Dr Sally Stephens, Director of Science
Which is more difficult: picking a flower or solving a complex mathematical problem?
Sweller, Ayers and Kalyuga (2011) draw on the work of noted cognitive developmental and evolutionary psychologist David C Geary to make a distinction between the two types of knowledge required to complete each task. According to Geary (2008), biologically-primary knowledge is the instinctive knowledge that humans have evolved to assimilate. It is learnable but not teachable. On the other hand, biologically-secondary knowledge results from social and cultural constructs, like money and time, which are invented by humans to improve the competencies needed for successful living in contemporary society. Biologically-secondary knowledge is learned through social interaction (Keating, 2013). Because we have not had to acquire this type of knowledge during our evolutionary history, it needs to be explicitly taught if we are to learn it. We have evolved to pick flowers and can do it without being taught. Moreover, the act of picking flowers causes us no discernible cognitive load, even though it requires vast amounts of information to coordinate all of the tasks involved in the whole process. Mathematics, however, is a human construct, and solving a maths problem, even a simple one, requires some knowledge that has to be acquired in a different way to biologically-primary knowledge; it requires some specific biologically-secondary knowledge (Sweller et al., 2011).
Another example of the distinction between these two types of knowledge is the act of speaking versus reading or writing. We have evolved to speak and can acquire our first language merely by being immersed in a culture that speaks it. On the other hand, we will not learn to read or write unless we undergo instruction (Sweller et al., 2011). Humans have been able to speak for thousands of years but up until 150 or so years ago, not more than one per cent of the population could read or write (Gary, 1993). Literacy rates only started to improve when the idea of compulsory, public education for all children gained some momentum. Of course, we can be coached to improve pronunciation and enunciation à la Eliza Doolittle, but essentially, biologically-primary skills that require a substantial alteration in their expression are no longer biologically-primary (Sweller et al., 2011).
It follows then that (at least according to cognitive scientists) the mechanism of learning depends on what one is trying to learn. Biologically-primary knowledge is easily learned and rapidly and automatically stored, whereas the acquisition and storage of culturally-invented, biologically-secondary knowledge is effortful and conscious. While we have not evolved to acquire biologically-secondary knowledge with the ease by which we acquire biologically-primary knowledge, we have evolved the cognitive wherewithal that permits the attainment of an infinite range of biologically-secondary skills (Sweller et al., 2011).
STEM (Science, Technology, Engineering and Mathematics) educators seek to understand, in order to eradicate the impediments to students’ problem-solving success. Clearly, the acquisition of germane biologically-secondary knowledge is crucial to a student’s ability to solve problems. However, according to Sweller et al., (2011), problem solving, planning and decision making are most likely biologically-primary, evolved skills which, as stated previously, are able to be learnt but not taught. Therefore, to solve a maths problem, students must have the relevant domain-specific, biologically-secondary knowledge (for example, algebra, trigonometry, geometry), plus the necessary problem-solving proficiency, which is a biologically-primary skill. Similarly, to solve a science problem, they must be able to select the problem-solving strategies that will work best with the pertinent scientific concepts. Teachers frequently see students struggle with problem solving — not because of a lack of conceptual understanding but because of underdeveloped biologically-primary skills. How then do students acquire the biologically-primary skills necessary for problem solving? The process is not straightforward but is best explained by looking at what we know about human memory.
Human cognitive architecture can be illustrated by the Atkinson and Shiffrin modal model of memory (Atkinson & Shiffrin, 1968). This model is oversimplified but is still frequently cited because of its explanatory capacity.
Human cognition requires a large store of information in order to interact with the external environment. We receive information from the environment through our senses. If we ignore these stimuli they disappear almost instantaneously; however, if they are perceived by us, they enter our sensory memory and the process of encoding that information begins. The sensory memory acts as a buffer for sensory inputs and allows the brain to retain impressions of sensory inputs after the stimulus has ceased (Mastin, 2010). It makes sense that each of the five senses would warrant its own buffer but only two — visual and auditory — have been extensively studied (Sweller at al., 2011). Visual information, such as text and images, is temporarily stored within the iconic memory, while auditory information is stored in the echoic memory. Written text is perceived visually but encoded in the echoic memory. In effect, we hear what we are reading (Ricker, 2014). Sensory memory is a very short-term memory and decays very quickly. Visual information is lost in less than one second and auditory information within three-to-four seconds, unless it is passed from the sensory memory into working memory via the process of attention. This is the cognitive process of selectively concentrating on one aspect of the environment while ignoring others (Mastin, 2010).
Working memory is very important in mental tasks involving the biologically-primary skill of problem solving and has two characteristics that impact on problem-solving success. First, it has a limited capacity to store information, a capacity that is determined by the novelty of the information, its complexity, and the quantity and quality of distractions that occur during the storage process. Miller’s Law suggests that the number of random objects an average human can hold in working memory is 7 ± 2. (See how many of the following numbers you can remember after a short period of examination: 23 42 16 87 91 56 78 21 38 63). Miller worked with simple items only. When more complex items are used, Miller’s magic number falls to three or even two (Mastin, 2010). Second, working memory is also limited in duration: novel information is only held for a few seconds before being lost unless something is done to refresh it. The primary function of the working memory is not to store information but to process it. Since cognitive tasks can only be completed if we have sufficient ability to hold relevant information while it is being processed, working memory capacity and duration can predict intellectual ability. Variations in students’ problem-solving success can be attributed to differences in their working memory capacities if they are working in a domain that is novel to them.
