Faceted Curriculum Project/Introduction

This page introduces the goals, structure, and development of the Faceted Curriculum Project.

Goals
The Faceted Curriculum Project (FCP) has the ambitious aim of changing the foundations of curriculum and textbook development, initially in mathematics, and initially at the 9-12 level. Possible audiences and uses of the FCP will include:
 * 1) Mathematicians who wish to contribute to 9-12 education will have a central repository:
 * 2) The project has strict organization and quality control guidelines to ensure consistency and quality of contributed content.
 * 3) The mathematics content will be developed only by mathematicians.
 * 4) Quality-control, community policing, and "page lockdowns" are available to ensure that content is open, but highly resistant to malicious or careless editing.
 * 5) School districts can develop curricula, and ensure that their curricula are pedagogically sound, mathematically sound, and attached to standards and assessment.
 * 6) The modular approach allows blocks of materials to be assembled flexibly.
 * 7) The "semantic links" between blocks ensure that blocks are assembled in a logical fashion.
 * 8) The multiple views (facets) on each block yield content that is appropriate for multiple audiences, including students, teachers, and professional developers.
 * 9) State and national education officials can perform "semantic queries" in order to obtain information that otherwise requires expensive studies.
 * 10) One can answer the question "What mathematics content is covered by California Standards, but not by Massachusetts Standards" with a one-line query.
 * 11) One can answer the question "What mathematics content must be learned in order to understand the proof of the Pythagorean theorem" with a one-line query.
 * 12) Teachers can use and develop "threads" as course outlines.
 * 13) A thread is a series of blocks, which are assembled into a course.
 * 14) Teachers can use discussion pages to perform lesson study on each thread.
 * 15) Threads can be tied to professional development.
 * 16) Teachers, mathematicians, and professionals can submit and discuss math problems.
 * 17) There are different kinds of math problems, for different audiences.
 * 18) Problems can be linked to strategies, for those wishing to follow Polya's problem-solving techniques.
 * 19) Problems can be tied to blocks, so that it is known what material is necessary to solve a problem.
 * 20) Teachers and professional developers can submit and discuss lessons.
 * 21) Lessons can be tied to blocks, which are tied to (state and national) standards.
 * 22) Lesson study can be accomplished on the "discussion page" for each lesson.
 * 23) Lessons can include various facets, problems, examples, and assessment.

Distinction from Existing Projects
While the FCP has educational improvement as a central goal, it differs from existing projects in numerous ways.


 * 1)  The FCP will have semantic data at its core.  For example, while the Pythagorean theorem is covered frequently on the web, and the equation describing a circle in the Cartesian plane is also covered elsewhere, the FCP will explicitly link them by pedagogical dependence; a teacher will know that the Pythagorean theorem must be understood/taught before the equation for a circle.  The semantic information will allow for the development of coherent threads to build a class/curriculum.
 * 2)  The FCP will have many facets available, for different users.  Students might require simple explanations of concepts, worked examples, and good problems.  Teachers might want to know/teach additional history, and they will want to understand how to assess students.  By having multiple facets on each topic, the usefulness of the material will be greatly improved.  Moreover, the built-in faceted approach will encourage contributors to write with specific audiences in mind, and improve consistency throughout the project.
 * 3)  The FCP will be structured around standards (state/national standards for various countries) for textbook/curriculum adoption, from the beginning.  Without this structure, it will automatically be excluded from serious consideration by school districts.
 * 4)  The FCP will have significantly more structure and quality-control enforcement than a typical wiki (such as wikipedia).  A thorough rigid skeleton of the project will be completed before editing is opened up to more authors.  Strict and transparent authorship guidelines will be created to ensure writer qualifications.

Structure
The FCP will have a strong foundational structure, based on blocks, facets, lexemes, standards, problems, and threads, linked semantically, as described below.

Blocks
A block is a unit of mathematical content. One may view blocks as an attempt to create universal standards, based solely on mathematical content (rather than pedagogy or representations).

