Cylindrical Toy Penholder for Multiplication-Division Practice
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Solution Overview
Problem
Primary school pupils face difficulties in learning forward-backward rhythmic counting and multiplication-division tables due to abstract concepts, and existing instructional materials are inefficient, difficult to use, and lack motivation, particularly for independent practice and group interaction.
Innovation Solution
A 3D cylindrical toy penholder that allows pupils to perform forward-backward rhythmic counting and write multiplication-division equations independently, with modular display of inverse equations and visual coding notation, enabling interactive games for enhanced learning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If teachers assign homework and check each pupil's work to teach multiplication-division tables, then learning effectiveness is improved, but teacher time and effort requirements increase significantly
Solution Approach 1:
The device enables pupils to practice multiplication-division tables independently through interactive gameplay. The toy includes a game board with multiplication tables, movable pieces for selecting problems, and immediate feedback mechanisms, allowing students to self-test and reinforce their knowledge without requiring continuous teacher intervention or homework checking.
Solution Approach 2:
The invention incorporates immediate feedback systems where the device provides correct/incorrect indicators after pupils answer multiplication-division problems. This immediate feedback loop reinforces learning effectiveness while eliminating the need for teachers to individually review each student's work, thereby reducing teacher time requirements.
2Loss of time
If teachers rely on peer assessment or parental support to save time, then teacher workload is reduced, but honesty and trust problems arise
Solution Approach 1:
The device provides an objective, standardized practice system that eliminates dependency on peer or parental assessment. Each pupil uses the same game board and rules independently, with the device itself providing standardized feedback, thereby removing the honesty and trust issues associated with peer or parental evaluation while maintaining time efficiency.
3Adaptability or versatility
If existing instructional materials are used for multiplication learning, then basic multiplication concepts are covered, but division operations and inverse equation relationships are not adequately addressed
Solution Approach 1:
The device serves multiple functions: it teaches multiplication tables, division tables, forward counting, backward counting, and the relationships between inverse equations. The game board includes both multiplication and division problems, and the movable pieces can be used to demonstrate both operations, making the device universally applicable to multiple mathematical concepts without requiring separate materials for each operation.
Solution Approach 2:
The invention merges multiplication and division learning into a single integrated device. The game board combines both operation types, and the same movable pieces serve dual purposes for demonstrating multiplication and division concepts, thereby reducing overall device complexity while increasing operational coverage.
4Adaptability or versatility
If block-based notation is used to display multiplication equations, then multiplication concepts are visualized, but division operations and equation relationships cannot be simultaneously displayed
Solution Approach 1:
The device uses movable pieces that can be dynamically repositioned on the game board to display different operations. The same physical pieces can represent multiplication factors, division divisors, or equation components depending on their position and configuration, allowing the system to dynamically adapt its notation to display both multiplication and division operations simultaneously without increasing structural complexity.
Data Source
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AI summary
This invention (product) is a concrete instructional material that helps primary school students learn and especially reinforce forward-backward rhythmic counting and multiplication-division tables, which they have difficulty in learning at mathematics courses, and allows them to play individually or in groups on the subject. The product consists of a penholder and a toy. The product looks like a vertical cylindrical penholder that the toy is attached at and detached from top face. Multiplication and division equations, which are inverse operations, are simultaneously written on penholder. The students multiply the numbers 1-10 with numbers 1- 10 whenever and wherever they want and write their equations on front side of penholder. They simultaneously write the inverse (division) equations on backside of it (e.g. 5 X 3 =15 and 15/3=5 and vice versa is possible. Students play games individually or in groups on product. In game, students randomly select one of 42 different numbers that are product/dividend in equations, and write equation/ equations of the number they selected on penholder and get points. Students monitor their game performance with game tracking-scoring form and this form gives them feedback-correction. In this product, students study, learn and reinforce forward-backward rhythmic counting and multiplication-division tables both as a whole and modularly.