A Vision of Effective Student Assessment in Mathematics
May 27, 2008
The teaching profession is a calling, a calling with the potential to do enormous good for students. Although we haven’t traditionally seen it in this light, assessment plays an indispensable role in fulfilling our calling. Used with skill, assessment can motivate the unmotivated, restore the desire to learn, and encourage students to keep learning, and it can actually create – not simply measure – increased achievement.
- Stiggins, et al., 2006
Purpose. The purpose of this document is to provide an overarching vision to guide the assessment initiatives and activities being planned and conducted as part of the Microsoft Math Partnership. As such, it has been developed as a resource for the Partnership’s
Student Assessment Working Group and for the teachers and administrators in the Partnership’s schools and districts.
Vision. As educators shift their focus from what was taught to what was learned, their
focus must also shift from narrowly evaluating what was taught to broadly assessing what has been learned. While tests and quizzes will continue to be important components of assessment, it is how the results of these quizzes and tests are used to analyze the impact of teaching, plan re-teaching, prepare individual instruction and design additional diagnosis that translates assessment into better teaching and learning. In addition, effective teachers use observations, student answers, class work, student work, and similar vehicles as evidence that is used to monitor the quality of learning. Finally, the results of a carefully aligned system of unit tests and end-of-grade and end-of-course assessments are regularly analyzed to make curricular and instructional modifications. Accordingly, we adopt a vision of effective student assessment that balances assessment for learning – making instructional decisions and monitoring the growth of student understanding – with assessment of learning – evaluating students’ achievement and
evaluating programs. Our vision assumes that the form and content of assessments match the form and content of instruction, and expects that our conception of assessment shifts from merely after-the-fact testing used to generate grades to an integral component of the planning, teaching, and assessment loop that characterizes high quality instruction. Background. Assessment is the third piece of the educational process captured by the three questions: “what do I teach?” (curriculum), “how do I teach it?” (instruction) and “how well was it learned?” (assessment). As such, assessment is the multi-faceted
process by which we gather information about students, teachers, schools and school districts that allows us to inform decision-making, adjust instruction and revise curriculum. Grounded in the on-going retrieval and analysis of information about the quality and quantity of student learning, effective assessment is the glue that connects the A Vision of Effective Student Assessment in Mathematics Page 1 of 4
components of a mathematics program (alignment), informs on-going instruction (formative) and provides insights into the degree of success of the overall program (summative).
Too often, assessment has been limited to summative tests and to high-stakes assessments that assign grades, scores and rankings without the expectation, or often even the capacity, to use this information to make improvements and adjustments. Too often, what has been tested is not tightly aligned with what is taught, nor how it is taught, nor widely known prior to instruction. Too often, classroom instruction has failed to take advantage of the wealth of formative information that can, and must, be gathered during every lesson. Too often decisions have been made, sometimes with serious consequences, on the basis of unreliable information or without attention to available data.
Alternatively, an effective system of assessment gathers and uses data that informs decision-making about:
; supporting the growth of student learning;
; identifying students’ strengths and weaknesses;
; assessing and informing the improvement of the effectiveness of instructional
; assessing and informing the improvement of the effectiveness of the mathematics
standards and curriculum; and
; communicating with and involving parents.
Converting this vision into practice. We know that assessment for learning occurs
when teachers – individually and collaboratively – use classroom assessment and other
information sources about student achievement in order to advance student learning. This formative assessment is using the questioning, the guided practice, the ongoing cumulative review, the student journal entries and short quizzes to gather evidence about what mathematics is and isn’t being learned and how well it is understood. Thus, teachers must fully understand the purposes of the assessment process; they must be astute at planning, developing and adapting assessments, gathering assessment data, analyzing and interpreting the data, and using and communicating the results of this analysis. As a result of this process, teachers connect “how did we do?” to “how can we do better?”
More specifically, this vision is converted into practice when:
; the mathematics that is taught, the way it is taught and how it is assessed are
deliberately and coherently aligned;
; students’ answers, solutions, errors, questions, explanations, homework, quizzes
and tests are seen as components of the formative assessment data that are used
to make decisions about moving forward, reteaching, intervening, and addressing
individual and small group needs;
; formative assessment processes and summative assessments are collaboratively
designed, adopted and/or adapted to generate meaningful evidence of learning;
A Vision of Effective Student Assessment in Mathematics Page 2 of 4
; the results and the student work that emerge from these assessments are carefully
analyzed to make decisions about how and where curricular and instructional
shifts must be made.
According to the Assessment Training Institute (2004), this requires that teachers, leaders, and teacher teams:
; understand and articulate in advance of teaching the achievement targets for
; become assessment literate so they can transform those expectations into
assessment exercises and scoring procedures that accurately reflect student
; use classroom assessments to build student confidence in themselves as
learners, helping students take responsibility for their own learning so as to
lay a foundation for lifelong learning;
; translate classroom assessment results into frequent, descriptive (versus
judgmental) feedback for students, providing them with specific insights
regarding their strengths as well as how to improve;
; adjust instruction continuously based on the results of classroom assessments;
; involve students in actively communicating with their teachers and their
families about their achievement status and improvement; and
; make sure that students understand how the achievement targets they strive to
achieve now relate to those that will come after.
Finally, since this vision of effective assessment focuses on students and their learning, its implementation depends on:
; teacher participation in the district-wide development or adoption of common
assessments and scoring rubrics that are well aligned with instructional practices
and that represent common agreement on exactly what students need to know and
be able to do;
; the implementation of high-quality summative assessments and formative
assessment processes that optimize opportunities for all students to learn;
; the skilled use of questioning strategies that challenge all students to reveal their
reasoning, think more deeply, and support conclusions with data;
; the analysis of student work and student scores to identify ways to shift
instruction and broaden understanding; and
; the scope and quality of the professional development necessary to accomplish
It is a goal of the Microsoft Math Partnership to provide guidance, resources and professional development to support the widespread implementation of this vision in each of the Partnership’s classrooms, schools and districts.
A Vision of Effective Student Assessment in Mathematics Page 3 of 4
A Field Guide to Student Success in Mathematics and Science. American Institutes for
Chappuis, S., Stiggins, R., Artez, J. and Chappuis, J. Assessment for Learning. Portland,
OR: Assessment Training Institute, 2004.
Conzemius, A. and Jan O'Neill. Building Shared Responsibility for Student Learning.
Washington, DC: Association for Supervision and Curriculum Development, 2001.
Chrispeels,, J., J. Strait, and J.Brown. The Paradoxes of Collaboration: What Works.
Thrust for Educational Leadeship, 29(2), 16 - 19, 1999.
Stiggins, R., Arter, J., Chappuis, J. and Chappuis, S. Classroom Assessment for Student Learning: Doing It Right-Using It Well. Princeton, NJ: Educational Testing Service, 2006. Teddlie, C. and S. Stringfield. Schools Do Make a Difference: Lessons Learned from a 10-Year Study on School Effects. New York: Teachers College Press
A Vision of Effective Student Assessment in Mathematics Page 4 of 4