Published December 27, 2025 | Version v1
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The Effect of the GeoGebra-Assisted APOS Model on Students' Numeracy Skills Regarding the Pythagorean Theorem

Authors/Creators

  • 1. Department of Mathematics Education, Faculty of Tarbiyah and Teacher Training (FTIK), State Islamic University of Syekh Ali Hasan Ahmad Addary Padangsidimpuan, Padangsidimpuan, North Sumatra, Indonesia
  • 2. Mathematics Education, Department of Mathematics Education, Padang State University, Padang, Indonesia
  • 3. Delft University of Technology, Delft, Zuid-Holland, Netherlands (NL), Windesheim University of Applied Sciences, NETHERLANDS

Description

This quasi-experimental study aimed to determine the influence of the GeoGebra-assisted APOS (Action, Process, Object, Schema) learning model on the numeracy skills of eighth-grade students regarding the Pythagorean Theorem. The research was conducted at SMP Negeri 1 in Padangsidimpuan, North Sumatra, Indonesia, during the first semester (July–December) of the 2025/2026 academic year. The population comprised all eighth-grade students at the school, with the sample selected using random sampling techniques. Data collection was carried out through a test instrument, utilizing methods of documentation, direct observation, a pretest, and a posttest. Hypothesis testing using a t-test yielded a two-tail P-value (T<=t) of 0.011686319 at a significance level (α) of 0.05. Since 0.011686319 < 0.05, the null hypothesis (H0) was rejected, and the alternative hypothesis (H1) was accepted. The results indicate a statistically significant positive influence of the GeoGebra-assisted APOS model on improving students' numeracy skills in the context of the Pythagorean Theorem. This finding suggests that integrating dynamic geometry software like GeoGebra within the structured phases of the APOS model can be an effective pedagogical strategy for enhancing numerical understanding and application in geometry.

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2025-12-27
This quasi-experimental study aimed to determine the influence of the GeoGebra-assisted APOS (Action, Process, Object, Schema) learning model on the numeracy skills of eighth-grade students regarding the Pythagorean Theorem. The research was conducted at SMP Negeri 1 in Padangsidimpuan, North Sumatra, Indonesia, during the first semester (July–December) of the 2025/2026 academic year. The population comprised all eighth-grade students at the school, with the sample selected using random sampling techniques. Data collection was carried out through a test instrument, utilizing methods of documentation, direct observation, a pretest, and a posttest. Hypothesis testing using a t-test yielded a two-tail P-value (T<=t) of 0.011686319 at a significance level (α) of 0.05. Since 0.011686319 < 0.05, the null hypothesis (H0) was rejected, and the alternative hypothesis (H1) was accepted. The results indicate a statistically significant positive influence of the GeoGebra-assisted APOS model on improving students' numeracy skills in the context of the Pythagorean Theorem. This finding suggests that integrating dynamic geometry software like GeoGebra within the structured phases of the APOS model can be an effective pedagogical strategy for enhancing numerical understanding and application in geometry.

References

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