On October 15, 2024, I conducted two mathematics classes for 9C and 8A, focusing on different topics for each class. For the 9C students, we dealt with problems related to similar triangles, while for the 8A students, we continued with the problems of the sum of square identity, specifically the expression
( a+b)^2= a^2 +b^2 + 2ab . My goal for these lessons was to guide the students through the logic and reasoning behind each problem, aiming to make the concepts more intuitive and understandable. However, I realized that I need to focus on reducing the number of steps involved in solving these problems to help the students grasp the concepts more efficiently.
In the 9C class, while teaching similar triangles, I aimed to ensure that the students could identify when two triangles are similar based on the similarity criteria—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS). I emphasized the importance of understanding these criteria as the foundation for solving problems involving similar triangles. We explored various problems that required the students to apply these criteria to determine whether two triangles were similar, as well as to find the lengths of unknown sides using the proportionality of sides in similar triangles.
During the session, I observed that some students were able to quickly catch on to the concept of similarity and could apply the criteria effectively. They were able to identify corresponding angles and sides in similar triangles and used the properties of proportions to solve problems accurately. However, a few students seemed to struggle with recognizing which criteria to apply in different scenarios. For these students, I realized that simplifying the approach could help them understand the underlying principles without getting overwhelmed by too many steps.
In an effort to make the learning process smoother, I plan to revise the structure of the lesson by breaking down the problems into more straightforward and easily understandable steps. By doing so, I hope to create a clearer path for students to follow, ensuring they can grasp the essential concepts without feeling lost or confused. My goal is to present these problems in a way that builds their confidence in applying similarity criteria, ultimately helping them to tackle more complex problems with ease.
In the 8A class, we continued working on the sum of square identity, which is expressed as
(
a
+
b
)
2
=
a
2
+
b
2
+
2
a
b
(a+b)
2
=a
2
+b
2
+2ab. The focus of the lesson was on solving problems using this identity and helping students understand its application in various algebraic contexts. I wanted to make sure that the students could not only memorize the identity but also understand how to use it in expanding expressions and simplifying algebraic equations.
As I guided the students through the problems, I noticed that while most of them were able to follow the steps involved in using the identity, there were instances where the solutions seemed overly lengthy. I realized that simplifying the method could be beneficial in making the process more straightforward and less time-consuming for the students. My aim was to help them reach the solution in a more efficient manner, without skipping any important steps that contribute to their understanding.
To address this issue, I plan to streamline the teaching process by focusing on the core elements of the identity and guiding the students on how to apply it directly to the problems at hand. By reducing unnecessary steps and emphasizing the most critical aspects of the calculation, I believe the students will find it easier to solve similar problems on their own. This approach will also encourage them to develop a logical way of thinking that is both practical and efficient.
One of the key takeaways from this lesson is the importance of adapting my teaching strategies to the needs of the students. I noticed that while some students were comfortable with a step-by-step approach, others could benefit from a more concise method that gets straight to the point. Balancing these needs requires a flexible teaching style that can cater to different learning paces and levels of comprehension.
Moving forward, I intend to make my lessons more interactive, encouraging students to participate actively in solving problems. By involving them in the process, I hope to create a classroom environment where they feel comfortable asking questions and sharing their thought processes. This kind of engagement will not only enhance their understanding of the concepts but also allow me to identify areas where they might need additional support.
In conclusion, the lessons on October 15, 2024, provided valuable insights into the effectiveness of my teaching methods. The focus on similar triangles in 9C and the sum of square identity in 8A revealed areas where I could make improvements to enhance the students' learning experience. By simplifying the steps involved in solving problems and creating a more inclusive learning atmosphere, I aim to help the students build a strong foundation in these mathematical concepts. My objective is to make mathematics a subject that is not only accessible but also enjoyable for all students, regardless of their individual learning pace.
