It's a shame that math texts don't work to make numbers interesting. I think that math classes should stress how numbers and number systems work for the first eight or nine years and then heavily stress how math is used in what ever career a student is thinking about so that the student can start thinking about that career through its mathematics.
Even if a person is not considering any kind of technical path, they should be able to do arithmetic in their heads and estimate more complex values just from knowing how the math works.
Algebra is something that you have to start off with very simple relationships and then build on that. After a while you start to see simple patterns in more complex structures.
If you stay in electronics, you won't be able to escape algebraic expressions that describe physical quantities and possibly some very advanced math if you get into signal processing and other fields.
Back in the 70's, my PhD advisor in E.E. told me the primary difference between Electrical Engineers and Electricial Technicians was the ability to describe a system (mathematically): note, he did not say "envision" or "design" or "build/construct."
The world needs Engineers, Technicians, as well as Software Architects and software coders... vive la différence.
Children getting frustrated at their simple arithmetic mistakes is a huge cause of frustration that pushes them away from math, in my experience. Getting all students down to 8 seconds for any 1 or 2 digit integer arithmetic is a big key to developing either a love of math or at bare minimum, a peaceful coexistence with it.
That's very interesting actually. But not all Engineers just do math. My Grandfather was a lead engineer for Qantas Airlines here in Australia in the mid to late 1900's. I'm not a mathematician by any stretch of the imagination yet my Grandfather will ring me up if he gets stuck on some math sometimes! (He still does machining for Automotive repair shops and also helps restore steam engines) Even as a Engineer for a airline his job was more about machining skills than being a mathematician.
On the other hand, my Uncle is a mathematician - and he is a extremely high level security systems engineer (for people like politicians, government agencies, the army, and the PM). He needs to be good at math. (He is also a serious Arduino enthusist - it doesn't matter what question I have, if it can't be solved here on the forum he will have the answer for me in a matter of minutes (** so jealous **))
Exactly. Something as seemingly simple as cutting a router template on the laser requires calculating how to size it based on what bushing you want/need to use.
Many woodworking projects involve geometry and trig and most everything requires you to divide and multiply and add and subtract ad infinitum.
Agreed. I'll never forget as a kid being drilled on my tables constantly by my mother, the accountant, from several rooms away. It makes a big difference when you get to the point where those relationships are almost intuitive.
Time to pull out that digital calculator (RPN anyone?) Now, this sounds silly probably, but knowing how to "do it" on paper is great for school work, but the use of a great calculator provides the correct answer; this is critically important when you are stressed, tired, or simply having a bad-day.
Math is like any language: the more you use it, the better you get and the easier it becomes to express yourself. But ambassadors in a strange land still rely on translators to avoid earth-scorching mistakes.
Point is, humans are fallible; just like math-in-the-mind is error prone. This has been known since counting things became important:
Or take a deep breath and keep drilling it. I've had students who would just sit and cry when it came to math and I'd spend hours and hours just drilling and encouraging them, and I haven't had one yet who couldn't get past it.
I have three favorite types of success with teaching and tutoring:
Helping a troubled student build enough confidence to hold their head up and move forward.
Working with the 20% or so that can learn abstract math around the age of 7.
A one off, I taught a girl who was a natural artist how to turn her art into 3D wooden reliefs so her parents, both of whom were blind, could 'see' her art for the first time.
I wish I could afford to have you tutor me.
I was homeschooled, so my teacher (my mother) is prematurely grey over me and my math. (Thankfully I only do practical "math" for school now - woodwork and HO scale modelling)
None. I'm just doing practical math - ie. whatever is needed for a modelling project or a woodwork project. But I want to learn advanced algebra and some calculus. My dream is to become either a Architect or a engineer/scientist.
Well, not entirely true. I've been teaching myself business math ever since I opened all my home businesses (currently trying to juggle four home businesses and move house at the same time )
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