Archived Information

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##  Summary of Independence Room Research Subgroup Discussion

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## DOMAINS 

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##  Curriculum and Instruction

**Issues**

1.  How to compare C & I programs

2.  Determining the elements of a good educational research design

3.  How to synthesize small-scale studies that have been carried out

4.  Do we know how to teach learners in special education?

**Ideal** (for Issue #1) -- arrive at consensus about results of
research in these areas

**Barriers** (for Issue #1)

-   No one solution or program will work for everyone

-   Different paths possible for getting to the same goal

-   Lack of coherent theory

-   Lack of agreement about goals of math ed

-   Lack of informed parental input

-   Vast differences in settings and programs

**Opportunities for Coordination** (for Issue #1)

-   Bring parents, mathematicians, and math educators together

-   Methods of communication

> \-- Need sustained communication

**Strategies (What)** (for Issue #1)

-   Neutral forums for continuing the dialogue

-   NAS/NRC

-   School boards

-   PTA meetings

-   The general public

#  [Cognitive Foundations of Mathematical Competency]{.underline}

#  Issues

1.  Evolution of math concepts over time for the individual learner

2.  Content and organization of math concepts (i.e., understanding of
    relations among concepts)

3.  Issues of symbolic representation, including natural language,
    tables, graphs, notation; relation between internal and external
    representations

4.  Social interaction and communication norms and engagement

**Ideal** (for Issues 2 & 3 combined)

-   What are the cognitive processes and empirical findings related to
    key concepts and contents in math?

**Barriers** (for Issues 2 & 3 combined)

-   Sense of isolation of different realms of research

-   Divergent views as to what constitutes evidence of understanding

(i.e., what constitutes valid research?)

-   Limited education of researchers themselves

> \-- (emphasis on basic research?)

-   Pressure that results of research should be immediately usable

-   Framing the most "effective"? (appropriate?) research questions

##  Assessment

**Issues**

-   How can mathematical learning be adequately assessed, and what kinds
    of assessment be used to advance student learning?

\-- Use of assessment for testing teacher knowledge of mathematics

> \-- Integration of assessment and curriculum (i.e., embedded
> assessment)

**Ideal**

-   Valid assessments that lead to valid inferences about what students
    know

> \-- Provide feedback to students, teachers, and researchers

**Barriers**

-   Sloppy use of language (e.g., testing, assessment, evaluation)

-   Professional development for teacher in use of assessment

-   "Scientifically-based research" is too narrowly focused

-   Assessments often take over (precedence?), especially high stakes
    "assessment"

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-   Quality of available assessments

#  Opportunities for Coordination

-   Bringing people together who have developed or are developing
    assessments

-   Building an assessment system around learning goals and testing it
    out

-   Types of questions used

-   Adaptive assessment

> \-- Use of technology