FAMILIAR DOMAINS

When confronted with a new task most problem-solvers do poorly. As has been shown, older problem-solvers do even worse than younger ones. In semantically rich domains, those domains requiring a large knowledge base for adequate performance, young and old novices alike can expect to perform poorly. To perform at expert levels takes about ten years of intensive preparation and practice, be it painting or music (Hayes, 1981), chess (Simon and Chase, 1973), telegraphy (Bryan and Harter, 1899), or reading, juggling, racing car driving, and even being a professional psychologist (Lindsay and Norman, 1977). Apparently it is necessary to learn a great many specific facts and procedures to master such domains. Given that the time to consolidate a new `chunk, of information averages about 5-10 s (Simon, 1981), and that the master has a recognition vocabulary on the order of 50,000 patterns (Simon and Gilmartin, 1973), it is obvious why between 1000 and 10,000 hours of study are necessary to acquire the relevant knowledge.

Expert problem-solvers operate very differently than do novices, in part because they represent the problem differently (e.g. for physics, see Chi et al, 1981 ) and hence search the problem space differently (e.g., see Simon and Simon, 1978; Larkin, 1981). In fact, a consistent difference between experts and novices is that the expert can grasp more of the problem configuration at a glance than can the novice (e.g. Allard et al., 1980; Chase and Simon, 1973; Charness, 1979; Egan and Schwartz, 1979; Reitman, 1976; Sloboda, 1976) in part because they can match larger chunks with their larger vocabulary of stored patterns. This perceptual advantage holds only for structured, sensible patterns from the domain, not for random patterns or patterns from other unfamiliar domains. A good chess player will not necessarily possess a large vocabulary of music patterns. There have been very few studies of how age affects performance in semantically rich domains. The few relevant studies suggest that experienced (skilled) older performers may not be disadvantaged relative to skilled younger ones.

Peak professional performance

Lehman (1953) provided a detailed review of the biographies of famous scientists, artists, athletes, and other professionals, from the perspective of assessing the age at which they achieved their finest performance. In many cases he was considering world championship performance for competitive sports, or Nobel prize winning work for scientists. The modal age decade for such outstanding performance was the 30s. There was significant variation across disciplines (e.g. mathematics achievements occurred earlier than history achievements). Nonetheless, the picture was remarkably consistent, from domains that had strong physical strength demands (e.g. weightlifting) to those demanding minimal physical exertion and maximal intellectual exertion (e.g., chess).

One of the problems with Lehman's analyses, pointed out by Cole (1979), is that Lehman looked at what proportion of important discoveries were made by scientists of different ages, rather than what proportion of scientists at different ages made important discoveries. (This problem resembles one familiar to psychologists worried about assessing the generalizability of results, and who therefore analyze their data across both subjects and experimental items.) Since the world's population has been consistently increasing, and the population of scientists, athletes, chess players, etc. has grown at about the same rate, young people are disproportionately represented in these sub-populations. (The famous statement: `half of all scientists who have ever lived are alive today', indicates this bias in the age distribution) .

Cole looked at the output of a sample of scientists of different ages cross-sectionally (rather than tracking achievements) and examined the production of a cohort of mathematicians longitudinally. He found very little evidence of a decline in research productivity (papers published or cited), although curvilinear relationships were observed, with productivity increasing to the middle 40s then decreasing slightly into the 60s. In other words, contrary to Lehman's findings, Cole did not find a major decline in professional performance.

As Salthouse (1982) has commented, Cole's study probably looked at competent scientific work, whereas Lehman looked at humanity's highest achievements. As the task complexity-hypothesis (Cerella et al., 1980) suggests, the most striking age effects are noticed when task complexity or difficulty is high. It is admittedly more difficult to do outstanding than competent scientific work. Nonetheless, even competent scientific work requires a significant intellectual effort. Cole's analysis provides a counterweight to Lehman's more gloomy view of the effects of aging on creativity and achievement.

