In contrast with theories of motivation based on biological and behavioral determinants are theories of motivation based on cognitive and social cognitive perspectives. Covington (1998) cited the following study, reported by Ferdinand Hoppe, as one of the precursors to the study of achievement motivation and “the key to the question of how, psychologically, humans define success and failure” (p. 27):
Professor Lewin’s laboratory was crowded with the research paraphernalia of his time, including an odd conveyor-belt device. This contraption allowed a series of pegs to move on circular rollers at a uniform rate and speed, much like a row of ducks in a shooting gallery…
Hoppe (1930) invited an assortment of local tradespeople and university students to practice tossing rings on the moving pegs at various distances from the target. He found that some subjects felt satisfied after placing, say, eight rings, while others expressed extreme frustration at only twelve correct tosses. Additionally, Hoppe found that the performance level needed to arouse feelings of success changed over time for each individual. A score that was initially judged a success might well be considered unacceptable on a later practice trial. (p. 28)
Covington (1998) noted several factors of motivation derivable from Hoppe’s findings (pp. 28 – 32):
- Levels of Aspiration – Judgments of success or failure depend less on actual levels of performance, and more on the relationship between the individual’s performances and aspirations. Feelings of success come when goals are achieved. Feelings of failure come when they are not.
- Self-Confidence – “Self-confidence reflects the extent to which individuals believe themselves able enough mentally to win the prize, strong enough to turn back the foe, or possessing sufficient hand-eye coordination to toss enough rings correctly” (pp. 28-29)
- Expectancy – “The term expectancy generally refers to perceived estimates of eventual success—how sure individuals are of doing well in the end, but not necessarily that they themselves are the cause of their success” (p. 29)
- Realistic Challenges – “The key to sustained involvement in learning requires that a realistic match be established between the individual’s present capabilities and the demands of the achievement task” (p. 30)
- Self-Generated Goals – Hoppe’s subjects set their own achievement goals, and altered them as necessary. The result was that “their aspirations spiraled upward just ahead of current achievement levels, but not so far ahead that their temporary goals could not be reached and surpassed through persistent effort and practice” (p. 32). In this manner, Hoppe’s subjects were constantly performing at their current maximum.
- Control of One’s Own Progress – The feeling of control of one’s own progress that came by way of setting one’s own goals generated a positive dynamic that sustained involvement in the task. (p. 32)
These same principles from Hoppe’s study can also be found in a theory of achievement motivation that is more well known, namely, Atkinson and McClelland’s theory of achievement motivation, also known as need achievement, need for achievement, and n Achievement. This theory comes from a broad program of research on achievement motivation that was initiated in the 1940s by McClelland and was first summarized in the 1953 publication by McClelland et al. of The Achievement Motive (J. W. Atkinson & Feather, 1966, p. vi). Achievement motivation is a theoretical model intended “to explain how the motive to achieve and the motive to avoid failure influence behavior in a situation where performance is evaluated against some standard of excellence” (J. W. Atkinson, 1957, p. 371). More specifically,
Achievement-oriented activity is activity undertaken by an individual with the expectation that his performance will be evaluated in terms of some standard of excellence. It is presumed that any situation which presents a challenge to achieve, by arousing an expectancy that action will lead to success, must also pose the threat of failure by arousing an expectancy that action may lead to failure. Thus achievement-oriented activity is always influenced by the resultant of a conflict between two opposed tendencies, the tendency to achieve success and the tendency to avoid failure. Normally, achievement-oriented activities are also influenced by other extrinsic motivational tendencies, which are attributable to other kinds of motive and incentive. The theory of achievement motivation focuses primarily upon the resolution of the conflict between the two opposed tendencies that are inherent in any achievement-oriented activity, but it also emphasizes the importance of extrinsic sources of motivation to undertake an activity, particularly when the resultant achievement-oriented tendency is negative. (J. W. Atkinson & Feather, 1966, p. 328)
Tendency to undertake an activity is defined as “the product of motive, expectancy, and incentive” (J. W. Atkinson & Feather, 1966, p. 328). There are two components to this tendency. The first is the tendency to achieve success (Ts). The second is the tendency to avoid failure (T-f). Tendency to achieve success is defined as the product of (a) the motive or need to achieve success (Ms), (b) the strength of expectancy (or subjective probability) that success will be the consequence of a particular activity (Ps), and (c) the incentive value of success at that particular activity (Is):
Ts = Ms x Ps x Is
Atkinson notes that this equation might be modified slightly by regrouping terms as follows:
Ts = Ps x (Ms x Is)
This regrouping highlights the compound of Ms and Is as “the subject value of success, the utility of success, or the valence of success at a particular activity to a particular person” (J. W. Atkinson & Feather, 1966, p. 329). An important special assumption about this function is that “the incentive value of success is assumed to be proportionate to the difficulty of the task (i.e., Is = 1 – Ps)” (p. 328). The equation for the tendency to achieve success, together with this special assumption, resulted in the following implications:
1. The tendency to achieve success should be strongest when a task is one of intermediate difficulty, but the difference in strength of tendency to achieve success that is attributable to a difference in the difficulty of the task (Ps) will be substantial only when Ms is relatively strong.
