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]]>Even though Wikipedia is not the final authority on all things, it does give a nice history of the concept:

http://en.wikipedia.org/wiki/History_of_the_function_concept

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]]>Computers and internet have diminished importance of human memory. We need people who possess enough understanding to search, process and use new information more than we need people with total recall. So, for students to achieve such understanding (deep learning) we need teachers who know their subjects and are able to engage students in discussions that reveal what is “inside their minds” so that these minds can be properly “formed” (“formation” is the word used in many languages to mean “education”). An ability to use group dynamics and emotional devices remains of utter importance. Ability to use technology is helpful but, in my view, its importance is sometimes exaggerated.

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]]>The post Numeracy appeared first on Sound Mathematics.

]]>extolling the virtues of teaching arithmetics as music. I

always feel sad when teachers put competency over

comprehension. Of course, at work, competency is king,

what matters is only whether you accomplish your tasks and

how quickly. But when learning, comprehension should be

paramount, eventually it will lead to greater competency.

Yes, one can learn the times table by heart without any

understanding. It takes a lot effort though and has

limited value. Yet, if one is explained how numbers work,

the times table can be learned in 2 weeks, working 10

minutes a day. And it is real fun!

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]]>is very important to find out what they know. No point in

going on about something most of the class are familiar

with anyway. Equally counter-productive is to skim over

the material students find puzzling.

Most teachers in higher education assume that students

can remove brackets. Many can’t. Dealing with a mix of

differently signed quantities is often a problem.

Several examples have to be considered to introduce what

in the UK schools is called a Smile Rule.

However, this is not enough. Throughout the

year, whenever the necessity for removing brackets arises,

it is advisable to get through the procedure, asking

students to talk about the necessary steps.

Most academics do not like doing that, thinking and saying

that they are not school teachers. But if the students failed

to acquire the necessary skills at school who would help

them if not us? And experience shows that they can be

helped. The teaching strategy I describe here has been

shown to work many times over.

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