Math Gateway Partners Meeting

Thursday, April 28 - Saturday April 30, 2005

Core Taxonomy and Metadata Issues

This breakout session on Core Taxonomy and Metadata Issues was co-chaired by Russ Herman (iLumina) and Robby Robson (Eduworks). It was attended by Russ Abbott (National Curve Bank), Mike Gage (WeBWorK), Terry Herrara (ENC), Dave Hill (Demos w/ Positive Impact), Susan Kornstein (College Board AP Central), Franda Liu (Ethnomathematics Digital Library), Robert Miner (Design Science), Jim Rutledge (MERLOT), and Roger Woodard (CAUSE). Russ Herman lead the Core Taxonomy discussion and Robby Robson lead the Metadata Issues discussion.

1. Core Taxonomy Motions

   Russ Herman reviewed the motions on the table, after recalling the general state of the Core Subject Taxonomy for Mathematical Sciences Education, which was posted on 4/2/2002. It was reiterated taht the taxonomy should be such that people using it can "map" into the core taxonomy, though it was suggested that "mapping" is not correct, as it suggests a one-to-one relationship.

   On May 24, 2004 CAUSE, a national group of statisticians, proposed a major change to the Probability and Statistics portion of the Core Taxonomy. Their proposal addressed concerns of alignment, vocabulary, and topics in the Core Taxonomy. Roger Woodard has represented CAUSE in the support of these changes. Over the past year there has been some discussion about this proposal. Jim Rutledge had provided an alternative proposal, which was based upon the two taxonomies and attempted to adhere to the general guidelines set during the finalization of the Core Taxonomy.

   During the breakout session we considered the alternative proposal. We looked at the items left out of the original taxonomy and then considered the changes from the CAUSE proposal. After considerable discussion and several competing motions, those present voted on the below final version and it was unanimously approved.

   9.0 Statistics and Probability
   	9.1 Data Collection
   		9.1.1 Experimental Design
   		9.1.2 Sampling and Surveys
   		9.1.3 Data and Measurement Issues
   	9.2 Data Summary and Presentation
   		9.2.1 Summary Statistics
   			9.2.1.1 Measures of Central Tendency
   			9.2.1.2 Measures of Spread
   		9.2.2 Data Representation
   			9.2.2.1 Graphs and Plots
   			9.2.2.2 Tables
   	9.3 Statistical Inference and Techniques
   		9.3.1 Sampling Distributions
   		9.3.2 Regression and Correlation
   		9.3.3 Confidence Intervals
   		9.3.4 Hypothesis Tests
   		9.3.5 Statistical Quality Control
   		9.3.6 Non-parametric Techniques
   		9.3.7 Multivariate Techniques
   		9.3.8 Survival Analysis
   		9.3.9 Bayesian Statistics
   	9.4 Probability
   		9.4.1 Elementary Probability
   			9.4.1.1 Sample Space and Events
   			9.4.1.2 General Rules
   			9.4.1.3 Combinations and Permutations
   			9.4.1.4 Random Variables
   		9.4.2 Univariate Distributions
   			9.4.2.1 Discrete Distributions
   			9.4.2.2 Continuous Distributions
   			9.4.2.3 Expected Value
   		9.4.3 Limit Theorems
   			9.4.3.1 Central Limit Theorem
   			9.4.3.2 Law of Large Numbers
   		9.4.4 Multivariate Distributions
   			9.4.4.1 Joint
   			9.4.4.2 Conditional
   			9.4.4.3 Expectations
   		9.4.5 Stochastic Processes
   			9.4.5.1 Brownian Motion
   			9.4.5.2 Markov Chains
   			9.4.5.3 Queuing Theory
   		9.4.6 Probability Measures
   		9.4.7 Simulation

2. Metadata Issues

   Robby Robson led this discussion. There were five subtopics that drove the discussion. The main ideas was to pose the issues that need to be addressed and then to think about the process by which these should be done. In many of these cases input and resources need to be provided by the Math Gateway, or partners.

   • Metadata Schema
     Do we need, or want a standard metadata schema? There are several choices if it is decided that a standard be adopted, such as the qualified Dublin Core (DC) as is being required by those being harvested by NSDL. What is the advantage to having a shared metadata schema? There will result some interoperability in the discipline. It would aid in advanced searches, such as providing the educational level of the resource, the technical requirements for using the resource, and help in dealing with rights issues for usage.
   • Policies
     Should the Math Gateway require partners to adopt the standard, or recommend it? Which metadata elements should be required? Are there mathematics education vocabularies that need to be adopted?
   • Metadata Services
     Requiring partners to adhere to a standard set of metadata would impose additional work, such as creating the metadata for each resource. If the Math Gateway, or some partner, could provide a metadata creation tool, this might be a useful service. The form of such a tool, existing or created, would require some exploration and financial resources. Further verification, or validation, of the metadata would also be needed.
   • Identifiers/Registries
     Unique identifiers and registration of the metadata databases would help in identifying resources. There are methods for doing this, but this issue needs exploration and needs to be addressed in the adopted policies.
   • How to get real work done
     These issues need to be addressed to make the Math Gateway work. This should be done in a timely fashion, though it is not clear if some of these need to be done involving all of the partners, or if a small group of people can get started working out the details. The current Gateway Partners should appoint a task force to begin working on this and should determin how much a small group can do and what all of the partners would agree to, especially about requiring a metadata schema. It was suggested that the small group put significang time into addressing these issues, such as having meetings for one hour per week with at least an hour of contemplation in between each meeting. However, there is concern that such a time investment should not be voluntary without reimbursement of some form.