Fig. 342a

The thing that inspired me most to learn and develop my mathematical concepts were the high school standards set out by the NCEA examinations. The concrete and well defined lines of where concepts sit, as well as the type of questions that were offered allowed me to have a strong grasp on where I needed to divert my attention. I guess you could say that clear learning objectives/outcomes are a good source of motivation for my learning. What frustrated me were when these lines began to blur. When concepts became inter-related, or when classes didn't have clearly set objectives. I felt that my understanding of mathematics had been blown apart and I couldn't find a way to comprehend and stay on top of my studies. This was most apparent during my university years studying as a math major, particularly in the field of applied mathematics. A math "teacher" that inspires me is Salman Khan, who is the creator of Khan Academy. His YouTube videos were clear in articulation ...

In response to Richard Skemp's article on Relational Understanding and Instrumental Understanding (available here ) The Skemp article prompted me to consider my own experiences in learning and teaching Mathematics, particularly in my home country, New Zealand. New Zealand has national assessment/certification for  all  high school subjects, the National Certificate of Educational Achievement (NCEA). All Year 11, 12, and 13 students - the final three years of high school - studying the same subject and level, will take the same exam at the end of the year, at exactly the same time. Due the set type of questions, year after year, teachers have become accustomed to teaching for the exam, more often than not, for instrumental understanding. Although the NCEA administration have made small changes to the exams year to year, in hopes of creating space for teachers to teach for more relational understanding, this is not always the case. I, myself, have been guilty for tutoring c...