Make a Memory... Build a Model vol.1
Try this little experiment... find someone who has never eaten a mango and try to explain what that is like. He/she will likely understand each word you use in your description, but will that mean they have an intuitive sense of mangos? Probably not.
What must that person do to access that kind of understanding? They actually have to experience a mango.
And that goes for any kind of learning. For understanding to take place at that deeper, conceptual level, the learner needs direct personal contact with the idea, be it riding a bicycle, knowing mangoes or mathematical ideas like making sense of mixed numbers.
Offering rich mathematical investigations where learners (including you) can build and manipulate models to ‘uncover’ ideas is one way of doing that. Through the manipulation of models, learners clarify thoughts, adjust thinking and notice patterns that boost their ability to reason and solve real problems.
Experiencing the math in this way has an added bonus as well... the chance of actually retaining the idea is significantly higher. Even after the models are gone, the learner will likely be able to visualize the idea in his/her mind, by recalling the experience.
Learners who have experienced mixed numbers through pattern blocks might use visualization to reason through a variety of mathematical situations.
What numbers of sixths would be needed to make only whole numbers? What numbers of sixths would it take to make mixed numbers? Track them on a 100 chart and notice the patterns.
What if the trapezoid was what we are calling ‘1’ (instead of the hexagon)... how would your patterns change? Predict first, then try it!
