Benjamin T

You definately have a very firm and immediately available knowledge of the content you were reviewing with the student! Your use of the whiteboard to give the classic drawing and graphical explanation oft he derivative was done very well and it is obvious that you are experienced both in the mathematical side of this but also in the tutoring side. While your drawings and explanations were very well done, they could have been slowed down a bit to ensure the student is completely following. While the principles you were explaining were relatviely straightforward, slowing down a bit and adding a few more details could help deliver your message more effectively. For example, your explanation jumped from secant lines to tangent lines very abruptly near the start of the session. Besides this, you did very well! I really liked how you admitted when you were unsure of a certain proof for a trignometric formula but proceeded to give the learner some resources on how they could find it out for themselves after the session.

Tutor · 17 hr. ago

I thought you did an excellent job engaging the learner. I like that you continuously checked in with them while you were explaining concepts to keep them "in the loop" and ensure they were understanding. I would recommend asking more open-ended questions to learners—questions that prompt the learner to share and apply some of their existing knowledge. For example, when you explaining the question with the derivative of sin(x), you could have asked something like "can you think of any trigonometry properties/identities that might be helpful here?" I think that particularly in calculus, learning and practicing applying the "foundational" trigonometry identities on the fly into more complex ones is really important since memorizing every identity is very burdensome.

Tutor · 17 hr. ago

Yes, the learner said they understood your explanations. Although, if time permits, I would recommend confirming learners' progress with a practice question or two after you've explained lots of concepts.

Tutor · 17 hr. ago

It seems like you have the basic knowledge of calculus and you do a great job explaining your thought process to the learners! I really enjoyed how you walked through the L'Hopital problem with Meklit and thoroughly explained all the steps. However, there were a few things that did seem to stump you a little - which is totally fine! For example, the 3-way partial decomposition and the integration with trig sub seemed a bit difficult for you, so maybe next time you can study those before coming to the session! (Side note: you could solve the trig sub integral using u sub on sqrt(9 + x^2)!)

Tutor · 2 days ago

There is definitely evidence that the learner's made progress as both students were able to understand your solution and followed along as you asked them questions throughout the process.

Tutor · 2 days ago

You did a great job adapting to the learner's unique needs, continuously engaging with James, and most of the part checked and confirmed his knowledge and progress throughout. The only advice I'll give is to maybe make practice questions prior to the session or ask James to solve specific questions on what he was struggling with, so you can make sure he mostly understands the concept and to show his progress. I think practice questions or exercises are a big deal, especially in calculus. Other than that, great job!!

Tutor · 16 days ago

Benjamin did strengthen the learner's confidence for the most part. What I liked a lot was the environment was very positive, opening, and respectful. It was a comfortable environment, where learners like James don't have to be shy and ask questions. Environment is one of the most important aspects of a meeting, so great job on that. Overall, you did a great job with this session!! I highly recommend you to make practice questions or exercises, and maybe even provide some practice resources in case the learner still doesn't understand what's going on after the session.

Tutor · 16 days ago

You addressed the learner's question directly and provided an explanation in a clear, structured manner. Your approach to solving the problem was logical, and they were responsive to the learner’s queries. To increase learner engagement and reinforce active learning: Ask probing questions to check for prior knowledge before diving into the solution. For example, ask the learner what they understand about linear functions or how they would approach solving the problem. Encourage active problem-solving. After explaining a concept, you could prompt the learner to try a similar problem on their own or explain the reasoning behind certain steps. This helps the learner gain confidence and ensures that the concept sticks. Provide opportunities for practice questions. You could ask the learner to solve problems independently, or work through progressively harder examples together, allowing the learner to test their understanding in real-time.

Tutor · 18 days ago

You made a good effort to engage the learners by asking questions throughout the session and prompting them to solve problems. The interactive component allowed learners to practice finding the equation of tangent lines and to apply the derivative formula, which reinforced their understanding. Additionally, you encouraged students to express their thought process, allowing for active participation and reflection on the material. Although you asked questions and encouraged participation, there could have been more active learning opportunities to deepen learners' engagement. For instance, after explaining the concept of tangent lines, you could have assigned learners to work on problems independently first, then compare and discuss their answers. This would encourage more critical thinking and foster a deeper connection with the material. Additionally, you could also incorporate more formative assessments during the session to check for understanding, such as quick polls or asking students to summarize key points in their own words. This would provide more real-time insight into learner progress and address any confusion immediately.

Tutor · 18 days ago

Thank you for hosting this session and teaching me U-Substitution! :)

Learner · 20 days ago

Thank you for this session and answering my math questions. You did a great job explaining clearly.

Learner · 27 days ago

Thank you for the zoom help! Looking forward to tomorrow's session!

