Assessment in Mathematics Classrooms

I’ve been doing some thinking, and writing, lately on the roles of assessment in mathematics classrooms. For many of us, assessment is a means to assign grades to students; we see assessment as following the learning. Certainly, we need to use assessments for grading purposes. However, learning can not be separated from assessment … learning without assessment is simply wandering in a city hoping to find that nice hotel or restaurant; little good is likely to result, and some damage is likely.

For general reading on assessments for learning mathematics, try one of these sources:

CUPM Guidelines for Assessment of Student Learning (at http://www.maa.org/saum/maanotes49/279.html)
Assessment and the Process of Learning Statistics (at http://www.amstat.org/publications/jse/v5n1/hubbard.html)
The Assessment Principle (NCTM) at https://www.usi.edu/science/math/sallyk/Standards/document/chapter2/assess.htm
IMAGINE: Mathematics Assessment For Learning (at http://www.gatesfoundation.org/edextranet/Pages/ImagineConvening2009.aspx)

The ideal assessment in my view would be a series of interviews with each student, where their work and comments are prompts for questions and discussion; an expert talking to the learner can identify problems and reinforce partially correct understanding, which are difficult goals for mass assessments. I have not managed to design a class to achieve this, although I have managed to create tools that enable some interviewing to support learning.

I’ll describe some of the assessment tools I am currently using to support student learning (and student motivation):

QUICK QUIZ
This is a traditional quiz, though very short (4 questions), with half of the items being concept or ‘no work’ items. The quiz is given at the start of a class, covering the learning that ‘should’ have occured prior to class (prior to any homework questions). Ten minutes is plenty of time, and then we review the quiz — by students explaining each item, and I reinforce & correct as needed. Since the Quick Quiz uses ideas and simpler problems, the process encourages students to attempt the learning; in class, we often say the “quiz is part of the learning process” to support good learning attitudes.

NO-TALK QUIZ
As a variation, a No-Talk Quiz involves students working 2 or 3 problems focusing on key processes or ideas. Their quiz is then reviewed by two other students, who can only write comments on the quiz. The student then has an opportunity to re-do any problem where they think the feedback suggests that they were wrong. As an assessment, this process involves every student doing two necessary steps: Critically reviewing work for accuracy and completeness, and explaining. In addition, each student has to judge their own understanding compared to the feedback they get; provides a little ‘meta-cognition’.

TEST DRIVES
During class, we develop ideas and reasoning as well as master procedures. After the large group discussion (5 to 10 minutes), I have every student try a Test Drive … their chance to try out what we have been learning. During a Test Drive, I talk to individual students about their work; this mini-interview does not involve every student for every Test Drive, but involves most students on any given class day. We review the Test Drive as a class, based on students explaining what we should do.

FOCUSED WORKSHEETS
My classes know these simply as ‘worksheets’ — they include material from all sections since the last test, and normally involve 5 or 6 items. My goal during worksheet time (20 to 35 minutes at the end of class), is to talk to every student at least once about their learning. Over a semester, I will ‘mini-interview’ every student enough to understand some of their learning needs ; this helps to inform my teaching decisions. As part of the worksheet process, students have an opportunity to work in groups; for my own purposes, I do not structure this nor require group work … though it is strongly encouraged.

Among the assessments I no longer use regularly, ‘writing’ is the primary category. I’ve tried different methods, such as explaining steps or sentence completion. I am sure that other people have developed a pattern with these so that they support learning; my own attempts seem to either frustrate students without benefit or actually reinforce learning wrong ideas.

For the curious, every class involves multiple “Test Drives”. Each class day involves either a quiz or worksheet; I have tried doing both a quiz and a worksheet in the same two-hour class, but the price is a considerable amount of stress for students. Overall, I try to do about 40 minutes of assessment activity in every 110-minute class period — not counting ‘test days’. I don’t label this time as ‘assessment’ for students, because they, too, view assessment as ‘grades’. Instead, I talk about improving our learning (which is exactly the goal of assessment).

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