NADE 33 nd Annual Conference February 25– 28, 2009 Greensboro, North Carolina NADE 33 nd Annual Conference February 25– 28, 2009 Greensboro, North Carolina Elena Litvinova, Bloomsburg University

 One-Unknown C-BIRD Method History  One-Unknown C-BIRD Method Effectiveness  Introduction of C-BIRD Method  One-Unknown C-BIRD Method Benefits  One-Unknown C-BIRD Method History  One-Unknown C-BIRD Method Effectiveness  Introduction of C-BIRD Method  One-Unknown C-BIRD Method Benefits

The method was born at Penn State Hazleton as part of the solution to the problem of remediation of elementary education major students in the area of problem solving.

Problem solving is one of the most important parts of early childhood development. Word problems convey mathematical meaning by using suitable concrete objects to represent abstract mathematical notions. They are allegories or mental manipulative, which paves a child’s way to abstractions. Let us remember that formal and abstract thinking, which is essential for success in the modern civilized technological society, does not come as a straightforward result of physiological maturation or social adjustment. The scientific experiments and observations showed that subjects who lived in remote villages and have not been influenced by school instruction were incapable of solving even the simplest word problems.

He proposed the Complete Box of Independent Raw Data (C-BIRD) method that he believes has the potential to provide education majors with the needed confidence in their ability to teach problem solving. Dr. Litvinov suggested that many Americans lack problem solving skills because their teachers were ineffective in explaining these crucial abilities.

The C-BIRD method is proven effective by analyzing the success rate of students in the PSMEM course offered at the Penn State - Hazleton campus. Originally, the majority of students who enroll in the course have deficient skills in problem solving and take it because the course is a requirement.

After completing the PSMEM course, and learning how to solve word problems through the use of C-BIRD, 80% of the students report feeling more confident in their ability to solve word problems. In the words of one PSMEM student, “The way [the course] is taught now allowed me to become good at problem solving, and I never thought I would be able to do that.” (The citation is taken from an anonymous essay)

Before I introduce the C-BIRD method for solving word problems I feel an obligation to explain why I think it might be extremely beneficial for all students. The traditional model of the problem –solving process, described by Mayer (1982), consists of a translation stage and solution stage. Students have more difficulty in the translation stage. Nevertheless, in the classroom more emphasis is given to the solution stage. The C-BIRD method is focused on the translation stage called problem modeling.

Traditionally, a student is required to break the problem into parts and hold a lot of information in the working memory. The C-BIRD method provides a tool for organizing and storing this data. As a result, the modeling part becomes more transparent.

Traditionally, word problems are divided into families, categories, and templates. Within this approach, teachers present concepts, procedures, routines and definitions piece by piece. A limitation of this model is that the problem has to fit one of those artificially developed structure types. The students would have to learn those structures, select the appropriate one and be able to take the information and place it in the matching structure. Unfortunately, standard methods can become mechanical and mysterious to the anxious students. They can also suggest that there is only one way to arrive to the solution and if one cannot recall it, the situation becomes hopeless.

In using this approach, teachers tend to forget that the delivery of knowledge is not the sole objective in teaching! It is more important to emphasize the development of a type of thinking that promotes solving problems than just giving the students a lot of tricks. The C-BIRD method stresses the use of common sense and encourages student suggestions by allowing multiple approaches during the modeling stage. It was proven by practice that in the course of one semester students developed confidence in their own ability in problem solving, and built an intuition for finding the most optimal solution.

Now I am ready to present a tool that helps to develop the student’s Intuitive Knowledge Base by allowing more flexibility and encouraging a heavy use of common sense.

Visual interpretation of data presented in the Complete Box of Independent Raw Data makes it easier to analyze data connections and make decisions about the variable choices.

Comparison of a number of unknowns to a number of equations in the Complete Box of Independent Raw Data helps to check if all the data in the problem was accounted for and if there is enough information to solve the problem.

Identification of the Master Equation and elimination of the modeling part helps to avoid common problems of the tautological equation.

Consistent use of the Complete Box of Independent Raw Data helps to develop an intuition for recognizing the best choice of the variable and simplest possible solution.

Thank you for being here today!