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I am a Senior at the University of Arizona majoring in Math and Ecology/Evolutionary Biology. I have also been working as a Math and Science Tutor at my former college since the Spring of 2013. While working there, I earned a CRLA Tutoring Certification and greatly refined my knowledge of Math and Science. I tutor a variety of subjects, but my passion definitely lies with Math. I am so passionate about Math that my ultimate goal is to become a Professor of Mathematics at the University of Arizona. I am a former athlete and it wasn't until I went to college that I realized that Math could be enjoyable. While working with students, I try to keep the environment lively. I want them to enjoy Math and Science too. In my free time, I like to be physically active and stay busy. I spend time at the gym, I go hiking and camping with my dog, play video games, and hang out with friends. I also do quite a bit of outdoor photography and I love going for long rides on my motorcycle.

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Lucas’ Qualifications

Education & Certification

Undergraduate Degree: University of Arizona - Bachelor of Science, Math, Ecology & Evolutionary Biology


Hiking, camping, on and off-road motorcycle riding, sports, and video games.

Q & A

What is your teaching philosophy?

Everyone can achieve at the highest level of academia with the right guidance. In order to push into the next level of understanding, a student must be tasked with a challenge that is just beyond their current ability. Overcoming the slight challenge causes a student to feel accomplished and thus makes them want to be challenged and succeed again. As a teacher, my job is to create those challenges and guide students through them in a way where it is clear that they did most of the work.

What might you do in a typical first session with a student?

The first session is where I establish a rapport with a student. One of my professors once shared a quote with me that I will never forget, "students won't care what you know until they know that you care." I go in with that mentality when I meet a student for the first time. I also have to be sure that the student knows I am an expert in the content so I don't end the session until the student's questions are answered and they begin to let their guard down.

How can you help a student become an independent learner?

When it comes to math, showing a student how to really use the TI-84 calculator is one of the best things I can do for them. Those calculators are an amazing tool and it still blows me away that we're allowed to use them since you can do most of the problems in math classes all the way up to Calculus 2 directly on the calculator. In science, I show students how to answer their own questions instead of directly giving them the answers. I've found that in general students have a hard time with science when they have a hard time organizing a large amount of material. Something as simple as showing a student how to quickly search through a textbook to find a definition can prove to be invaluable when it comes to helping them become an independent learner.

How would you help a student stay motivated?

Students lose motivation for two main reasons. Either because they are totally lost in a class or they are so far ahead that the class bores them. The fastest way to overcome these obstacles is through the use of scaffolding for the student who is totally lost and providing opportunities for enrichment when a student is way ahead of the class. A student who is lost in a differential equations class likely needs more instruction in factoring and integration before they are ready to keep up with the rest of the class. A student who is bored in college algebra likely had the class in high school and thus could benefit from being asked to do an extra credit application problem where they must integrate skills from the entire class.

If a student has difficulty learning a skill or concept, what would you do?

It depends on the content area and whether it is a skill or concept. Learning a skill such as addition or multiplication unfortunately is boring and the best way to get better at it is to simply practice it over and over. A concept on the other hand can be explained in many different ways. For example, the derivative of a function can be thought of using the limit definition you'll see in a textbook and it can also be explained as the slope of the tangent line to a function at a given point. It can also be thought of as the slope of a secant line over an infinitely small interval. A concept such as independent assortment in genetics can be explained the way Gregor Mendel did way back in the day or it can be explained using a couple of pencils lying around on the table. To answer the question, the only reliable way to learn a skill is to practice it but a concept can be explained in multiple ways until one of the approaches works for a student.

How do you help students who are struggling with reading comprehension?

Reading comprehension skills are precisely the reason that word problems in math and science are so difficult for students. When I have a student who is behind in reading comprehension I share the 4-step process for solving word problems with them. I've found that process to be extremely helpful for students and once they get used to using it I can assign increasingly difficult word problems and before we know it, the student is answering SAT level word problems and the reading comprehension skills are back up to grade level.

What strategies have you found to be most successful when you start to work with a student?

With tutoring, one of the most important things is to start off by developing a positive relationship with a student. No one can learn one on one from someone they don't like, so that means that one of my first priorities is to ensure that I come off in a professional and friendly manner to students.

How would you help a student get excited/engaged with a subject that they are struggling in?

Generally, once a student starts to struggle in a subject, the relevance of the content starts to be questioned. Showing the student a problem that can be solved using the content they are learning can drastically increase the relevance of the content. We don't necessarily have to solve the problem; sometimes just knowing that you can use math or science principles to solve this problem will be enough motivation to make a difference. If not, one of the best motivators is success. Giving a student a problem that I know they can succeed in will help raise their self-confidence, and thus increase their motivation to continue to succeed.

What techniques would you use to be sure that a student understands the material?

When doing math, I can always make up a similar problem and ask the student to solve it. I can also ask the student to rephrase an explanation of a mathematical or scientific concept in a way that is different from the way I, or their textbook, explained it. In science, I can ask the student how they think this could be applied in a real world or laboratory setting. That would take them all the way up to the top of Bloom's taxonomy, and if they can come up with a reasonable application of the concept then we are golden.

How do you build a student's confidence in a subject?

Success is the most reliable way to build confidence. The more a student succeeds, the more confident they will fell with a specific subject. Thus, in order to make a struggling student feel more confident I would first bring the material down to a level they can currently handle. Then we would slowly step up the difficulty until the student is solving problems and asking questions at a higher level than what is currently being presented in class.

How do you evaluate a student's needs?

This depends on the age level of the student. College students generally know exactly what they need form a tutor, so there isn't much work to do in those cases. Younger students need to be informally assessed to find out what the best course of action is. I try to generalize and say that most students need a tutor to be either a coach or a second teacher. The coach just hangs out in the background and pushes the student forward whenever they are struggling. A second teacher explains concepts in a new manner and will model exactly how to do problems and study strategies for the student. A student who needs a coach will generally be able to fill in the blanks when I ask an open ended question, and a student who needs a second teacher will be completely lost when set on their own to do problems. Thus I try to let a student try a problem on their own and evaluate whether they need a coach or a teacher by the way they approach the problems they are presented with.

How do you adapt your tutoring to the student's needs?

Going back to the coach and second teacher analogies I gave earlier, I will constantly bounce between the two roles during a session. If a student is stumped, I will take on the role of second teacher and explain the concept to the student while asking leading questions until they are confident enough to pick up their pencil and write something on the paper. That's when I become a coach and push the student through the problem from the dugout. Once the student finished the problem, I generally take up the role of second teacher again and summarize the logical process taken to solve it. Sometimes, students don't need me to take the role of second teacher at all in order to begin a problem, and sometimes the student needs me to be a second teacher all the way through a problem by modeling it for them and then giving them a similar one to coach them through. In short, depending on what the student needs, I can go from solving problems for students all the way to not even touching my pencil and using Socratic questioning techniques to push a student through a problem.

What types of materials do you typically use during a tutoring session?

I try to get students used to using the TI-84 calculator as much as possible, since those things are amazing and they can do anything that a student might need to do all the way up to a Calculus 2 class, and the calculator continues to be useful all the way up until proof-focused courses. I also use Wolfram Alpha all the time, as it is both an incredible resource and a nice way to get students used to typing mathematics into a computer. Other than that I just bring pencil and paper with me, since a computer with internet really can do more than we would ever need nowadays.

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