1. Clarifying the problem, Proposing some solutions 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 1 What Are the Features of Coherent Assessment Programs?

2. 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 2 We live in the age of assessment. At no other time in the history of education in the United States, and for that matter in other countries, have so many people, resources, and time been devoted to measuring students’ knowledge and performance in mathematics. Assessment has come to be viewed by policy makers and others to be more a lever for reform than merely an indication of the effectiveness of reform. The loosely coupled assessment system pervades every classroom in every school in the nation, at least in grades 3–8 and high school. (Webb, 2007, p. 1821; emphasis added)

3. Key issues: But not for this meeting 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 3 Why a national assessment? Who are the stakeholders and who do we wish to inform? Conditions: When administered, under what conditions, and in what format? Consequences of a national assessment — for funding, for curriculum choices, for instruction, for student learning How closely is the assessment tied to a curriculum and which is the driving force? °°°

4. Key Issues: What we should address 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 4 What would it mean for an assessment program to be coherent? What are the criteria for a program to be coherent? Is it possible to have a coherent assessment program? If so, what has to be put in place? If not, what are the obstacles? How can we ensure that the program continues to be coherent? What standards should we have for the appropriate use of the assessment program?

5. My primary references 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 5 5 chapters in the Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007) by — Jan de Lange (ch. 25) Joan Ferrini-Mundy & Robert Floden (ch. 29) Norman Webb (ch. 30) Dylan Wiliam (ch. 23) Linda Dager Wilson (ch. 24) A monograph prepared by Webb in 1997 for CCSSO

6. (Some) features of a coherent program 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 6 Content specifications Degree of alignment of the assessments with standards, curriculum, and instruction Technical considerations: validity, reliability, equity Standards for appropriate use.

7. With regard to content specifications 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 7 Need to identify criteria for specifying attributes of assessments that are aligned with the system components.

8. Criteria for specifying the extent of alignment of assessments (Webb, 1997, 2007) 10/14/2015 CBMS Forum on the Content and Assessment of School Mathematics 8 Categorical concurrence Depth-of-knowledge consistency Range-of-knowledge correspondence Balance of representation Structure-of-knowledge comparability ________________________________ Dispositional consonance