September 12, 2020
The Mystery of Who Invented Calculus
Let’s say you were the creator of one of the world’s most useful and lifechanging inventions, but someone else discovered that invention at the same time and wanted to claim the credit. Wouldn’t you be … I don’t know … furious?! Wouldn’t you fight tooth and nail to be recognized for coming up with the essential mathematics behind engineering, computer science, and economics? That’s exactly what happened between Sir Isaac Newton and Gottfried Leibniz over the claim of who invented calculus. The problem is, there’s still some major controversy over who really created it despite there being hard evidence of both their work. Maybe you can decide for yourself…
While today’s scandals circulate around notorious twitter feeds, Newton and Leibniz’s battle for recognition over who invented calculus rocked the entirety of Europe in the 17^{th} century. England was so invested in the mathematician from their country that they stuck with Newton’s theory setting them back 100 years in mathematical progress. So does that mean Leibniz was the first inventor? Well it’s not actually that simple.
And up close, the debate gets ugly and personal. There are intimidation tactics, receipts, slander, cliques (looking at you British Royal Society), and lots of shade. This isn’t the stuff you’ll find in your textbooks, but it was enough to make two scientists go to war to prove their accomplishments. They knew that being named the inventor of calculus was too significant to be left in the dust, forgotten. If they fought hard enough for the title, they knew we’d be talking about them today.
Background
When you think about who invented calculus, you might imagine some pompous aristocrat in a powdered wig. But early traces of calculusrelated math were actually initiated in the time of the toga, long before the 1600s.
Around 250 BC, Archimedes of Syracuse was the first person to conceptualize the tangent, which is a straight line that grazes a curve and an instrumental concept in today’s calculus. This concept was described in the Archimedes Palimpsest, a document that uses a variety of rudimentary concepts to solve problems now treated by modern calculus. This kind of math would later be used by both Newton and Leibniz.
Other Greek philosophers built off Archimedes’ work in calculus, and in 500 AD India, mathematicians wrestled with the same early concepts. The astronomer and mathematical theorist, Aryabhata, began using infinitesimals to study the rate of change. He was later succeeded by astronomer Vatasseri Parameshvara Nambudiri, who invented calculus fragments, like an early version of the mean value theorem^{ [1]} from the 15^{th} century.
So, if calculus has been around for a while, why are Newton and Leibniz fighting over who gets all the royalties? Weren’t they just two links in a long chain of people who invented calculus before? Because it didn’t have the legs to stand on as an independent type of study before they put all the pieces together. In order to understand their contributions and why it’s important to know who invented calculus, you first need to know what calculus is in the first place.
Essentially, calculus is a branch of mathematics that quantifies how a thing changes. It’s kind of like how geometry examines the properties of shapes and how algebra is the study of arithmetic (numbers). More specifically, calculus uses infinitesimals, or an endlessly smaller measurement than real numbers, to describe the size of a change. So, the person who invented calculus would be recognized as a genius! This is what Newton and Leibniz were at war over.
Now, our mystery of who invented calculus takes place during The Scientific Revolution in Europe between 1543 – 1687. This was a time when developments in math, physics, astronomy, biology, anatomy, and chemistry dramatically changed how people thought about nature. Seriously, people began challenging archaic religious beliefs with scientific discovery about the center of the universe^{[2]} and fundamental human rights. ^{[3]}
You can imagine how heartbreaking it must have felt for both Newton and Leibniz to get their names among the ranks of Galileo, Kepler, and Copernicus. They created a feasible means of doing math with numbers that didn’t totally exist yet! Not only were they fighting to protect their honor and pride in their work, but the chance to become an Alist celebrity. These guys were fighting over Oprah vs. Robert Downey Jr. levels of fame. Indeed, being the person who invented calculus is the kind of stuff that puts you in history books and is precisely what was at stake for both theorists.
Who are the Defendants?
Let’s start with the more wellknown contender for who invented calculus. Sir Isaac Newton was born on December 25, 1642 (a Christmas baby!) in the United Kingdom and became a mathematician, physicist, astronomer, theologian, refusing to stay sequestered on his mother’s lowincome farm.
Isaac is recognized for discovering gravity when he allegedly witnessed an apple falling while contemplating the literal forces of nature. He later realized that gravitational forces constantly exist between all objects and used this theory to explain that the Earth moves in relation to the Sun.
Newton also has many other accomplishments. He discovered ways to describe how thing’s move with force [4], how colors are actually made up of light, and he initiated groundbreaking studies on the speed of sound! Newton was also mentored by Isaac Barrow, one of the foremost thinkers of calculusish mathematics^{[5]} during the European Enlightenment. It wouldn’t be that surprising if such an accomplished mathematician as Newton came up with this branch of the subject. Why not say he was the one who invented calculus as well and call it a day?
Because…
Gottfried Leibniz was also an ambitious scholar and a passionate thinker in his own right. Born on July 1^{st}, 1646 to wealthy German parents, Leibniz inherited an impressive collection of advanced philosophy at the age of six when his Father passed away. Many of the works he read weren’t available to general school audiences, so he took an interest in the exclusive material because, well, it’s not like they had Youtube back then.
By the age of 18, Leibniz graduated with a Master of Philosophy and was awarded a Bachelor of Law after just one year of legal studies. He later developed the binary system,^{[6]} invented modern formal logic, predicted problems later addressed by Albert Einstein, and daydreamt about computing systems that could do algebra. Leibniz’s accomplishments made him a valid response to the question of “who invented calculus.”
