A Lesson Plan to Boost Confidence for Palo Alto High School Students

Introduction and Backstory

Calculus is a challenging topic, and the California curriculum sits on a pedestal in terms of content and challenge level. Having been raised in a Chinese household by two doctors, I always put pressure on myself to reach their level of success and be the best possible version of myself. Despite my love for math, I found calculus to be daunting and challenging, laregely because I couldn't relate to my teacher or their approach to the content.

Fortunately, everything changed for me in college. While pursuing a degree in applied mathematical engineering, I was lucky to have Dr. Roth as my professor. In one specific lesson, I struggled with quadruple integrals because I couldn't understand the concept of more than three dimensions. Knowing I was a two-time Olympic-qualified swimmer, Dr. Roth intuitively explained the concept by relating it to a dive, breaking down the x, y, z, and t coordinates for me. He further enhanced his lesson with visuals from a YouTube video. The real learning moment, though, was when he pulled up another video to have me explain it back to him. This boosted my confidence and enthusiasm for the content, enriching my appreciation for math and physics in everyday life.

Dr. Roth is part of what inspired me to become a teacher, and helped spark my love for math and its applications in everyday life. He didn't just tell me, but taught me to teach myself. Now, I'm thrilled to be following similar steps in my approach to teaching.

Below is a breakdown of how I approach how I taught a lesson to Simon, a student who was struggling with high school calculus. Inspired by Dr. Roth and my pedagogical research, I used relationships, relatability, success criteria, and a gradual release of responsibility to build Simon's confidence and understanding.

1. Initial Meeting

During the initial meeting with any student, the focus is on understanding their background in mathematics, their experiences, and their goals related to learning calculus. Finally, it's meant to break the ice and set the stage for a comfortable and productive learning environment.

• Exloring the student's subjects of interest, areas of excitement, and what they're proud of.

• Exploring the student's previous experiences with math, particularly calculus or functions.

• Identifying how the current class and topic is going, and their relationship with their teacher. As a tutor, it's always best to work as a team with teachers, parents, and students to build a network of support.

• Discussing learning preferences and styles. Does the student prefer checklists to try? Do they like to talk aloud while processing information?

  
  

In Simon's case, he had struggled with advanced functions in the prior semester, didn't feel confident with math, and was nervous to ask his teacher for more help. He was interested in baseball and Marvel movies, learned best when conversing about concepts, and wanted to achieve an 80% in the course.

2. Personalized Lesson Plan

Motivation

It can be hard to learn something that's boring or unrelatable. Tutoring is the best possible medium to motivate students because I can take unfamiliar concepts and place them in familiar settings. In Simon's case, I hooked him by having him draw two x,y graphs of projectile motion. I like to use two examples of the same concept: one for me to guide and one for him to practice.

Success Criteria

John Hattie's research shows that success criteria is one of the highest-yield strategies to boost learning. As such, I always start my lessons with a list of goals for the session. In this case, I use the following success criteria:

1. I can visually identify the limit of a continuous 2D function

2. I can algebraically identify the limit of a continuous 2D function

3. I can visually identify the limit of a step 2D function

4. I can algebraically identify the limit of a step 2D function

Gradual Release of Responsibility

Hook (5 min)

Using Simon's hand-drawn projectile motion, I began asking him about the ball's height at various horizontal positions and had him identify them for me. From there, I proceeded to ask more challenging questions, like "where do you think the ball would go if x continued forever?" This approach helped boost Simon's confidence with low-stress questions.

Adding Complexity (5 min)

From that point, I provided Simon with several graph options to choose from, allowing him to select one to depict the projectile motion for each illustration. I chose a multiple-choice format because I was aware that Simon had difficulties with functions last semester. This approach allowed him to encounter more examples beyond our own and engage in a low-pressure critical-thinking exercise. Using our y=-(1/2)x^2 and y=-x^2 graphs, I created a few limit problems to tackle. I demonstrated the solution to one problem using the first equation and then asked him to explain his solution to me in his own words.

Practice (10 min)

At this stage, Simon didn't have any questions for me, so we moved onto the practice questions provided by his teacher. I prefer to use the teacher's materials because they are the assessors and typically design their tests based on practice problems. This is also where I can touch upon some of the more challenging concepts and level 3 problems.

Hook for next topic (5 min)

Next, we proceeded to step functions, a challenging concept for many of us. For this illustration, we used Dr. Strange's teleportation portals as an example, knowing that Simon is a Marvel fan. I then presented the idea of determining Dr. Strange's location at the moment of teleportation. This allowed us to explore the step function when approaching from the left or the right.

Adding Complexity (5 min)

I then asked Simon to write the function for me and create a new scenario of his own. I didn't need to show him anything because he had already understood the concept. He quickly demonstrated mastery of this concept and was ready to move on. It's a great feeling as an educator when students take off with their learning!

Practice (10 min)

Having met the day's success criteria, it was time to reinforce understanding through additional practice. I ensured that Simon focused solely on the most challenging problems he could tackle to make the most of his tutoring session.

Self-Reflection (5 min)

The final step of our session is to review the success criteria and mark them as completed. I spent a few minutes having Simon reflect on the learning process and provide feedback for our next session.

Additionally, I suggested that Simon communicate openly with his teacher about any difficulties. Most teachers, myself included, appreciate when students seek help. This enhances our relationship and allows us to proactively address challenging topics and offer support during class.

Self-Reflection

Following each session, I reflect on the lesson to evaluate what was successful and what wasn't. In this instance, Simon understood the concepts more quickly than expected, prompting me to think about accelerating the pace for our upcoming session.

Overall, it was an excellent lesson, and I was proud of Simon's progress and increased confidence. Occasionally, making early advancements can significantly impact the entire semester.