Read more about blocks.

Facets
A facet is a way of looking at a block. A block is only a chunk of mathematics. A facet is a way of looking at the mathematics: a perspective with a purpose. Facets are written with a very specific audience, and a very specific purpose in mind.

Read more about facets.

Lexemes
A lexeme is a technical linguistic term, which can be thought of as a dictionary entry. Each block will be summarized with a collection of lexemes, and each lexeme will have a definition given. These definitions will also be faceted -- there will be definitions appropriate for mathematicians, teachers, and students, as well as a discussion of common definitions.

Read more about lexemes.

Standards
A standard is an existing standard for mathematics content. Examples of standards include:
 * 1) State and National standards for high-school mathematics content.
 * 2) Standards used for test preparation (SAT, A-level or O-level, CSET, MCAS, etc...)
 * 3) National curricula standards for countries.

Standards often consist of published and copyrighted material. On the other hand, there is an open-content license linked at the bottom of every page in this wiki.

To resolve this incompatibility, we follow some guidelines:
 * 1) Each standard will have its own page.
 * 2) The main text of the standard will not be reproduced on this wiki. In this way, copyright will not be violated.
 * 3) The section, subsection numbers and codes will be placed on the standard pages on this wiki, in addition to an external link to the original source of the standard. In this way, there can be semantic data linking to standards, without actually displaying the standard text on this wiki.

You may read more about standards

Problems
A problem is simply a math problem. These will be roughly classified as follows:


 * 1)  Drill problems.  These are the problems which are repetetive, easy to randomly generate, and which involve an isolated mathematical ability.
 * 2)  Synthesis problems.  These are problems which require multiple mathematical techniques, language comprehension, and are individually interesting.
 * 3)  Assessment problems.  These are problems which are meant to assess a specific ability.  Such problems may be multiple-choice, in order to detect specific ways that students might be going astray.

You may read more about problems.

Threads
A thread is a collection of blocks, linked according to the desires of a specific audience. Here are some examples of threads:


 * 1)  A linear thread, which develops a mathematically coherent, pedagogically sound, and standards-based curriculum for Algebra I.
 * 2)  A directed, but non-linear, thread, which develops high-school geometry deductively from a set of axioms.
 * 3)  A linear thread, which outlines a two-week professional development program for teachers of Algebra II.

You may read more about threads.

Semantic Information
For the development of the FCP, a large amount of semantic data will be created before mathematical content. In other words, a lightweight ontology will be developed (probably without sophisticated tools). This will rely on the Semantic MediaWiki extension. Examples of types of semantic data (in subject-predicate-object form) are the following:


 * 1)  A problem assesses students understanding of a block.
 * 2)  A block should be understood before a block.
 * 3)  A block must be developed mathematically before a block.
 * 4)  A (synthesis) problem requires understanding of a block.

Development Status
This project is still in the early planning stages. The project is being developed by Marty Weissman.

Here is the current To Do List.

Here is an early description of the FCP Semantics.

Quality Control
It is hoped that a self-enforced system of quality-control can be implemented through well-posted guidelines. Such guidelines would ensure that purely mathematical content is developed by professional mathematicians, that problems are written and checked by multiple parties, and teaching methodology is written by highly qualified teachers and teacher-educators. A "network of trust" can be established using Semantic Mediawiki annotations.

Technical Hurdles
Most of the required software exists within Semantic MediaWiki package.

After the development of content, it will be useful to have custom skins, displaying various facets for various audiences. In this way, teachers might be able to view the mathematical, learners, teachers, and standards facet, for example. This might require some custom CSS, or perhaps something fancier like the Fresnel package for viewing RDF data.

In addition, some software might be useful which automates the process of checking whether a curriculum satisfies all standards within a domain, or is pedagogically sound. Such a process would require the development of the semantic content described above. It is possible that the SWiM project and additional OMDoc markup will facilitate such additional features.