Leibniz even created his own theory of truth. Seriously, he thought he could explain the entire universe through simple logic statements. He was so famous, even before being considered as a potential mathematician who invented calculus, that the internationally renowned German chocolate covered biscuits were named LeibnizKeks. Apparently that’s what happens when you’re the most notable person to reside in Hanover, where the manufacturer is located.
Now that you’ve got an idea of who Isaac Newton and Gottfried Leibniz are and what they’re capable of, it’s time to figure out who invented calculus and review the hard evidence.
The Evidence
Despite the controversy over who invented calculus, there is actually a welldocumented record of each mathematician’s findings over the years. We’ll use this here to paint a picture of how things went down so you can really be the judge of who deserves the sole title of inventor.
1666
This is Newton’s annus mirabilis, the “miracle year” when he discovered gravity and started to theorize about colors. In 1666, Newton was sent home from Cambridge University after graduating due to the bubonic plague. With all this time on his hands, he initiated work on calculus, calling it then, “the method of fluxions.” Newton focused on geometry and the physical world in his work rather than theoretical concepts.
However, all of this thinking was off the books and in the early stages of development. Nothing had been published yet and his work largely remained in his personal collection or resided in letters to correspondents…
1674
Leibniz started working on his theory of calculus a few years before making a breakthrough in 1675. While he was in Paris on November 11^{th}, 1675, he made a breakthrough, inventing a new system of notation. This breakthrough is important because it was unique from Newton’s methodology in that it approached calculus from a completely different side of math. Ultimately, it was more robust and practical.
1686
Leibniz published the Discourse on Metaphysics, his formal explanation of calculus in 1686. This book is significant because it means that Leibniz published his calculus work before Newton.
1687
A year after Leibniz’s publication, Newton published his findings in the Philosophiæ Naturalis Principia Mathematica. This is the big one, the publication that is praised as one of, if not, the greatest science book of all time. Despite some early problems in the work, Newton used this new calculus in his book to support the theories in his book.
The Principia Mathematica is where Newton presents his findings about gravity, motion, and planets, basically all the stuff that he’s famous for. It swiftly won him presidency of The Royal Society, the highest independent scientific academy from the United Kingdom that still operates today. Newton’s esteemed position as the head of the most influential scientific group garnered him a steep advantage over Leibniz in terms of cultural recognition.
The Rivalry
At first, Newton and Leibniz didn’t have an ugly conflict. They were both highly publicized members of the scientific community, so it was likely that they had seen each other’s work. But since Leibniz had published first, it was Leibniz not Newton who had sole credit for inventing this amazing new field of mathematics. The recognition Leibniz won for Discourse on Metaphysics, may have left Newton with the need to center his own accomplishments.
 Leibniz published work on calculus in Discourse on Metaphysics: 1686
 Newton’s published work on calculus in Principia Mathematica: 1687
Newton notably led The Royal Society through an aggressive agenda to publish the Commercium Epistolicum, a ledger containing letters from both Leibniz and Newton to correspondents about their work on calculus. The point of publishing this ledger was to publicize dated documents proving that Newton started working on calculus before Leibniz.
The two key pieces of evidence from the Commercium Epistolicum that Newton used to prove he was truly the one who invented calculus include: 1) Letters submitted to The Royal Society from Isaac Barrow, Newton’s mentor. These letters showed that Newton’s work in calculus began in 1666, and 2) Letters submitted to The Royal Society from Leibniz, explicitly expressing an early interest in calculus dated in 1673, clearly after Newton’s work began on the subject.
 Newton’s letters to Isaac Barrow about calculus: 1666
 Leibniz’s letters to The Royal Society expressing interest in calculus: 1673
But Newton wasn’t satisfied. Proving that he started working on calculus first wasn’t enough; he wanted to completely annihilate Leibniz’s credibility. After all, Leibniz’s method is superior to Newton’s, and Newton knew it. Newton also knew that this branch of mathematics was too important to become irrelevant in its history, so he embarked on a complete smear campaign to prove that Leibniz plagiarized.
It devolved into an allout war to prove who invented calculus. Both Newton and Leibniz tried publishing several statements expanding on how each one’s math was superior to the other’s. But Newton had a huge advantage: he was the president of The Royal Society, and no one dared challenge the establishment.
The one notable scientist that stood up on Leibniz’s behalf was a mathematician named Johann Bernoulli. When Bernoulli publicly announced support for Leibniz’s credibility as the one who invented calculus, Newton swooped in with a silent brigade of intimidation tactics. Bernoulli eventually retracted his statements, and Leibniz was left alone, again, to fend for himself.
The finishing blow of Newton’s attack came in the form of a devious claim: Newton argued that because his letters were circulating around the scientific community at the time, Leibniz must have seen them and started copying off Newton’s invention. However, Leibniz’s methodology is dramatically different from Newton’s. More than anything, Newton’s evidence proves that both Newton and Leibniz independently discovered calculus using their own approaches to the work.
Conclusions
In the end, The Royal Society deemed their president the sole discoverer of calculus in 1715, using Newton’s name to proudly answer “who invented calculus” while Leibniz’s credibility dwindled until his death a year later. As a result of the UK’s nationalistic pride in Newton, they refused to use Leibniz’s superior method and suffered for it as the rest of Europe progressed without them.
Today, the scientific community recognizes both mathematicians for their work and respects that they individually made discoveries about calculus independently. Knowing who invented calculus is the kind of history that isn’t taught in textbooks, but it can make math more interesting when you learn where it came from.
