###### March 29, 2020

### The Benefits of Active Tutoring

I always struggled trying to learn math and science. It wasn’t natural for me. Some students “got it.” They understood math. But I never did. I “got by.” Friends helped me with assignments, or I copied off my neighbors. I never really took the time to learn and invest in my mathematics abilities. This was because I had a **fixed mindset** when it came to math. I thought—well I always do poorly at math—I must **be bad** at math. In a weird, sort-of-rational way, I believed that I was permanently bad at math. I didn’t have any successes to prove otherwise!

Many other students and families feel this same way. These families are frustrated because they know their student is bright and smart. She is just having a hard time learning math. I believe this is more about the way that math and science are currently being taught in schools than it is about the learner. Math is being taught as a lecture. Teachers have a strict agenda of what they want to teach. They give their lecture, pass out a worksheet, and then expect the students to learn the ideas. This is outdated and simply doesn’t work.

This style of teaching doesn’t hold its ground when compared to the new research being published on math and science education. The research today shows that students learn math and science **when they hear themselves verbalize their own mathematical and scientific thinking.** *This is a huge finding.* Up until now, teachers have been relying mainly on lecture-based teaching. They lecture during class, maybe assign some worksheets to keep the students busy, and they send them home with work to complete.

I grew up taking math courses centered around lecture. They were all about one person presenting the ideas. The problem with lecture-based mathematics and STEM courses is that students often think they understand what is going on, but in reality they are missing a few small distinctions on how to complete the problem or activity. These small misunderstandings compound on each other until eventually the student is so far behind that they need massive assistance in order to catch up. *But these small misunderstandings don’t have to compound! *We can stop them in their tracks!

If students were allowed the opportunity to simply discuss the concepts every day, then they would learn them much quicker. This is because when we discuss ideas we are better able to see the small holes in our own understanding. This allows learners to ask questions and fill in the gaps. Specifically, in active learning class rooms students spend the majority of the class discussing concepts, ideas, and working together on practice problems. This is the ideal way to learn math and science. But these courses require professors who invest a significant amount of time and energy into planning their courses and their course structure.

In college, I was fortunate enough to study under such a teacher. She not only knew mathematics, but also had a Ph.D. in mathematics education. She knew **how** to teach math. The entire course was centered around small groups. This is where everything started. We sat at a small table of 3-4 people and we discussed ideas *before* she taught us what the core concepts were. Most of the time we were able to figure things out in our small group!

Learning like this was difficult. It was challenging to learn this way because we weren’t simply spoon-fed the answer. We had to find it ourselves. We had to discover it. I took algebra 1/2, and algebra 3/4 this way. I also took pre-calculus and even two discovery-based calc I and calc II courses.

In my calculus classes, we spent weeks at our table discussing the concept of “rate-of-change.” We looked at graphs and got a good feel for what rate of change was. We learned that when you look at a graph, you can determine at what rate it is changing at any certain moment. Imagine zooming in on one small square of a graph. How fast is the line changing in that moment? **That is what a derivative is.** We learned that before ever hearing the word “derivative.” By the time she wrote the equation for a derivative on the board, we had already learned what it was. It was as if we built the meaning with our own hands. We felt as if we owned that word. We knew it inside and out.

Most people walk away from calculus course not learning anything. I’ve asked many people what they learned. (Try asking people yourself)! People generally say that calculus was useless and that they didn’t learn anything. “I can’t remember anything from that class,” they say. **And that is a total shame! **Because the concepts of calculus are so incredible. These concepts are fundamental to our lives. I think about rate of change all the time. You can apply it to the stock market, to human psychology, to climate change. What I find really fascinating, is that **you can even apply rate of change concepts to your own learning.** Think about it: *every course moves at a certain rate.* And each chapter moves at a different rate. It is also important to be able to think about your own rate of learning in each moment. How fast are you improving? Is your rate of change fast enough to learn all the material? If you aren’t learning at a fast enough rate, then you simply won’t do well in the course. If you realize you aren’t currently learning things at a fast enough rate, then you have to come up with a new plan or strategy. It’s all about having the right approach and mindset when it comes to learning.

One method we use with our clients—to increase their rate of learning—is to use **active tutoring** strategies. This means that we engage with out students. No longer are these students simply passively learning new knowledge. We believe that passive education is demoralizing. It reduces students’ confidence. It erodes their belief in themselves and their own ability to learn. Because essentially the message of lecture based STEM education is that: *we are the intelligent people with all of the answers, and all you can do is sit down in front of us and diligently take notes and learn. *Active learning flips this around and empowers students.

