Nicole Wessman-Enzinger

problem solvers: problem: Base-ten block challenge

Wessman-Enzinger., presents a group-worthy task an intellectually challenging task that encourages positive interdependence among group members through the defined roles and task construction. Wessman-Enzinger et al adds that, understanding place value in the base-ten number system is an essential component of mathematics instruction from first grade to fifth grade

Nuances of Prospective Teachers’ Interpretations of Integer Word Problems

This chapter identifies the ways in which 15 prospective teachers engage the strands of mathematical proficiency as they solve word problems involving integer addition and subtraction. The prospective teachers, through think-aloud interviews, demonstrated a strong focus on solving problems using procedures, which some did not explain and others explained in detail. Number line representations were popular ways to illustrate solution methods, especially to highlight distances to and from zero. Further, some problems elicited a variety of strategies, while others mainly elicited procedures. The collective think-aloud data reveal strong, interconnected strands that could help individuals reflect on procedural versus conceptual knowledge and how best to explain and make connections among the ideas involved in the problems.

Integer Play and Playing with Integers

This chapter describes instances of play within a teaching episode on integer addition and subtraction. Specifically, this chapter makes the theoretical distinction between integer play and playing with integers. Describing instances of integer play and playing with integers is important for facilitating this type of intellectual play in the future. The playful curiosities arising out of integer addition and subtraction tended to be concepts that we think of prerequisite knowledge (e.g., magnitude or order, sign of zero) or knowledge that is more nuanced for integer addition and subtraction (e.g., how negative and positive integers can “balance” each other). Instances of integer play and playing with integers are connected to the work of mathematicians, highlighting the importance of play in school mathematics.

Prospective Teachers’ Attention to Children’s Thinking About Integers, Temperature, and Distance

The study reported on in this chapter describes the justifications that elementary and middle school prospective teachers (PTs) made as they examined the temperature story that a Grade 5 student posed for an integer subtraction number sentence. The ways that the PTs made sense of the student’s story that used integer subtraction as distance are described, providing further insight into the ways that PTs may reason about temperature stories in relation to an integer subtraction number sentence. PTs’ justifications focused on attributes like order, rather than a magnitude discrepancy in the story. PTs need more experience examining stories for integer addition and subtraction in order to promote discussion and reflection on the various complexities of posing stories for integer addition and subtraction number sentences: consistency, realism, and subtraction as distance.

Conclusion: Reflecting on the Landscape: Concluding Remarks

The conclusion contains a response to the chapters and commentary in this book describing the thinking, models, and metaphors for integer addition and subtraction. This response includes three main sections: establishing landmarks, valuing emergent thinking, and critiquing integer instructional models. First, we further discuss the need to establish landmarks, or use clearly defined language (e.g., order, magnitude, strategies), in our work with integers. Second, we suggest that valuing emergent thinking within the research on thinking and learning of integer operations is important and entails less focus on correct strategies and places more value on the development of integer understanding. And, last, we critique the consistent rhetoric of “meaningful” for both contexts and instructional models by highlighting that what is meaningful to children may not be meaningful to teachers and researchers (and vice versa). We end the conclusion by posing questions for future research in the realm of thinking and learning within integer addition and subtraction.