Student engagement: it means that students are actively and productively moving through the learning process. This does not necessarily mean to me that students are always getting everything right, but they are on the right track to learning the material. Learning is a process, which means that there needs to be an action to get them to the final product.
In the first video, the teacher goes right into the lesson. While she explains what she is going to do, there is little "need" for the students to pay attention. The students are not given a prompt to truly start learning other than being expected to answer right away. However, it is clear from her teaching style that the students will not need to participate as long as they all stay quiet as the teacher will do the work for them. The teacher asks "okay" for clarification, but this almost seems like more of a habit as she does not get, and probably does not expect to get, a true response. When asking questions, she says "somebody" which diffuses the students' responsibility as she doesn't engage specific students. To make it worse, there are no consequences for not answering as the teacher then goes ahead with the lesson by giving the students the answer. Meanwhile, students doodle, listen to music, look away, yawn, and are most likely NOT truly learning French.
This is not the case in the second video. This engaging math teacher breaks the "wall" that is place between her and her students by moving from the front of the class and walking into the aisles. I have found this strategy most effective with students. Going up and down aisles means that the students can't doodle due to fear or getting into trouble and are more likely to watch me 1) because I am moving or 2) in order to make sure that they are not caught doing anything they shouldn't be doing. In addition to good classroom management, this also shows a deeper connection to the students by being physically closer to them. The math students from the second video clearly show that they are engaged with the teacher and their fellow students. The students know that they will have to answer questions. This teacher is in control of the class, yet has given students the chance to take control of their own learning.
The students are also physically engaged. In fact, they are required to gesture and be engaged. What's more, they're enjoying it! Students "teach" fellow students. This allows the teacher to measure student learning by asking student sto "give me gestures please." If they're not all engaged, students, who could have been "pretending," are called out, and then made to use gestures. Students are expected to model and teach. This shows that there are reinforcements for learning. Not to mention that there is a sense of ownership if the students know the answers, especially since there is a rapport between the teacher and students, shown by their respect toward her, and the fact that she actively knows and uses students' names. Students are engaged in their learning process and are clearly on the right track to learning what they need to know.
(I apologize about my oversight of the due date.)