**Why is active learning so powerful?**

Active learning is inherently engaging. It gets students involved in the process of their own education. They cease to be passive observers of knowledge and become actively engaged in their own learning. This is empowering. It teaches them that they have control over what and how they learn. Active learning teaches kids to have a GROWTH MINDSET. It helps to **shatter** the fixed mindset which is inherently limiting. The whole idea of active learning is built around the growth mindset–that if you apply yourself, you can grow, you can improve, you can become better. And you do this by rolling up your sleeves and getting to work…. NOT sitting back and watching.

Importantly, active learning has been shown to do two main things: 1) it **increases students’ overall academic achievement** and 2) it **improves students’ attitude towards math and science**. It does all of this while also reducing misunderstandings about science and improving students’ understanding of big ideas and concepts.

Active learning works so well because it shifts learning from a one-size-fits-all approach to one that is inherently personalized and tailored to each student.

At Tutor Portland, we use an active approach to tutoring. Instead of simply giving answers or showing students how to solve problems, we ask them questions. We engage our students in critical thinking and in-depth discussions about concepts and topics. We ask questions and try to get students to connect the ideas they are currently learning to ones they learned last term or last chapter.

**This is often the first time they have *ever* thought critically about the ideas they are learning in school.** It’s a dramatic difference once students become engaged with the material. It changes from something abstract to something up-close and personal.

**We follow a few “active tutoring” rules very closely:**

- The tutor is simply
*a guide*, a facilitator — the tutor is not a teacher. - We give students time to
*think.* - We create a comfortable and relaxed learning environment.
- We ask open-ended questions.
- Curiosity is a quality which we embody, and which we attempt to bring forth within our students.
- Teach ethical behavior and thinking.
- Focus the session on the student. Not on the tutor or the parent or anyone else.

These are guidelines which help us create a positive and active tutoring environment.

*Updated March 2020.*

###### March 28, 2020

### Math Tutor Portland Oregon

**Math is a hard subject.** It’s *really, really* hard. I know. I’ve been there. My name is Eric M Earle and I’m the founder of Tutor Portland. As a middle school and high school student, I fell behind in mathematics. [I mean, I fell *way* behind]. And that made math and science really challenging for me because math is a cumulative subject. Math is inherently based on what came before it.

Courses and teachers don’t wait. They move on. This teacher had 25 other students to focus on. I simply wasn’t their top priority. I got lost as their attention was consumed by others. And my ability and confidence in mathematics suffered.

I wish I knew back then the things that I know now. At the time, I didn’t realize that math was important! I thought I would never need to know it. But I didn’t understand that math and science are everywhere in society. And additionally, there are a number of “mental-models” or frameworks for viewing the world—big concept ideas—that you can learn by studying math and science. You can apply these “mental models” in any career: finance, law, entrepreneurship, health-care, teaching—whatever the case, you can always use the big lessons from mathematics and apply those to everyday life and situations.

But when I was little I didn’t think about these things. I wish someone told me! My parents spent time looking for a private math tutor, but they didn’t find one because hiring and finding the right tutor can be challenging. As a result, I fell behind and was largely unsuccessful at math and science in high school. I fell behind and never caught back up. And *that’s* why I didn’t like math. I wasn’t good at it and because I didn’t focus on it. My lack of skill in mathematics caused me a lot of stress and anxiety. I remember once in grade school when I sat at the kitchen counter pulling my hair out and crying 😢 because I simply couldn’t understand math. I wanted to work on it but I was too far behind to even begin.

It would have been possible for me to catch up, but I wasn’t **resourceful enough.** I had all the resources 📚 in the world. My parents could have helped me. I could have asked my teacher. I could have found someone to help me. But I didn’t use those resources. I wasn’t resourceful. I was too young and didn’t have the drive and motivation to succeed. I look back now and realize that the right mentor or tutor could have really helped me. I wish that 27-year-old Eric could have had a conversation with my younger self.

*What would you have told him? *

I would have told him how important math is. I would have encouraged him to work harder, be persistent, and just sit down with tough ideas and eventually he would start to figure them out. I would have shown him that he could learn anything if he set his mind to it. And I would have sat down with him and helped him.

When you’re trying to learn a hard subject, it is helpful to have someone sitting down next to you. They can be the one reminding you: “together, we can learn anything” and “we are going to figure this stuff out.” I often make comments such as these with my clients. I want to reassure them that we are going to get through it. We can solve this. We can figure this out.

I ask my students to get the syllabus of the course. That way we can look at and analyze their course rationally—see what every assignment is worth—and craft a winning game plan for their course.

A lot of learning is about having the right mental attitude and frame of mind. Actually, so much of life is about that!

