CM . . .
. Volume XX Number 36. . . .May 16, 2014
The ANIE: A Math Assessment Tool that Reveals Learning and Informs Teaching.
Kevin Bird & Kirk Savage.
Markham, ON: Pembroke, 2014.
95 pp., trade pbk. & pdf, $24.95 (pbk.).
ISBN 978-1-55138-296-8 (pbk.), ISBN 978-1-55138-861-8 (pdf).
Mathematics-Study and teaching (Elementary).
Review by Martha Koch.
The ANIE is a one-page assessment of students’ understanding of a single learning outcome or standard. The ANIE is designed for students from Grades 1 to 12 and takes about 10 minutes to administer. Grading is relatively quick and most importantly, teachers can use the results to plan timely and targeted intervention. The ANIE is unique because it is complex enough to assess conceptual and procedural understandings that align with performance standards and yet simple enough to use as a learning tool every day. (p. 9)
The Assessment of Numeracy in Education (ANIE) was developed by two school administrators in British Columbia for use in Grades 1 to 12 mathematics classrooms. The book is written to encourage teachers and school administrators to use the ANIE in their mathematics program. It includes seven chapters that describe the ANIE and the ANIE Junior, a version for use with primary students or students with special needs. The first three chapters outline the features of the tool and suggest ways to introduce the assessment to students. Chapter 4 explains how the assessment is graded while chapter 5 provides annotated examples of the tool. More specifically, responses from five Grade 4 students who completed the ANIE for “37 ÷ 4 = n” and responses from four Grade 2 students who completed the ANIE Junior for “12 – 5 = _____” are shown. In chapter 6, the authors provide a vignette describing the use of the assessment by a Grade 4 teacher. The final chapter contains two brief case studies suggesting the positive impact the ANIE may have on students’ mathematics achievement. Templates for the ANIE and ANIE Junior are provided along with a glossary and responses to “frequently asked questions”.
Before explaining my reasons for not recommending this book, I will describe the one-page templates that form the core of this assessment. The top of each template provides a space for classroom teachers to insert a mathematics question which must be expressed in standard notation (i.e. 37 ÷ 4 = n) rather than as a word problem. Students are required to complete a sequence of steps (estimate, calculate, represent, explain, apply to real life, and reflect) to solve the question and demonstrate their understanding. The same sequence of steps is followed on each ANIE or ANIE Junior, regardless of the math content area being assessed. As indicated in the excerpt, the assessment can be administered in as little as 10 minutes. The template includes small boxes where students record their responses to each step. Students are encouraged to complete the steps in order. For instance, they are expected to calculate their answer and then create a visual representation. These representations are an additional means of communicating the answer rather than a mathematical thinking tool that students might use to find an answer. The bottom of the template contains a four-category, four-level scoring rubric. As with the sequence of steps, the scoring rubric does not change for different mathematics content areas or grade levels. Thus, the ANIE and ANIE Junior are assessment templates intended for use across grade levels and math content areas.
The authors of the ANIE demonstrate an appreciation for the central role of assessment in guiding a math teacher’s next instructional steps. Indeed, the powerful impact that ongoing classroom assessment can have on students’ mathematics learning is well established and extensively documented. Regrettably, the authors do not draw on this literature either as a theoretical framework for the development of the ANIE or to strengthen their rationale for various features of the tool. For instance, the ANIE highlights the value of having students connect their mathematics understanding to “real life”, of asking students to create math stories and of encouraging them to reflect on their learning process. However, the authors have not situated these praiseworthy features of the ANIE within the current research literature. Instead, they refer to a few relatively obscure and, in some cases, outdated sources.
A more serious concern is that the authors make several claims about the ANIE that are not adequately substantiated in the book. For instance, they state that repeated use of the ANIE “works to create efficient and strong neural connections between the brain cells used to complete the different steps of the ANIE” (p. 13). While such a claim may lend an air of scientific rigor to the assessment, supporting it would require extensive empirical research. The authors also state that the ANIE has been used with hundreds of students in many classrooms and that it “has a positive impact on students’ learning” (p. 61). Unfortunately, details about these classrooms are not provided, and no reports or publications documenting the development or use of the ANIE are cited. Moreover, the authors claim that the tool can lead to increased scores on provincial assessments, but the brief case studies in chapter 7 do not provide adequate contextual or statistical evidence for this claim. The book is clearly intended as a professional resource rather than an academic publication. Nonetheless, the authors have not provided the empirical evidence mathematics teachers and school administrators would need to evaluate the quality of this tool and decide whether to use it in their program.
Another problematic aspect of the ANIE is the suggestion that it be used on a daily basis rather than as one of a variety of classroom assessment tools. Evidence that the authors advocate frequent use of the tool is found in the vignette of Mr. W whose “students complete the equivalent of four ANIEs on most days” (p. 60) and in the claim that “students who regularly use the ANIE framework begin to view a math question though the framework . . . an ANIE-trained brain automatically cues all the steps of the template” (p. 13). In sharp contrast, numerous peer-reviewed research articles, assessment publications of the National Council of Teachers of Mathematics (NCTM) and provincial and state curricula explicitly emphasize the need to use a variety of assessment tools that enable diverse learners to communicate their understanding and can assess the full range of mathematics knowledge and skills. Use of the ANIE as the principal assessment approach in a classroom is particularly worrisome because of the tool’s emphasis on arithmetic. While completing an occasional ANIE as a learning activity may help develop students’ computation skills, it is not well suited for assessing many other important mathematics concepts and processes. In fact, even within the domain of arithmetic, many mathematics educators maintain that approaching every question using one routinized approach results in less flexible problem solving and more restricted mathematical thinking.
Along a somewhat different dimension, an additional concern I have with this book is the unnecessarily mechanistic vision of mathematics teaching and learning that it presents. Drawing on a discourse of teaching as a series of interventions, the authors characterize assessment as a tool for revealing gaps and identifying shortcomings. They state, the ANIE “allows teachers to identify serious deficiencies that were not evident using other assessment methods” (p. 16). Their perspective centres on finding and remedying student weaknesses rather than situating assessment as a natural part of the dynamic process of mathematics learning. Classroom assessments, well-conceived and carefully used, are an integral part of the ongoing process of mathematics learning where students engage in a variety of experiences, communicate their understanding and receive meaningful feedback that helps them deepen that understanding. In my view, the ANIE has a limited capacity to achieve such goals.
Martha Koch is a teacher educator and researcher in the areas of mathematics education and classroom assessment at the Faculty of Education, University of Manitoba in Winnipeg, MB.
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