Dim 5: Formative Assessment

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Formative assessment involves orchestrating classroom activities that reveal the current state of student understanding during the learning process. Revealing the ways in which students are making sense of the content as they learn provides the teacher and the students opportunities to build upon the understandings that students have developed, and to address emerging misunderstandings. Formative assessment may involve quizzes or tests, but it involves much more. It often includes informal information gathering, e.g., posing questions that may bring out into the open incorrect assumptions or ideas that need to be challenged, or that help students realize that they need to dig more deeply into the content. The use of formative assessment contrasts strongly with the use of summative assessment – the formal end-of-unit or end-of-year tests that can reveal what students know and can do, but provide that information too late for it to be useful in helping students develop deeper understandings as they are learning.

In formative assessment, the information gathered about student reasoning and understanding gathered plays a major role in shaping the classroom activities that follow (Black et al., 2003; Shepard, 2000). This may seem challenging at first – who knows what students will say, given the chance? – but it is essential in order to meet students where they are. Once one starts providing students opportunities for students to engage openly in the discipline, it becomes an easily sustained habit. There are large literatures on student misconceptions, or “alternative conceptions,” that document the kinds of partial understandings students typically develop in specific content areas. Knowing about these typical patterns of student reasoning can help teachers to be prepared to deal with them. For more detail in mathematics, see the Formative Assessment Lessons described in the partners section of this document.

Through deliberately attending to student reasoning and understanding, and then shaping instruction in response, teaching “becomes clearer, more focused, and more effective” (National Research Council, 2001, p.350). In addition, hearing student reasoning provides the information that allows teachers to adjust the level of cognitive demand, so that students are positioned to engage in meaningful sense making. That is, Dimension 5 (formative assessment) provides the support structure for Dimension 2 (cognitive demand).

Black and Wiliam’s (1998 a,b) widely cited reviews document the substantial learning gains that result from teachers’ use of formative assessment. When assessment becomes an integral and ongoing part of the learning process, as opposed to an interruption of classroom activities, student thinking takes on a more central role in determining the direction and shape of classroom activities (Shepard, 2000; Shafer & Romberg, 1999; de Lange, 1999).

Of course, formative assessment is only useful if there is something interesting and important to assess – namely, meaningful disciplinary understandings and the ability to apply those understandings in powerful ways. Thus, Dimension 1 (the content) is implicated in establishing the disciplinary context for Dimension 5 (formative assessment).

In every discipline, multiple cycles of writing (pre-writes, outlines, drafts, revised drafts, etc.) provide students with opportunities to refine their ideas and to improve their writing. Sharing and critiquing ideas with other students places all students within a zone of productive thinking, as well as providing opportunities for the refinement and ownership of ideas. Thus, effective formative assessment (and the use of classroom structures to support student interactions) supports the right levels of cognitive demand for students (Dimension 2) and opens up opportunities for the development of student voice (Dimension 4). If supportive classroom norms are established, and the tasks have multiple entry points (which supports rich disciplinary conversations), then the major goal of equitable access (Dimension 3) is served as well.

It is important to note that the teacher is not necessarily responsible for addressing all of the issues that emerge when student thinking is solicited. When groups or the whole class work on rich tasks, students can serve as powerful resources for each other, in eliciting and building on each other’s thinking.

The Mathematics Assessment Project’s Formative Assessment Lessons, provide numerous examples of how this can be done, with tasks that invite student collaboration and critique.

See the tools sections for a deeper discussion and pointers to further resources.