Sometimes learning challenging concepts and ideas takes time. You have to commit to them. **Sit with them.** You have to sit down and start researching and learning. But when you’re a beginner and lack confidence in yourself, this can feel so overwhelming that many students fail to even start. I know this—because I used to be one of those students. *And that is such a hard place to be in.*

When thinking about tutoring and some of the big ideas & themes in education and education research—I often sit back and think to myself—what type of qualities would a tutor have needed in order to help me? There are a few core ideas that always come to mind:

- A great understanding of math & and the ability to explain difficult concepts in simple ways 👍
- A pleasing personality and pleasant demeanor 👍
- Somewhat that I looked up to 👍
- Strong understanding of communication and psychology 👍
- The drive to teach and improve others 👍

Wow! What a great list of attributes. Those are the top qualities I’d want in any great tutor. Tutors are able to help in multiple ways. They provide resources and assistance to students. They can also teach students how to be more resourceful and self-directed learners themselves. The best tutors *empower* their students to achieve their own learning goals. The best tutors also have a sense of persistence. They sit down and say—in a reassuring way, “we are going to figure this stuff out, okay?” That alone is incredibly helpful to a student. Normally, when I say this, I see the student visibly relax. I can almost feel my sense of calm and confidence being transferred to the student. The best tutors come from a place of knowing confidence. The best tutors are people who themselves had to struggle with the subject. And because they were able to overcome their own learning struggles time and time again, they are now in a blessed place to help others.

## My Story (continued…)

I got decent grades in math and science, but I never understood the subjects. It wasn’t until my early to mid-twenties that I developed the desire to start relearning mathematics. I had a life changing volunteer trip to India. I was volunteering at a neurology clinic up in northern India and I witnessed first-hand the incredible amount of poverty [and absolute lack of access to healthcare]. **And it moved me.** I saw people

*suffering*and I realized that I had to help. That’s when I became a pre-medical post-grad student. At that point, my mathematics was so terrible that I couldn’t get into a college math class. I took the placement test at Portland State University, but it was so bad I

**couldn’t even get into math 70 [high school pre-algebra].**

*So I started working with a tutor.*We met at the Multnomah Athletic Club twice a week. And slowly I started to improve. By fall term I was ready and enrolled myself into math 95. I remember once telling a woman this and she laughed at me. She laughed because I was starting back in such a low level of math. This didn’t bother me because I knew deep inside of me that in due time I would be taking advanced mathematics courses. And that is exactly what happened.

**I earned straight A’s in math 95, 111, and 112.**

**I fell in love ❤️ with mathematics **because of my trigonometry professor, who taught our class with **active learning** strategies. [This is something we now employ at Tutor Portland]. These **active learning techniques** helped me learn math easily and effortlessly. **I went on to earn over 100% in both Calculus I and Calculus II. **

Learning math has continued to pay benefits. It has helped me in every area of my life. Learning math teaches you mathematical reasoning and “number sense.” It gives you the ability to look at numbers and data and just *make sense* of them without extensive analysis. *You just start to *get* math and numbers.* This has taught me that I can truly learn anything. I took my most challenging subject and mastered it. *That* is empowering. *That* is what we strive to do for students at **Tutor Portland**.

## Eric’s Perspective

👍 All of this has given me perspective. It has given me a unique point of view on 1) how hard it can be to learn math and 2) how rewarding it can be to finally understand it! As a 20-something, I started tutoring students in the liberal arts. I taught public speaking, communication, writing, and Spanish. Soon after I started, parents began asking if I knew any good Portland, OR math tutors. I began interviewing math tutors. Eventually, I found a mechanical engineering student at PSU who was a good fit. He had a great ability to explain difficult concepts in simple ways. Soon I became a math tutor as well.

I realized that my unique view on math and learning was something that had to be available to more Portland families. Together, my math tutors and I have developed and honed our **active tutoring approach** that works to engage students in their course material and get them thinking deeply about math. We have also developed our own **private mathematics curriculum**. All of the research today shows that** students learn math when they hear themselves verbalize their mathematical thinking. **So that’s what we focus on. We ask questions which encourage students to engage with and think critically about the course material. 👍

## If I can learn it…

As you have read already, math used to be a huge challenge for me. I avoided it at all costs. And my attitude was that “math doesn’t matter.” This is a defensive and protective attitude. And I was holding it because I was afraid. I was engaging with math from a place of fear and lack.

Now, that has all changed. I relate to math from a place of confidence, abundance, and curiosity. My mathematical reasoning skills are highly developed. I can **use and apply** the mathematics that I know to real-world situations. And math has provided me with different **mental models, **or ways to think about and analyze the world. Mental models are things all disciplines have. They are frameworks—or guiding visions—that help us see the world in certain ways. That’s why an **interdisciplinary approach** to learning is so favored because it allows you to think about complex problems through various lenses.

