Polyhedral Dice System for Math Fact Fluency
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Solution Overview
Problem
Traditional dice systems are limited in teaching more complex mathematical operations, such as harder-to-learn number combinations and 'math fact fluency', leading to deficiencies in students' math skills, particularly in addition and multiplication, which persist throughout their education.
Innovation Solution
A polyhedral dice system with non-traditional number series and combinations that focus on harder-to-master math operations, allowing for adaptive gameplay to target individual students' needs, by eliminating or deemphasizing easy math facts and emphasizing specific operations through different dice configurations and color-coding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional dice with ordinal numbers (1-6) are used, then the dice are simple to manufacture and easy to understand, but they produce overly simple math operations that fail to teach harder-to-learn number combinations
Solution Approach 1:
The patent changes the numerical parameters on the dice faces from traditional ordinal sequences (1-6) to non-traditional number series specifically selected to emphasize harder-to-learn math facts. For example, dice may feature numbers like 7, 8, 9, 10, 11, 12 instead of 1-6, or use repeated numbers strategically to create challenging addition and multiplication combinations that target specific learning gaps.
2Adaptability or versatility
If dice emphasize harder-to-learn number combinations, then math fact fluency is improved, but the dice design becomes more complex and less adaptable to individual student needs
Solution Approach 1:
The patent divides the educational task into segments by creating multiple specialized dice sets, each targeting specific math fact categories (e.g., addition facts, multiplication facts, specific number ranges). This allows students to select and use only the dice sets relevant to their current learning needs, making the overall complex system manageable and adaptable through modular selection.
Solution Approach 2:
The patent enables dynamic adaptation by allowing students to choose different dice combinations based on their individual learning progress and needs. The system transitions from static traditional dice to a dynamic set where dice selection and combination can be adjusted as students master certain math facts and move on to more challenging operations.
3Reliability
If traditional dice are used, then all number combinations are equally distributed, but this uniform distribution fails to target specific learning gaps in math facts
Solution Approach 1:
The patent applies local quality by designing dice with non-uniform number distributions that are optimized for specific educational purposes. Different regions or faces of the dice emphasize different number combinations based on learning research about which math facts are hardest to master, rather than distributing all numbers uniformly across all dice faces.
Data Source
AI summary
A math learning process uses a first set of dice and a second set of dice. The process includes configuring the first set of dice and the second set of dice to respectively produce equal probabilities of occurrence of two different sums. A first player rolls the first set of dice and records the sum. A second player rolls the second set of dice and records the sum. These steps are repeated until one of the first player and the second player rolls a particular sum a predetermined number of times. Other dice configurations facilitate focus on specific math facts and operations.