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The concept of " function" is corner stone of mathematics. Those who had basic idea of " function" can be well versed and will be able to understand concept of calculus: LIMITS, CONTINUITY, DIFFERENTIABLITY.

please give suggestions how to dovelop this idea
Development may be
1)Giving examples: Area of circle is function of radius , and establishing there is a relation between two variables and establishing how one quantity will depend on another quantity
2)Giving idea of taking equation:
a)making table of values:
b)ploting equation graphically
3)Function as a relation
4)Establishing a fact that a  line parallel to y axis cuts the graph of a function at one point.
4)Giving examples of expression which is  not a function
5) with conclusion   etc etc
please suggest the steps to be involved systematically

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Replies to This Discussion

The metaphor of a machine is appropriate for explaining a function. When a function is computerised, as in a graphing calculator, that is exactly how the function is implemented, as a machine, with floating point numbers representing real numbers. On the other hand, an analog computer can be constructed from operational amplifiers which use non-digitised voltages to represent real numbers. Complicated functions can be achieved by connecting the inputs and outputs of multiple operational amplifiers with passive components such as resistors and capacitors. In an electronic circuit, everything is connected to something else. A circuit designer must be creative to construct a circuit where the output is NOT a function of the inputs, such as a clock frequency that is not dependent on temperature or a D.C. power supply that provides a constant voltage even when the A.C. supply is drifting. The mathematical functions in a circuit, especially voltages that are a function of time, become very visible when the circuit is probed with an oscilloscope.
Colin, check out ANALOG (!!!) machine for solving differential equations:
http://www.youtube.com/watch?v=NmX151Jd3_o
http://www.marshall.edu/mu-advance/news-MU-Differential-Analyzer-Gr...

I was fortunate to get a tour this Fall. Bonita Lawrence will present at Math 2.0 series soon.
Hi !

I am currently pursuing my master in math and my focus is on an applet called Algebra Arrows. I try to use Instrumentation/Instrumentalisation in order to exploit this so students/pupils may build a concept of function (This is related to 2 of the 4 components that O'Callaghan mentions in (O'Callaghan, 1998). The 2 components are
1. MODELING
This means the transition from a problem situation to a mathematical representation of that situation. Usually this means making an equation, a graph or a table.
2. INTERPRETING
The reverse procedure of modeling. A mathematical representation is interpreted and the transition will be to a suitable situation. This can be explained as the ability to read an equation, table or graph.

I kindly ask of you to consider trying this applet and tell me what you perceive as strengths concerning the introduction of the concept of function when you consider the 2 components mentioned earlier.

The applet: http://www.fi.uu.nl/toepassingen/02008/toepassing_wisweb.en.html
Manual for the applet: http://www.fi.uu.nl/en/fius/rmeconference/handouts/vanderkooij/wedn...


O'Callaghan, Brian R. (1998). Computer-intensive algebra and students' conceptual knowledge of functions. Journal for Research in Mathematics Education, 29(1), 21-40.

Thanks in advance !

Dag Rune Kvittem

Here's my contribution to this discussion on introducing the concept of function:







I find it useful to use a situation where students themselves will:

  1. identify the changing and unchanging quantities;
  2. determine the effect of the change of one quantity over the others;
  3. describe the properties of the relationship; and,
  4. think of ways for describing and representing these relationships.

Click this link to read more and for sample activity

 

Function - starts in class XI onwards.  Students already knew about linear equations in two variables and their graph in class X.  one can explain from linear equation or can explain set/cross product/relation and a particular relation is a function.  Every function is a relation but converse not true.  by the by , graphical representation of relation will help students to understand better.

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