Evaluation of Lesson Study on Lines and Angles

The intersection of two lines was studied in grade 7, junior high school. This geometry material is very important, as the basic 3 dimensions that students will learn at the high school level. Exploring and persuading the two properties of vertical lines is the most difficult thing in teaching. Traditional teaching uses methods such as observation, drawing, measurement, and comparison to derive the properties of vertical lines, and expresses the properties of vertical lines in finer words, which easily create greater difficulty for students to understand. This research uses research and development methods, tries to use mathematical software to teach lines and angles and optimizes the basic concept of lines and angles. The results of this study provide specific references to the graphs and geometry of junior high school mathematics.


INTRODUCTION
The "Vertical Line" lesson comes from the content of "Intersecting Lines and Parallel Lines" in the second volume of the grade 7, Junior High School (Andriyani, 2018;X. Zhang, Zhou, & Wijaya, 2020). It is an important content of material on geometry (Ikhsan & Juandi, 2015). It is when students have a preliminary understanding of basic graphics points, lines and angles (Ramdhani & Suryadi, 2018). A special positional relationship based on learning, initially infiltrating students' ideas from general to special, is the key content of the school, math material material is difficult to understand (Dewi, Mediyani, Hidayat, Rohaeti, & Wijaya, 2019;T.T. Wijaya, Sukma, Purnama, & Tanuwijaya, 2020). Traditional teaching is prone to two phenomena: one is to draw a vertical line of a known straight line through hands-on manipulation, and to directly give the nature of the vertical line through observation; the other is to obtain the shortest vertical line segment by measuring the line segment between the point and the straight line nature. Because the graphics are immutable and static, this kind of teaching is not conducive to the correct grasp of the nature of the vertical line, and it is  Wijaya, Ying, & Purnama, 2020b;Tommy Tanu Wijaya, Murni, Purnama, & Tanuwijaya, 2020;Tommy Tanu Wijaya, Ying, Chotimah, & Bernard, 2020;X. Zhang et al., 2020). This article tries to explore how to use dynamic mathematics technology to optimize teaching design, while highlighting the key points and solving the difficulties.
The "Compulsory Education Mathematics Curriculum Standard (2011 Edition)" pointed out that it is necessary to fully consider the impact of information technology on the content and methods of mathematics learning (Aixia, Ying, & Wijaya, 2020), develop and provide students with abundant learning resources (Yi, Ying, & Wijaya, 2019), and use modern information technology as a powerful tool for students to learn mathematics and solve problems Tools to effectively improve the way of teaching and learning (Lin, Zhou, Wang, & Wijaya, 2020). Information technology to improve classroom teaching is the choice and requirement of the times (Suan, Ying, & Wijaya, 2020; T.T. L. Zhang, Zhou, & Wijaya, 2020). Mathematical dynamic technology can not only visually and dynamically present mathematical knowledge (Chotimah, Wijaya, Aprianti, Akbar, & Bernard, 2020;Cunhua, Ying, Qunzhuang, & Wijaya, 2019;Tan, Zou, Wijaya, Suci, & Dewi, 2020), highlight the essence of mathematical concepts, and promote students' deep understanding of learning content (T.T. Wijaya, Ying, & Purnama, 2020a), but also has the functions of strengthening students' hands-on operation, enhancing their interest in mathematical learning (Dikovic, 2009;Newhouse, 2017;Yu, Niemi, & Mason, 2019), and improving students' learning methods. As a result, dynamic mathematics technology is deeply integrated into the mathematics classroom to provide guarantee for promoting students' in-depth learning and improving mathematics literacy (Chai, Lim, & Tan, 2016;Koh, 2019;Listiawan, Purwanto, As'Ari, & Muksar, 2018;Oner, 2020).
Based on the above guiding ideology, this class first designed the link of "reviewing the past and learning the new". In classroom teaching, introduction is an important link, and the quality of introduction directly affects the teaching effect of the entire class to some extent. From the review of the intersection of two straight lines, four corners will be formed. Through the change, the straight line is rotated to discover the special situation of the intersection, and then the concept of verticality is introduced; secondly, the link of "hands-on operation, inductive nature" is designed. Students have already drawn a point of a vertical line with a known straight line. The teacher dynamically displays the process of drawing a vertical line, guides students to observe the change of the vertical line when the position of the known line or point is changed, and allows students to conclude the first vertical line Article nature. Finally, design the link of "thinking about the problem and re-exploring the nature" and set the problem context. The teacher uses dynamic mathematics technology to dynamically present the length of the vertical line segment compared with the length of other line segments, and guide students to summarize the second nature of the vertical line. At the same time, the concept of "distance from point to straight line" is effectively established. Based on the abovementioned course ideas, the following is a record of the course creation of "the concept and nature of the vertical line".

