Algorithm: A process or set of rules to be followed in calculations or other problem-solving operations, especially by a computer.
Heuristic: any approach to problem solving, learning, or discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal.
I want to show how we can teach students certain algorithms to help them diagnose the aim of a particular question and apply the right knowledge to answer it correctly, rather than using their own less accurate heuristic approaches.
Algorithms and heuristics in decision making
Cognitive psychology explores people’s decision-making by using three main concepts. People use algorithms to weigh pros and cons of outcomes to try and create the best possible result (in their opinion), and develop schemas (patterns of thought or behaviour that organises information based on prior experience) over time. But to solve some things algorithmically would be unnecessarily demanding on the working memory, either because we do not have all the information, or we do not have time to spare, or simple because it is not worth the effort. For these processes we use heuristics. These ‘rules of thumb’ help streamline our life, although they are often sub-optimal.
When I teach this in A-level Psychology my two favourite examples of heuristics are finding the milk in a supermarket and finding my keys.
If I need to buy milk in my local supermarket I have a strong schema on the location of the milk as I know its location. So I can route-plan the shortest route simply adjusting for factors like how busy an aisle is. But if I go to a new supermarket I don’t know the location of the milk. So I apply the ‘availability heuristic’, and apply my same schema. In my local supermarket the milk is in the back corner so I head straight there. I don’t systematically search the entire shop algorithmically, I take an educated guess and head to the other back corner. It’s not there either, but it was more likely to be there than at the front, based on my experience.
It’s the same when you lose your keys. You do not search the entire house. You employ heuristic strategies like yelling “ANYONE SEEN MY KEYS! I’M LATE!” and checking the most common places you put them down or have been that day. You don’t move to a room-by-room sweep of all surfaces, drawers and pockets (algorithm) until you get desperate.
Linking it to teaching.
It struck me this morning when reading Niki Kaiser’s blog on the RSC research project that students that don’t have a really strong grasp of threshold concepts will have developed a heuristic approach to those questions. They will have been taught the concepts in detail and will have a understanding of the concepts involved. They just can’t put it all together to make a reliable model that can be applied to all scenarios. This could be further evidence of the idea that application is a domain specific skill and not transferable.
This became really apparent when I marked my Year 13 chemistry mocks. There is an excellent question at the end on bonding.
A couple of students who answered this question applied their availability heuristic and assumed that one of the compounds must be covalent, because ‘why would a question not include all 3 types of bonding?’
This lead to lots of accurate work on covalent bonding completely misapplied to this question.
I believe that those students who got the question wrong did so because they did not have an algorithmical understanding of bonding, so they jumped ahead, possibly due to pressure, or due to poor understanding and their ‘rule of thumb’ let them down. They definitely know the bonding models individually but because our practice had always focused on individual types of bonding, or comparing all three, they just created simple heuristic strategies instead of a deeper understanding of how to apply bonding.
I need to combat this by creating a more explicit algorithm for them to adopt. I need to use explicit instruction to ensure they know the steps to follow and how to decide which way to go. A flow diagram should do the trick, created on the board to live-model its construction and incorporating the diagrammatic representation of each type of bonding to support.
Above is the overall structure without any visuals of the bonding types and various positions of the periodic table, which I will have to source later.
If you are looking at the above and thinking “Isn’t this is something that should have been taught to them in Year 10?” – yes, the above is incredibly simple, but it is clearly missing from some of the students’ schema on bonding. One of the things I have really learnt from this cohort is not to assume prior knowledge, even for the students with the top grades. It’s really changed my teaching of the Year 12 cohort and we do lots more diagnostic activities of GCSE gaps than before to compensate.
I also think it’s illustrative of just how far students can get with a heuristic understanding of the threshold concepts and why as teachers we have to induce cognitive conflict to find those gaps and consolidate them.