The Interactive Classroom
New Rochelle, NY 10804
Pic-Jour Math is a guidebook for both teachers and parents to assist them in developing in children a unique understanding of the essential numerical equations taught at the elementary and middle school levels. The approach is multi-modal, integrating a visual, numerical, and linguistic mode of explanation at each step of problem solving. This multi-modal form responds to the diverse ways in which a multi-cultural society integrates information; it also recognizes the importance of addressing the multiplicity of individual learning styles.
This book is divided into two sections. The first section, a narrative, gives historical perspective to learning differences, the importance of spatial and tactile experiences in promoting mathematical comprehension, and the significance of encouraging children to express themselves through language and drawing. The second section, journal writing evaluations, offers examples of how teachers may appropriately use the journal evaluation form. The final section, and the core of the book, is a series of sample lessons for grades three through eight. The subjects covered in this final section range from whole numbers through introductory algebra. Every lesson targets one level of understanding for each major topic and gives readers suggestions on how these topics may be dynamically presented to students.
Within each topic a word problem is presented and solved in three correlated modes, with one mode reaffirming the other. The steps are all clearly defined. Each lesson in the guide presents the standard explanations of required algorithms (numerical expressions). Of course, there are many ways to prove these algorithms, and many materials which may be used to help students visualize this math. Pic-Jour Math offers samples that are most cogent to me, but readers are urged to view these samples as flexible tools with which they can create their own proofs.
Pic-Jour Math strives to accomplish a number of goals. The first goal encourages teachers and parents to open their minds to a multi-modal approach in teaching math in grades three through eight. As teachers become comfortable with this method, they will be more able to help students visualize math rather than learn by rote.
The second goal, aligned with the first, encourages teachers to create a learning environment which urges children to express their understanding of math in a variety of modes. By stimulating students to draw, verbalize and write, instructors can help them bridge the gap between understanding math using manipulatives and applying that understanding to math alone. Teachers can use the students’ drawings, numbers, and journal writing in a variety of formats, including as a diagnostic tool to follow their thinking and to see where they may be confused. Students will feel more empowered because they will now be able to identify for themselves what they understand and where they may be having difficulty. The likelihood of students both owning the information and retaining it in long-term memory is far greater when they can actively participate and freely express themselves in the learning process.
A third goal suggests to both teachers and students that standard algorithms which have been taken at face value for too long, may be challenged and understood by children in grades three through eight. For example, it can be satisfying and fun to discover why the reciprocal function is used in the division of fractions or why pi equals approximately 3.14. As students learn to appreciate the search for answers, they may then be motivated to develop their own solutions to a variety of mathematical problems.