METHOD
This study uses the Research and development (RnD) method (Abadi, Asih, & Jupri, 2018). The researcher took a difficult junior high school material, then redesigned the learning using technology.
The object of this research is the lines and angles material. Angles and lines material is in grade 7, Junior High School. The lesson plan consists of 3 sections, namely, the Opening Section, the main section and the discussion and evaluation section.

Opening Section
Teacher: Earlier we learned that the intersection of two straight lines AB and CD can form four angles. If you rotate the straight lines AB and CD, what will you find? (Dynamic presentation of the linear rotation process, as shown in Figure 1).

Figure 1. Two lines intersect
Student 1: With the rotation of the straight line, the size of the four corners formed will change.
Student 2: When the straight line rotates to a specific position, ∠1 is equal to 90°, and the other angles are equal, which is also equal to 90°.
Teacher: Yes, when the straight line rotates to a certain position, the degrees of the four angles are all 90°. Mark ∠1 with a right angle symbol. At this time, we call these two straight lines perpendicular to each other. That is, when one of the angles formed by the intersection of two straight lines is a right angle (it is easy to know that the other three angles are also right angles), the two straight lines are called perpendicular to each other, and one of the straight lines is called the perpendicular of the other straight line, and their intersection point It's called a vertical foot. Perpendicular is indicated by the symbol "", the straight line AB and CD are perpendicular to each other (O is the vertical foot), recorded as "AB CD", read as "AB perpendicular to CD".

Main Section
Teacher: After we understand the concept of vertical, if we give a point and a straight line, where the point can be on the straight line or outside the straight line, and it is required to draw a vertical line that passes through a known straight line, will students draw it? Please do it yourself. Teacher: How to ensure that the two intersecting straight lines are 90°? Which 90° angle models have we been exposed to?
Student 4: You can use the right angle of a right triangle to draw a straight line that forms a 90° angle with a known straight line, and ensure that the drawn straight line passes through point P.  Journal on Education, Volume 03, No. 01, Desember 2020, hal. 42-50  Teacher: Finally, we use a mind map to summarize the content of this lesson:

Figure 4. lines and angles mind map
This lesson will focus on breaking through a difficult point: the exploration of the two properties of vertical lines. Because these two properties are only obtained through drawing, measurement, and comparison, and the textual expression of the two properties is very concise, it will be difficult for students to summarize and understand. At the same time, the seventh grade students are mainly based on experience-based logical thinking. They need to go through the process of inquiry, accumulate experience in the process, and summarize the nature of the vertical line through guessing. Therefore, in teaching, teachers mainly use student experience as the starting point for new knowledge. Let students go through three links to understand the concept of vertical and master the two properties of vertical Regarding the first property of the vertical line, the teacher first guides the students to do it by hand, draw a picture through a point to make a known straight vertical line, and then the students go through the process of drawing the vertical line, guess the first property, and finally the teacher passes Dynamically present "when changing the position of a known straight line or point, only a vertical line can still be drawn" to verify the conjecture. Regarding the second nature of the vertical line, the teacher first asks students how to accurately measure the performance of the long jump to stimulate students' thinking, and then introduces the concepts of vertical and oblique line segments, uses technology to measure the length of these line segments, and finally uses the form of dragging.
Change the position of the point to abstract the concept of the distance from the point to the straight line, and then deduce the shortest vertical line segment. At the end of this lesson, organize the content of this lesson with a mind map, which is not only easy to remember knowledge, but also can effectively improve students' thinking ability and cultivate students' core qualities.
Of course, the above teaching process is not static. Teachers should make adjustments or changes according to their academic conditions to help students effectively understand and master the two properties of the vertical.

CONCLUSION
Lines and angles material has many formulas and theories that students must master. This study shows that using technology in learning can improve students' mathematical abilities and help students understand the lines and angles material. In the next research, a study can be carried out on the influence of technology learning media on lines and angles material to see the differences in the ability of classes that use technology and classes that do not use technology.

ACKNOWLEDGEMENT
The researcher thanks Tommy Tanu Wijaya who has helped author to revised this paper. The author also thanks Professor Tang Jianlan as a supervisor who always supports everything. This paper would not have been this good without the support of all parties.