The concept of aptitude and how differences in aptitude influencing learning could be reduced through mastery strategies have interested me throughout my academic career. I understood aptitude as something I thought of as intelligence. Intelligence is an abstraction that researchers attempt to measure with intelligence tests and investigate in practice through correlations with academic progress. Intelligence tests are not a direct measure of aptitude, but really an estimate based on differences in what individuals have learned and can do. Even the simple representation of intelligence as IQ (intelligence quotient) imagines intelligence as how much has been learned (mental age or MA) divided by age (chronological age).
Intelligence tests have come under a great deal of criticism based on potential racial/SES biases. These criticisms are certainly fair, but the tests do predict academic achievement and I was never convinced to support the abandonment of the development and use of such tests. The correlations measure something, and whatever this is does not disappear when tests are not given. If both tests and educational practice are biased, why not recognize that this is the case?
The theoretical basis for mastery learning (see Arlin and Bloom references) proposes that educators consider the rate of learning and accept that the rate of learning differs greatly among individuals. To me, this sounded very much like intelligence, and the concept of IQ is obviously related to learning rate (how much was learned per unit of time). However, what these researchers and educational theorists proposed was that other factors were involved in traditional educational practice and these other factors had a significant impact on achievement. While time required for learning was determined by aptitude, it was also influenced by whether the method of instruction met individual needs and by differences in existing knowledge. Think of it this way. If aptitude-based differences in learning create a range of learning speeds and a class of students moves through learning experiences faster than some students can master some important skills and concepts, in the future some students will be burdened not only by learning at a slower rate, but also by missing knowledge prerequisite to new skills and concepts they are trying to learn. Over time, these missing elements (Sal Kahn calls this Swiss cheese learning) will accumulate increasing failure and frustration in some learners. Mastery learning strategies focus on limiting the accumulation of knowledge prerequisites by individualizing the rate of learning to the rate of mastery. Some students in completely individualized approaches do move more slowly (and some faster), but the theory proposes that the rate of actual mastery would be faster than without mastery for all learners because deficits would not accumulate in learners needing more time and more capable students could move more quickly. The work of Arlin attempted to demonstrate what these changes in the rate of learning might be. When ratios such as 5:1 or 7:1 are proposed, it is easy to see why some students would fall hopelessly behind.
Individualization is challenging. Tutoring has always been a personal interest, but not economically feasible. With access to personal computers in the 1990s I saw the first method that might be available to provide individualization and this continues as an interest. Many attack present attempts to make use of technology in direct instruction as boring and depersonalizing. I think these folks have the wrong idea, but this is a topic I address elsewhere. Here, I want to recognize recent research that claims individualized instruction with technology (Koedinger, et al) may not only deal with individual differences in background knowledge, but also challenge the notion there are meaningful differences in the rate of learning.
How variable is the impact of aptitude?
Koedinger and colleagues studied the work of thousands of students from all grade levels working on different types of content using the type of technology-enabled methods I described above. Their focus was different in being based on the mastery of very specific capabilities rather than courses or even weeks of work. The learning experiences consisted of initial exposure to information (video or written) followed by a sequence of worked activities. I suppose a worksheet would be an example of a worked activity, but the variety and type of activities included a many different activities. The goal was to reach 80% mastery on a worked activity. The authors found that in the first attempt following the acquisition phase, the top half of students scored 75% and the bottom half scored 50%. The top half then required 3.7 practice trials to reach mastery (80%) and the bottom half 13 trials. What startled the researchers was that the gain per practice trial was very similar leading the researchers to conclude learning rate was very similar once existing knowledge was addressed. Aptitude (if I can be allowed to switch terms here) accounts for little difference in speed.
I am not convinced I would interpret these results in the same way given the method, but I do like the demonstration that allowing additional learning trials allows students the same level of achievement. I encourage interested parties to review the study themselves and see if they agree with my assessment. The statistical method is quite sophisticated and I wonder what interpretations the method allows. I would be more convinced had the researchers carried their research over an extended period of time and actually determined what happens when individual differences in existing knowledge are eliminated. The difference in understanding after the individual phase of exposure to new content was substantial and while likely a partial product of existing differences in background it does not seem to me that the difference would not partially also be due to aptitude differences. Since learners with existing background knowledge are not involved, it seems to me there is no demonstration that aptitude does not play a role in determining the number of practice trials that are required.
I am pleased to see that this type of research continues and assume this study will generate replications and hopefully extensions.
Additional comments on mastery learning and learning speed
Arlin, M. (1984). Time variability in mastery learning. American Educational Research Journal, 21(1), 103–120.
Arlin, M. (1984b). Time, equality, and mastery learning. Review of Educational Research, 54(1), 65–86.
Bloom, B. S. (1974). Time and learning. American Psychologist, 29(9), 682–688.
Koedinger, K. R., Carvalho, P. F., Liu, R., & McLaughlin, E. A. (2023). An astonishing regularity in student learning rate. Proceedings of the National Academy of Sciences, 120(13), e2221311120.
Khan, S. (2012) The One World Schoolhouse?—?Education Reimagined. Hodder and Stoughton, London, 2012 and Twelwe, Boston & New York.