According to Sweller et al. (2011), we are intuitively aware of our personal working memory limitations: they become obvious when we are engaged in tasks such as copying a sentence from the board by the number of words that we can transcribe before we have to look up again. Mental arithmetic also exposes our personal working memory limitations. Can you do the following sums without pen and paper?
24 + 38 =
24538974 + 38296749 =
Most adults would have no trouble with the first sum, and the second is no more taxing mathematically than the first — if you are allowed to write your answers down as you go. Jotting the results of your computations as you go effectively clears working memory space. If pen and paper are not allowed, most would struggle to provide an answer for the second sum because the task exceeds working memory capacity. Significantly, when information is retrieved from long-term memory to working memory, the latter is neither limited in capacity nor duration as it is when novel information is acquired from sensory input.
Long-term memory has unlimited capacity and duration. Given that the greater part of our everyday activity is familiar to us, much of our long-term memory consists of biologically-primary knowledge. This is essential for our survival. But all of the higher-level cognitive processing that characterises our lives is reliant also on the biologically-secondary knowledge that is also stored in our long-term memories. This knowledge is organised into schemas that allow us to treat multiple elements as a single entity, thus providing the templates for problem solving.
Problem-solving success in one domain does not automatically lead to success in another. Chase and Simon (1973) stopped a chess game mid-play and asked master chess players and novices to reconstruct the placement of the chess pieces. They then counted the number of times each player needed to refer to the original board to reconstruct it from memory. As predicted, the masters needed fewer referrals. Then they repeated the experiment with randomly placed chess pieces on a board. The performance of the experts was worse than the novices because the masters’ schemas were useless in a random environment.
The difference between an expert and a novice is found in the quality and quantity of their schemas. Experts in a particular domain have a large, complex knowledge network constructed via the large variety of situations in that domain with which they have experience and to which they have learned how to respond. Most problems emanating from this domain would be routine for them and automatic. On the other hand, a novice in a domain has relatively few relevant schemas and few domain-specific situations within their experience. The domain remains novel and each problem requires attention to be given to many different elements in the pursuit of a solution.
So, back to the original question.
The reason that picking a flower and talking are so easy for us, even though they are among the most difficult tasks that humans ever master, is that we have evolved to perform these tasks, hence the associated schemas are so comprehensive and held so strongly in long-term memory that such activities present little burden on working memory (Cooper, 1998). Similarly, reading and writing present little cognitive load for most adults because of the expansive set of task-related schemas that we have acquired. But think about how young children struggle to encode the required schemas to enable them to read and write. Still, as familiarity with the processes of reading and writing increases, the cognitive demands decrease so that working memory can handle them more efficiently, and they progress from ‘clumsy, error-prone, slow and difficult to smooth and effortless’ (Cooper, 1998). With practice, they become more automatic readers and writers.
It is the same for problem solving. The reason it presents such cognitive challenges for students is that they have not yet acquired the necessary schemas to reduce cognitive load. Learning to solve problems requires students to augment the schematic structures of long-term memory for each of the domains they are studying until they are able to perform tasks with low levels of mental effort. With practice, they will become more automatic problem solvers.
Problem solving serves a critical role in STEM curricula and improving it must remain a key goal of STEM education. Students often fail to apply knowledge that they have acquired to novel situations because of their underdeveloped repertoire of problem-solving skills. It is clear that problem-solving ability in any domain is contingent upon familiarity with its concepts. As students work to improve the quality and quantity of schemas and how readily they can be retrieved, they gain expertise, reduce the cognitive demands on working memory and move closer towards problem-solving success.
References
Atkinson R.C, & Shiffrin, R.M. (1968). Human Memory: A proposed system and its control processes. In K.W. Spence & J.T. Spence (Ed.), The psychology of learning and motivation (Vol. 2, p. 89–195). New York: Academic Press.
Chase, W. G., & Simon, H. A. (1973). Perception in chess. Cognitive Psychology, 4, 55–81. Retrieved March 19, 2014, from http://matt.colorado.edu/teaching/highcog/fall8/cs73.pdf
Cooper, G. (1998). Research into Cognitive Load Theory and Instructional Design at UNSW. Sydney, Australia: University of New South Wales (UNSW). Retrieved February 11, 2014, from http://dwb4.unl.edu/Diss/Cooper/UNSW.htm
Gary, B.L. (1993). A new timescale for placing human events, derivation of per capita rate of innovation, and a speculation on the timing of the demise of humanity. Retrieved February 11, 2014 from http://reductionism.net.seanic.net/brucegary3/Speculations/innovations(t).html
Geary, D. C. (2008). An evolutionarily informed education science. Educational Psychologist, 43, 179-195.
Keating, J. (2013). Why Time is a Social Construct. Psychologists and anthropologists debate how different cultures answer the question, ‘What time is it?’ Smithsonian Magazine. Retrieved March 2014, from http://www.smithsonianmag.com/science-nature/why-time-is-a-social-construct-164139110/
Mastin, L. (2010). The Human Memory. Retrieved March 19, 2014, from http://www.human-memory.net/types.html
Ricker, J. (2014). PSY 101 – Introduction to Psychology. Section 5-5: Encoding, Storing, & Retrieving Memories. Retrieved March 19, 2014, from http://sccpsy101.com/home/chapter-5/section-5/
Sweller, J., Ayres, P., & Kalyuga S. (2011). Cognitive load theory. New York: Springer.
Published 15 May 2014