There are many influential factors that play a part in how mathematics are taught or learnt. In addition, to be effective in teaching mathematics, we need to have the mathematics knowledge and also knowing how learners learn.There are six principles involved in teaching mathematics. These principles allow us to know that it is not just the concept that learners need to know when learning mathematics. Furthermore, there are five process standards to show how learners should practice and gain mathematical knowledge. The principles and standards illustrate how experiences should be for learners and how it means to understand mathematics.
Doing or learning mathematics is not by memory like what we always thought of. It is by understanding the pattern. Doing mathematics is being able to generate strategies to problem solve, applying the strategies to see if it works and also if the answers make sense. “Productive struggle” helps learners to learn mathematics. It is not leaving the learner with a question or problem without equipping him or her with prior knowledge. It is to allow them to try different approaches to find the solution and not directly intervene to help when the learners got stuck. This act is supported by the six principles and five process standards. Knowing the patterns and understanding the concepts, that is doing mathematics!
There are two learning theories which complement to how learners do mathematics. The constructivism theory explains how learners can construct new knowledge upon prior knowledge. Just like building blocks, having a foundation base in order to add on more.
Sociocultural theory explains how learners can be supported by peers or people who are more knowledgeable to reach their zone of proximal development (ZPD). In this way, learning mathematics will be productive!