Clearly, it’s important to engage in ideas beyond the text with peers, mentors, tutors, and teachers. You might even be able to bring up who invented calculus at a party as a secretly dramatic tale of scandal and sabotage.
Sources & Citations
^{[1]} The mean value theorem is a type of formula that calculates the sine, or a specific angle’s dimensions.
^{[2]} In 1543, Nicholaus Copernicus argued that the Sun was near the center of the Universe and that the Earth along with all the other planets orbited around it in circular paths.
^{[3]} John Locke argued for the fundamental human rights of “life, liberty, and property” in An Essay Concerning Human Understanding in 1689.
^{[4]} Newton’s Three Laws of Motion: 1. An object is equal to its mass times its acceleration, 2. The force of an object is equal to its mass times its acceleration, and 3. When two objects collide, they apply force to each other of equal magnitude and opposite direction
^{[5]} Barrow pursued the concept of the derivative and linked calculus concepts like differentiation and integration.
^{[6]} The binary number system serves as an alternative to the decimal system that is used in our day to day actions. Rather than using a 10digitbased system, the binary number system uses 1’s and 0’s to simplify the design of technology. Essentially, it makes up the basis of all contemporary electronics and computers.
April 2, 2020
How Tutoring Can Benefit Students
The Benefits of Tutoring
The benefits of tutoring vary from student to student, but there is no doubt that any student, of any skill level, can benefit from tutoring. Tutoring can assist students that are struggling to keep up with subject matter or challenge those who need an extra push. Tutors can challenge students without evoking feelings of judgment, or the emotional baggage students often feel when working with parents or teachers on school work. We see this a lot. Students time and time again prefer to work with a tutor rather than with their parents or teacher. And this makes sense! A relationship with a tutor is more downtoearth and relaxed. Students feel comfortable around tutors. They know that they can ask questions without being judged.
Below we discuss how tutoring benefits students and why you should consider enrolling your child, or self, in a tutoring program.
Students that are enrolled in private tutoring benefit from an individualized learning experience. They can learn difficult subjects like math and science better when they verbalize their own mathematical/scientific thinking in a tutoring session. This is critical. Many students are never given the chance in large classrooms to hear themselves speak and think about mathematics. During our tutoring sessions we employ an “active learning” strategy. There is a lot of evidence showing that active learning strategies help students learn and improve their retention of subject matter. The whole idea of active learning is that students are engaged in the process. They are asked to think about what they are doing. This is a form of metacognition. Metacognition is critical to learning. It provides the bridge between the worksheet or the problems that the students are doing—and the actual learning itself. Learning does not just happen. It doesn’t simply occur when students do homework. Learning functions when the learning environment has been intentionally designed based on scientific evidence.
There is a wide body of evidence that shows that when students solve difficult problems with the support of a tutor, instructor, or peers, they are better able to retain information and achieve their desired learning goals.
Tutors help students build academic skills and assist them in areas they struggle in whilst preparing them with improved work and study skills. The extra layer of preparedness and confidence students gain through tutoring will increase their overall academic achievement. This confidence radiates out to every aspect of a student’s life. It affects how they show up to the classroom. It improves their ability to make connections between complex ideas. It gives them a solid foundation and confidence upon which other successes are built.
The accountability a tutor provides encourages students to stay on track with their coursework and follow through with tasks. When a student is prepared for their subject matter, and don’t feel overwhelmed, they are more inclined to finish homework and other schoolrelated tasks. This helps in so many ways. Firstly, it is always better to be prepared! This alone really helps students. They start turning in assignments on time. They understand when HW is due and what is expected of them.
Customized tutoring programs help ensure your child is learning effectively in a way that works for them. This is good for students who need an extra challenge, as well as students that need a slower pace and more individualized teaching. Simply put: not every student learns at the same pace. This is why lecturebasedlearning often fails students and leaves many behind. The course must continue. And the teacher has to “sacrifice” some students for the benefit of others.
Through tutoring, students can learn work and study habits they might miss out on through standardized public schooling alone. The social, behavioral, and independence skills students learn through tutoring will benefit them inside and outside of school. These skills really apply to every area of life. Tutoring helps students learn how to set goals. It teaches them the importance of sitting down with a subject and just sticking with it. Tutoring also helps students learn that it is okay to ask for help and seek assistance from others.
Through tutoring, students learn how to recognize and control their learning pace and take initiative when doing their coursework. When a student feels like they are able to learn better thanks to the tools tutoring prepares them with, they are less likely to feel “leftbehind” or too nervous to seek help when needed. Tutoring puts the learner in the driver’s seat. They are instantly incharge of their own learning. Rather than being passive observers—like they are during class—students are transported to a block of time where they have to direct their own learning. With help, of course! Often it is the student who directs the tutor. The student says, “this is where I need help. This is what I’m struggling with.” Those are invaluable skills! In this way, tutoring helps students become better at recognizing their own weaknesses and strengths. This is helpful when attempting to learn or improve at any skill.
Tutoring can help school become fun for students. Encouragement and praise surrounding school can help with feelings of frustration toward school. Additionally, the confidence students gain via tutoring makes them feel more prepared going into school and other academic settings.
When a student feels more confident in their ability to succeed in school, and other academic settings, their overall confidence will increase. The tools learned in personalized tutoring boosts student’s selfesteem and confidence as they become more successful students.
Tutoring helps identify and manage any learning difficulties students may face resulting in an improved attitude towards school and learning. The oneonone teaching that tutoring provides can help identify any issues that may get looked over in a large classroom setting.
