Why is it important for students to understand more than one interpretation of each mathematical operation?
371713
It is important because the different interpretations will be encountered as they try to apply their knowledge.  It's like teaching the use of a comma in a sentence is to separate a list, but then leave out the other uses of a comma.  Just knowing how to multiply isn't enough to get an understanding of when to multiply.  \n\nSo much of school and math in particular is sets of seemingly aribitrary rules.  But one of the main points of math is that the rules are, in fact, logical and not arbitrary.  So, if students learn that the mathetical operations are aribitrary rules and not steeped in a logical base, it gets very difficult for them to understand math at all.  That is to say that teaching more than one interpretation of mathematical operations can allow the students to see the logic behind the operation as opposed to memorizing the "hows"
714870
This is one of the overstated things - depends greatly on whether you want to be a coder, analyst, tester, theoretical scientist or whatever:\n- discrete mathematics, proofs, logical reasoning, induction, set theory, graph theory are pretty important to most algorithms\n- calculus, algebra, geometry and even less relevant domains etc. are *not* particularly directly important except in general insofar as they build necessary theoretical rigor as above, depending on how much you need\n\nThere are many different schools of thought on teaching and learning computer science concepts, and they can all be simultaneously right, depending on what level you're talking about.
1017111
In the history of math, it took certain conditions to kindle an interest in various branches of maths and related interests (astronomy, geometry, algebra). Accounting was necessary only where personal consumption varied strongly from personal production, i.e. in cities where communal irrigation or similar communal activities overrode the pure agricultural (or otherwise primary production) activity. Keeping a calendar became another agricultural necessity tied in to maths (or at least counting and accounting).\n\nMore recently, under the Nazi regime there was a school of German physicists which aimed at teaching physics not from mathematical formulary but in a purely textual approach, to counter the presumed "jewish" way we still practise at university.\n\nWhen I started school, another teaching paradigm was to start maths education with set theory.\n\nBoth of these approaches were ideologically based rather than culturally, but if a few generations of mathematicians are taught that way, it might change their outlook at maths to make a cultural difference.
503325
talk to your math teachers, ask them what you don't understand so you can understand everything. so when they introduce a new concept, you can figure it out from prior knowledge.
166221
Gaining new understanding about why things work.
280051
I'm no mathamatician myself but,\n\nMath is a subject that builds on itself, starting with simple addition and subtraction, then building on that for multiplication and division, then an understanding of fractions and decimals, then algebraic equations and trigonometry, then calculus etc etc etc…\n\nMy point is that often having trouble at one level in math, is the result of not having a good enough grasp of a lower level of math. Example small children who haven't learned their numbers cannot grasp the idea of addition, adding multi digit numbers is hard if you don't memorize addition tables (single digit addition) likewise multiplication is impossible without knowing addition, learning the multiplication tables is necessary to advance to higher forms of mathematics.\nAlso, most of math is memorization, and the best way to memorize anything is repetition. In order to memorize the multiplication (times) tables, you must either say or write them over and over again... regular daily quizzing yourself until the answers just come from memory, instead of having to think about them... it's the same with most of the basics in math.\nSo to answer your question, in general terms since I don't know what type of math is giving you difficulty, is to back up one step and be sure you have complete understanding of the lower level which will help alot with your current level.\nRemember, we are all born without an understanding of math, it is something that each of us have to work on.. Sure there are a few people born who seem to just be born with the skill, but most of us had to work to learn it :)\nYou can do this, just back up and study the basics, building on the basics with make the more complicated come easier.\n\nGood luck.
434590
because in more complex fields of mathematics, equations are as yet unsolvable, and the best we can do is make approximations. in fact there is an entire field of math devoted to this.
824865
The same universal laws govern the simple life issues and the complex ones, so it make sense to observe them and try to understand them in the simple issues first and later try to move on to the complexities of life. Let say someone tries to understand humanity as a whole; it is a very complex issue, but understanding one person--myself, for example, is a bit easier, isn't it? That is my understanding of the quote, but I enjoyed other answers also, they seem to answer your question well, each from a different angle and to me it is a great way to learn. Thank you for asking good questions.
382957
I you can express the problems in mathematical relations, yuo can use calculus  everywhere. For businesses you can use differentiation to find sensitivity of for example of profit to  a unit change in cost or sales or production.  you can use integration to find out over all profit or production, etc.
379804
math, because it is challenging and you have to think a lot to solve of the problems.
829946
I'd say that this is open to interpretation. you are best to ask your teacher or tutor, you cant trust our advice, cos none of us would know for sure.
786259
You won't understand why you need to learn most of this "math crap" until you get to college algebra--or more like calculus.\n\nIn the mean time, it may not seem like you'll ever use this "crap", and maybe you never will, but at least it's helping you learn how to think logically.
810795
Not if the student is just playing lazy and looking for someone to give them the answers.  That's not help.....that's wanting someone to do the work for them.\n\nIf a student needs opinions or ideas, then it's not a bad place to get a little thought material.  It's also helpful if you have a math problem you have tried, but can't find the mistake.\n\nAs with anything else.  It's a great idea that gets abused by those looking for the easy way out of doing the work themselves.
1128846
I majored in math in college.  All my professors said the hard part about math is the English.  If you cant read it properly then you cant do the problems.  Another part is people dont want to learn the postulates and theoroms needed to solve the problems.
281262
well look at it this way, math is the language of alot of sciences...its how we describe the world around us.  I would say most definetly, once you understand the rules and (more importantly but the harder of teh two)how to ready teh symbols and notations one could speak the mathematical language.  One big problem is that there are limited people who can understand high level mathematics and oen doesnt get a full grasp of math till they are say a Graduate Student in college.
590399
An interpretation of something tells always more about the person who interprets (yourself) than about the object that is being interpreted. I bet you can also find some more positive anagrams.
809456
The practical applications of math are endless. The basic math like algebra and geometry is vital knowledge for being able to solve everyday problems. The higher math is very useful in professions. If you're any kind of scientist, you'll need to know everything up until at least differential equations, and definitely further for chemistry and physics. Statistics is a real, very common application of mathematics that shows up everywhere- being able to take a set of real data that probably isn't perfect and still managing to analyze it to find patterns. Calculus also shows up frequently in businesses when they are attempting to optimize conditions in order to maximize profit or decrease cost.\n\nAside from applications, math fosters more analytical, rational thinking. This is why Plato taught geometry and arithmetic to his students before subjecting them to philosophy: so that he could develop their critical thinking skills. Just being able to solve complex problems is a wonderful skill that can be developed through mathematics. The mathematical study of logic is also quite practical.\n\nAnd surely you don't think that all of the world's technology just popped out of the air without somebody doing a lot of math along the way?