Ryan W

Ryan demonstrates a complete understanding of limits and continuity. For example, when doing limits as they approached infinity, he demonstrated a technique through dividing all the terms through the biggest term before using the comparison of terms to solve them. Additionally, Ryan helped explain the analogy of a limit through using very small values when Elizabeth was struggling with her warm-up from class, which made it very helpful on why limits are the value they approach, not what they are defined at that point before explaining left and right hand limits with it as well. Additionally, Ryan also gave a technique with the sin(x)/x limit as x approaches 0 without using L'Hopitial's Rule to solve other limits that are similar to it through using the constant coefficient.

Tutor · 2 mo. ago

Yes, Elizabeth made progress from learning. She asked the questions needed and sounded confident when Ryan confirmed her learning progress. She also explained her thinking behind problems that she solved incorrectly before turning them into a learning experience, understanding why her teacher's answer key or explanations was the way they were in the worksheet. Also, she's willing to put in the effort since she doesn't want Ryan to solve all the problems on her HW, meaning she wants to apply what she learned to solve problems, meaning she's trying to grow further outside of the session as well.

Tutor · 2 mo. ago

Ryan did all of the above in this session; he checked Elizabeth's prior knowledge on limits before solving the problems that she had from school. This made it helpful since it gave him the background to adapt to Elizabeth's understanding of limits so she could apply what he knew on them. Additionally, both were engaged for the entire session, with Elizabeth clearly not doing something else as they were collaborating the whole time, with Ryan being a supporter, not the person who directly works on the work. Additionally, he ,consistently on the way through solving problems, confirms Elizabeth's progress, confirming if she understood the concept for all the examples done and had a follow-up, being open to questions from her after the session.

Tutor · 2 mo. ago

Ryan did an excellent job conducting a comfortable learning session with Elizabeth. For example, when Elizabeth had misconceptions on how a limit worked to the defined values, Ryan helped explain what the proper definition of a limit was and find the one-handed limits. Additionally, both felt very comfortable collaborating with each other and shared screens solving problems. Elizabeth had no trouble asking questions for the entire session which symbolizes this session being respectful.

Tutor · 2 mo. ago