In 2001 the Mathematical Association of America (MAA) began a three-year project named *Supporting Assessment in Undergraduate Mathematics* (SAUM). The MAA has, in this book, published an accounting of the now-completed project. The book’s content consists of papers by scholars who participated in the project. The papers are, roughly, of two types, thematic essays and case studies.

In a thematic essay, Madison reports on the goals and activities of SAUM and on resistence within professional mathematics to “effective assessment” (as Madison calls it). The goal of SAUM was “to encourage and support faculty in designing and implementing effective programs of assessment of student learning in some curricular block of undergraduate mathematics” (p. 3). Its activities included “[promoting] assessment to hundreds of faculty in professional forums and [working] directly with 68 teams of one to five faculty from 66 colleges or universities in SAUM workshops” (p. 3). The resistance to effective assessment, Madison writes, comes in two varieties, “tensions” and “tethers”. Resistence involving “tensions” takes the form of opting for easier but less effective models, including anecdotal assessment. Resistence involving “tethers” takes the form of staying with current practices regarding program evaluations, faculty reward systems, lecture-style teaching, and curriculum.

Steen, in another thematic essay, levels a critique of current assessment practices in undergraduate mathematics. Problem solving, she observes, plays an inordinately large role in assessment: “[F]or virtually everyone associated with mathematics education, assessing mathematics means asking students to solve problems” (p. 14). This practice ranges from high-profile competitions like the Putnam competition to routine examinations. (Steen does not address the significance for a mathematics student of doing problem sets. For myself, doing problem sets stood at the centre of my university mathematics education.) Additionally, Steen questions the reliability and validity of current assessment practices:

[U]ndergraduate mathematics assessment is rather like the Wild West — a libertarian free-for-all with few rules and no established standards of accountability. In most institutions, faculty just make up the test based on a mixture of experience and hunch, administer them without any of the careful reviewing that is required for the development of commercial tests, and grade them by simply adding and subtracting arbitrarily assigned points. (p. 16)

Moreover, “collegiate mathematics… assessment is still a minority culture beset by ignorance, prejudice, and the power of a dominant discipline backed by centuries of practice” (p. 18).

A route towards engendering a culture of assessment, Steen feels, involves engaging mathematicians in dialogue about assessment issues by, in particular, asking the right questions, of which she suggests a number. (“Is assessment being used for improvement or for judgement?” is one such question, p. 18.)

In another thematic essay, Ewell, too, is concerned about engendering a culture of assessment within mathematics undergraduate education. He notes, in his generally positive evaluation of the project, that the project helped established a degree of “colleagueship” with respect to assessment, while also noting that there is a long way to go in this respect.

The heart of the book consists of more than twenty assessment case studies conducted under the umbrella of SAUM. These are grouped under the headings “Developmental, Quantitative, and Precalculus Programs”, “Mathematics-Intensive Programs”, “Mathematics Programs to Prepare Future Teachers”, and “Undergraduate Major in Mathematics”.

The book would seem to be invaluable as an introduction to an emerging field of systematic assessment in undergraduate mathematics education. This book is available as a free download here. The MAA also offers a companion volume, **Assessment Practices in Undergraduate Mathematics**, as a free download.

**References:** (Each of the papers below is in the book under review.)

- Ewell, P. “Assessing Assessment: The SAUM Evaluator’s Perspective.”
- Madison, B.L. “Tensions and tethers: assessing learning in undergraduate mathematics.”
- Steen, L. A. “Asking the right questions”.

Dennis Lomas (dlomas@upei.ca) has studied computer science (MSc), mathematics (half dozen, or so, graduate courses), and philosophy (PhD). He resides in Prince Edward Island (Canada).