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The TetractysTM Rule

Learn about...
  • Why the rule is the heart of the puzzle
  • The importance of rule-following
  • The multifunctional nature of digits according to the rule
Benefits to the student:
  • Learning to follow an arbitrary rule helps thinking abstractly
  • Understanding a rule involves concept formation
  • Rules teach normative behavior, that is, correct and incorrect usage

The Heart of the Puzzle

While the focus of the Tetractys™ Number Puzzle is to help students learn how to think abstractly, the heart of the Tetractys™ Number Puzzle is the rule which governs the four digits of each puzzle.

The Tetractys™ Number Puzzle is based on sets of four digits, each from 0 to 9 and related to one another by a simple, arbitrary rule. It is this rule which defines every puzzle and makes each digit in a set of four significant. In fact, the rule of the Tetractys™ Number Puzzle is so simple, that all that is required to understand it is a basic knowledge of the multiplication table up to 9 × 9 and the decimal place value system.

Once a student has sufficiently memorized the multiplication table up to 9 × 9 and has a reasonably good grasp of place value notation, this puzzle can be introduced to the student not only to deepen that knowledge but to show that this knowledge is just the starting point to even deeper knowledge about these same numbers. We believe that if you can accomplish this much early on in a student’s learning of mathematics, you are well on your way to preparing that student for more advanced topics, especially those that invariably involve learning more complex symbolism at greater levels of abstraction.

Understand the Rule


    The Tetractys™ Number Puzzle's rule is not only simple to learn but is designed to demonstrate the student's understanding of the multiplication table up to 9 x 9 and place value notation. Once they understand these basic facts, the rule can be used to deepen this understanding.

  • The arbitrary nature of the rule helps abstract thinking
  • The rule is simple yet exhibits subtle complexity
  • The nature of the rule allows for thorough analysis
  • Students can learn the rule as early as Grade 4

Analyze the Rule


    The nature of the Tetractys™ Number Puzzle's rule helps students learn how to think abstractly once they understand the multifunctional nature of the digits under the rule. Because the rule determines the multiple meanings of the digits, the rule can be analyzed step-by-step.

  • Analyzing the rule in-depth clarifies the multifunctional nature of digits
  • The rule actually compresses what the student already knows but in a new form!
  • Analyzing the rule gives the student confidence when solving the puzzle

Solve the Puzzle


    The rule of the Tetractys™ Number Puzzle allows the puzzle and its solutions to be presented in a systematic and compressed form. Not only that, but the way in which puzzles and solutions can be referenced is also in a systematic and compressed form. This further enhances rule-following skills.

  • The puzzle grid essentially encodes the rule systematically
  • Analyzing and solving the puzzle involves decoding the rule
  • Encoding and decoding information using digits facilitates abstract thinking

The Importance of Rule-following in Mathematics

Rule-following is more than just blind adherence to a rule-formulation. On the contrary, rule-following provides the clearest demonstration of a student's understanding of a rule.

Many people have a negative view of rules and rule-following, likening these things to blind obedience, mechanical actions, or simply to something lifeless or 'deadening' or perhaps even 'boring'. But rule-following is actually something entirely different: it is the outward manifestation of someone's understanding of a rule or how someone grasps the concept behind a rule. To grasp a concept or follow a rule is no mean thing, no trivial skill. In mathematics in particular rule-following gets to the heart of doing mathematics and above all of creating new mathematical concepts.

The rule underlying the Tetractys Number Puzzle provides yet one way in which a student can demonstrate his or her mastery of basic mathematical facts concerning multiplication and place value notation. But this rule, once understood, is also one way in which an original concept can additionally be formed out of these same basic facts. A rule, once understood and followed, becomes a new mathematical object in its own right, one that can be studied further, explored, and mined for new information. Moreover, since a rule always governs or rules over something, the behavior exhibited in following a rule is normative, that is, a rule distinguishes between correct and incorrect behavior. Without rule-following there would be no correct from incorrect behavior in mathematics, and hence no proof in mathematics. Without rule-following what would be left of mathematics?

The Tetractys Number Puzzle aims to teach one such rule in order to show not only how well students have grasped basic facts of arithmetic and mathematical notation but also how well they are able to conceive these basic facts in a novel form or 'rule'.

Tetractys Number Puzzle: A Mathematical Learning System for Students

ONLY$9.95
Product Details

  • Publisher: POIS Research; First edition
  • Language: English
  • ISBN-13: 978-0-9959504-0-5
  • Product Dimensions: 8.5" x 5.5" x 0.2"
  • Paperback: 64 pages in full color (Saddle Stitch)

  • Note: Dry Erase Marker and Dry Eraser not included.
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