Fig. 342a

As I read through Gerofsky's " Battleground schools: Mathematics education", it struck me to recall my mathematics education in New Zealand, and how much it pointed towards elements of the conservative and progressive approaches. I quite enjoyed mathematics up until the senior years of high school. However, at the university level, lectures and tutorials seemed to point to a conservative view. As I scanned down the table comparing the different elements of mathematics education (2008, p. 392-393), I found myself ticking off the assumptions belonging to the conservative column, although as Gerofsky mentions, this dichotomy is not always the healthiest ways to understand approaches to math education. However, it does reveal how much of my pre-conceived notions of mathematic education derive from my background as a mathematics learner, and how I now face a paradigm shift in the way I orient myself as a mathematics educator. In a bullet point that described who conservative...

Eisner sets out to explain the three curricula taught by schools, including the 1. Explicit curriculum - what is made public through course announcements 2. Implicit curriculum - the socialization through physical and behavioural structures of the school and classroom 3. Null curriculum - what is left out from our explicit curriculum Through his theory of implicit education, Eisner makes his case that is it usually more important for a student to study the teacher, rather than the course content, in an attempt to achieve a good grade. The students reads the environment created by the teacher to establish to determine how much effort they should put into a class, particularly in systems that use behaviour modification techniques. How is it that we should go about cultivating student initiative and to develop intrinsic motivation so that students find the joy of learning for themselves, rather than to please their community - teachers, parents, and peers - through their achievements...

 I took the TPI test twice, the first time through the lens of myself after my first year as a high school music teacher, and the second time as a mathematics tutor and prospective math classroom teacher.  Other than answering questions on the five perspectives differently, I also tried to vary my responses more dramatically the second time. Fig. 1. TPI results as a Music Educator   Fig. 2. TPI results as a Math Educator I would agree with the overall result that perspective that I find strongest is Nurturing; my greatest aim in teaching, no matter what subjects, is for students to develop a sense of confidence - the bravery to reach for goals, and the realisation that the capacity they have for impact. Mistake making is an important part of my teaching philosophy, particularly music where one's mistake is audibly heard by the rest of the group. It's imperative for my students change their mindset from embarrassment ...

Peter Gustainis and I worked together to recreate Felicia Tabing's Knotical . We created the 4 tiles digitally to represent her artwork presented at Bridges Math Art 2017, then arranged the tiles in the same fashion as her original block print.To extend this artwork, we incorporated colours associated with Andy Warhol's work with pop art, giving each tile a different gradient. This allowed for a clearer representation of the transformations (symmetry, rotation, translation) present in this artwork. As you can see in the color schemes below, the work almost has a complete rotational symmetry. As a challenge, we provided an activity where students were given a set of tiles and asked to represent 2 common knots - Solomon, and Trefoil - mosaically. Here is the link to our Google Slides presentation This project was a fun inquiry to the ways that we can teach mathematical concepts alongside concepts in aesthetics - the ways that mathematicians create art through vis...

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...