WHAT IS GOING ON?

I have two anecdotes. The first incident occurred in a math class that is struggling. Some grades are extremely low, and the overall grades are the lowest of all my classes. At the end of a whole group instruction and before anyone began independent practice, I asked if there were any questions. Every student in that class firmly maintained they knew the material and understood what to do. It was not surprising to find that most of their independent classwork was inaccurate and based on a confused and inadequate understanding of the new mathematical concept.

The other incident occurred in the math class that is excelling. Some grades are extremely high, and the overall grades are the highest of all my classes. At the end of instruction and before anyone began independent practice, I asked if there were any questions. A few hands went up in the air, and they started asking questions before I had a chance to call on anyone. When I explained it further, most of the students in the class acknowledged that there was still a little uncertainty, but they would give it a try. It was not surprising to find that most of their independent work was accurate and based on a rudimentary understanding of the new math concept.

What do these two incidents suggest?

- Some would say the first class' lack of ability refutes the value of self-esteem.
- Others would suggest that cognitive awareness, or the ability to reflect and evaluate one's thinking process, can benefit understanding, and the first class has less cognitive awareness than the second.
- Others would say that the first class lacks intellectual curiosity and just wants to be done with it.
- Some would say that peer pressure in the first class forces all the students to keep a low profile and not attempt to please the teacher by showing some interest.
- Others would recommend that more data needs to be gathered in order to verify a hypothesis.

You parents may have a clue as to what's going on. All I know is that I have observed this type of phenomenon all my teaching career, and in middle school the phenomenon is more pronounced and observable.