Learner · 1 mo. ago

Your explanations were the some of the best I've ever seen in a peer review. You were helpful, intuitive, and went at a good pace. That tangent line problem was challenging with lots of steps, but your explanation made it highly understandable. I like that you used different colors on your whiteboard to help differentiate between different variables/symbols/etc. Adding in links to relevant Khan videos was a nice touch, too. I'm going to try using the same whiteboard website as you! No recommendations.

Tutor · 17 hr. ago

I thought you were friendly, approachable, and respectful throughout the session. I would recommend briefly introducing yourself at the start of sessions as well as referring to learners by name. I would also recommend deliberately commending learners when they get something correct, especially when solving challenging problems. For example, when the learner figured out cos(h-1)/h wasn't necessarily undefined, adding some brief words of encouragement (e.g. "Great job! That was a difficult question") after confirming they were right would have helped keep the learner encouraged.

Tutor · 17 hr. ago

Thanks for explaining derivative rules!

Learner · 1 day ago

Great job interacting with learners! I really loved how you comfortable talked with the students like it was a conversation, and it wasn't one-sided at all. Before you begin solving problems, however, try to get a feel for what level they are, by checking their prior knowledge. Perhaps on the first problem, after recognizing partial decomposition, you could ask about if they've learned it and how they would go about using that to solve this problem. I think you did a great job adapting to learners' needs - although like I said earlier, brushing up on some of the more advanced topics would help you better accommodate learners' problems. I love that you continuously engaged learners one-on-one, however instead of keeping people waiting, you could ask other learners about their thoughts on the current problem! Finally, one tiny thing I think you should do is to give some extra problems at the end to check if the learner has comprehended the topic. Other that that amazing job!

Tutor · 2 days ago

Thank you so much Ben! You helped me more than I could expect.

Learner · 6 days ago

Yes, there is somewhat evidence that the learners made progress throughout the session , by telling Benjamin he understands it and has a pretty solid understanding of what is happening. Nice job on helping James with the MVT Theorem and the different types of concepts part of it! It seems like you have a solid understanding of calculus, specifically, the MVT Theorem, proving differential, continuous functions, etc. Although, calculus is a tough subject and it can be forgetting, you did a great job explaining to James the MVT Theorem and many challenging concepts part of it. Great job!

Tutor · 16 days ago

You demonstrated a good grasp of the calculus topic of linear functions and was able to explain the essential concepts. You addressed the learner's specific question effectively, providing clear answers and breaking down the steps involved in understanding linear functions. You communicated the key ideas well, which would have helped the learner gain a foundational understanding of the topic. You could benefit from incorporating more examples to further solidify the learner's understanding. For example, showing a few more linear function problems with varying complexity would help the learner better grasp the different scenarios they might encounter. Visual aids like graphs or equations plotted on a whiteboard would enhance understanding, particularly when discussing linear functions. A visual representation of the questions, for instance, would make abstract concepts more tangible.

Tutor · 18 days ago

You demonstrated a clear understanding of the core concepts related to tangent lines and their significance in calculus. The explanations provided a solid foundation for learners to understand the geometric interpretation of derivatives, specifically focusing on how tangent lines represent the instantaneous rate of change of a function at a given point. You used appropriate terminology and reinforced key ideas with examples that highlighted the relevance of tangent lines in both theoretical and practical contexts. The visual aids, such as graphs of functions and their tangent lines, were effective in reinforcing the concept. You were able to explain the connection between the derivative and the slope of the tangent line, making the topic more accessible for students. While the content was accurate and well-explained, you could benefit from providing more detailed step-by-step examples to clarify the process of finding tangent lines from a given function. For instance, a more structured breakdown of the derivative calculation and its application to tangent lines—especially in more complex functions—would help solidify the learner's understanding. Additionally, explaining the conceptual background of how derivatives are derived (such as limits and slopes of secant lines approaching the tangent) might provide learners with a deeper understanding of the foundations behind tangent lines. In future sessions, it would be helpful to include more variety in the types of problems discussed, including those involving functions with more complex behaviors (e.g., piecewise functions or non-differentiable points), as this will challenge learners and expand their comprehension of tangent lines beyond basic examples.

Tutor · 18 days ago

You have overall fostered a positive and supportive learning environment. They consistently provided encouragement, reinforcing the value of mistakes as learning opportunities. This approach helped boost learners' confidence, especially when they struggled with difficult problems. You was patient and took the time to explain concepts multiple times when necessary, ensuring all learners felt comfortable and supported throughout the session. You created a respectful and nurturing environment. However, personalized encouragement could be further emphasized by highlighting individual learner progress or effort, especially for students who may have initially struggled with the material. Recognizing incremental improvements or unique problem-solving approaches would further strengthen learners' confidence.

Tutor · 18 days ago

Thank you very much for the live session! I got the most out of it and I'm looking forward to the next one.

Learner · 26 days ago

THANK YOU

Learner · 30 days ago