Compare & Contrast

Both papers discuss similar aspects of tangles, but in very different ways. Tanton writes to an audience that may not have much background in math and/or knots. Tanton breaks down each idea step by step with lots of diagrams, making it very easy to follow. Kauffman and Lambropoulou write much more academically focused. In order to be able to fully follow and understand Kauffman and Lambropoulou's article, you must have some sort of background in mathematical knowledge (especially proofs). Both papers discuss what it means for tangles to be isotopic as well as operations on tangles, but as I have previously mentioned, Tanton's paper, is much easier to understand and follow. 

The advantage to Tanton's paper is that anyone could read it and follow it. The disadvantage is if the reader was someone well versed in mathematics and knot theory, than they may be bored with the basic explanations and humor that is embedded throughout the paper. 

The advantage to Kauffman and Lambropoulou's paper is that it goes much more in-depth with each concept, thoroughly proving and explaining every idea. The language used is also much more academic compared to Tanton's. This could be a disadvantage depending on who the reader is. Also, Kauffman and Lambropoulou do not use as many visuals in their paper, which may put them at a disadvantage to a reader who is more of a visual learner. 

As a reader with a mathematics degree, I was able to follow both papers, but I connected most with Tanton's paper. As my knowledge of knot theory is developing, Tanton's paper was easy to follow, and I was able to make connections and develop take-aways rather quickly. I also enjoyed the whit and humor that was embedded throughout Tanton's paper. I felt that Kauffman and Lambropoulou's paper was extremely dry, and it was difficult to get through. Yes I could understand the majority of what was being discussed and proved, but it was just SO in-depth, it was very easy for me to get distracted. 

If I were to give math teachers one of these readings to introduce them to tangles, I definitely would have them read Tanton's paper. I think that teachers would be thoroughly engaged in the paper, and they would not feel like they are swimming in a pile of academic jargon.