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How Math Can Be Taught Better

Victor Aguilar

posted on 01 October 2015

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I have observed that exponents and logarithms are the stopping point for most failed high school math students.  In this paper I will discuss how this subject can be taught better.  The points I make apply to all topics in high school mathematics.  For instance, I offer a geometric solution for carbon dating problems that provides two digits of accuracy and can be done in seconds, which is handy on timed multiple-choice tests.  Also, I discuss what math is needed by tradesmen.  That such practical men feel their high school math classes were irrelevant is one reason why so many dislike mathematics. 


In the real world, this widespread dislike for mathematics is concealed by an almost religious belief in “data driven” research, which means statistics.  But their mathiness is achieved by feeding empirical data into statistical software that they downloaded from the internet, not by actually doing any math.  I have observed that the more strident a researcher is about proclaiming himself to be data driven, the more harshly he denounces deductivism, by which he means any type of mathematics other than statistics. 


If hate for math were restricted to people who do not need it, then we could just say that math is not for everyone.  But when even those who need it hate it, then we must look for systemic problems in how math is being taught.  Thus, while this paper is primarily written for educators, it is of interest to everyone whose profession requires the use of mathematics.


I added new material.


I decided that my focus on exponents and logarithms was too narrow.  I have added a discussion of trigonometry and geometry, as well as a section on mathematics for the tradesman, as I recognize that not all high school students will be going on to college.

the reason why lots of kids detest math is that they don't think it will be of use in future..either logarithm or various formulas wouldn't tdo you much good unless your future career has something to do with why not teach all kids some general math but teach more only tose are interested in math so that all those who don't care at all about wouldn't try this instead of doing their homework on their own???

Thank you for your thoughtful comment.


My current project is writing a textbook about geometry called Geometry-Do.  I attempt to address the needs of both talented students who are preparing for mathematical competitions as well as practical people like masons and carpenters that use geometry to build things.  Most of these students will drop out in the yellow- or green-belt chapter when Geometry-Do starts getting difficult, but I earnestly hope that they will not sell their textbook to the used book store because they believe the white- and orange-belt chapters are useful enough that they want to keep the book for reference.


Could you please read the white- and orange-belt chapters and tell me if this looks useful?

"If hate for math were restricted to people who do not need it, then we could just say that math is not for everyone."

Incredibly enlightning sentence. It makes sense on so many levels, when you think of Math pragmatic applicabilities as well as the experimentation with abstract. I mean the pragmatism as any it's use in any proffession which is marked for use within scope of Economic universe. Abstract theories, on the other hand, are marvelling in "immaterial' structures limited; at least initially to the workings of imagination. Scientist working with theories for theories sake, may be less focused on how these could materialise in form of better engineered bridge, or stock market model.

Reading your paper I realised that probably the schooling, even at primary education goes immediately into abstract, rather than real-life. I hope I understood your paper correctly?

I am myself a student of Financial Engineering at WQU, with background in social sciences. I really enjoy reading this forum, from point of view of transition from Sociological / Economic interest into more scientific. It's so many amazing contributions.

If you agree, could I share reference to your work - as this is very impactful work - and especially statement. 




You may share reference to my work.


My current project is a textbook on geometry: