WikiCurriculum

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WikiCurriculum

I have decided to host this project outside of the wikimedia setting The project, now known as the Faceted Curriculum Project (FCP) can be found at: [1] Thank you all for your advice! -- Marty 12:48, 4 September 2007 (UTC)

Mission

The WikiCurriculum project has the ambitious aim of changing the foundations of textbook and curriculum development, initially in mathematics at the 9-12 level. We hope that electronic ink technology, as well as wireless connectivity, improve to the point that internet distribution can replace traditional print publishing, and eventually an electronic device can replace a print textbook in the classroom.

When such technologies are readily available, it is hoped that the project can provide a dynamic interface to mathematics content, so that:

1. School districts can easily "snap together" a mathematics curriculum from basic blocks. The project interface will ensure that curricula are mathematically and pedagogically sound, and in-line with state standards. In addition, the semantic information will automate the assembly of a textbook to accompany the chosen curriculum.
2. Teachers can view blocks of mathematical content, using facets that display pedagogical tips, assessment guidelines, mathematical background, and linking to relevant information and activities.
3. Students can view blocks of mathematical content, using facets that provide explanations, rigorous proofs, worked examples, and exercises.

Distinction from Existing Projects

While the WikiCurriculum project has educational improvement as a central goal, it differs from the WikiBooks and Wikiversity projects in numerous ways.

1. The WikiCurriculum 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 WikiCurriculum project 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 WikiCurriculum 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.
3. The WikiCurriculum 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.

Basic Structure

The WikiCurriculum project will have a strong foundational structure, based on blocks, problems, facets, and threads, linked semantically, as described below.

Blocks

A block is a unit of material. Here are two examples of blocks:

1. Solving systems of two linear equations in two variables.
2. Setting up word problems with rates.

The following are suggested criteria for creating a new block:

1. The block must address a national/state mathematics standard.
2. Within the block, only one new mathematical technique (algorithm, construction, or theorem) may be used.
3. The block must not be properly contained in another block.

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.

Facets

A facet is a lens for viewing a block. For example, let us consider a block about solving systems of two linear equations in two variables. The following are relevant facets:

1. The purely mathematical facet. In this facet, the technical term "systems of two linear equations in two variables" is defined in a rigorous mathematical way. A criteria for solubility is given and proven. A general algorithm for solving such systems is given. Specific-use algorithms are also given. Such algorithms are proven to work.
2. A learners facet. In this facet, the terms are defined in a less formal, but still rigorous way. Methods of analyzing systems of equations are given, such as graphing, and algebraic techniques. Worked examples are given. Possible confusions are discussed, such as nonexistence of solutions, uniqueness of solutions, and infinitude of solutions. Practical algorithms are given, which can be done by hand, or with graphing calculator.
3. A real-world facet. In this facet, real-world examples are given. For example, an example from basic economics (intersection of supply and demand lines) might be given.
4. A teachers facet. In this facet, techniques are discussed for teaching the material. Activities are discussed for usage with students, and lesson-study is developed. In addition, methods of assessment are given, both for pre- and post-assessment. Frequent student problems are discussed.
5. A standards facet. In this facet, it is discussed which state and NCTM (national U.S.) standards are addressed in the block.

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.

Semantic Information

For the development of the WikiCurriculum, a large amount of semantic data will be created. 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.

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.

Technical Hurdles

Most of the required software exists within the MediaWiki software, given the Semantic Mediawiki extension.

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.

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.