Representation And Structure In Mastery

 

Representation and structure is the second over lying idea when discussing teaching mastery in math.  It is easy to learn the big ideas but it can be much harder if you have no idea how to use it in your classroom.  Today, we'll look at ways to incorporate  representation and structure into your classroom.

Representation and structure refers to the different ways in which mathematical topics or concepts can be represented.  In addition, these representations can be used to show how certain concepts or topics are connected.

For instance, one can represent an equation concretely, pictorially, or abstractly.  Concrete refers to using manipulatives to represent the equation or problem.  Pictorially refers to drawing pictures to show the idea while abstractly uses the symbols or written form to take it a step further. Abstract is also known as  Students need this because we have discovered that there is not a single way to do any mathematical equation.

The thing is that the concept or topic needs to be presented in the correct order.  The best way is to begin with a pictorial representation so students "see" what it looks like. I will admit that this can be more difficult in higher level math classes but it can be done.  Once they've explored and gotten the pictorial representation, then its time to move on connecting this to the representation in the text book.  Finally, connect these to more abstract view of the concept by connecting the idea with prior knowledge. 

It is important for students to use language, written words, and reading mathematics is extremely important to learning mathematics.  This is part of the abstract stage and students have to be able to read and understand the textbook.  

As far as representations, there are so many possibilities to use, even in middle school and high school maths.  There are base 10 manipulatives, math balance scales, and so many more.  In fact, manipulatives can be found either in virtual or manipulative form and some are free, some do cost but if you look around, you can find things.  One can even find free apps for student devices so students can use their phones or computers.  These manipulatives can really help students make connections.

Next time, we'll look at mathematical thinking in more detail.  Let me know what you think, I'd love to hear.  Have a great day.