Steps to Tracing a Mathematical Concept Central San Diego Math PLC 11/5/10
Concept Selection and Tracing of Development
1. Review math concepts that develop from the lower grades and are essential in higher mathematics and based on common errors (Comment: I don't understand this sentence, in particular the "based on common errors part". Do we mean something like "...mathematics. Note common errors in the development of these concepts."?) .I agree this is confusing.
2. Identify the target concept.
3. Select sources for tracking the development of the concept.
4. Set limits of tracing the development of the concept (Pre-K-Statistics or 3rd-Calculus…).
5. Collect standards/learning outcomes and problems that trace the development of the concept through the levels:
Isolate CA Standards and Framework having to do with the concept in order of grade level and class.
Collect standards and problems from backwards mapping documents such as the San Diego County Office of Education Algebra Backwards Mapping
Isolate Common Core Standards having to do with concepts in order of grade level and class.
Isolate CA and Core Standards of other disciplines for the concept and order in terms of grade level.
Review the NCTM documents to see if they have anything to contribute to the development of the concept.
Collect standards and sample problems from Community College Student Learning Outcomes and Assessments and University Materials.
Examine Cal-PASS Deconstructions for sample problems.
Create missing problem examples.
6. Make notations about what is missing in the development of the concept.
7. Make notations about common errors made by students due to the developmental gaps.
Document Creation, Editing, and Commentary
1. Remove from the documents any standards or problems that do not really trace the development of the concept.
2. Make notations about how to correct errors in thinking or steps in understanding critical that might be missing in the development of the concept.
3. Comment on gaps in development of the concept and issues with sample problems or standards
5. Create a Cover Sheet which denotes audience, purpose, and use of this training of a concepts development.
6. Create an introduction that highlights findings.
7. Create a Conclusion which makes recommendation.
8. Create Table of Contents and Contributors page.
Next Steps: Creating activities that can be done at each level that will reveal student errors in understanding and create inventions for learning the concept (Comment: What do we mean by "create inventions"?).I think we mean interventions.
Central San Diego Math PLC
11/5/10
Concept Selection and Tracing of Development
1. Review math concepts that develop from the lower grades and are essential in higher mathematics and based on common errors (Comment: I don't understand this sentence, in particular the "based on common errors part". Do we mean something like "...mathematics. Note common errors in the development of these concepts."?) .I agree this is confusing.
2. Identify the target concept.
3. Select sources for tracking the development of the concept.
4. Set limits of tracing the development of the concept (Pre-K-Statistics or 3rd-Calculus…).
5. Collect standards/learning outcomes and problems that trace the development of the concept through the levels:
6. Make notations about what is missing in the development of the concept.
7. Make notations about common errors made by students due to the developmental gaps.
Document Creation, Editing, and Commentary
1. Remove from the documents any standards or problems that do not really trace the development of the concept.
2. Make notations about how to correct errors in thinking or steps in understanding critical that might be missing in the development of the concept.
3. Comment on gaps in development of the concept and issues with sample problems or standards
4. Reference ICAS Competencies in Mathematics http://icas-ca.org/competencies-in-mathematics and other ICAS Competencies that may apply in commentary
5. Create a Cover Sheet which denotes audience, purpose, and use of this training of a concepts development.
6. Create an introduction that highlights findings.
7. Create a Conclusion which makes recommendation.
8. Create Table of Contents and Contributors page.
Next Steps: Creating activities that can be done at each level that will reveal student errors in understanding and create inventions for learning the concept (Comment: What do we mean by "create inventions"?).I think we mean interventions.