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Some things anyone can do to understand science and math better
and then use them to solve problems.

Get familiar with the many reasons that we must seek out disconfirmations . . . and we might then often just ignore confirmations. 
Disconfirmation is the key.
Disconfirmation is our first line of defense against deception.  In the 1940’s advertisers successfully sold cigarettes as a panacea for most medical ailments  They picked out any evidence they could find that might support their panacea hypothesis, and then invented evidence as needed.  Today’s advertisers have perfected their old techniques; and most of their targets still believe that confirmation is the key to proving hypotheses.  It isn’t.  Wason’s card selection puzzle reveals more about this point.
Pack a portfolio of understood abstractions: this means understanding why certain common beliefs are the pre-scientific misunderstandings while the abstractions are the real science of the past several centuries.  Abstractions make life richer. Energy is a nice starting place to recognize how familiar words have a colloquial meaning and a science meaning.  We sense a metaphorical connection between food, fuel, rest, sleep, etc.  And so in everyday language, energy means a kind of capacity for doing work.  Science of the early19th century told us that energy can be unavailable for doing work.  The energy concept of science quickly grew more abstract and developed into a peculiar force-times-distance concept.  Figuring out what that means is a valuable exercise.  But “capacity for doing work” is the really relevant thing. (Not the energy of science.) 
Learn to recognize oversimplifications, figure out the damage they can do; then figure out how to do the right thing. Oversimplification is a downer. One oversimplification is being self-centered and not recognizing that Mother Nature neglected to endow us with perceptions of most of the wonders of the universe. Science breaks some of our intellectual bonds by carrying us beyond our evolved perceptions and reasoning skills. 
Discover things that we cannot deny ... even if we fervently desire the opposite.  Look especially in those scientific abstractions we hadn't understood. The undeniable can drop you down a deep hole. When we don’t understand some science or math principle, we probably don’t sense some things we are missing that would force us to change our ideas about our problem. Then we goof. The 5X5X5 cube puzzle illustrates this principle.  We gain a lot by looking for as many of these undeniable points as we can discover.  Think about the lottery!
Get some skill at separating relevance from irrelevance.  Irrelevance is a sometimes deadly lure. Air temperature is irrelevant to the actinicity (sunburning ability) of sunlight.  Logical analysis of simple observations can establish this irrelevance.  Further study can reveal what is relevant.