Challenge Students to Describe and Analyze their Solution Methods
An important step in advancing children's thinking is to challenge them to describe and analyze their solution methods. The following paragraphs illustrate instructional strategies that Ms. Smith used to elicit children's solution methods
Elicit many solution methods for one problem. Rather than focus on a single answer to a mathematics problem, Ms. Smith attempted to foster discussion about how students solved a problem. She asked such questions as "Who did this problem another way?", "Did anyone do something else, that Allan did not do?" and "Can you use anything else besides your fingers and a number line to solve this problem?" By asking these types of questions, Ms. Smith encouraged children to share their ideas. Moreover, children in this classroom readily discovered that many approaches are available to solve problems.
Wait for, and listen to, students' descriptions of solution methods. A sense of calm and patience is needed to encourage children to express their ideas. Providing sufficient wait-time and listening to ideas lets children know that thoughtful explanations are more valuable than quick answers.
Encourage elaboration. Often, children need prompting to explain their thinking more completely. Even though Ms. Smith may have understood a child's response, she encouraged clarifications for the benefit of the entire class. On occasion, she assisted students in articulating their methods.
Use students' explanations for the lesson's content. Students' articulated ideas can furnish the content of class discussions.
Remind students of conceptually similar problem situations. To "jump-start" their thinking, children may need to be reminded that one problem is like another one that they have solved previously.
Review background knowledge. Reviewing necessary background knowledge with students is another effective support strategy. For example, Ms. Smith reviewed coin values for a student who was having trouble counting money.
Lead students through instant replays. Teachers can support the understanding of all children in the class by revisiting one child's elicited solution method in a slow and step-by-step fashion. This strategy is very different from that of a teacher who offers his or her own solution method as the only sanctioned method.
Write symbolic representations of each solution method on the board. Writing the symbols for the children's solution methods on the board helps children link the verbal descriptions of their thinking with the written mathematical marks. Ms. Smith noted another benefit of this strategy: "Recording on the board assists students in following the procedure. Some students must see the numbers. Constant review of this helps them write the digits."
Encourage students to request assistance. Ms. Smith expected children to request additional help when necessary. She attached no stigma to the requirement for extra help; on the contrary, students who requested assistance received extra time and attention from the teacher. This acceptance and expectation is an important aspect of a teacher's support of students' learning
Fraivilig,
J. (2001). Strategies for advancing Children's Mathematical Thinking.
Teaching
Children Mathematics. 7(8), 454.