Nowadays, maths is so much more than being able to add, subtract, multiply and divide. Essentially it is the study of number, measurement and space. When teachers 'teach maths' they want to guide children into discovering answers to real life problems themselves. It is a process of coming to a solution using their mathematical skills. And it is the process of getting to the solution which contributes to mathematical understanding.
Solving problems requires the children to add, subtract, multiply and divide, so these skills are taught in this context. Children should be encouraged to investigate numbers: 5+3=8 but so does 50-42 and 64/8 and 4+4. Teachers aim for children to be curious about numbers so that they discover the properties of numbers themselves.
To aid understanding in maths, the use of concrete materials is widespread. Materials such as pop sticks, blocks, counters, string, shells, even food (or representations of it) can be used to enhance understanding. With these materials, children sort, order, classify, manipulate, group, add together, measure, tessellate and do lots of other things to further their understanding of mathematical concepts.
Other skills that are taught include estimating predicting, measuring, ordering, classifying and interpreting. It's all a part of discovering the Maths in everyday situations and giving meaning to the numbers and symbols that we use to represent the mathematical concepts in our lives.