Age and practice

As Rabbitt (1981) and many others have pointed out, age is a relatively poor predictor of individual differences in performance. Practice level with a task is a much better predictor. To put it another way, any age differences in initial level of performance are likely to be very small compared to the change that takes place for every individual following practice. People are adaptive. If given the opportunity to practice people become more efficient. They acquire skill (Anderson, 1982; Bryan and Harter, 1899; Welford, 1951). In fact, learning a task follows a power law (see Newell and Rosenbloom, 1981) such that initial improvements are large, but further improvements become more and more difficult.

Older people show improvements with practice even on psychometric tasks such as digit-symbol substitution (Beres and Baron, 1981; Grant et al., 1978), induction (Baltes and Willis, 1982; Labouvie-Vief and Gonda, 1976) and concept formation (e.g. Sanders and Sanders, 1978). They show remarkable improvement on reaction time tasks (Murrell, 1970) and even on elementary processes such as motion detection, memory scanning, and visual discrimination (Salthouse and Somberg, 1982). In fact, in some studies, practice by itself is as effective or more effective in modifying initial performance than more elaborate training procedures such as cognitive behavior modification (Labouvie-Vief and Gonda, 1976).

The rates of improvement for older vs. younger groups when practicing appears to be reasonably well-fit by a simple power function, an equation that represents performance on trial T = aT^b, where a and b are constants and T represents the trial or block of trials. The constant a represents the trial 1 or initial performance level. The exponent b provides the rate of improvement. (As Stones and Kozma point out in their chapter, exponential and power laws provide good fits to physical performance, such as running times for different distances by elite athletes.)

Interestingly, the exponent (rate of improvement parameter) does not vary too much with age (see Charness, 1982), though it is difficult to generalize since the initial level of performance often affects the rate of improvement.

Age and skill tradeoff

Why does the relation between age and performance often take the form of an inverted U-shaped function, such as the Lehman functions? One explanation often advanced is that two factors combine to create this curvilinear relation. With increasing age a person builds up a large store of useful experience. Also associated with aging in adulthood is a decline in biological systems that support performance. Even as a large library of efficient software is being acquired, the physical system (hardware) responsible for running these programs goes into decline. One way to think of this decline, using the computer ana1ogy, is that there is a slow, random loss of memory storage elements (neurons), and possibly slowing in the `clock', regulating the timing of elementary processes. Thus each `line', in the program is executed more slowly.

The brief discussion of practice effects is meant to sensitize you to the idea that experience in a task is a very powerful predictor of performance. As this volume indicates, we also believe that age is a significant factor in human performance. What happens when you play off these two factors against each other? If aging is seen to reflect negative changes in cognitive architecture (hardware) whereas experience is believed to reflect positive changes in task strategy (software), how does an experienced older person perform? This theme was first raised in Welford's early books (1951, 1958), though the tasks explored in the Nuffield project were for the most part not well suited to address this question.

One of the favorite images that people summon up when imagining a typical activity for seniors is a group sitting around playing cards, or perhaps two old men playing chess outdoors in a city park. (More realistic would be the image, common to all age groups, of sitting around the television set.)

Games present the psychologist with the opportunity to examine intellectual performance in a `cohort-insensitive, ecologically valid' task environment. (The term `cohort-insensitive' means that the environment has not changed in any way that might disadvantage one cohort in a cross-sectional study. The term 'ecologically valid' means that the behavior under investigation actually occurs in ecological niches other than psychology laboratories.) As seen, party games such as `twenty questions' have been used to examine problem-solving in a classification task. Chess and bridge problem solving tasks have been used in my laboratory to assess how age and experience trade off to predict performance.

Chess

The rules of chess have remained stable for well over a hundred years. Although there has been a marked secular trend toward improved levels of performance by world champions over the past century (Elo, 1978), this is due in part to the larger population base of tournament players. Human players today play chess the same way players did a century ago. The task environment has not changed, so the technique for searching the problem space, called `progressive deepening, (de Groot, 1978), has also remained the same. In short, chess is a cohort-insensitive task environment, making it ideal for cross-sectional investigation.

