## 4 Results
### Results of Correlation Analysis  
To explore the reasons for the inconsistent significance of the differences in the scores of the four science subjects, the researchers analyzed the data from the perspective of technological support for teachers and students. Teachers: Three intelligent teaching system functions that are frequently used by teachers in daily teaching were selected, as shown on the x-axis of the following Figure 7A, and their usage frequency in the four subjects was compared. From the bar chart, it can be seen that mathematics has the highest usage frequency for the three major functions, and biology ranks last in usage frequency for all subjects, which is consistent with the trend in the above-mentioned significant differences. The physics subject has a lower usage frequency of the \"homework question\" function than the chemistry subject, but has a higher usage frequency for the other two functions, yet it did not show a corresponding impact on teaching effectiveness. Through the correlation analysis in Figure 7B, it can be seen that the slopes of the three functional curves are positive, all positively correlated, with the slope values being \"homework questions\" (26.46) > \"homework reports viewed\" (5.238) > \"homework assign  
Figure 6: Average score frequency distribution. Note. The chart shows the distribution of scores from the pre-test and post-test in math (**A**) and chemistry (**B**). In the histogram, each bar represents the number of students within a specific score range. The superimposed normal distribution curve illustrates the distribution of the data, with its peak (the middle line) indicating the median, highlighted with a blue line. The shape and position of the curve represent the concentration tendency and dispersion of the score distribution. The quartile table for each graph is displayed on the right side of the chart. Figure 7: Class student self-directed learning. ment\" (1.734), proving that \"homework questions\" have a more significant impact on the variability of score changes across different subjects. In the precision teaching model, in addition to teachers, another important role is the student. Teachers are responsible for teaching, monitoring, and feedback, while the initiative of learning lies with the students. Therefore, the reasons affecting teaching effectiveness should also be explored from the perspective of students' self-directed learning effectiveness. The following parts analyze the effectiveness of self-directed learning from the perspective of the class and typical students. Students: The correlation between students' self-directed learning through the intelligent system and their final exam scores was explored. This study, from the perspective of various disciplines, conducts a correlation analysis on the relationship between the difference in pre and post average scores of intervention classes and students' self-directed learning, including homework completion rate, the number of similar problems completed, and the number of personalized exercises completed. The homework completion rate reflects students' enthusiasm and seriousness towards the subject, the number of similar problems completed reflects the ability of identifying and filling gaps, and the personalized exercises reflect the ability of improvement and advancement; the \"Personalized Learning Pathways\" diagram can be referred to for context. The results of the correlation analysis are represented by a linear function, where the sign of the slope reflects whether there is a correlation, and the magnitude of the slope value reflects the degree of correlation. The analysis results are shown in Table 3 below. From Table 3, it can be seen that the correlation data for each subject follows different patterns. The patterns for mathematics and chemistry are approximately the same. The improvement in mathematics scores is negatively correlated with the number of similar problem exercises, and positively correlated with the other two autonomous practice data.