The accountability that tutoring provides can go a long way in student’s overall dedication, and persistence in completing schoolwork and other schoolrelated tasks. Through tutoring, students will eventually realize their personal growth and begin to take ownership of their own studies and other responsibilities.
Want more resources? Check out our free resource on how to create an effective home learning program for your child!
REFERENCES
Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
Article Updated April 2020
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, sortofrational 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 lecturebased 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 lecturebased 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 34 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 spoonfed 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 precalculus and even two discoverybased calc I and calc II courses.
In my calculus classes, we spent weeks at our table discussing the concept of “rateofchange.” 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 onesizefitsall 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 indepth 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 upclose 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 openended 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 “mentalmodels” 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, healthcare, 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 27yearold 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 selfdirected 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 midtwenties 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 firsthand 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 premedical postgrad 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 prealgebra]. 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 20something, 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 realworld 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 wellmeaning 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 indepth 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 call us at (503) 347 7102.
Post updated March 2020.
Tutor Portland  Math Tutoring
950 SW 21st Ave #1117
Portland, OR 97205
(503) 3477120
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
September 1, 2019
General Chemistry Tutor
The Benefits Of Having A General Chemistry Tutor
Chemistry is one of the hardest subjects. It’s one of the most popular and common subjects that we assist with at Tutor Portland. General chemistry concepts (in both college and high school) are challenging because gen chem forces you to think and understand what is going on. In addition, the subject is highly quantitative.
But the best students are able to weave in both a qualitative and quantitative understanding. This is something that I worked very hard at developing. I was always trying to understand big concepts. I figured that if I understood how the molecules were interacting and what was happening in the beaker, then I would do just fine on the exams. And that played out to be true. In chemistry, even highly quantitative problems can often be solved without crunching any numbers. If you have a really good understanding of the laws and properties of chemistry—and the definitions of the terms—then you can often figure out the answer to multiplechoice problems without using your calculator.
Challenges With General Chemistry In School
Another reason that general chemistry is challenging is that there is often intense timepressure on the examinations. You might have two or three minutes per problem. And some easily require four or five. That means you have to use your time very wisely. You have to have calculated so many practice problems, that you are acting on muscle memory. When you see a simple problem, you don’t even have to think about it, you just start plugging numbers into your calculator instantly. And you can’t be slowly typing numbers in. You are *flying* through that exam.
One of the best tricks is to be able to answer some of the longer quantitative problems instantly without having to calculate. If you have a really solid understanding of the principles of chemistry, then you should be able to do this. While your friends are struggling to calculate these long problems, you will have moved on and will have more time to spend on other difficult problems. That’s why learning concepts is so valuable.
Learning about the concepts of chemistry is valuable for other reasons, too. These are powerful concepts that you can apply to everyday life. They help you think about the world. They also help you ponder the world around you. It’s fascinating to learn about the autoionization of water. H2O is constantly changing form right in front of our eyes, switching back and forth between water, hydronium, and hydroxide. That makes you realize the law of imperanance—that nothing in life is truly permanent, everything is constantly changing shape. Things are unstable. When you truly feel and grasp this concept, you will have peace because it teaches you that there is nothing to cling to or hold onto. If things are constantly changing, it doesn’t make rational sense to try and cling to anything. Without clinging there is no attachment. Without attachment, there is no agitation. And without agitation one is able to attain nirvana. That’s one of the many connections between chemistry and Buddhism. Chemistry can also connect to investing. Just as water is constantly changing, so too is the stock market. Everyday “Mr. Market” comes to you and tries to offer you stock at a certain price. And all you have to do is wait. You can wait for the day when that price is low enough, and then you buy.
Other science courses also teach us lessons about life. For example, Biology teaches us about “fundamental” and “realized” niches. Fundamental niches are the total amount of space and resources that a species could possibly occupy. But no species ever realizes it’s entire fundamental niche. Species are only able to attain their “realized” niche. This is the same in your life. It has brought me a great deal of peace to realize that it’s natural that I won’t reach *all* of my goals. I won’t attain my entire fundamental niche. But I can attain my realized niche!
In addition, many species in biology are able to find coniches. Instead of complete competition, they are able to live sidebyside and even benefit from each other. We can see this play out in life as companies compete with each other in the market. They often don’t entirely destroy other companies. Each company is able to carve out its niche. This is the same with people, too.
Other ideas in chemistry help us think about life. For example, we can consider how the ideas in bonding theory relate to our life. I like to think about how when a bond is created there is actually a decrease in potential energy, and the new molecule is more stable. This is one of the benefits that relationships and other people bring to our life. When we engage with intimate relationships and close friendships and family, our lives actually become more stable than they were before.
One huge idea in chemistry and biology is the old “structure and function” lesson. This concept says that the structure of something correlates very closely with its function. This gets very specific in subjects such as organic chemistry. The smallest changes in structure—the placement of an atom or even the 3D shape of something—can dramatically change its function. This can help us ponder our own structure. What are our strengths? What function in society would we be best suited for? What will my life look like at a certain school, job, or occupation? The structure of the day is so different depending on what you choose.
But most importantly, underneath all of this, chemistry is simply inherently interesting. It is fascinating to learn about these ideas. Still, even with the vast beauty of chemistry, it’s very challenging to convince kids and students to like it. It takes finesse. It requires good communication skills and an open, likable personality. You have to think about things from the kid’s perspective. How can you connect with them? How can you empathize with their life? Try to think, connect, and feel what might be going on in their life. Chemistry is probably the last thing in the world they want to focus on. I always thank my students and tell them: “I know that Chemistry is the last thing you want to be doing on a Sunday, so thanks for putting the time and effort in. It won’t be too long or terrible, and we’ll get through it.”