There is remarkably little information about the relation between age and skill in chess via cross-sectional studies. Secondary analysis of a mail-in questionnaire study completed by the Chess Federation of Canada in 1979 revealed that there was no relation between chess rating and age (r=0.08, for a reasonably representative sample of 243 respondents).

Elo (1965, 1978) has shown that the longitudinal performance of chess masters follows a Lehman-like function, with improvement from the early 20s to a peak in the later 30s and a slow decline that steepens in the 60s. Nonetheless, the absolute level of decline is about one half of a standard deviation unit. The chess rating scale is an interval scale that has a standard deviation of about 200 rating points, with the world's best player typically reaching 2700 points and an inexperienced tournament newcomer performing at about 800-1000 points. (See Elo, 1978, to see how the scale scores are derived from tournament performance.)

Unfortunately, since chess careers may span 40-50 years, the secular trend of improving chess play may in part accentuate any measured decline of ageing players who are competing against a larger number of new skilled players. This trend may be balanced by selective withdrawal from tournament competition by players who recognize a diminution in their performance and retire at, or near, their peak. Nonetheless, considering the incredible strain (physical and mental) that tournament players undergo, the remarkable success of current players in their 50s (Korchnoi, at 55, challenger for the 1980 world chess championship), early 60s (Smyslov, at 61 qualifying for the 1984 World Championship candidates semi-final match), and even 70s (Reshevsky, tying for 1st place in a 1983 Reykjavik Tournament, at 72) testifies to their vitality and persistence.

Nevertheless, chess seems to be a young man's game. The mean age when a player first won or tied a match for the world championship is 30 years (SD = 4.8) for the last 8 world champions since the world championship format was standardized in 1948. Further, there seems to be a relation between the age at which the game is first learned and the length of successful tournament performance (Krogius, cited in Charness, 1981a) with those learning early having longer successful careers. It is not that uncommon for teenagers to reach master level play (2200 rating points), though grandmaster status (2500 rating points) is rarely achieved in less that ten years of effort (Simon and Chase, 1973). Chess can be learned by children as young as 4-5 years old.

Chess is quite a simple game, conceptually. A player when on move must attempt to choose the best move for his side. Since there are usually no more than 25-50 candidates possible from a position, it is not that difficult to generate all the alternative first moves; perhaps no more than a minute is necessary, if move generation takes about a second.

The factor that makes chess difficult to play is that it is nearly impossible to evaluate a candidate move without evaluating countermoves by your opponent, yourself, etc. The tree representing all possible moves and countermoves is estimated to be in the range of 10¹²⁰ nodes (1 with 120 zeros following it!) Thus human players must search selectively, using all the knowledge they can bring to bear on generating only plausible moves. It is rare for humans to examine more than 100 nodes for a single move (Charness, 1981b). Selectivity in move generation seems to depend heavily on pattern recognition. Players rarely generate more than 10% of the possible candidate (initial) moves, and the best move (even if not eventually chosen) is more likely to be generated by better players (Charness, 1981b; de Groot, 1978). Chase and Simon (1973) have proposed that move generation is guided by recognizing critical features (patterns) which in turn trigger plausible move generation. Productions such as 'if you see an open file, then consider putting a rook on it, are envisaged as the link between perception and search activity.

As de Groot (1978) and others have pointed out, the master seems to have a large vocabulary of such patterns stored in memory. Skill in chess depends on knowing (recognizing) what to do in a great many specific situations, rather than being able to 'out-calculate', search more extensively or deeply than, your opponent.

