How teachers can use questions while students play games to develop their mathematical reasoning. Games for primary as well as intermediate grades are provided, as well as questions one may ask of students who play them.

### Ok-Kyeong Kim and Lisa Kasmer

Mathematical reasoning is fundamental to the learning of mathematics. when reasoning is effectively and routinely promoted and fostered in the classroom through justifying solutions, developing ideas, predicting results, or making sense of observed phenomena, students can develop a deeper understanding of mathematical ideas.

### Eric A. Pandiscio

Construction tools in most high school Euclidean geometry classes have typically been limited to a compass for drawing circular arcs and a straightedge for drawing line segments. The strengths of these tools include both mathematical precision and a long history of use. However, alternatives can provide fresh possibilities for engaging students in the mathematical reasoning that lies at the heart of traditional geometry (Gibb 1982; Robertson 1986). This article proposes that a single task completed with a variety of construction tools fosters a greater sense of mathematical contemplation than multiple tasks done with the same tool. The premises are simple: each tool fosters different mathematical ideas, and using multiple tools not only requires understanding of a greater breadth and depth of geometric concepts but also highlights the connections that exist among different ideas.

### Jean M. McGivney-Burelle

How a group of third-grade students engaged in mathematical reasoning while solving mathematics problems involving networks. Examples of the project and classroom ideas for teachers are included in this article.

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (Principles and Standards for School Mathematics, p. 56).

Mathematical reasoning and sense making are critical aspects of learning and doing math. “People who reason and think analytically tend to note patterns, structure, or regularities in both real-world situations and symbolic objects; they ask if those patterns are accidental or if they occur for a reason; and they conjecture and prove. Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts” (*Principles and Standards for School Mathematics*, p. 56).