Faceted Curriculum Project/About Blocks

This page describes, in more detail, the category FCP Block.

New Block Guidelines
The following are guidelines for creating a new block.


 * 1) A block page only contains a simple description of a small chunk of mathematical content.
 * 2) The main purpose of a block page is a very short summary (one sentence, adaptable to the ontology described below), together with a larger amount of semantic information. The semantic information ties the block to standards, and to more detailed views of the block from the standpoint of mathematics, teaching, learning, assessment, etc...
 * 3) Blocks can be thought of as universal standards. The creation of blocks corresponds to finding universal content standards which encompass all existing state and national content standards.  However, more than one block may address the same standard, and one block may itself address many standards.
 * 4) Each block should be minimalist. They should encompass individual techniques, classifications, etc...  The richness of mathematics is expressed in the connections between these blocks.
 * 5) At the initial stage of development, the standards of California, Massachusetts, Indiana, and Singapore should be used to guide the creation of blocks.

Block Summary Ontology
Since blocks are meant to be universal standards, it would be quite useful to have semantic information available in the block summary.

The block summary is meant to be a single sentence summarizing the content of the block. One example might be: "Multiplying binomials using the distributive law and FOIL".

Traditional sources of standards arrange standards by threads, subtopics, grade level, and other methods. By storing the block summary with a semantic framework, one should be able to flexibly categorize blocks. This avoids problems with overlapping standards, and artificial categorization/hierarchies. Semantics can also be linked easily to glossaries for further clarification.

In order to construct such a semantic framework, the FCP will use a single format for Block Summaries, known as the $S^5$ format.

Interblock Ontology
There can be many types of semantic links between pairs of blocks. Some are inversely related to others. Since blocks are "chunks of mathematics", the semantic links may include the following: Deductive dependence: If a proof, contained in Block X, depends on a result, contained in Block Y, then we say that "Block X mathematically depends on Block Y". This should be annotated, in the text of Block X, with: Mathematically Depends On::Block Y Pedagogical dependence: If a student's learning of Block X relies on a student's understanding of Block Y, then we say that "Block X pedagogically depends on Block Y". This should be annotated, in the text of Block X, with: Pedagogically Depends On::Block Y