Since word vocabulary grows over the adult years, it might be expected that older players would maintain and improve their vocabulary of chess patterns. On the other hand, since perceptual processes seem to decline in efficiency with age (see the Verrillo and Verrillo chapter), one could predict that the ability to access this vocabulary might decline with age. I found such pattern-access decline when I matched young and old players on skill level and evaluated recall of briefly presented chess positions (Charness, 1981c). although there were no age differences in the time to initiate recall (p1ace the first piece on the board) the accuracy of what was recalled declined with age, implying an encoding deficit. Nonetheless, the older players still recalled more with a 1 s exposure than do unskilled college undergraduates in classroom demonstrations with a 5 s exposure!

More interesting are the results of a study of problem solving performance (Charness, 1981a,b). Players were selected such that skill (measured by chess rating, Elo, 1978) and age were un-correlated. Players were asked to think out loud while choosing the best move for their side in each of four chess positions. They were also asked to evaluate end-game positions as rapidly as possible as win, draw, or loss. The former task mimics the activity carried out 40 or more times in a real game ­ choosing the best move for your side. If chess ratings are valid indicators of skill in chess at all ages, no age effects should be observed for the value of the move chosen by the players. No age effects were observed for the value of the chosen move, and as expected, the value of the move did vary with skill level. The major point of this exercise, however, was to examine the process used to select the move, to see how it varied with age and skill. Tape recordings of the think-aloud protocols were transcribed and converted to problem behavior graphs (see Charness 1981b) to trace out the search process.

Search

From the data obtained in concept formation, twenty questions, and logic problem tasks we could predict that older players would (a) generate more base (initial) moves (use inefficient moves and hence need more of them to answer the `what's the best move' problem); (b) repeat moves more frequently (both base moves and other moves); (c) generate poorer candidates on average (ask inefficient questions); and (d) examine more moves in total before arriving at the solution. We would probably also expect them to take longer to solve the problem. We cannot predict that they would be less likely to generate a good solution, because they were selected to be equal in chess problem-solving skill.

As it turns out, only one of these predictions is correct. Older players were less likely to include the best move among their candidate moves. But because the problems were quite difficult, very rarely was the best move generated by anyone in this moderate skill range. All the other predictions were exactly reversed! Younger players took longer to select their move repeated moves more frequently, generated more base moves, and more total moves than equally skilled older players.

If there is something to the hypothesis that older people have more `wisdom' than younger people (Clayton and Birren, 1980), then we might claim that this study provides the first 'hard' piece of evidence. Older players came up with an acceptable move with less search than their younger counterparts. I am inclined to believe that this result is somewhat artifactual, since it could be explained by assuming that younger players wanted to search right up to the time limit (about 600 s), whereas older ones stopped when they were satisfied that their candidate move was acceptable.

Perhaps even more intriguing is that no age differences were evident in the depth of search statistics. Depth of search refers to how far ahead the player looked (e.g., 1, 2, 3, 4 ply deep into the search tree). It is roughly equivalent to a measure of working memory, since it indicates how many changes in piece positions can be retained before a player becomes unsure of the resulting position.

Depth varied with skill, but not with age. Since the oldest player in this sample was 64, and since memory span does not change much with age until the 70s (Talland, 1968) this result is not too surprising. On the other hand, players need to remember the results of previous search episodes in order to evaluate their current move, making chess search much like problem solving with a memory load. Wright (1981) has shown that older people are quite inconvenienced in such situations when doing unfamiliar reasoning tasks.

Speed of search

It was also possible to provide rough estimates of the time to generate moves, that is, look at speed of search apart from the extent of search statistics. No age differences were observed. Even though older players searched less extensively, they searched at approximately the same rate. It is possible that older players were thinking more slowly, but the measure of moves per minute was too insensitive to find the effect. Most of the time in problem-solving is probably spent on encoding and evaluating the position initially, and evaluating nodes reached in search, rather than generating moves. People averaged about 10-15 s at each node in the tree.

Evaluation

In the rapid evaluation problem-solving task players were required to categorize an end-game position as a win, draw, or loss as quickly as possible. The evaluation process is a critical component of search in chess, since each terminal node in a search episode (the final position generated from a sequence of moves) must be evaluated properly or a wrong inference will be drawn about the base move under consideration. Move generation and position evaluation are intimately related in heuristic search.

