Seamless Assessment/instruction = Good Teaching
Lambdin, Diana V., Forseth, Clare, Teaching Children Mathematics
[Assessment serves] to help teachers better understand what students know and make meaningful instructional decisions. (NCTM 1989, 189)
Assessment of students and analysis of instruction are fundamentally interconnected. Mathematics teachers should monitor students' learning on an ongoing basis in order to assess and adjust their teaching. (NCTM 1991, 63)
Effective teachers have known it for years, though the recent assessment movement sometimes trumpets it as news:
Good teaching and effective assessment are often hard to distinguish.
Teachers use assessment to make decisions throughout the instructional process - in planning for the year, in deciding how to organize individual lessons, and even in orchestrating classroom activities.
Instructional decisions include identifying appropriate content, sequencing and pacing lessons, modifying or extending activities for students' special needs, and choosing effective methodologies. Teachers cycle repeatedly through the decision-making process as they reflect on information gathered about what students know and can do - information collected not only from such written work as assignments, quizzes, and tests but also from observing, listening to, and questioning students. Clearly, the quality of teachers' decisions is determined by how accurately they can infer what their students need from the assessment data that they have collected.
The recently published Assessment Standards for School Mathematics (NCTM 1995) identifies six standards, or criteria, to be used for judging assessment practices: mathematics, learning, equity, openness, inferences, and coherence. Since assessment and instruction are so often intertwined in the classroom, applying these assessment standards to instruction makes perfect sense, too. Experienced teachers have internalized and frequently use such questions as the following to monitor their practice:
* How does the mathematics of this assessment/instruction fit within a framework of important mathematics? (Mathematics Standard)
* How does this assessment/instruction contribute to students' learning mathematics? (Learning Standard)
* What opportunities does each student have to engage in this assessment/instruction? (Equity Standard)
* How have students become familiar with the assessment/instruction and its purposes, expectations, and consequences? (Openness Standard)
* How are multiple sources of evidence being used for drawing the inferences that lead to assessment/instructional decisions? (Inferences Standard)
* How does this assessment/instruction match specific goals? (Coherence Standard)
Uses of assessment in instructional decision making permeate the entire teaching process. At the beginning of each unit, semester, or year, teachers make long-range decisions about the content, the methods, and the frequency and types of assessments they will use. Throughout the year, they make short-range decisions about the next investigation or unit. And every day in the classroom, they make moment-by-moment decisions that affect the immediate lesson.
Using Assessment in Long-Range Planning
The first tasks for a teacher considering assessment in long-range planning are to decide what mathematics is important for students to learn and how evidence can be collected about students' progress in learning it. The state's, school district's, or perhaps a textbook's curriculum framework often guides long-range planning.
A long-range plan also includes establishing such classroom routines as deciding when to use daily warm-up or calendar activities, problems of the week, journals, or portfolios. Such routines are chosen, in part, with an eye to their potential for rendering assessment evidence about students' progress. For example, a teacher who particularly wants to document students' communication and self-reflection might ask them to keep journals. …