Week 2

I found the examples in the boxes to be extremely interesting. When I read Fish is Fish (Box 1.2), I immediately thought of past instances where pre-existing knowledge affected my teaching. (I also plan on purchasing the book for some of the classes I teach!) Finding the Area of a Figure (Box 3.4), made me wonder which method I had been originally taught. Did I really understand or just memorize at first? In the cottage cheese example (Box 3.10), I think I too would have used the contextualized reasoning rather than the school strategy of multiplying the fractions. The diverse examples from biology, mathematics and everyday settings increased my understanding of the concepts and thus in theory should lead to more flexible transfer, hopefully into my teaching. It appears the authors “practiced what they preached”.

When I first read the assignment, almost everything seemed over my head. However, after I read it again the concepts and the ideas were much clearer, I was mainly getting hung up on the terminology and the vocabulary. For instance, I think I understand prior knowledge, but “topic-associative oral style” was used as an example and I don’t know what that means. Also, are “formative assessments” any activities or projects that reveal to the teacher and learner what is actually understood and what needs further work? (Thus, the reflections we’re doing for class are “formative assessments”.) Does “inquiry based instruction” refer to instruction that uses formative assessments and metacognition while “conventional instruction” refers to memorizing and regurgitating? Lastly, what I really had trouble with, what is abstract instruction and abstract problem representations? Is it the core concept or a generalization of the problem so that it will by easier to transfer across different contexts? I need an example.

I was teaching a group of elementary school age children about pollution and water conservation and I thought things were going well – they must have gone over it in other classes. They were able to tell me various ways to conserve water along with ways to not pollute. However, when I tried to discuss why it was important – what would we do if there was no clean water to drink or we “ran out” I discovered that they couldn’t grasp those possibilities. Their pre-existing knowledge was hindering the learning process. They informed me that water comes from sinks. One girl said that “when that stops your mom just calls the repair man and someone comes to your house and fixes it”. They had memorized a list of ways to conserve water and ways to not pollute from previous classes, but hadn’t learned with understanding and competence.