Multiplication Abacus with Sliding Matrix for Intuitive Learning
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Solution Overview
Problem
Multiplication learning tools, such as multiplication tables, are abstract and not intuitive for primary school students, relying heavily on rote memorization rather than understanding, which hinders the development of mathematical thinking.
Innovation Solution
A multiplication abacus device with a detachable result display area and sliding members arranged in a matrix, allowing students to visually demonstrate and calculate the product of two numbers by moving the sliding members, combining hands-on operation with visual and cognitive learning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If a multiplication table is used for learning, then students can access multiplication formulas, but the learning process becomes abstract and not intuitive enough
Solution Approach 1:
The patent transforms the traditional two-dimensional multiplication table into a three-dimensional abacus structure with sliding members that can move vertically and horizontally. This spatial dimensionality allows students to visually and physically represent multiplication as area coverage, making the abstract concept concrete and intuitive while preserving all multiplication formula information.
Solution Approach 2:
The sliding members act as intermediaries between the student's manual operation and the multiplication concept. By moving these physical components across the abacus grid, students create a tangible representation of multiplication that bridges the gap between rote memorization and conceptual understanding.
2Reliability
If students rely on rote memorization to learn multiplication, then they can remember formulas, but they cannot fundamentally understand multiplication
Solution Approach 1:
The abacus employs dynamic sliding members that can be moved to different positions, transforming static multiplication formulas into dynamic visual representations. This allows students to actively manipulate the tool to understand the relationship between factors and products, enhancing both memory retention and conceptual understanding without adding unnecessary complexity.
Solution Approach 2:
The multiplication abacus is segmented into a grid structure with individual sliding members for each cell, allowing students to focus on one multiplication fact at a time. This segmentation breaks down the complex task of learning all multiplication formulas into manageable units while maintaining the overall structure for comprehensive learning.
3Productivity
If traditional multiplication teaching methods are used, then students can complete calculations, but their spatial thinking and mathematical modeling abilities are not enhanced
Solution Approach 1:
The multiplication abacus serves multiple functions: it calculates multiplication results, develops spatial thinking through manual manipulation, enhances mathematical modeling by representing area concepts, and improves memory retention. This multi-functionality allows students to achieve calculation proficiency while simultaneously developing broader mathematical thinking abilities.
Data Source
AI summary
A multiplication abacus device is provided, which includes a main body with a result display area, where the result display area has calculation result bits arranged in a matrix, the calculation result bits have numbers for displaying a calculation result, a plurality of sliding members, arranged in a matrix that can slide horizontally and longitudinally on the main body, and located on the calculation result bits, where adjacent M rows of sliding members slide longitudinally, and adjacent N columns of sliding members slide horizontally. After the sliding members do not obstruct one row of calculation result bits and do not obstruct one column of calculation result bits, a number of the calculation result bits in a crossed position is a calculation result of M×N. Through the above technical solution, a technical problem of learning multiplication in existing technologies being abstract and not intuitive enough has been solved.