No age effects were observed for the number of correct evaluations, though the expected skill effects were found. Even when evaluations were separated into fast (less than 10 s) and slow (greater than 10 s) categories there was still no evidence of any age-related inaccuracy. This result is a bit unexpected since older people tend to be disadvantaged in speeded tasks. Older players were able to carry out an accurate evaluation of an end-game position as quickly as their younger counterparts. Because end-game positions are well-defined and usually contain few pieces, it is possible that weak equivalent to a measure of working memory, since it indicates how many changes in piece positions can be retained before a player becomes unsure of the resulting position.

Depth varied with skill, but not with age. Since the oldest player in this sample was 64, and since memory span does not change much with age until the 70s (Talland, 1968) this result is not too surprising. On the other hand, players need to remember the results of previous search episodes in order to evaluate their current move, making chess search much like problem solving with a memory load. Wright (1981) has shown that older people are quite inconvenienced in such situations when doing unfamiliar reasoning tasks.

Speed of search

It was also possible to provide rough estimates of the time to generate moves, that is, look at speed of search apart from the extent of search statistics. No age differences were observed. Even though older players searched less extensively, they searched at approximately the same rate. It is possible that older players were thinking more slowly, but the measure of moves per minute was too insensitive to find the effect. Most of the time in problem-solving is probably spent on encoding and evaluating the position initially, and evaluating nodes reached in search, rather than generating moves. People averaged about 10-15 s at each node in the tree.

Evaluation

In the rapid evaluation problem-solving task players were required to categorize an end-game position as a win, draw, or loss as quickly as possible The evaluation process is a critical component of search in chess, since each terminal node in a search episode (the final position generated from a sequence of moves) must be evaluated properly or a wrong inference will be drawn about the base move under consideration. Move generation and position evaluation are intimately related in heuristic search.

No age effects were observed for the number of correct evaluations, though the expected skill effects were found. Even when evaluations were separated into fast (less than 10 s) and slow (greater than 10 s) categories there was still no evidence of any age-related inaccuracy. This result is a bit unexpected since older people tend to be disadvantaged in speeded tasks Older players were able to carry out an accurate evaluation of an end-game position as quickly as their younger counterparts. Because end-game positions are well-defined and usually contain few pieces, it is possible that weak age effects were not detected.

Memory performance

The rosy picture of aging emerging from search and eva1uation performance might lead you to suspect that older chess players represent an elite population. They don't! All you need to do is give them some traditional laboratory memory tasks and they resemble their peers in countless other laboratories. At the end of the study players were asked to recall the four problems that they worked on earlier by placing pieces on an empty chessboard. Following recall, they were given a recognition confidence rating task where the four problem positions were embedded in a set of photographic slides containing the 20 end-game positions and 6 additional positions that were never presented.

Recall accuracy both for correct placements and errors of commission depended on both age and skill. As expected the more skilled player recalled positions more accurately (more pieces p1aced correctly and fewer errors of commission). Older players recalled positions less accurately than their skill-equivalent younger counterparts. That is, the usual finding that incidental recall declines with age was observed here, though it fails to fit with Kausler's (this volume) report that memory for prob1em-solving activity was unrelated to age. Recognition accuracy, however, was unrelated to age, as Schonfield and Robertson (1966) have shown. Recognition confidence was related to age, however, with older players less confident of their classification of a chess position slide as a target versus a non-target.

Chunking in recall

Because recall was videotaped, it was possible to examine the pattern of piece placements in great detail. Chase and Simon (1973) have shown that when consecutive pieces have a short latency of placement they come from the same symbol structure or chunk in memory. It is thus possible to use recall data to infer the player's units of encoding. Recall provides a window on the way the player represented the problem position.

