formative assessment – UBC Education Library Booklists

Listed below are selected resources related to teaching mathematics.

Challenging mathematical tasks: Unlocking the potential of all students

by Peter Sullivan

Sullivan’s research shows that many students do not fear challenges in mathematics, but welcome them, and rather than having teachers instruct them, prefer to work out solutions for themselves. This book includes activities that allow for sustained thinking, decision-making and risk-taking by the students, and features a ‘Learning Focus’, ‘Key Mathematical Language’, ‘Pedagogical Considerations’, and ‘Enabling and Extending Prompts’ for each task.

Teaching student-centered mathematics: Developmentally appropriate instruction for grades pre-K – 2

by John A. Van de Walle, LouAnn H. Lovin, Karen S. Karp, and Jennifer M. Bay-Williams

Grades: K-2

Part of the Student-Centered Mathematics Series, this book is designed to illustrate what it means to teach student-centered, problem-based mathematics, to serve as a reference for the mathematics content and research-based instructional strategies suggested for the specific grade levels, and to present a large collection of high quality tasks and activities that can engage students in the mathematics that is important for them to learn.

Teaching student-centered mathematics: Developmentally appropriate instruction for grades 3-5

by John A. Van de Walle, Karen S. Karp, LouAnn H. Lovin, and Jennifer M. Bay-Williams.

Grades: 3-5

The math teacher’s toolbox: Hundreds of practical ideas to support your students

by Bobson Wong & Larisa Bukalov

Grades: K-12

The Math Teacher’s Toolbox contains hundreds of student-friendly classroom lessons and teaching strategies….Topics range from the planning of units, lessons, tests, and homework to conducting formative assessments, differentiating instruction, motivating students, dealing with “math anxiety,” and culturally responsive teaching.

Every math learner: A doable approach to teaching with learning differences in mind, grades K-5

by Nanci N. Smith

Grades: K-5

Smith debunks the myths around what math differentiation is and is not, and offers a practical approach to teaching mathematics for real learning differences.

Good questions: Great ways to differentiate mathematics instruction in the standards-based classroom

by Marian Small

Grades: K-8

This resource helps experienced and novice teachers to effectively and efficiently differentiate mathematics instruction in grades K-8 using two strategies: Open Questions and Parallel Tasks.

Visible learning for mathematics, grades K-12: What works best to optimize student learning

by John Hattie, Douglas Fisher, and Nancy Frey

Grades: K-12

The authors discuss three important phases of learning mathematics: the surface learning phase, where students explore new concepts and make connections to procedural skills; the deep learning phase, where students make connections among conceptual ideas and form generalizations; and the transfer phase, when they can independently approach more complex concepts and situations.

Using formative assessment to drive mathematics instruction in grades preK-2

by Christine Oberdorf and Jennifer Taylor-Cox

Grades: K-2

The authors illustrate the distinction between a “traditional” assessment and an “enhanced” assessment; describe specific differentiated activities; provide “Questions to Assess” to determine what each child understands about the math concept; show how to move students to higher-level mathematics thinking and to apply math concepts; and share extension activities to offer challenging work for children who have achieved skill mastery level.

Using formative assessment to drive mathematics instruction in grades 3-5

by Christine Oberdorf and Jennifer Taylor-Cox

Grades: 3-5

Yes, but why? Teaching for understanding in mathematics

by Ed Southall

Grades: K-12

Getting the right answers in math is only half the problem; understanding why the processes work is the part that often stumps students and teachers alike. This book answers a range of questions about why mathematics works, and sheds light on the hidden connections between everything in mathematics at school.

Math for real life: Teaching practical uses for algebra, geometry and trigonometry

by Jim Libby

Grades: 7-12

This book presents hundreds of practical applications for mathematics—from baseball statistics to the theory of relativity—that can be understood by anyone with a knowledge of high school algebra, geometry and trigonometry. It will help teachers to answer the inevitable question “When are we ever going to use this?”

We reason & we prove for ALL mathematics: Building students’ critical thinking, grades 6-12

by Fran Arbaugh et al.

Grades: 6-12

This book spans all mathematical content areas to provide teachers with strategies to help build students’ reasoning and proving skills. Activities include solving and discussing high-level mathematical tasks; analyzing narrative cases that make the relationship between teaching and learning salient; examining and interpreting student work; and modifying curriculum materials and evaluating learning environments to better support students.

Math wise! Over 100 hands-on activities that promote real math understanding, grades K-8

by Jim Overholt and Laurie Kincheloe

Grades: K-8

This activity book is a resource teachers can use to give students a firm grounding to work with more advanced math concepts. Contains over 100 activities that address topics like number sense, geometry, computation, problem-solving, and logical thinking. Activities are presented in order of difficulty and address different learning styles

Finding More Resources

To find more resources in this area, try the following:

Search using the General tab on the UBC Library website to look for material in all UBC Library branches.
Search using “Search Education Resources” box in the left hand bar on the Education Library website to limit your results to physical materials in the Education Library.
Use specific search terms, such as “mathematics – study and teaching” or “mathematical ability – testing”.
To find lesson plans, include “lesson plans”, “lesson planning”, or “activity programs” in your search terms.

