Development and Evaluation of the Remainder Clock Device for Teaching Polynomial Remainders to IDSC Senior High School Learners

Author(s): Alcaldeza, Joshua L.
Publication year: 2026
Material type: Research paper
Subject: Secondary Mathematics Education — Polynomial Division and Remainders
Program: Teacher Education

Description

Polynomial division is challenging for many learners because long and synthetic division require several sequential operations that can result in sign errors and procedural confusion. Learners may also complete the procedures without understanding how a remainder is obtained. This study developed and evaluated the Remainder Clock, a hands-on instructional device designed to help learners visualize and calculate polynomial remainders. It examined the device’s effectiveness among senior high school learners at Infotech Development Systems Colleges.

The study employed a quasi-experimental pretest–posttest design involving 46 Grade 11 Science, Technology, Engineering, and Mathematics students selected through purposive sampling. Pretests and posttests were administered through Google Forms. The intervention consisted of demonstrations of the Remainder Clock supported by presentation slides and video tutorials. Weighted mean, percentage, and a paired-samples t-test were used to analyze the learners’ performance before and after the intervention.

The learners obtained low mean scores in the pretest but showed marked improvement in the posttest after the introduction of the device. The results suggest that the Remainder Clock supported instruction on polynomial remainders when the divisors were binomials. The device helped connect physical manipulation with the abstract logic involved in polynomial division.

The study concludes that the Remainder Clock can serve as an instructional scaffold for teaching polynomial remainders. Mathematics teachers may incorporate the device into lessons on polynomial division to support visualization and procedural accuracy. Recommended improvements include increasing the durability of the device, using high-contrast labels, and investigating whether an expanded version can also help learners determine polynomial quotients.