This builds connection and rapport. With that little sentence, you have separated yourself from teachers and other educators who only care about imparting their agenda. This sentence shows that you are actually taking an interest in *their* life and attempting to see things from their perspective. If you ever want a student to try and see your perspective on something, you first have to try seeing theirs. That is how you build a connection. And connection and rapport are how any great learning process begins.
Hire A Chemistry Tutor
If you would like to learn more about hiring a chemistry tutor, reach out to us here:
Other General Tutoring & Help We Offer:
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General Help
September 1, 2019
Organic Chemistry Tutor Portland Oregon
Organic chemistry is widely accepted—and universally feared—as one of the most difficult and challenging college courses. It’s incredibly complex because of the sheer amount of content you are forced to learn in a short time. There are hundreds (if not thousands) of rules to memorize and commit to memory. One small mistake with these can cost you a significant number of points. But that’s just the beginning.
Organic chemistry is challenging because it requires you to think critically. Successful students need to have an understanding of a vast framework of conceptual ideas. They need to be able to visualize molecules and understand and predict entire reaction sequences in their head. Students are asked to do all of this while remembering thousands of rules, each with multiple distinctions and degrees of nuance.
Because organic chemistry is so hard, many of the teachers aren’t good at teaching it! This compounds the problem. Most organic chemistry professors aren’t good at explaining the difficult concepts they teach. Thus, many students struggle. And some choose to not take the class entirely. I’ve met people who chose not to become doctors, or who avoiding studying science altogether, because of their fear of organic chemistry.
People are right when they say: “you can’t wait until the last minute to try and cram and learn O chem.” It doesn’t work. There is a lot of evidence which shows that we learn better when force ourselves to access information more frequently throughout extended periods. And this is especially true with subjects like organic chemistry: courses which require you to synthesize vast bodies of knowledge and apply them in new ways to solve challenging problems.
When I first started studying organic chemistry, I purchased the textbook and spent all summer reading it. I even sat in on the summer lectures and absorbed everything I could. I didn’t always understand what the teacher was saying because the summer course moves very quickly and I was also a bit behind in my reading. But struggling to think about the ideas in the class was helpful. And I saw from a unique angle what core ideas were used throughout the entire course and thus would be very useful to know and understand well.
I realized that as with other subjects, it’s not about the number of resources you have available to you, it’s about how resourceful you are. Their resources are there. You can attend the Ochem course the year before you take the class. You can buy ten textbooks online and read them all. You can go to your professor’s office hours. You can find videos online. You can hire a tutor who works with you on an unlimited basis. The resources are all there. What matters is how badly *you* want to succeed. College is different from high school. In high school, the drive didn’t matter as much. You could get by
That being said, if you want to take your chemistry to the next level, we certainly offer organic chemistry tutoring here at Tutor Portland. I (Eric) do this tutoring myself. Since finding a good organic chemistry tutor is so rare, our rates for this are separate from our regular tutoring. Our organic tutoring is billed on a perhour basis.
Organic Chemistry Tutor Portland Oregon
Having been through Organic Chemistry myself, I think that tutoring is a good option if the subject of chemistry is starting to make you feel stressed or if you are starting to fall behind. But I strongly encourage students to seek help as early as they can because organic chemistry is a very challenging subject to learn. It’s a difficult subject to learn if you only have a handful of days before your exam.
One of the biggest recommendations I make for any learning program is that students invest a little bit of time each day learning and working with the material from a subject. There is a lot of research that shows when students force themselves to access information on different occasions spread out over time, they learn better and have improved recall of the concepts. This is especially true with Organic Chemistry. This subject is no joke. There is a reason why everyone thinks it is so difficult. It earned its reputation for a good reason. You have to start studying early for Organic Chemistry.
When I first started learning OChem I spent my summer studying the subject for 1.5 to 2 hours every single day. Before the course even started in the fall, I had already spent nearly 200 hours studying the subject.
My attitude was this: I don’t want to *just* earn an A in this course. I don’t want to *just* be top of my class. I want my professor to say, “this is the best organic chemistry student we have seen in fifty years.” And my work ethic backed this up.
That’s the type of work ethic and attitude I will bring to our tutoring sessions. I don’t just want you to pass organic chemistry. I want you to dominate the subject. And that is certainly possible. It will take a lot of hard work and dedication on your part, though having an experienced tutor can save you hundreds of hours. One key I learned is that some certain chapters and concepts repeat themselves. For example, when I was taking OChem II in the summer, I made a note when the professor said, “the acidbase chapter is the most important content in the whole Ochem series. It comes up time and time again. So make sure you know that stuff.” I took note of that and when I read the chapter I invested a lot of time into it.
That’s the way Ochem goes. There are some small concepts you think are nominal and not important. But actually, those might be the most important concepts in the entire course. That’s one reason why it is helpful to have a tutor guiding you in your studies.
Get Started
If you would like to get started with tutoring today, click the button below to schedule a free tutoring session:
Pre Medical Tutoring In Portland Oregon (PDX)
If you want to become a doctor, your future likely rests on your ability to succeed in organic chemistry. Medical schools use this course as a test. They want to ensure that you can handle the rigor of medical school. Organic chemistry requires you to learn, synthesize, and apply vast quantities of knowledge and countless interweaving concepts. Having someone to help you is a *huge* advantage. If you’d like to schedule a session, please contact me personally: eric@mentorportland.com.