## Tutor Portland’s Mission

That’s why we’ve made it our mission to help all students—from middle or high school to adult learners—understand mathematics and apply their learning to other subjects. We’ve made it our mission to help children and families overcome the stress and anxiety around math.

[And – hey! – this is totally normal. It’s normal to have anxiety about math]. But it’s not acceptable to never overcome your fear. The world needs young people who know mathematics. More and more the jobs and positions are shifting towards students who understand STEM (science, technology, engineering, and mathematics). All of the research shows this. America is being an economy built on math, technology, and science. The best employees in the future will need to know these ideas and be able to think critically about math, science, and more.

High school students often wonder what the point of studying math is. “When will I ever use this?” They ask.

I used to ask those exact same questions!!!

We get it. It’s natural to ask that. 👍

It’s our mission to help them learn math! (Leave that stuff up to us!!!!!). Our goal is to help students understand how critically important math is to their future. Do they want to be a doctor, an engineer, a scientist, a businessman? All of these occupations require math! Math will make you better at whatever it is that you decide to do. At Tutor Portland, we have an element of mentoring in all the tutoring that we do. We believe it’s important to inspire students and **make them want to learn math, **instead of forcing them. We’ve found that by connecting a student’s future goals with what they are learning today, they become ten times more motivated to study and put the effort it. 👍

But it’s important not to push subjects on students. We often hear about teacher and parents who, in a very well-meaning way, tell their students the reasons they need to learn math. This doesn’t work 🚫. Countless studies have shown that people become **more motivated** to do things when they **hear themselves give their reasons** for **why** they want to do something. Therefore, we like to ask questions. We ask students questions like: “So, we know you probably aren’t interested in learning all this mathematics stuff—especially not on Sunday!—but if you were interested, why might you be?” **Questions like this do a lot. **First, they provide students with autonomy. Autonomy is something that is important for *anyone,* but it is especially, especially important to teenagers. Second, this question gets the student thinking about why they might want to learn math. There are several other follow up questions to ask.

It’s important to note that questions such as these need to be asked **in the setting of a relationship with strong rapport. **This is where many teachers and tutors go wrong. They try to “motivate” their students without first developing a relationship with them. This erodes trust. **Students don’t need to be “motivated.”** Students have all the motivation they could ever need already inside of them. We just need to coax it out. **But it’s elusive.** That’s why tutoring is an art as well as a skill.

## Math Tutors in Portland, Oregon

😃 At Tutor Portland, we’ve learned a few things about how to find a great math tutor. The first, most important thing that we look for is integrity and character. In order to gain the trust and respect of a student, it is necessary that a tutor must first show and demonstrate these deeply held qualities. In addition, it’s really important that a prospective tutor knows how to teach math. I once hired a physics tutor who was very brilliant. He had a Ph.D. in physics and was clearly smart. But he couldn’t get through to kids. He couldn’t explain challenging ideas in simple ways. This is the most important thing that is required of a tutor. I spoke with our clients regarding the Ph.D. tutor. These families told me that he was explaining concepts in a way that was over the students’ ability to grasp them. Eventually, we had to let him go. It’s not enough to be good at a subject, tutors have to know how to teach ideas and concepts in multiple ways. In fact, **the ability to teach tough concepts in easy effortless ways is the number one ability of a good tutor. **Understanding the material should be a given. That is baseline stuff. A lot of people understand mathematics. **But very few people know how to teach math in a way that anyone can understand. **

Over time we have developed a comprehensive checklist regarding what we look for in math tutors. Here are *just some* of the key elements that we look for:

- 👍 Can this tutor explain tough concepts in 5 different ways?
- 👍 Can this tutor use metaphors [which are relevant to the student’s life]?
- 👍 Is the tutor able to adopt an
**active learning approach**where he engages the client in in-depth discussions about mathematics? - 👍 Does this tutor embody virtues and integrity?
- 👍 How adept is this tutor at teaching mathematics?

😃 These are some of the key questions that we can ask ourselves before hiring any math tutor.

If you want to learn more about us, please feel free to email us or call us at (503) 347 7102.

*Post updated March 2020.*

Tutor Portland | Math Tutoring

950 SW 21st Ave #1117

Portland, OR 97205

eric@tutorportland.com

(503) 347-7102

We offer **Math Tutor** services in:

- Lake Oswego
- Milwaukie
- Vancouver WA
- West Linn
- NW Portland

We offer tutors in the following specific Math subjects:

- Tutoring algebra
- Geometry tutors
- Calculus tutors
- Statistics tutors
- Basic mathematics tutoring