Site here,
https://buildingmathematicians.wordpress.com/2016/06/29/a-few-simple-beliefs/
“One way to think of a person’s understanding of mathematics is that it exists along a continuum. At one end is a rich set of connections. At the other end of the continuum, ideas are isolated or viewed as disconnected bits of information. A sound understanding of mathematics is one that sees the connections within mathematics and between mathematics and the world”
TIPS4RM: Developing Mathematical Literacy, 2005
A statements like this is easy to agree with. Sounds great, doesn’t it? The ideas in mathematics should connect! The above quote speaks to what Richard Skemp calls Relational Understanding (an article you need to read!) which I believe is a major goal of learning mathematics. However, I am not sure we would all agree on HOW we help our students achieve this relational understanding.
I think Willingham is onto something here. We have all become educators because we want our students to be successful… and we want to do our best to help them do well. However, we are often so eager to get the results we want, that we don’t take enough time to allow our students to think… to explore… to make sense of the math… to realize WHY we are learning what we are learning. In our eagerness to have our students get answers, we often miss the developmental pieces that our students need to be successful!
If we were to focus on mean conceptually, we would likely have students who understood the procedures in ways that they are ready to use them in different ways… If we focused on visuals we would likely have students who could mentally reason these numbers on a number line… If we focused on reasoning, we would likely have students who were ready to adapt because they were used to making sense of things…
When we help orchestrate situations where our students make these connections, we are building mathematical thinkers… we are building mathematicians!
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