Additional Tutoring We Offer:

College Math

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Pre Medical
September 1, 2019
Tutors Portland, OR
How to find Tutors in Portland, OR
Finding a good tutor in Portland, OR can be challenging. Many families are looking for a great tutor who will come out to their home within a few days. Tutoring can be a time pressing issue. Grades need to be fixed quickly. Exams can’t be delayed or postponed. At Tutor Portland, we commonly send tutors out the very same day that people ask. But even we admit that finding good tutors is really hard. We have to interview scores of applicants before we find a good tutor. And we have long made it our internal motto that we would rather grow at a slower rate—and be limited by the number of great tutors we have—then grow at a faster rate by hiring mediocre tutors.
I think this should be your philosophy, too. It is better to spend time researching and finding a great tutor, than quickly signing up and accepting a mediocre one.
Portland, OR is growing incredibly quickly
Portland, OR is growing. Albeit, the rate of growth has cooled slightly in 2019 relative to the 20152016 years of rapid growth. But still, Portland, OR has been growing by well over 30,000 residents every year for decades. This has caused a strain to Portland, OR’s school system—and a rapidly increasing demand for educational services. Since the mid2010’s Portland, OR has been growing at an average growth rate of over 1.0% per year. As far as population growth is concerned, this is an incredibly high rate of change. In fact, Portland, OR is growing twice as fast as the broader nation is. Still, the population growth doesn’t tell the entire story. Portland, OR has grown it’s GDP by 48% between 2001 and 2014. That is significantly more than double the rate of growth of San Francisco. This means that workers have been hard to find in Portland. This has increased the difficulty of finding highquality tutors in Portland, OR.
How does tutoring in Portland, OR work?
Tutoring in Portland, OR is becoming more difficult do the increasing population density. Tutors have to travel for longer distances. And there are more students who need help. Portland has a shortage of workers. However, the few good tutors still remain in Portland, OR. It just takes time to track them down. Once you find a good tutor, you normally set an initial session or phone call with them. At Tutor Portland, we always offer the first session for free. The tutor comes out to your home and you get to see if it’s a good fit.
Most other tutoring companies provide an initial “free consultation.” Essentially, this is a free sales pitch. They come out to your home and try to sell you thousands of dollars worth of tutoring. That is how “tutordoctor” does it. We think this is sleazy and a waste of everyone’s time. Therefore, we decided to bypass this sales pitch. (Our founder, Eric Earle, hates hard pressure sales. He vowed to never let his company use those tactics. He thinks that people should be offered something—and, if they like it, they might decide to purchase it).
On top of that, most of the time tutoring is a timesensitive issue. Families who are looking for tutors in Portland, OR, need to find them quickly—often within a day or two. That’s why we offer a free session. We don’t want there to be any barriers between you and homework help and exam prep. Just call us, and we’ll send a great tutor out to your home—as long as you are located in the greater Portland, OR area.
What subjects can Portland, OR tutors help with?
Tutors can help Portland students with just about every subject. Over the years that we’ve been in business, we’ve found that the vast majority of students need help in Chemistry, Mathematics, and Spanish. So we’ve chosen to hone in and focus on those. In addition, those are the subjects we’re best at. They are also the subjects that Portland, OR students struggle with the most. Every market and every city is different! But in Portland, OR that’s what students struggle the most with.
How much do tutors in Portland, OR cost?
The price of tutors in Portland, OR has a pretty big variation. For test prep services, tutoring can cost upwards of $300 per hour. Our subject tutoring costs around $100 per hour (as of 2019). There are certainly other cheaper options. Some people choose to use a family friend, or someone they found on Facebook or Craigslist. But the market for professional tutoring is expanding rapidly. We think this is because parents see the value in professional tutors. Families now view tutoring as one of the best investments they can make in their children—and we all know that children are the biggest investment that any family has.
When should I sign up for tutors in Portland, OR?
Families choose to sign up for tutoring at different times. Many families wait until their children are far behind before they sign up. This isn’t something that we would recommend! But often that is just the nature of the situation, and we understand. Many families choose to start tutoring before their child’s grade start to drop. This is a great idea because it ensures success and is more preventative. We highly, highly recommend this!
Families might also choose tutoring at different times throughout the year. Some families choose to start tutoring in the fall, and others start in the winter or summer. This is entirely up to you! We would recommend starting in the fall and working throughout the entire school year with a tutor. This provides the best results.
Why Tutor Portland?
Tutor Portland is unique for three reasons:
 We focus on active tutoring.
 We are a membership company.
 We hire handselected elite tutors. Most companies are focused on rapid growth and hiring any tutor they can get their hands on. We would rather grow at a slower rate and ensure that our tutoring is top notch. This means that sometimes we get so busy, we simply can’t offer our services to everyone.
August 28, 2019
Tutoring in Portland, Oregon
Finding good tutoring in Portland, Oregon can be a unique and challenging journey. This is because Portland has many different educational subsystems to navigate. We are firm believers that good tutors know and understand how a given school system works. A tutor has to know how a school system works in order to best help a student.
Portland has seven different public school districts and a vast array of private schools. It also has many colleges, including Portland State University, which is located in downtown Portland, Oregon. With regards to primary and secondary education, Portland has seven school districts which include: Lake Oswego, Parkrose, David Douglas, Beaverton, TigardTualatin, Reynolds, Riverdale, and the Portland Public School District. The latter is by far the largest school district. There are over 45,000 students who attend one of the ~ 100 schools in the Portland Public School District.
Portland also has many private schools, including Central Catholic High School, Catlin Gabel, De La Salle, The International School, and Oregon Episcopal School, among many others. Portland is also home to OHSU School of Medicine and Lewis and Clark Law School.
