A DIDACTIC SOLUTION FOR INTEGERS: A METHODOLOGICAL VARIANT WITH PRACTICAL DEMONSTRATION
Abstract
This study examines the effectiveness of using a symbol counter methodology to teach integer operations within a three-tiered didactic framework: concrete application, visual representation, and symbolic notation. The experimental approach was designed to address common student challenges, such as sign errors, incomplete understanding, and flawed reasoning in mathematical problem-solving. The pilot lesson incorporated student-centered teaching strategies, including hands-on activities, teamwork, discussion, and reflection.
The symbol counter, a tool utilizing physical symbols like paper circles with plus or minus signs, helped students grasp concepts such as positive and negative numbers, opposite numbers, and zero through tactile and visual experiences. This method facilitated a deeper understanding of integer properties and operations, including addition, subtraction, multiplication, and division. By transitioning from physical manipulation to mental visualization and symbolic abstraction, students were able to internalize mathematical concepts more effectively.
To validate the hypotheses proposed in the study, we explored the feasibility of employing methodological approaches that encourage student engagement in the lesson, critical thinking, self-directed learning, and collaboration. To achieve the established objectives, the following tasks were undertaken:
- Identifying the experimental group
- Creating the experimental lesson plan
- Conducting the experiment
- Evaluating the experimental outcomes
In high school math classes, we learned the rules for performing operations with integers. The sign calculations were written and formulated as follows:
- (+) × (+) = (+)
- (+) × (-) = (-)
- (-) × (+) = (-)
- (-) × (-) = (-)
These notations can be found in various textbooks and educational materials.
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