Framework Construction Documents

Sarah Donaldson

 

Situations Project documents (that contribute to Framework discussion)
Jan. 30, 2008

DATE

ITEM

DESCRIPTION

USEFULNESS

LOCATION

050325

Some thoughts on thinking about [MKTS]

Early discussion of trying to identify MKTS (P. Wilson, J. Kilpatrick, K. Heid).

Includes guiding questions for developing a Framework.

webpage

060525

Theoretical Framework

Description of the project and how the Situations and theoretical framework work together to characterize MKTS (J. Kilpatrick, G. Blume, B. Allen)

Proposes two dimensions to MKTS: math content and math proficiency. Math proficiency list comes from Adding It Up (2001).

webpage, CD

060910

Purposes and characteristics of good Situations

Discussion of what makes a good Situation, and why good Situations are useful (UGA).

 

Includes items that might be useful for characterizing MKTS.

webpage, CD

061024

Intro to PSU’s Process and Drawing on Mathematics categories

Description of Processes (proving/justifying, defining, and generalizing) and Drawing on Mathematics; analysis of Situation 40 using this Framework (PSU).

 

Early attempt at a Framework for MKT, and analysis of a Situation using it.

hard copy (Sarah)

061031

UGA comments on above

UGA response to categories discussed by PSU.

 

 

CD

061118

Powerpoint for NSF-CLT conference in MD

 

 

 

CD

 

070127

Powerpoint for AMTE

 

 

 

CD

0701

Mathematical lenses for teaching mathematics

As presented at AMTE 0701: mathematical objects, big math’l ideas, and math’l activities of teachers.

Ideas for how to organize MKTS.

CD

070226

Mathematical activity of teaching (“Snow Camp”)

 

List of mathematical activities of teaching (UGA/PSU).

This was used to create future lists (MTTM).

CD

??

“Draw on” examples

 

Examples of when a teacher draws on mathematical knowledge (PSU).

This was used to create future lists (MTTM).

CD

070520

Powerpoint from Expert Meeting

 

 

 

CD

070522

Expert’s response to final question

What are the 5 most important things you would put in a content course designed to develop MKTS? 

 

Ideas from experts about key elements of MKTS.

CD

070625

PSU categories of MTTM

Compilation of MTTM from 0705 Expert Meeting, Draw-on list, “Snow Camp” list (PSU).

 

Large list that was eventually condensed to actions and entities

CD

070710

 

 

070718?
070719
070723
070724
0707??

Framework for mathematical tasks for teaching mathematics (MTTM)

Situation 39
Situation 43
Situation 21
Situation 39b
Situation 49

Situation 10

List of actions and entities that combine to characterize MTTM. The list was made by examining past attempts to characterize MKT and notes including those from the 0705 Expert Meeting (UGA).

MTTM Framework applied to specific Situations. We looked for entities in the Situations: objects, representations, statements, procedures, and connections. These categories were later revised.

 

We used this to analyze situations to see if it was a valid way of looking at the work of teaching. Another attempt at a Framework—is it helpful to look at the tasks of teaching mathematics?

CD

070722

Diagram of framework building process

Shows relationship of situations, framework of MKT, MTTM (UGA).

 

Connects MTTM to MKTS.

CD

070731

Representation

Description/definition of Representation (UGA grad students).

 

Includes description, examples (geometric, analytical, etc.)

 

070911

Process

Description/definition of Process (UGA grad students).

Includes description, examples (proof, geom. construction, etc.)

 

071005

Concept

Description/definition of Concept (UGA grad students).

 

Discussion of concept.

 

071029

Defined actions from Framework for MTTM

Definitions of actions: recognize, choose, create, use representations, assess the math of the situation, extend, connect, demonstrate/explain, prove, investigate, apply, reason, coordinate, reflect (PSU).

 

Thorough descriptions, including examples. Also includes comments about mathematical disposition.

CD

071030, 080116

Decision making moments in teaching

Flowchart. Issues: Where is the MKT? Where is the framework? (UGA)

 

Shows dynamic process.

CD

07Fall

A report from the Framework and Definitions group

Overview of this group’s work on defining entities* (representation, process, concept, operation, and relation) and looking at literature. Includes explanation of “Decision making moments in teaching” flowchart (UGA).

*This document doesn’t include those definitions.
They would definitely be useful—where are they?

 

071116

Powerpoint presentation from UGA colloquium

MKTS: Examples from the Situations Project

Gives overview of the project, including goals.

CD

 

 

 

 

 

Articles and resources from others


AUTHOR

DATE

TITLE

LOCATION

Sharon Senk

0704

060420

TEDS, Teacher Education Study in Mathematics (conceptual framework of from IEA study)

TNE Mathematics standards. Mathematical knowledge teachers must possess.

hard copy

hard copy

Joan Ferrini-Mundy, et al.

070705

Conceptual knowledge framework for teaching school algebra

CD

Deborah Ball

 

What mathematical knowledge is needed for teaching mathematics?

hard copy

Al Cuoco

Cuoco et al.

0102

96

Mathematics for Teaching  (Notices of AMS)

Habits of mind: An organizing principle for mathematics curricula (Journal of Mathematical Behavior)

 

hard copy

CD

Jill Adler & Zain Davis

06

Opening another black box: researching mathematics for teaching in mathematics teacher education (JRME Vol. 37 No.4)

 

hard copy

Ruhama Even

9012

Subject matter knowledge for teaching and the case of functions (Educational Studies in Mathematics Vol. 21 No. 6)

 

CD

McEwan & Bull

91

The pedagogic nature of subject matter knowledge (American Educational Research Journal Vol. 28 No. 2)

 

CD

Peressini et al.

04

A conceptual framework for learning to teach secondary mathematics: A situative perspective (Educational Studies in Mathematics)

CD