Monthly Archives: December 2009

Groupings, Shopping Lists, Vectors: part 9

Posted on 2009/12/29 by Bert Speelpenning

In earlier parts of this series we’ve looked at shopping lists as both an example and a model for something that in math class is called a vector. We’ve looked at the sum of two vectors by imagining you join … Continue reading →

Posted in Uncategorized | Tagged denominations, extending patterns, math class, models, naming, representations, whole vs. parts | 1 Comment

Groupings, Shopping Lists, Vectors: part 8

Posted on 2009/12/29 by Bert Speelpenning

In part 7 of this series, one of the examples for the use of inner product of two vectors was that of a final score based on a series of tests with different weights. We have a vector of weights … Continue reading →

Posted in Uncategorized | Tagged denominations, extending patterns, models, naming, representations, whole vs. parts | 2 Comments

Groupings, Shopping Lists, Vectors: part 7

Posted on 2009/12/23 by Bert Speelpenning

In part 6 of this series, I introduced an operation called inner product between two vectors, as a way to find the total price of an order using a price list. In this post, I want to give a bunch … Continue reading →

Posted in Uncategorized | Tagged denominations, look-up, math class, models, naming, representations, whole vs. parts | 2 Comments

Groupings, Shopping Lists, Vectors: part 6

Posted on 2009/12/20 by Bert Speelpenning

In this series on vectors we showed vector addition in this post, and then took a small excursion to show a surprising connection between some vector additions and the distributive property. In this post, I will combine vectors with look-up … Continue reading →

Posted in Uncategorized | Tagged denominations, look-up, naming, representations, whole vs. parts | 4 Comments

Groupings, Shopping Lists, Vectors: part 5

Posted on 2009/12/19 by Bert Speelpenning

In the previous post, I introduced vector addition in terms of combining two piles of stuff, while keeping track of what kind of stuff is in our piles, and how many of each of the stuff we’ve got. In this … Continue reading →

Posted in Uncategorized | Tagged education, math class, models, representations, whole vs. parts | 2 Comments

Groupings, Shopping Lists, Vectors: part 4

Posted on 2009/12/18 by Bert Speelpenning

Part 1, part 2, and part 3 of this series looked at a particular model for vector algebra, based on some simple notions such as that of a shopping list. In this post, I want to play with vector addition … Continue reading →

Posted in Uncategorized | Tagged denominations, models, naming, representations, whole vs. parts | 3 Comments

Groupings, Shopping lists, Vectors: part 3

Posted on 2009/12/16 by Bert Speelpenning

The previous installments in this series can be found here and here. What I am after is a natural way to develop the usefulness of the idea of a vector, and in the previous post I suggested that a shopping … Continue reading →

Posted in Uncategorized | Tagged denominations, math class, models, naming, representations, whole vs. parts | 2 Comments

Groupings, Shopping Lists, Vectors: part 2

Posted on 2009/12/16 by Bert Speelpenning

For an introduction to this series of posts, see here. Imagine Joe going up to the drive-through, to order for himself and his room mates. Their orders are all combined on a piece of paper. He reads it at the … Continue reading →

Posted in Uncategorized | Tagged denominations, models, naming, representations, whole vs. parts | 3 Comments

Groupings, Shopping Lists, Vectors: part 1

Posted on 2009/12/15 by Bert Speelpenning

There is a surprisingly versatile part of mathematics that deals with groupings and collections of things. The main ideas involved are really quite easy and practical. If you can make sense of a shopping list written by a spouse or … Continue reading →

Posted in Uncategorized | Tagged denominations, math class, models, naming, representations, whole vs. parts | 6 Comments