Indeed, if no one followed up on original ideas, we would be buried in fresh starts going nowhere. I think this is a really interesting idea, and one that we continually see in the STEM areas of learning. If we were to take everything for face value when it was first discovered, we would never progress and always be reliving the past. Part of the fun of science and mathematics is exploring theorems and formulas that were brought up from the past and linking them to new ideas and bridging them in ways that ancient mathematicians wouldn't think possible when they first discovered them. it is also the catalyst for improvement, change, and exploration. Finding and creating theories takes time and patience, and we cannot be scared to continue to progress with our own ideas, even if we fail. If we do fail, we can still learn from these experiences and bridge that knowledge to other ideas to continue to learn and grow. Learning is a never ending process unless we give up and stop following our ideas.
We have many ways of dismissing new observations, of explaining them away as if our goal were to be rid of them as quickly as possible...If those fail, then another pair of techniques will succeed for sure. Connecting to the previous point, this is very interesting because I find it analogous to politics and conspiracy theorists. In the digital age, where ads are targeted and tailored towards our individual desires, we are pumped full of information that continually attempts to validate our beliefs. Videos that are recommended, ads online, and 'explore' pages on social media all target the person's beliefs and enhance them to the point where they cannot accept another point of view. I think this is such a dangerous belief that goes beyond science and is dividing our world apart. In politics (especially in America) the divide between left and right wing politics have never felt greater, and it only continues to grow. Neither side is willing to agree with the other or even meet halfway and come to an agreement. We are constantly trying to validate our own beliefs and say that failure or the opposite of what we want is acceptable.
Analogies form a bridge to the ultimate necessity, words. I found this really interesting because my SA has mentioned the same things and has tried implementing this idea into her classroom. Math has some extremely technical and confusing terms that anyone would find hard to understand, so how can we expect 13 year-olds to pick it up right away? Formal definitions are important, but having them understand through visual representations or analogies from their daily life can really help them understand the ideas more seamlessly. I found that using analogies that are within the classroom really helps the students understand visually; for example I used a box found in the room to help communicate 3D objects, nets, and surface area and mentioned how if the students were ever stuck, they could always refer to that example. Some analogies can be personal to the student like using sports as an analogy to angles, or they could be general like the box idea. Either way it gives the students words to technical meaning and makes translation on the teachers' part easier.
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