Exit Slip: Some beginning questions for discussion of the Skemp article

 

When talking about instrumental and relational mathematics, our group collectively decided that it is better to teach instrumental mathematics first. The reason is that instrumental mathematics is often easier to understand. We described the class distribution as a Gaussian Distribution (Bell Curve), where students in the higher percentiles seek more challenging (relational) mathemtics and students in the lower percentiles are often just wanting to pass the class (and therefore seeking a basic understanding of instrumental mathematics. (We aren't saying that the class distribution fits a bell curve exactly, but it is an example.) We talked about how traditionally. teachers will try to teach mathematics somewhere in the middle region of the Gaussian distribution (plus or minus 1 standard deviation; 68% of the class). However, teachers would neglect the bottom and the top students of the class by doing so. The top students would find the class boring and would not be reaching their potential, and the students who are struggling will continue to not understand the concepts. We then asked ourselves: "How do we teach to the whole class?" As a group, we decided that the best way to do it is to start with instrumental math, gauge where the class is at with the course content, ease our way into relational mathematics (the whys), then go back and forth between the two depending on the students' capabilities. Every student has different goals. Some students are looking to be physicists and mathematicians, while others are going into the humanitites and arts. That being said, our aim as math teachers should be to help students reach their goals in the class while making math enjoyable and as engaging as possible for students.