I grew up in Portland, Oregon. I attended a number of the Portland Public Schools, including Duniway Elementary, Sellwood Middle School, and Cleveland High School. I also spent some time at Central Catholic High School. Growing up in Portland taught me a lot about the Portland Public School system as well as the surrounding school systems. Now I own and run Tutor Portland, which is a local tutoring company serving a countless number of schools in the Portland area. We focus mainly on mathematics, science (mostly chemistry!), and Spanish. We focus on these because we have found through experience that these are generally the subjects that Portland, Oregon students struggle most with. They are also subjects which students can learn! And we’ve seen the biggest benefits when students reach out for help in these subjects. But, we’ve also learned that not all tutoring is created equal. We’ve discovered that often a college student with strong communication and psychology skills makes for a better tutor than a Ph.D. who has trouble explaining his or her ideas. The college student is likely more approachable. And if they are experienced at working with youth and have the ability to create rapport then that’s a strong foundation for a tutoring relationship to flourish. They also have to know and understand the Portland, Oregon school system—especially the school district within Portland that your child attends. Each district has different standards and programs.
Finding tutors who are knowledgable about the various different school districts and curriculums in Portland is not easy. Portland, Oregon is a growing city. There are more students needing tutoring—and more people claiming that they can offer it! How do you sort out a trustworthy tutor from one that doesn’t really know how to teach?
We like tutors who:
 Grew up in Portland, Oregon and know the local school system
 Have strong communication skills & understand human psychology
 Are downtoearth and approachable*
*This one is really important. Learning is really hard. Math and science are difficult subjects. The last thing you need is a teacher or tutor who is uptight and too serious. That makes these subjects even more challenging and frightening to approach. When the tutor is downtoearth and relaxed, the student will naturally feel this and adopt this attitude. In addition, math and science are generally not the most important things in a teenager’s life. And that’s fine! Tutors need to be accepting and understanding of this. If they aren’t, if they try and tell students that math is the most important thing in life, the student will be offput by that. This puts the learning relationship at risk.
In addition, *you* are likely getting busier and busier. Your kids do sports, your daughter has music lessons, and you have to drive them around all day. Traffic is getting worse. It takes hours to get across town. That’s why many parents find it hard to secure good tutoring. Maybe they think about online tutoring, but generally realize it’s not as high quality as inhome or inperson tutoring, and they can’t monitor what is going on during online sessions. That’s why many Portland, Oregon families ask about our inhome tutoring. This is a good option because we drive out to you. This allows your student to learn in the comfort of their own home. In addition, it is just simply convenient. You save time and money not having to drive your kids all around town during rush hour.
Many families are telling us that the current education their child is receiving is inadequate. Often they have a teacher who moves too quickly for their child. Many times these teachers are bythebook and not very accommodating to students who learn math and science at a different pace or in another way. And lessthanstellar teachers are not the only thing putting downward pressure on Portland students. The Portland Public School system is also facing budget cuts and other funding pressures. To compound this problem, Portland has a housing crisis for many families. This means that many children go to sleep each night without a stable home to sleep in. Because of this, nearly 4% of Portland Public school students are deemed homeless. This puts pressure on all of the students in school.
One neat thing about the Portland Public school district is that they offer language immersion programs. The Spanish immersion is the most popular program and it is offered at ten elementary schools. The program is also offered at the middle and high schools that these elementary schools feed into. At Tutor Portland, we work closely with these programs and provide support for students who are struggling, and students who simply wish to excel.
Many Portland schools also offer International Baccalaureate (IB) programs. The IB program is run by a nonprofit organization. It allows students to take more challenging courses and receive advanced credit for them. There are four different IB programs: Primary, Middle, Diploma, and CareerRelated. These programs are offered at various schools throughout the Portland area. Some of the schools are: Lincoln High School, International School of Beaverton, Southridge, Tualatin, and Cleveland High School.
The Diploma IB Program is for high school students aged 1619. Schools all across the world offer this program. There are six core subject areas within the program: Arts, Mathematics, Language, Science, Literature, and Societies. Each subject area has specific courses that fall within it. Many schools will let students take just a few courses instead of testing for the entire IB Diploma program. For example, it’s possible to just enroll in IB English, IB Science, and IB Mathematics. And we can help you with those subjects! We’ve done quite a bit of work helping students in these challenging IB courses and preparing for difficult IB and AP examinations.
We think that the IB Program is great because they focus on developing students who are:
 Thinkers
 Communicators
 Principled
 Reflective
 Caring
Those are great qualities for students to have.
Portland Public Schools also have other programs, which many families voice concerns over and feel frustrated with. We listen to many complaints about the Common Core State Standards Initiative. The Oregon School Board of Education put these standards in place in 2010. The standards were placed in English and mathematics. The majority of issues families have are with the mathematics standards. Families are frustrated because the Common Core Standards and their corresponding teaching methods are different than they grew up with.
The standards outline different categories for students. For example, high school students are expected to learn and gain mastery over six different areas:
 Numbers & Quantities
 Algebra
 Functions
 Modeling
 Geometry
 Statistics & Probability
As a way to gauge success within the given categories, annual standardized tests are conducted for each child. This strong emphasis and focus on persistent testing of students has led to backlash and outrage across the nation and throughout schools in Portland, Oregon. Teachers have taken to the streets to protest the Common Core Standards and corresponding standardized testing.
