Uncovering Student Thinking in Mathematics Grades 6–12: 30 Formative Assessment Probes for the Secondary Classroom

This 225 page book is a nice compilation of a variety of ideas. While the title indicates this book is for the purposes of assessment, in that it has assessment probes included, it goes much deeper than the title indicates. To begin with, there is a discussion of types of student misunderstanding and how this gives rise to the need for different types of assessment. This is backed by research and supported by NCTM standards.

There is also discussion of the instructional implications of assessment, as well as the distinction between assessment and evaluation. While we often use these words interchangeably, the authors make it very clear that their probes are not for the purpose of evaluation, ie: grades. Their probes are to unearth student thinking and understanding in a way that will help the teacher make better teaching decisions as they move forward with their class. Slightly over 10% of the book is dedicated to the types of issues described above.

Following the research based discussion above, there are three distinctly different components of the book, all of which are related to the probes alluded to in the book’s title. The three different sections of the book are

1. Number and Operations
2. Geometry, Measurement, and Data
3. Algebra

Within these sections, 30 different probes are presented. These probes are designed to assess student thinking in different areas. Each probe is followed by teacher’s notes regarding the reasoning behind the probe.

Most probes also have variations given to alter the way the probe could be deployed. For example, one may look like a matching exercise, while a secondary option is more of a game format. In addition to the probes, sample responses from students are given, as well as responses from teachers who have used the probe. This would give then reader a chance to see what they might expect as they try the probe for the first time.

I see two distinctly different ways this book could be used. In one frame of mind I can see how a teacher could use this when teaching topics for the first time, trying to get the correct understandings across to her students and assessing her ability to do so. This would enable a teacher to see where she may need to spend more time or address misconceptions.

However, from a personal perspective, working with older students (late high school and early college) I think this would be a great tool to start discussion. I can see it used as an ice breaker or a prior-knowledge kind of assessment. This would allow a teacher to see the misconceptions she may need to address before she can start a related, but more advanced topic.

In my teaching of pre-service teachers, using this book would allow me to address two kinds of issues. First, misconceptions the pre-service teachers themselves may have, and second, the misconceptions their students may have once they start teaching. I am very excited to see this resource and plan to start using it next semester as I work with pre-service teachers at my university.

Krista B. Hands is an Assistant Professor of Mathematics at Ashland University, Ashland, Ohio. Her research is in mathematics pedagogy with a focus in undergraduate mathematics. She teaches mathematics content courses to pre-service teachers as well as other mathematics courses. She resides in Medina, Ohio with her husband, daughter, and son.