Activating Intuitive Heuristics in Math

          I really enjoyed this chapter because it talks about heuristics.  It refers to the self-discovering on the part of the learner.  As I look back at my mathematics classes in elementary school I feel as if there was no intuitive heuristics that took place.  My teachers used the deductive teaching strategies in that they gave us the rules and we applied them in our work.  Although deductive teaching strategies have there advantages, such as multiplication facts (memorization), it did not always work for me when solving word problems.  So, I created a personal theory of my own to activate heuristics in my prospective mathematics classroom.

        If the teacher first introduces mathematical symbols such as, ‘-’ , ‘+’, and ‘=’ and asks the students to write what they think that these symbols mean in 5 different ways, then the teacher is not explicitly giving the rules.  Rather, the teacher is giving the students the opportunity to come up with their own meaning.  According to Carpenter, “With opportunity and encouragement, children construct themselves strategies that model the action or relationships in the problem” (Carpenter, 1999, p. 3).  Therefore, the teacher need not explicitly give the rules because with opportunity and encouragement children will able able to construct strategies by themseleves.  Students can create their own meaning to the symbols, then as a class, the students could share their responses to their peers and the teacher. 

After the symbols are introduced, word problems could come next with the use of manipulatives.  If the teacher gives every student a certain amount of blocks and writes a word problem on the board, the student can use the manipulatives to come up with the answer.  In the book,  Children’s Mathematics: Cognitively Guided Instruction, the author states that “Children do not have to be taught that a particular strategy goes with a particular type of problem” (Carpenter, 1999, p. 3).  An example of this is a student named Jose who came up with counting strategies all by himself.  The word problem read, “Eliz has 3 dollars to buy cookies.  How many more dollars does she need to have 8 dollars?”  Jose solved this problem by counting on his fingers.  Prior to this, Jose was never taught how to count, it just came naturally to him.  Therefore, Carpenter is correct; children do not have to be taught that particular strategy goes with a particular type of problem.

If the students are coming up with answers to various word problems, the easier it will be for the student to create  a number sentence.  As I said, if the teacher first introduces mathematical symbols and asks the students as to what they all mean, the student will have the ability to identify certain phrases or words in word problems that are equivalent to mathematical symbols.

Students do what comes naturally, and teachers work as facilitators to prompt students to explain how they come about getting the answer. With encouragement, children will feel self-confident in sharing ideas about what certain mathematical symbols mean.  After, students will do what comes naturally when solving word problems, and then finally, will be able to write number sentences by looking at words and phrases in the world problems.