## The Four Strands

Strand 1: The Drills Component
Drill, drill, drill is an ineffective and outdated way of doing mathematics. The Spirit of Math approach combines cooperative learning drills with an in-depth mathematics problem-solving program that has proved popular and effective with students. The drills component encourages cooperation among the students, helps build self-confidence and develops the students’ accuracy in mental calculation. Improvement and group cooperation in reaching the required class average are emphasized as part of the system.
In grades 5 and 6 students are given 10 minutes to complete the grid. They each keep a graph of their progress, and a large graph showing progress of the class average is displayed in the classroom. When the class average reaches 70 out of 80, the students move on to the next drill: a short division drill. A similar process is used with all students in grades 1 through 6. The drills for the younger students also include addition.

Strand 2: Problem Solving
In every grade in Spirit of Math there are hundreds of problems that students must answer. The problems are presented to students as the Problem of the Day (POW) for the younger students, and progress to larger assignments. These assignments provide for research and experimentation with numbers, but are largely aimed at developing both problem solving and relationship skills. In various ways, students are encouraged to share their insights and understandings without just giving away answers.

Strand 3: Core Program
The core program was developed with the intent to give students the opportunity to delve deeper into concepts and to expose students to ideas that they don’t normally meet in the day-schools. It is also skill-based, developing the skill sets that need students for their future work in mathematics.
Spirit of Math initially focuses on number theory for the younger grades, beginning with the “Relocation Property” from grade 1 through 5, which involves students moving numbers for ease of calculation in questions which involve addition and subtraction (grade 1 and up), or multiplication and division (grade 3 and up).
Prime numbers are introduced in grade 2 and thoroughly explored in grade 5 to help promote mental calculation abilities in multiplication and division.
“Signed Numbers” is first taught in grade 1 so that all the basic work with positives and negatives is put into place. As a consequence, we find that students at an early age develop a much broader understanding of numbers. This skill, combined with their fluency in the use of number facts, allows younger students to easily manipulate numbers, providing them with “wings” to fly through much of the procedural mathematics. This provides the opportunity for the young people to spend more time sorting out the conceptual ideas and problems that test their conceptual understanding.
“Order of Operations” is another fundamental math skill that is introduced very quickly in grade 1, first in the Assignment of the Year, and then consolidated in the extremely intensive Order of Operations unit in grade 5. This unit in grade 5 requires all the skills learned from previous topics, combining all four operations. Brackets and exponents are introduced here.
The concept of “Factors, Multiples and Primes” is introduced in grade 2 and continues through to grade 5, ensuring that the students have a solid foundation in number theory.
Finally, “Number Sets” (including fractions) complete the last of the topics that combine to form a solid set of skills from which students are able to propel themselves forward in any topic in mathematics.
You will note that many of the topics covered in the math texts used in schools are not included in the above description. The text material is, however, incorporated in the applications of the Spirit of Math program and in the problem solving exercises.
Three or four specific topics are covered in depth in each grade after grade 5.

Strand 4: Cooperative Learning
Cooperative group work and presentation skills are stressed in class, not only for their essential life-skills benefits, but because teamwork is often essential for a student to get the solution to a problem. Through teamwork, students develop the ability to work effectively with others, learning from their peers, and learning how to make helpful contributions to group learning.
Cooperative learning is an integral part of the Spirit of Math approach. Our experience has shown that when we present mathematics at an appropriately complex and thought-provoking level, students naturally want to analyze their work and discuss ideas with one another. New understandings emerge and new ideas are generated more effectively.