Problem solving, reasoning and proof
Christine Hopkins, Sue Pope, Sandy Pepperell · David Fulton Publishers eBooks · 2013
Human beings have always been involved in problem solving and mathematics has played its part in our search for answers. The Egyptians made use of their mathematical knowledge for practical purposes relying heavily on previous experience to ‘get the job done’. The exploration of mathematics is conducted in the search for greater knowledge and deeper understanding. The ‘problem’ to be solved is within the mathematics itself. Constructing chains of reasoning like this to solve a problem is at the heart of mathematics and children start this process of reasoning from a very young age. Mathematicians have been interested in paradoxes since the time of the Ancient Greeks because they make us look very carefully at our reasoning. Many of the conclusions which mathematicians have come to about infinity are counter intuitive and yet they have led to the development of powerful areas of mathematics such as calculus.