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Page 2
This page last updated on: Monday, January 10, 2011 7:58 PM
I have spent a good hour completing the selected exercises from Problem Set 1.1 in "Introduction to Linear Algebra". I then had a first reading of section 1.2 on the dot product of two (or more) vectors. From here it was a small jump to recalling APL and the notation +.x .
Then stepping back and realizing that understanding involves a variety of modalities. Sometimes we use language (e.g. English, German, mandarin, ...), sometimes we use algebra (i.e. mathematical symbolism, APL, Mathematica, ...), sometimes we use imagery (e.g. geometry, sketching, ... ), sometimes it may even involve sound or taste or tactile. Shades of Jerome Bruner and his three-fold model of enactive, iconic, and symbolic modes of thinking.
But the deep understanding comes from some subtle combination of all of the above. And the more practice and experience one has within a particular domain, the richer and deeper the understanding. Practice is closely tied to time-on-task, but it is also critical that the practice involve variety. The variety may come from asking good questions such as, what happens when I change this? when something gets very small, or very large, or is repetitive (i.e. something times itself).
There have been volumes written on quantitative versus qualitative versus narrative versus ... They are all different ways of viewing and thinking about an elephant. In different contexts, each may have priority. But to exclude a view limits one's perspective. Education is about developing and appreciating many viewpoints. I began this morning thinking about vectors. I am now thinking about Education. Quite right.
Now for some hard problem solving as I have a look at my Ship It! files for my model train layout.
Yes, it has been snowing, and with the wind there has been substantial drifting. This is followed by shovelling to keep the driveway (relatively) clear. Here is a photo taken from the front steps. The camera was about 5 feet off the ground when I took the photo:
Model Trains: I have finally generated a new set of starting positions as well as a switching list for Session 1. This took me much of the day as I encountered a couple of errors that required me to restart my entire system from a position since my last backup (about 2 hours earlier). Still, I am pleased to finally have it working again.
I spent an hour before bed reading "Freedom".
Technology: APLX Technology: Lesson 4 of "Adobe Dreamweaver CS5 Classroom in a Book" Mathematics: Chap. 1 of "Introduction to Linear Algebra" by Gilbert Strang Model Trains: Review and revise my Ship It! files Continue reading "Freedom" by Jonathan Franzen
| Learning Category | Planned Activities for Today | Time |
|---|---|---|
| Technology | Use APLX | 1 hr |
| Technology | Lesson 4 of "Adobe Dreamweaver CS5 Classroom in a Book" | 1 hr |
| Mathematics | Chap. 1 of "Introduction to Linear Algebra" by Gilbert Strang | 1 hr |
| Model Trains | Review and revise my Ship It! files | 7 hr |
| Literature | Continue reading "Freedom" by Jonathan Franzen | 1 hr |
