How do we construct meaning?

One reoccurring question from parents and teachers new to PYP is usually about math: Why don’t we use text books to teach math.
I usually answer with another question:

How do children learn math?

Now that usually brings the conversation to an unintended halt, I am actually curious, it is a genuine question. As I have traveled and taught on three different continents and seen many different countries it still baffles me that there seems to be many ways to teach math.

For a PYP school it is made pretty simple: our learning theory is based on Socio-Constructivist understanding. Therefore we believe that the learner is an active participator and constructs their own understanding. IB Scope and Sequence states

First, children need an opportunity to construct their own meaning about mathematical ideas and concepts. Then, they need the guidance and support to transfer their own meaning into conventional symbols, vocabulary. Finally, they need a chance to apply their understanding. These three phases are fluid and children move back and forth through them in an on-going cycle.

 

To summarize:

• Students construct their own meaning about math (Conceptual approach, e.g. Concrete Manipulatives –> Abstract representation –> Concrete language)
• Students transfer their meaning into conventional symbols (vocabulary, notations, )
• Students apply their understanding of learned mathematical concepts in situations that require higher order of thinking

A lot of the teachers are confident about that first stage in the math steps,  but many are still wondering how to bring all three of the stages together.

In an attempt to step back and see the big picture of how the stages fit together, we will generate a visual to help us on our journey towards.

I will update this post once we have collected some evidence and strategies.