Here too there was a tradeoff between age and skill. Skilled players represented a position as a small number of large chunks. Older players, however, were more likely to represent the position as a larger number of smaller chunks than their skill-equivalent counterparts. Worse yet, the advantage of being skilled declined with increasing age. By about age 60 there was no longer any advantage to being skilled.

The combination of age-invariant problem-solving and evaluation accuracy together with age-sensitive memory performance provides a paradoxical picture. It implies that the memory deficits uncovered in many investigations are very situation-specific, and may have nothing to do with how successfully older people tackle their usual problems. When older people can rely on previously compiled well-practiced search strategies (programs) they can perform as well as their younger counterparts. When they need to create and interpret new programs for the task at hand they are at a marked disadvantage. It is perhaps not surprising to learn that players in the chess study averaged about 6 hours a week of chess playing or study, with reported study/playing time not varying with age. Most studies aimed at modifying the cognitive performance of older people rarely intervene for as long as these people voluntarily study or practice in one week. In some cases these chess players have been following such a regimen for 20 or more years!

Bridge playing

In an early study not designed specifically to examine aging, I found the same pattern that had been previously observed with chess players (Charness, 1979). Namely, in a plan-the-play-of-a-bridge-contract task and in a rapid select-an-opening-bid task, skill but not age effects were obtained for solution accuracy. In an incidental and an intentional recall task both age and skill predicted recall. Older players recalled fewer bridge cards correctly than equally skilled younger players.

In a later study (Charness, 1983) 45 players were selected from a duplicate bridge club such that age and skill were unrelated. A questionnaire revealed that, as expected, older players were less educated than younger ones, and that level of education was unrelated to skill in bridge. (The latter follows from the fact that bridge playing is a semantically rich domain. Bridge instruction is usually not in the formal school curriculum.)

The main task was to announce an opening bridge bid as quickly as possible. Varying amounts of information were available about the bridge hand before it was actually displayed. This task was expected to tap different stages in the processing of a bridge hand. To bid a hand, the player must first translate honour cards into points (an analog to an intelligence subtest, the digit-symbol substitution test, which is quite sensitive to age). Then, or perhaps concurrently, the player must notice the length of the suits. Finally, after encoding both points and distribution, the player must access an appropriate bid from memory and respond with the bid.

Despite the fact that accuracy in bidding was quite high, it improved with increased skill level, and it was unrelated to age. Latency to bid was sensitive to skill and to age, with better players bidding faster, and older players bidding more slowly. Bidding latency increased about two thirds of a second more for each decade of age. Nonetheless, in a real bridge game, there is no need to bid as quickly as possible, so again we fail to find any effect of age on an ecologically sensible measure, bidding accuracy, though we do see an age decline in speed.

Again, players no longer derived any benefit by being more skilled in terms of response speed, past age 58. This study underlines the general finding that mental processes slow down as you age. It also appears to support the view that major declines in speed occur in the 60s, since there is apparently no longer any benefit to having compiled procedures or programs for doing mental tasks at this age.

A closer look at the data qualifies this view. When performance is examined over the two halves of the experiment, most of the age effects appear in the first half. Older players improved their performance more than younger ones did over the second half. I interpret this to mean that once a stable program was constructed for doing the task, older players were as fast as younger ones. Older players took longer to arrive at their program.

Further research with the same sample has shown that the interaction of age and skill has disappeared. When a similar task was provided ­ simply providing the number of points, instead of going on to announce the bid-age and skill traded off directly for reaction time, rather than interactively. Again, accuracy increased with skill, but was unrelated to age.

In summary, as bridge players and chess players age they may become slower at encoding information about the problem, but once the problem space has been represented, they search it as effectively as their level of acquired skill permits. The one strong constraint on this research is that older players were not very old ­ the upper age range was the early 70s. Nonetheless, the age range was sufficiently broad to demonstrate marked memory and speed declines.

