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The variables for getting dressed are the same for most people but the weightings (the number representing how important or influential that variable is) will vary, which is why we all end up buying different clothes and dressing differently. We each have a unique equation for getting dressed, and that will change for each day. As we can see there is an underlying pattern of decision making for each person and how they dress. But if we knew what clothes were in their wardrobe, and we knew the person well by understanding the pattern of how they dress (based on all the different variables), we could predict what someone might wear to a specific event. We can make this prediction because our brain has created a pattern for how that person dresses for different situations (contexts).
The key here is that our brain loves working out patterns between variables. Everyone understands and applies this type of algebra continually throughout every day. We apply this process to the trips we plan, the meals we cook, the choice of a book we download, the car we buy, the people we like and take on as friends, who we sit next to on the bus, and we compute these algebraic equations very quickly. Our lives are all about the patterns that cause and effect creates.
The extraordinary nature of concepts is that our brain loves them and is constantly looking for patterns in our world. We spend a large part of our lives looking for patterns in people’s behaviour, the weather, our partner’s mood, judging whether mortgage rates will go up or down, or is this a good time to buy a new car, whether we should visit the grandparents, or where we should we go for a holiday ...
We are walking algebra experts, despite our possible failure in algebra at school. Once we understand variables and how they affect outcomes, we can create concepts and predict possible outcomes. ‘Concreate variables are ‘things’ that are tangible that we can see or feel. When learners become familiar with ‘concrete’ variables, learners can begin to come to terms with abstract variables, make sense of them and use them to find the unknown quantities in our lives.
In mathematics, the same principle applies to the concept of number and measurement and for every mathematical concept, BUT each concept must be introduced using only the knowledge that is required and then that knowledge is applied to ‘safe’ contexts that the learner can relate to. The task of all educators is to keep the concepts at the forefront of the learning and not to burden learners with knowledge and processes, Just-In-Case they may need it sometime in the future. Smartphones are far better at remembering things like that, so let the learner’s minds play with concepts, as that is what it is designed to do and does very efficiently.
Getting the exact answer in school is viewed as being important, whereas in life it is far more important to be able to approximate, and that requires the ability to predict and that requires us understanding the concept of number. To predict approximately what ‘15% off’ might mean in a supermarket store, we must understand the concept of both number and percentage. The extraordinary thing about learning a concept is that once we understand it, we can predict what the discount will approximately be, for anything. Understanding the concept of algebra and number are fundamental to life, especially in the complex world of decision-making.
Building patterns between variables allows us to make predictions and human beings are the only species on planet Earth that can make predictions, as we are the only species with this very powerful learning system. If we can develop our learning programmes based on concepts, learners will learn to understand more deeply and they will achieve this very quickly.
We need to evaluate and look at how we teach what is worth learning, whatever the learning domain may be. Educating for understanding allows us to focus on learning to learn, rather than remembering scores of inane facts or processes that the learners will never remember after the test has been completed and marked. Many of the facts we learned in school have little relevance in an era where we carry the world’s most complex and dynamic library of words, imagery and video in our pockets, courtesy of our smartphones.
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