Concrete and formal operations are part of Piaget’s genetic epistemology framework. This study of how knowledge is developed is based on cognitive structures that correspond with stages of development. Piaget theory of cognitive development identifies four cognitive structures of sensorimotor, pre-operations, concrete operations, and formal operations.
As discussed by Culatta (2021) the concrete operational stage is roughly 8 to 11 years, and formal operations start roughly between the ages of 12 to 15 and last into adulthood. McLeod (2010) discusses the concrete operational stage as the beginning of logical and rational thinking, with an ability to work problems in reverse. These operations are applied to physical objects, it is not yet possible to hypothesize or process abstract concepts. For example, a child could see an object and answer questions based on what they observe and know. The formal operational stage, as discussed by McLeod (2010) is the ability to think and reason in an abstract manner. This thought process does not require physical objects. For example, deductive reasoning can be applied to predict outcomes and then apply a systematic approach to test an idea. Most literature indicates Piaget’s theory is associated with constructivism. This makes sense in the concreate and formal operations stages since previous knowledge is necessary to rationalize and reason.
One way to promote concrete operations is by using worked examples. For children that could mean giving them a mathematical formula with the solution and requiring them to work through the steps to show how to get to that solution. In adult training an HTML course could use completed blocks of code allowing students to make adjustments to see how other tags affect how the page looks and works. In comparison to formal operations the HTML lesson would be having students create a page from scratch. For children this could mean posing a mathematical problem where the actual functions need to be determined before actually working the problem.
Culatta, R. (2021) Genetic epistemology (Jean Piaget). Instructional Design. Retrieved from: https://www.instructionaldesign.org/theories/genetic-epistemology/
McLeod, S. (2010) Formal operational stage. Simply Psychology. Retrieved from: https://www.simplypsychology.org/formal-operational.html#:~:text=Concrete%20operations%20are%20carried%20out,for%20planning%20regarding%20the%20future.