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Monthly Archives: January 2010
Groupings, Shopping Lists, Vectors: part 19
In this post, I will try to connect a set of equations with matrices and vectors in a way that isn’t simply a notational shift. In part 18 of this series, I brought up the vast preponderance of square matrices … Continue reading
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Tagged denominations, matrix multiplication, models, naming, representations, whole vs. parts
1 Comment
Groupings, Shopping Lists, Vectors: part 18
If you have read earlier installments of this series – and I know it has gotten long – you may have noticed that very few of the matrices that appeared there have the same number of rows and columns. A … Continue reading
Posted in Uncategorized
Tagged denominations, extending patterns, math class, matrix multiplication, models, naming, representations, whole vs. parts
6 Comments
Groupings, Shopping Lists, Vectors: part 17
In this post I will show a full-fledged matrix multiplication done in a spreadsheet, Excel. (This series starts here; two recent posts part 15 and part 16 introduce vector inner products done in Excel.) Above you see one approach, though … Continue reading
Posted in Uncategorized
Tagged education, extending patterns, matrix multiplication, models, naming, representations, whole vs. parts
5 Comments
Groupings, Shopping Lists, Vectors: part 16
This has become a long series, and we’re not done yet. Here is where we started, looking for natural models that give power and flavor to the mathematical idea of a vector. Since then, we’ve looked at vector inner products, … Continue reading
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Tagged denominations, extending patterns, matrix multiplication, models, naming, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 15
This post is part of a series, starting here, about models and ideas that underlie the rather abstract stuff called vectors and matrices in math textbooks. In this series, we’ve looked at shopping lists, pricing out orders, weighted averages, perspective … Continue reading
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Tagged denominations, extending patterns, math class, matrix multiplication, models, naming, representations
3 Comments
Groupings, Shopping Lists, Vectors: part 14
In the prior parts of this series, I have look at a number of problem situations from which a certain notion of grouping data and organizing data and operating on data arises straightforwardly, a way of grouping data that is … Continue reading
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Tagged denominations, math class, matrix multiplication, models, naming, representations, whole vs. parts
1 Comment
Groupings, Shopping Lists, Vectors: part 13
In prior posts in this series we have seen two completely different kinds of applications for the idea of matrix multiplication: in part 11 we looked at pricing out an order, and in part 12 we looked at drawing a … Continue reading
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Tagged denominations, extending patterns, math class, matrix multiplication, models, naming, reverse engineering, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 12
After the work we’ve done in prior parts of this series, e.g. part 11, to show vector inner products and matrix multiplication using an example of pricing out an order at a fast food place, I’d like to work through … Continue reading
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Tagged denominations, extending patterns, matrix multiplication, models, representations, whole vs. parts
2 Comments
Groupings, Shopping Lists, Vectors: part 11
Let’s look some more at matrix multiplication, which we introduced in part 10 of this series. We showed three rectangular arrangements, and called each a matrix, and called one the product of the other two. (The accepted plural of matrix … Continue reading
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Tagged denominations, extending patterns, math class, matrix multiplication, models, naming, reverse engineering, whole vs. parts
2 Comments
On Discoverability and Conventions
Chances are that if I asked you to add 1756678 and 99810023 together without using a calculator, you would have a way to accomplish that. This is already pretty interesting, if you think about it, in that it is likely … Continue reading
Posted in Uncategorized
Tagged discoverable, extending patterns, math class, models, naming, representations
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Learning and Unlearning Math 