Reflection about a Mathematics Teacher in Grade 10

Lesson: Absolute Value Approximation


Topic: Clarity











As we know, the teacher behavior in "Clarity" is divided into five functions:

1- Framing the Learning
2- Presenting Information
3- Creating Mental Engagement
4- Getting Inside Students' Heads (Cognitive Empathy)
5- Consolidating and Anchoring the Learning

And each function holds many main titles and subtitles.

Based on my observation, it was shown that the teacher was working on achieving “Clarity” in his lesson. He had a great emphasis on being clear in his teaching process to reach the desired academic aims. This was shown in stating the objective of the mathematics lesson “How to Find the Absolute Value of Certain Functions?” at the beginning of the lecture which falls under the title “Communicating the Objective”. Also, when the students complained from some parts in the homework, he told them that this lecture will be a solving session to remove the vagueness in some parts. This reminds us with “Explaining the Reason for an Activity”. And these lie under the title “Framing the Big Picture”.

Moreover, when the teacher gave a hint about the bound in the absolute value before starting solving, students remembered that everything negative will be positive within the bound, stimulating their background knowledge which is the same as “Activating Students’ Current Knowledge”. Also, the teacher emphasized students to solve firstly the product ab and then to find its absolute value and that since he knows that students will solve it incorrectly by making │ a│ and│ b│ and then multiplying them. In fact, this is false where: │a│×│b│≠│ab│. So by stating the procedure in steps, wrong results will be avoided. This reminds us with “Anticipating Confusions and Misconceptions”. And these lie under the title “Getting Ready for Instruction”.

In addition to the hints the teacher gave before starting solving as a mean for helping students to follow correct strategy to reach the desired result (absolute value), plus to the hints he stated at the end of the lecture to give the idea of the question. These are considered “Progressive Minimal Cues”. Moreover, when the student started thinking about “ab”, he mentioned the procedure in steps while speaking in loud as a way to check themselves in solving. This is known by “Modeling Thinking Aloud”. And these lie under the title “Explanatory Devices”.

Note that when he stated that the bound of the absolute value is the same as the bound of the square (students already know) to make the idea more clear and closer to the students’ mind, this in known by “Showing Resemblance to Something Students Already Know”. Also, the teacher practiced these exercises from the simplest to the most complex, where when he was sure that the idea of “Absolute Value” is clear, he gave students higher level exercises to solve, reminding us with “Signaling Shift in Level”. And these lie under the title “Making Cognitive Connections”.