Michael T. Battista, Jae
Meen Baek, Kathleen Cramer, Maria Blanton
Based on extensive research conducted by the authors, Reasoning and Sense Making in the
Mathematics Classroom, Grades 3–5, is designed to help classroom teachers
understand, monitor, and guide the development of students’ reasoning and sense
making about core ideas in elementary school mathematics. It describes and
illustrates the nature of these skills using classroom vignettes and actual
student work in conjunction with instructional tasks and learning progressions
to show how reasoning and sense making develop and how instruction can support
students in that development.
Students who can make sense of mathematical ideas can apply
those ideas in problem solving, even in unfamiliar situations, and can use them
as a foundation for future learning. Without them, students are reduced to rote
learning, often experiencing frustration and failure.
But what do reasoning and sense making during learning and
teaching look like?
Each chapter of Reasoning
and Sense Making in the Mathematics Classroom, Grades 3–5 explores a
different topic that children encounter in mathematics, demonstrating with
actual student work and classroom dialogue how their mathematical knowledge and
reasoning ability move through “levels of sophistication” or learning
After opening with a discussion of the nature of
reasoning and sense making and their critical importance in developing
mathematical thinking, chapter 1 examines how students attempt to make sense of
the concept of length measurement.
Chapter 2 focuses on student strategies that
exemplify conceptually sound reasoning and sense making in the context of
multiplication word problems, and discusses how instruction can support
students’ growth in this reasoning. The critical topic of properties of numbers
that underlie reasoning about multiplication is also examined.
Chapter 3 describes how students in grades 3–5
extend their understanding of number to include fractions and how they can build
reasoning and sense making for fractions through explorations of different
representations such as physical materials, pictures, and story contexts.
Discussions on the nature of early algebraic
reasoning, including research-based descriptions of this reasoning in children,
classroom practices that can support this reasoning, and how algebra can be
appropriately integrated in elementary mathematical content are provided in
Chapter 5 discusses practices and processes
connected to reasoning about geometric decomposition and structuring as applied
to arrays of squares and cubes and to area and volume problems. A learning
progression for the development of such reasoning is examined, and
instructional practices that are consistent with this learning progression are
Not just a theoretical discussion,the book also provides specific suggestions for related
instructional activities for each topic. Reasoning
and Sense Making in the Mathematics Classroom, Grades 3–5 will be a
valuable and practical addition to your professional library.