As Murrell also demonstrated numerous times with tasks such as drilling (Murrell et al., 1962), response initiation time (Murrell, 1970), and shadowing (Murrell and Humphries, 1978), experience does count for older performers.

LIKELY SOURCES OF AGE DECLINE IN PROBLEM-SOLVING

Software

As is obvious from this review, most studies of problem-solving are cross-sectional. Thus age is confounded with cohort factors such as education. The two longitudinal studies by Arenberg ( 1974, 1982) show that age decline only appears to be significant in the 60s and 70s.

Cohort, however, is not a very helpful explanatory concept. Sometimes education differences seem responsible for age differences (Kesler et al., 1976), but at other times, even with the same task, age adds independently to the effects of education (Denney and Denney, 1982).

For most novel tasks both how the problem is represented by the problem solver and what operators are available for generating new knowledge states in search seem critical. Education is likely to provide people with general problem-solving skills such as subgoaling ­ finding ways to partition a problem space. It may also provide them with specific operators ­ e.g. the `halving' operator for twenty questions. To the extent that older people are less likely to have experienced much of the formal problem-solving that higher education demands (such as occurs in experimental sciences and mathematics), they will perform less well than younger people with that education. Likewise, highly educated people should perform better than less educated ones. Gardner and Monge (1977) provided a great deal of evidence supporting this view from a battery of cognitive abilities tests such as vocabulary, arithmetic, and knowledge of facts. Nonetheless, even though education was as powerful or more powerful than age as a predictor, patterns of performance across age were very similar in high and low education groups.

Hardware

It appears that two factors can account for much of the decline in problem solving performance: changes in speed of execution of elementary information processes ('eip's', see Chase, 1978) and changes in the capacity of working memory. It is also possible that speed alone can account for all the changes, to the extent that working memory relies on the speed of processes such as rehearsal.

Speed

Many theorists have pointed out how critical speed of processing is to an information processing system (cf. Birren et al., 1980; Botwinick, 1978 Cerella et al., 1980; Salthouse, 1982). Some have attempted to find direct evidence that the internal clock of the human processor ticks more slowly with increasing age (cf. Salthouse et al, 1979; Surwillo, 1968) but have obtained inconsistent results.

Nonetheless, there is much direct and indirect evidence for age-related slowing in processing. The age-complexity hypothesis (Cerella et al, 1980), showing that for many reaction time tasks the old group is proportionately slower than the young group, fits nicely. If each 'eip' takes slightly longer in an older person, then on simple tasks any age differences are likely to be small. As tasks demand the concatenation of many 'eip's' in a performance program, the age differences will become larger in proportion to the number of 'eip's'.

Nonetheless, unless you can demonstrate that the same program is used by old and young alike ­ unless you can equate task strategies ­ this hypothesis cannot be tested fairly. Some recent work by Cohen and Faulkner (1983) suggests that older people do not differ much from younger people in the types of strategies that they adopt. They are much less efficient in implementing strategies, particularly those that demand more memory capacity.

More importantly, unless you can demonstrate that practice with the same program is equivalent, you still cannot assert that slowing is attributable to age-induced changes in hardware. When a program is repeated, practiced, by a human processor it speeds up. When practice is suspended, the program is executed more slowly at its next instantiation. (See Salthouse and Somberg, 1982, for a noteworthy example.)

It is quite unclear whether practice represents a software effect (a new, more efficient program develops), or a hardware effect (semi-permanent changes in neural structure result in increased efficiency). Further, it is not yet evident whether practice-performance functions are parallel in old and young (Charness, 1982).

We can plausibly assert that in the classic cross-sectional experiment, when an old community-dwelling group and a young group of college undergraduates are compared on a task, performance differences can be attributed at least in part to differences in the position of the two groups on a practice function. As Craik and Byrd (1982) observe, however, there is probably more to age differences than practice.