For more help with searching, please visit the Library Service Desk or e-mail ed.lib@ubc.ca.

Listed below are selected resources for teachers related to formative assessment.

An introduction to student-involved assessment for learning

by Jan Chappuis and Richard J. Stiggins

Grades: K-12

This book is intended to help teachers establish clear learning targets as the basis for instruction and assessment, select assessment methods that align with those targets, select and/or create high-quality assessments that accurately measure student progress to the learning targets, clearly communicate assessment results to learners for both formative and summative purposes, and involve students in the assessment process to develop their capabilities to be self-directed learners.

Embedded formative assessment

by Dylan Wiliam

Grades: K-12

The author introduces five strategies are introduced building formative assessment into the classroom: clarifying, sharing and understanding learning intentions and success criteria; engineering discussions and activities that elicit evidence of learning; providing feedback that moves learners forward; activating students as learning resources for each other; and activating students as owners of their own learning.

Embedding formative assessment: Practical techniques for F-12 classrooms,

by Dylan Wiliam and Siobhan Leahy

Grades: K-12

Building on the five strategies for formative assessment described in Embedded formative assessment, the authors provide an overview of each strategy and a number of practical formative assessment techniques for implementing the strategies in the classroom. Along with guidance on when and how to use the specific techniques, they provide tips, cautions and enhancements to sustain formative assessment. A student reflection form, peer observation form and self-reflection checklist accompany each strategy.

The formative assessment action plan: Practical steps to more successful teaching and learning

by Nancy Frey and Douglas Fisher

Grades: K-12

The book describes a four-step approach to implementing formative assessment in the classroom: ensuring that students understand the purpose of an assignment, task, or lesson, including how they will be assessed; checking for understanding to guide instruction and determine if students are making progress toward their goals; providing feedback to students; and building on that feedback to facilitate student achievement.

Checking for understanding: Formative assessment techniques for your classroom

by Douglas Fisher and Nancy Frey

Grades: K-12

The authors present five formative assessment techniques that can be used to check for understanding: oral language strategies that close the gap between what students need to know and what they already know; using writing to check for understanding in any subject; student response techniques that increase participation and engagement; projects and performances that are easily integrated into daily classroom practice; and test items that help plan further instruction.

20 formative assessment strategies that work: A guide across content and grade levels

by Kate Wolfe Maxlow and Karen L. Sanzo

Grades: K-12

The authors present a range of formative assessment strategies and ways to implement them, using activities involving collaboration, movement, and/or selecting and supplying responses. (E-book)

Mastering formative assessment moves: 7 high-leverage practices to advance student learning

by Brent Duckor and Carrie Holmberg

Grades: K-12

The authors present seven strategies that can be used as part of formative assessment: priming (building on background knowledge), posing (asking questions), pausing (waiting after questions), probing (deepening discussions), bouncing (sampling student responses), tagging (recording student responses), and binning (interpreting student responses). (E-book)

Leading the way to assessment for learning: A practical guide

by Anne Davies, Sandra Herbst, and Beth Parrott Reynolds

Grades: K-12

This book presents a number of strategies for formative assessment, including describing success, beginning with the end in mind, involving students in instruction, and using assessment to guide instruction.

100 ideas for secondary teachers: Assessment for learning

by David Spendlove

Grades: 9-12

The author suggests that assessment for learning (AfL) can help to increase student autonomy and ensure progress is taking place for every student. Key topics covered are questioning and dialogue, written and verbal feedback, and improving behaviour using AfL strategies and explaining its importance to parents.

Formative classroom assessment: Theory into practice

edited by James H. McMillan

Grades: K-12

The essays in this book present a state-of-the-art review of formative assessment in the classroom. Experts examine what is currently known about formative assessment and its application to teaching, balancing theory and research with practical applications.

Student assessment: Fast, frequent, and formative

by Debra J. Dirksen

Grades: K-12

Just as video games often have a ‘reset button’, this book suggests that formative assessment can be used in the classroom as a virtual ‘reset button’ for student learning. A range of formative assessment strategies and techniques are discussed, such as the use of graphic organizers, quick writes, and journaling.

Finding More Resources

To find more resources in this area, try the following:

Search using the General tab on the UBC Library website to look for material in all UBC Library branches.
Search using “Search Education Resources” box in the left-hand bar on the Education Library website to limit your results to physical materials in the Education Library.
Use specific search terms, such as “formative assessment”, “formative assessment techniques”, or “educational tests and measurements”.
To find lesson plans, include “lesson plans”, “lesson planning”, or “activity programs” in your search terms.

PDF Booklist

For more help with searching, please visit the Library Service Desk or e-mail ed.lib@ubc.ca.