Finding out what they could do.... or Couldn't!

To no surprise, the students at Amber Hill were outperformed by the students at Phoenix Park on both assessments administered by Boaler, and the state-wide assessments (the GCSE’s). The issue is not which method of teaching is better than the other, rather how do we ensure students develop the appropriated mathematical knowledge required. The students at Amber Hill were of the opinion that math was fragmented and consisted largely of rote memorization of formulas and algorithms. A technique which essentially, failed them when they needed it. In contrast, the students at Phoenix Park developed and discovered the concepts for themselves through a series of open-ended questions. They had the ability to take this developed knowledge and apply it to multiple situations. This self-developed knowledge led to a better understanding of the material and proved to be beneficial in not only test situations but also in situations outside the math class which required mathematics.

It was alarming to discover the poor retention rates of the students (only 9% of Amber Hill students had the ability to retain mathematical information for any extended period of time). Students at Amber Hill felt increased pressure and anxiety to remember formulas not knowing where they came from, or even when to use them. As we all know from personal experiences, understanding and developing formulas and theorems, as the students at Phoenix Park did, results in an increased ability to retain the learned information. In one of the previous sections a student from Amber Hill made the comment “as soon as you walk out the class.... you don’t really know anything, cause you’ve already switched off... as soon as you’ve walked out, you’ve forgotten about that lesson”. Thus providing some insight as to why the students did not retain information.

It was interesting to note that the students at Amber Hill did not “think” about the math. They simply looked for cue words as indicators of which formula to use. If, for some reason, the cues were absent, they were unaware of which approach or method to apply. As a teacher, I am guilty of telling my students to look for “key” words as indicators of how to go about solving a particular problem. As discussed in class, many common exams and public exams have questions appear in the order in which they were taught in class. For example on the 2009 Math 3204 public exam, students knew that the first series of multiple choice questions were going to deal with quadratics, as this is the first unit taught in 3204. Therefore, students knew how to accurately select the correct answer based on this.

I reflect back on my own learning experiences, which were very much traditional and very similar to those experienced by the students at Amber Hill. I remember just trying to get through yet another lesson, devising songs, poems, acrostics, doing just about anything to aid in the memorization of the “math”. It worked, for the most part, but only for the duration of that particular unit. As soon as the test was finished, I would push those math concepts to the back of my mind, only to make use of them when mid-year and final examinations came around. I only wish I were given the opportunity to delve into mathematics as the students at Phoenix Park were.