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Monday / May 29

Assessing As You Teach!

Close to ten years ago, while serving as President of the National Council of Teachers of Mathematics (NCTM) I wrote a President’s Message that was entitled “Go Ahead, Teach to the Test!” I had very deliberately chosen the title of my message to “grab” readers, since, to this day, there is much confusion, misunderstanding and, frankly, angst at the school district and classroom level, relative to the role of assessment in teaching and learning. Consider the comment below:

“I actually never knew that my end-of-year and end-of-marking period benchmark tests in mathematics were summative assessments. Thinking about how I can use both formative and summative assessments has been an eye-opening experience to me, AND I’m in my fifth year of teaching!”
—Fourth grade teacher

For many, the word assessment is directly associated with major summative tests and not nearly as everyday-connected to the reason all teachers assess, which is to inform instruction. In our work (Fennell, Kobett, & Wray, 2017) with teachers of mathematics and mathematics specialists/leaders we have literally seen how deliberate everyday connections between planning, instruction, and assessment truly impacts and influences student learning and empowers teachers.

Formative assessment includes all activities that provide information to be used as feedback to modify teaching and learning, while summative assessments are typically used to evaluate student learning at the end of an experience. This could be a unit assessment, school district assessment, or the more high-stakes and high-profile end-of-year state assessments. Your assessment portfolio will include both formative and summative assessments, but the use of formative assessments will have greater everyday impact on your planning and instruction.

But let’s move away from the specifics of formative and summative assessment and consider how ongoing use of formative assessment can become summative. What? Consider the following examples of two classroom-based formative assessment techniques, “Observation” and “Show Me,” and how their use can grow to frame summative decisions about student progress.


You observe your students doing mathematics every day. But observation is often overlooked as a formative assessment technique—why is that? In our work we encourage teachers to think about, as they plan, what they might observe their students doing when engaged in the lesson. We routinely ask—what would you expect to observe students doing in this lesson? And, importantly, how would you know “it” if you saw “it”? The feedback you provide to students as they are engaged in doing mathematics, and observed, is also important. This could be oral feedback or actually recording student responses or comments about their work habits, attention to the mathematics tasks, solution strategies used, etc. What you observe is constantly updated based on the responses of your students, and monitors your teaching within a lesson and certainly impacts what you do the next day and beyond.

Show Me

An extension of what you might observe is a technique my colleagues and I refer to as a Show Me (Fennell, Kobett & Wray, 2017). A Show Me is a performance response by a student or group of students that extends and often deepens what you have observed. Its use is, to some extent, serendipitous and planned. All teachers are often caught off guard by or wonder about a student response and can ask a student to show what he or she did. Similarly, teachers can and should plan for particular elements within a lesson where a Show Me may be warranted.

These two classroom-based formative assessment techniques, observation and Show Me, help to monitor and guide your planning and teaching. They inform instruction. And, as you continue to use them, and you should, they inform you about each and every one of your students. What they can do. Where and when they are challenged. How successful they might be in using particular representations (e.g. base ten materials, the number line, etc.). In short, as your dedicated use of observations and Show Me responses accumulate your assessment of their progress becomes summative. You can speak with confidence at that parent teacher conference or meeting with your principal or grade level team about particular students because your evaluative comments are based on everyday use of these two classroom-based formative assessment techniques.

Yes, all formative assessments must be very directly connected to your everyday planning and teaching to monitor your progress instructionally, as well as the progress of your students. And the bonus, for you, is that their accumulation then becomes that living evaluative portfolio that validates summative comments about your students and their mathematical understandings.

Written by

McDaniel College Professor Emeritus Dr. Francis “Skip” Fennell, the inaugural recipient of the L. Stanley Bowlsbey Chair in Education and Graduate and Professional Studies, is an internationally renowned expert in mathematics education who developed the first graduate program for elementary mathematics teachers in Maryland.

Follow Skip on Twitter @SkipFennell or check out his website


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