I hope you don't mind some late night thoughts on this.
What I take away from my own training is that basic maths such as adding and subtracting or multiplying and dividing when done repeatedly and in a new way such as matrix work in college show that basic skills can be extended. Personally I am weak at the knowledge in advanced maths having left advanced maths for years at a time but my basic skills still pull me along so I succeed in applied statistics but not theoretical. The knowledge such as Navy knowledge in my case knowledge of consumer tasks such as buying and advertising would I think allow someone with the basic skills of working with numbers to then learn the applied problems. I don't want to say more about military maths because I am anti-war. But I also want to point out the big sell of computer companies and software sales firms for the term knowledge. This affects statistics education where we are trained at advanced levels to think critically of helping the social scientists with their statistics which they need help with but in other courses we are taught to build complex models in probability and knowledge searching that aid business improvement processes, i.e managing to get the most out of underpaid workers by recording and timing work tasks and driving for efficiency. I am a little off topic here but back to knowledge searching as a paradigm of the computer age and thus as an agenda for educational reform. I think I am being over the top here but I hope you are aware that advanced computer and statistics is seeking to manage, find, and discover, knowledge rather than impart it to others.
I also just read some math education papers from Europe about concepts and the fact that both teachers and students can make big mistakes when they pervert math concepts. In my marking of regular university students as a teaching assistant I mark for correct method rather than correct skills meaning basic maths. Your final answer can be off but if you used the right formulas and so forth and did correct reasoning with your wrong result you still can score A. The skills taught in university are more problem solving and decision making skills. We try to let the students learn techniques and when to use which technique and reasons for statistical methodology decisions.
I am sorry I can add more in the adult education field but I am mostly working elsewhere these days.
Peter Timusk, B.Math statistics, B.A. legal studies M.A. legal studies applicant just trying to stay linear. Read by hundreds of lurkers every week.
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