Working memory

Multiply 8 x 78 mentally. Depending on how calculator-dependent you've become, you can probably strain a bit and do the task successfully. Now try to multiply 78 x 78 mentally. You may have reached your limit on this problem. Why? Operations such as 7 x 8, 8 x 8, 7 x 7, are probably quite easy to carry out in isolation. Where you bog down is in remembering the results of previous operations or subgoals so that you can retrieve them for later ones (such as addition, carrying, etc.). You run out of 'working memory' (see Baddeley, 1976; Welford, 1980). Mental calculators devise strategies that override these problems-see Chase and Ericsson (1983)-and those strategies can be taught successfully to university students (Campbell, 1982).

The complexity of the problem you can successfully tackle depends strongly on the demands it makes on working memory. Much human problem-solving demands that the results of subgoals be output to a more permanent memory (to long-term memory, or to external memory devices such as paper). Recent work by Parkinson and his col1eagues (e.g. Parkinson et al., 1982; Inman and Parkinson, 1983) and by Hayslip and Kennelly (1982) using backward digit span, demonstrates that there are pronounced age effects on working memory capacity. Work on reading comprehension by Spilich (this volume) also points strongly to the idea that working memory capacity declines with age.

Much of the age decline in problem solving on unfamiliar tasks can be attributed to working memory declines. Both the failure to carry out operations, (e.g., inferences in concept formation) and repetition of the same operations, suggest that older solvers are dealing with less working memory capacity than their younger counterparts. The same explanation may underlie Cohen's (1979) finding that older people draw fewer inferences when trying to comprehend prose passages.

The why of memory capacity decline is more difficult to establish. Older people may have to deal with 'noisier' data (Welford, 1958), or they may suffer from greater interference from previous operations (e.g. Schonfield et al., 1983; Winocur and Moscovitch, 1983). One view is that information in short-term memory decays if it is not attended to or rehearsed. If older people carry out operations more slowly, they will return to previously processed material that has decayed further than that available to younger people who return to it more quickly. At any rate, we can expect that the general integrity of the neural substrate underlying efficient memory processes shows decline to the same extent that other organ systems in the body show age-related decrement.

Perhaps a worthwhile analogy is to consider two computers with different memory capacities. When tasks demand a great deal of working memory, execution may slow down for the computer with less memory, particularly for programs that are executed in an 'interpreted, or one-statement-at-a-time mode. A 'compiled' program, one that has most processes in ready-to-execute mode, may still run quite efficiently on a machine with less memory. Perhaps one explanation for the age-insensitivity of problem-solving in familiar domains is that expert programs are compiled. A small (memory size) computer with a slow rate of execution of instructions can run an efficient program more quickly than a larger, faster machine with an inefficient program. Experience in working on problems can be viewed as the process that allows an adaptive information processing system to develop the most efficient program to do a task.

It is fashionable to end a chapter by calling for more and better research to understand phenomenon X, where X stands for topics such as problem solving and aging. A more basic question needs to be addressed first: for what aspects of problem solving do older people feel that they need remediation?

I doubt that too many older or, for that matter, younger people want to learn the optimal strategy for 'twenty questions' or concept formation tasks. Even in semantically rich domains, few bridge players or chess players spontaneously complained to me that they could not solve game-related problems the way they used to in earlier years. More than a few commented that they were still funding ways to improve their game. The rapidly growing number of courses offered for elderly people at adult recreation centers, community colleges, and other community centers (and even within institutions) suggests that many older citizens are quite eager to acquire new skills, or improve existing ones.

I suspect that acquiring skill at problem solving in a specific domain resembles many other complex learning tasks. The challenge we face is to find more effective ways to help people acquire new information, both facts and search procedures. Perhaps the critical question is the same one addressed by the educators of the young: how can we successfully engineer individualized learning environments?

Where research into problem-solving may help is to identify particular bottlenecks, be they hardware-related or software-related, that are unique to the aging individual.

This work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC-A0790). 1 am grateful to Len Giambra, Alan Welford, Don Kausler, and John Cerella for comments on early drafts of this chapter.

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