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Defense against bias, superstition, and preconceived notions
- By guiding researchers towards objective results based on transparency and reproducibility, the scientific method acts as a defense against bias, superstition, and preconceived notions.
www.aje.com/arc/what-is-the-scientific-method/What is the Scientific Method: How does it work and why is it ...
Apr 18, 2014 · When learning mathematics, it's useful to prove "obvious" results in addition to "non-obvious" ones because: you "know" they're true before you start, which can save some frustration. the ease or difficulty of proving the obvious teaches you something interesting about the area you're working in.
Jul 20, 2014 · Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures.
- Why Does Math Need Proofs?
- Why Do I Need to Learn Proofs?
- Where Will I Need Proofs?
- Logic in Law
First, from 2000: I replied: Math, that is, is abstract reasoning, which is guaranteed to be true as long as the assumptions we make are true. In arithmetic, we start with basic assumptions about how numbers combine, and reach a conclusion that will be true as long as the things we are counting are actually suitable for counting (as opposed to, say...
Consider this question from 2002: Doctor Roy answered, starting with a teaser and some parallel questions: The same could be said of many things taught in schools. He went on to give examples where school teaches ways of thinking, not just specifically useful facts. He concluded:
Here’s one more question, focused on a particular kind of proof in geometry but really applicable to all of math. This is from 2000: We’ve seen above that all of math is built on provable facts, not just blind assumptions. But why learn it when you will not be a mathematician? Two of us replied, starting with Doctor Ian, mentioning facts you might ...
Doctor Alicia added her thoughts: Of course, they don’t really use “two-column proofs”, which are a particular way to organize a proof meant to help beginners be sure that every step of reasoning is justified. Step by step, we would use the given information to show, in the end, that angles A and B are complementary. (This is a typical very brief p...
Why do We Need Proofs? It's clear why we need to prove mathematically something that's not obvious, like the Pythagorean Theorem, but why should we prove something that "common sense" tells us is obviously true. First, if something cannot be proved, there may be something missing. For example, suppose we set up some equations that describe a ...
Aug 8, 2013 · Attaching numbers to a problem can help local, provincial or federal governments decide what kind of action they need to take to solve it. In fact, collecting enough evidence to convince people to make changes is one of the biggest reasons we see so much “obvious” research.
Jul 30, 2022 · Students believe what they are told by their teachers, especially in math class, and with good reason because math teachers rarely teach an untrue theorem, and proofs often are used instead of good explanations. The proofs are looked at, and then forgotten, with nothing gained.
Apr 10, 2015 · A proof is a logical argument that establishes, beyond any doubt, that something is true. How do you go about constructing such an argument? And why are mathematicians so crazy about proofs? Which way around? What can maths prove about sheep?