2. When the difficulty of a task is held constant, the tendency to achieve success is stronger when Ms is strong than when it is weak, but the difference in strength of tendency to achieve success that is attributable to a difference in strength of achievement motive (Ms) will be substantial only when the task is one of intermediate difficulty. (J. W. Atkinson & Feather, 1966, p. 329)
The tendency to avoid failure is defined as a parallel product of (a) the motive to avoid failure (MAF), (b) the expectancy of failure (Pf), and (c) the incentive value of failure (If).
T-f = MAF x Pf x If
Similar to the equation for tendency to achieve success, this equation for tendency to avoid failure is accompanied by a special assumption. In this case, that assumption is that “the incentive value of failure is more negative the easier the task” (J. W. Atkinson & Feather, 1966, p. 331) (i.e., Is = – Ps). The implications that followed are
1. The tendency to avoid failure should be strongest when a task is one of intermediate difficulty, but the difference in strength of tendency to avoid failure that is attributable to a difference in the difficulty of the task (Pf) will be substantial only when MAF is relatively strong.
2. When the difficulty of a task is held constant, the tendency to avoid failure is stronger when MAF is strong than when it is weak, but the difference in strength of tendency to avoid failure that is attributable to a difference in motive (MAF) will be substantial only when the task is one of intermediate difficulty. (J. W. Atkinson & Feather, 1966, pp. 331-332)
Together, the tendency to achieve success and the tendency to avoid failure are combined to provide a measure of resultant-oriented tendency (TA):
TA = Ts + T-f
“When the resultant achievement-oriented tendency is negative, there will be no active impulse to undertake a particular achievement-oriented activity (TA) unless some positive extrinsic tendency to perform the activity (Text) overcomes the resistance of Ts + T-f ” (J. W. Atkinson & Feather, 1966, p. 333). The modified equation, that includes a term to account for such extrinsic motivation is as follows:
TA = Ts + T-f + Text
In summary, achievement motivation, described as a tendency to engage in an achievement-oriented task, is “a joint multiplicative function of motive, expectancy (subjective probability), and incentive” (J. W. Atkinson, 1957, p. 371). It is a model that offers an explanation for the selection of one task over other alternatives which differ in difficulty, and an explanation for the level of performance exhibited in a given task once initiated. The two major implications of the theory are (a) that “performance level should be greatest when there is greatest uncertainty about the outcome” (p. 371), and (b) that people with strong achievement motive “should prefer intermediate risk while persons in whom the motive to avoid failure is stronger should avoid intermediate risk, preferring instead either very easy and safe undertakings or extremely difficult and speculative undertakings” (p. 371).
 Covington (1998, p. 28) attributes use of the term aspiration for describing the individual’s personal goals to Diggory (1966).
 Covington notes here that “expectations” and “confidence” are not interchangeable concepts, inasmuch as confidence implies a belief in success due to one’s own ability.
 Covington cites an experiment by Charles Woodson, reported in 1975, in which varying degrees of match and mismatch were set up between student ability levels and the difficulty of a school test. Students who experienced the closest match (i.e., high ability, difficult test; low ability, easy test) learned the most. A mismatch interfered at all levels, with more able students becoming bored with easy standards, and less able students becoming frustrated when they failed to deliver against high standards.
 There seems to be some confusion in the motivation literature regarding who the theory should be attributed to. For example, based on the publications cited when introduction achievement motivation, Covington (1984, p. 6; 1998, pp. 13, 33) gives the impression that Atkinson (1957; 1981) is the initial author of the theory, later accompanied by McClelland (McClelland, 1965). However, Weiner’s (1972, pp. 169-175) account of the historical evolution of the theory is that it was McClelland who, influenced by Henry Murray’s theory of behavior based on need, lead out in articulation of the theory, publishing some initial ideas in 1951, and then shortly after published The Achievement Motive (1953) with Atkinson, Clark, and Lowell. Being that McClelland is listed as the first author, and that Atkinson himself (J. W. Atkinson & Feather, 1966, p. vi) attributed achievement motivation to McClelland’s research program, it seems that McClelland did, in fact, initiate the theory, but that the two worked closely together in its articulation and elaboration.
 Use here of the phrase a particular person provides an indication of the importance of accounting for individual differences in the theory of achievement motivation. Weiner (1972) stated that “[Atkinson’s] concern with individual differences in the understanding of motivational processes cannot be overemphasized” (p. 194) and quoted the following statement made by Atkinson:
A most encouraging development in recent experimental analysis of motivation…is the use of tests to assess individual differences in the strength of theoretically-relevant motivational dispositions of humans. Here again, the broad implication of Lewinian ideas is apparent. The guiding hypothesis, B = f (P,E), is now represented in a methodological development that may provide a means of bridging the gap between the study of individual differences in personality and the search for basic explanatory principles which has so far seriously handicapped both enterprises in psychology’s relatively short history….
It is to be hoped that contemporary research on n[eed] achievement…and contemporary research on individual differences in anxiety, within the context of Drive X Habit theory, will point the way towards more fruitful systematic use of personality tests in future research on human motivation. (Atkinson, 1964, pp. 271, 272, as cited in Weiner, 1972p. 194)
 To clarify, although Atkinson used the term proportionate, the mathematical relationship described between Is and Ps is one of inverse proportion, meaning as Ps grows larger, Is grows smaller, and vice versa.