The development of the cycle model and its effect on mathematics learning using GeoGebra mathematical software

Figures & data

Figure 1. Graph of $f\left(x\right)=\frac{\mathrm{s}\mathrm{i}\mathrm{n}\left(5x\right)}{2x}$

Figure 2. Graph of diving board function

Figure 3. Values where the function is continuous

Table 1. Stages of the cycle model.

Stages	Name of the stages	Activities
1	Environment	Identification of area (environment) (such as laboratory class setting).
2	Individual behaviour	Identification of individual areas (teacher professional development and student ability, perception). As the researcher was a teacher, the MKO applies, thus teaching and learning can take place. The pre-test was used to identify students’ abilities.
3	State objectives	State objectives of teaching a lesson with Technology/GeoGebra (by using review literature).
4	Design	Design teaching materials (lesson plan that is compatible with GeoGebra)
5	Implementation	Implementation of a lesson plan in the classroom (start scaffolding student-student, teacher-student interaction)
6	Feedback	Get feedback from students (responses). This feedback could be in the form of an intermediate test, post-test and interview
7	Evaluation	Evaluation of whether the method achieved what was intended. Comparison of abilities before and after the intervention
8	Internalisation and externalisation	Disseminate and practice the knowledge they obtained in the next stages of the cycle model, Stage 9
9	Environment	Practising the knowledge they obtained within the environment by becoming a MKO (such as teachers, and other experts according to the types of intervention given)

Source: Bedada and Machaba (2022b, p. 4).

Figure 4. Participants’ demographic information.

Table 2. Summary of item analysis of DCAT.

Item analysis
Tests	Difficulty index (P)	Reliability Coefficient (KR-20)	Remark
Procedural (P) test items	0.2131	0.649	Four items needed to be revised (Q9,11,14,19) as all were marginal and difficult items.
Conceptual (C) test items	0.213	0.525	Three items needed to be revised: Q12 was a poor and very difficult item; Q16 was average in terms of difficulty and a poor item in terms of differentiation between students, and Q4 was a very difficult item and only marginally useful for identifying students). In addition, one item (Q15) was rejected and replaced as it had a negative discrimination index and was very difficult (Sharma, 2021).

Table 3. Normality of pre-test.

	Group	Kolmogorov-Smirnov			Shapiro-Wilk
		Statistic	Df	Sig.	Statistic	df	Sig.
Pre-test	Experimental	.119	30	.200	.946	30	.133
	Control	.145	36	.055	.957	36	.172

Source: Bedada and Machaba (2022b, p. 7)

Table 4. Overall descriptive statistics of the two groups’ proficiency in differential calculus before the intervention.

Groups	Differential calculus achievement (Before intervention)
	N	Mean	SD	Std. Error
Experimental	30	27.0000	9.96546	1.81944
Control	36	26.6667	10.82326	1.80388
Total	66	26.8182	10.36400	1.27572

Source: Bedada and Machaba (2022b, p. 6)

Table 5. Overall one-way analysis of variance summary table comparing groups’ achievement in differential calculus before intervention.

Differential Calculus Achievement Test (Before Intervention)
	Sum of Squares	Df	Mean Square	F	Sig.
Between Groups	1.818	1	1.818	.017	.898
Within Groups	6980.000	64	109.063
Total	6981.818	65

Source: Bedada and Machaba (2022b, p. 7)

Table 6. Overall descriptive statistics for two groups on differential calculus achievement after the treatment.

Comparison of Pre-test Scores and Post-test Scores of Groups
Interventions		Pre-test Scores	Post-test Scores
Experimental (N = 30)	Mean	27.0000	41.1667
	Std. Deviation	9.96546	13.81424
Control (N = 36)	Mean	26.6667	31.1111
	Std. Deviation	10.82326	11.40871
Total	Mean	26.8182	35.6818
	Std. Deviation	10.36400	13.44179

Source: Source: Bedada and Machaba (2022b, p. 10)

Table 7. Descriptive analysis of student proficiency in conceptual and procedural understanding.

Pre-test conceptual-procedural, Post-test conceptual and post-test procedural with Groups
Groups		Pre-test Conceptual	Pre-test Procedural	Post-test Conceptual	Post-test Procedural
Experimental	Mean	16.3333	10.6667	16.8333	24.3333
	Std. Deviation	6.55656	5.83292	8.14559	7.51244
Control	Mean	13.8889	12.7778	20.0000	11.2500
	Std. Deviation	7.28120	5.90937	9.56183	8.39855
Total	Mean	15.0000	11.8182	18.5606	17.1970
	Std. Deviation	7.01646	5.92494	9.01986	10.30791

Source: Bedada and Machaba (2022b, p. 7)

Table 8. Descriptive analysis of normality test of post-test data.

Tests of Normality of post-test
	Groups	Kolmogorov-Smirnov			Shapiro-Wilk
		Statistic	Df	Sig.	Statistic	df	Sig.
Post-test Scores	Experimental	.139	30	.144	.924	30	.033
	Control	.128	36	.145	.962	36	.253

Table 9. Descriptive analysis of normality test of post-test proficiency data.

Tests of Normality
Post-test	Groups	Kolmogorov-Smirnov			Shapiro-Wilk
		Statistic	Df	Sig.	Statistic	df	Sig.
Conceptual	Experimental	.199	30	.004	.909	30	.014
	Control	.144	36	.057	.970	36	.434
Procedural	Experimental	.251	30	.000	.887	30	.004
	Control	.145	36	.055	.923	36	.016

Table 10. Mann-Whitney U test on students’ scores in differential calculus.

Time Groups		N	Effect size(r)	Mean Rank	Median	Sum of Ranks	Z-value	U	P
Pre-test conceptual	Experimental	30	.19	37.42	15	1122.50	−1.551	422.5	.121
	Control	36		30.24	15	1088.50
	Total	66
Pre-test procedural	Experimental	30	.71	30.03	10	901.00	−1.385	436	.166
	Control	36		36.39	15	1310.00
	Total	66
Post-test Conceptual	Experimental	30	.72	29.93	17.5	898.00	−1.397	433	.163
	Control	36		36.47	20	1313.00
	Total	66
Post-test Procedural	Experimental	30	.83	47.10	20	1413.00	−6.729	132	.000
	Control	36		22.17	10	798.00
	Total	66

Table 11. Interpretation of the effect sizes.

Observations	Computed effect size	Percentile gain	Interpretation
Pre-test – post-test	−1.7	46%	Improvement is high as the value is greater than Cohen’s d standard of 0.8.
Pre-C – Post-C	−0.06	2%	Improvement is low as the value is smaller than Cohen’s d standard 0.2.
Pre-P – Post-P	−2.35	49%	Improvement is high as the value is greater than Cohen’s d standard of 0.8.

Bedada, T. B., & Machaba, M. F. (2022b). The effect of GeoGebra on students’ abilities to study calculus. Education Research International, 2022, 1–14. https://doi.org/10.1155/2022/4400024

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Sharma, L. R. (2021). Analysis of difficulty index, discrimination index and distractor efficiency of multiple choice questions of speech sounds of English. International Research Journal of MMC, 2(1), 15–28.

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Data availability statement

The data and materials used in the current study are available from the corresponding author upon request.