However, there are some organizations that support Common Core. Notably, the Bill & Melinda Gates Foundation supports it. They support it because they believe that Common Core gives our schools a set of standards which help make our students competitive in the global economy.
Regardless of the perceived benefits or disadvantages of common core, one thing is clear: it can be tricky for families to navigate. That’s why we’ve found that having a tutor or assistant who can help you greatly improves student performance and reduces stress.
However, not all students fit within the neat categories or school districts. There are many students who choose to home school, at least for a few years. We have worked with a number of families who were deciding to homeschool their children and wanted to provide some structure to their day by adding an hour or two of tutoring each weekday. We have helped create custom learning programs for students in subjects ranging from mathematics, English, to Spanish. These students often see great results in their learning. They have the advantage of being more selfdirected in their learning and more focused on mastery of subjects and ideas, rather than on simply earning good grades.
The legal requirements and standards for homeschooling in Portland, Oregon are pretty simple. The government simply asks that you register your child with your local school district service. This can be done online! Parents are given a lot of leeway with how they want to educate their children. Parents can choose what subjects they want their kids to learn and what resources they will use. Parents can choose textbooks, online resources, private tutoring, and online charter schools. There are many free resources to use! KhanAcademy is a great free tool.
There are a lot of different ways parents like to use tutoring. We have covered many different ways in this post. Sometimes families choose unlimited [or full time] tutoring for their children instead of school. This is common for parents who are homeschooling their children. Other times, parents use tutoring as an addition and boost to their current education.
Portland, Oregon can be a tricky place when it comes to navigating the local school systems and finding a good tutor. This is our specialty. This is what we do. Please let us serve you.
August 24, 2019
InHome Math Tutoring
What is inhome math tutoring?
Inhome math tutoring is one of the most common and popular types of tutoring for several reasons. Inhome tutoring is incredibly popular because families love the convenience and lack of stress that comes with having a tutor come out directly to your home at a time of your choosing. Families have busy schedules these days! We get it. Everyone is packed full and overloaded. You simply don’t have time to drive all over town. That’s why inhome math tutors come to you! Another reason this type of tutoring is so popular is that math is one of the most difficult subjects for students to learn. Time and time again we see students struggling in courses such as geometry and algebra and trigonometry.
How does inhome math tutoring work?
Inhome math tutoring is really pretty simple. The first step is scheduling your free session. That’s right, every first time Tutor Portland member gets access to a free tutoring session. You will have an initial phone call with our founder, Eric. In this quick free introductory call, we will cover all the details prior to the session. We will ask about your child and your learning goals. We will ask some initial discovery questions to assess where exactly your student is at, and what skills and tools will benefit them the most. Then we will pick a tutor who we believe to be the best match. And we will set a time for your initial free session. 99% of the time this first session is a good fit. And nearly everyone who receives the session signs up to become a paying member.
What is an inhome math tutoring membership?
An inhome math tutoring membership is something that we offer at Tutor Portland. Our memberships are designed to be incredibly customerfocused. Our mission is to be the most customerfocused company in the world. We believe in the customer. Our founder was tired of brands not treating customers right. He wanted his brand, Tutor Portland, to stand for something. And we chose to stand for the customer. That’s why our tutoring membership is flexible. You can cancel anytime. The sessions are yours to keep, they never expire. And the first session is always free. We also have a better grades guarantee. This means that for our top two membership tiers we guarantee that your child’s grades will improve.
We set up our membership this way because we realized that customers are the most important thing in the world. Your satisfaction means everything to us. The only reason that we are here in business is to serve you. Please consider letting us do just that.
Why learn mathematics?
There are countless reasons why it’s important to learn mathematics. Many students complain about learning math. They say: “when will I ever need to learn this?” I get it! I used to be one of those students. But there are so many jobs that require math. Here are just a few positions which are generally filled by mathematicians or which math majors are normally hired for:
 Accountant
 Biostatistician
 Computer Programmer
 Computer Systems Analyst
 Doctor
 Financial Analyst
 Financial Manager
 Information Systems Analyst
 Insurance Underwriter
 Inventory Control Specialist
 Investment Manager
 Market Research Analyst
 Professor
 Risk Manager
 Securities Analyst
 Statistician
These are some of the most common jobs you can get from learning math.
Two of the most common responses for why it’s important to learn math is because A) it can prepare you for STEMrelated jobs and positions and B) because math is inherently beautiful. Some mathematicians have called these the classical reasons. These classical reasons are indeed very strong reasons to learn mathematics. But there are also other reasons why someone might want to learn mathematics. Learning mathematics can add to the diversity of your knowledge. Mathematics—especially ideas such as ratios, rate of change, and simple algebra concepts—can be used to think about our world in unique and compelling ways. Mathematics can make you a better person by giving you a mental framework to think about the philosophical problems of fairness and equity. In addition, learning mathematics will make you more rational and reasonable. It will help you see that most of life is statistics, it comes down to odds and chances.
What are Tutor Portland’s beliefs about math education?
Tutor Portland believes that mathematics tutors and teachers should take an active approach. Most students don’t do well at math because they aren’t interested and they are not engaged in the course. This is usually because the course is lecturebased and they fall behind in the course. However, small & active group work allows students to engage with others. Working with others allows students to attempt to put their mathematical thinking into coherent sentences. Normally, when doing this, students will begin to see the holes and gaps in their own learning and reasoning. They can then ask questions and try to dive deeper.
Therefore, at Tutor Portland, we take an active learning approach. We don’t believe in bland memorization of facts or rules. We want students to understand the rules. We want them to feel what a derivative is. To experience it. To know what it is before they are taught the formula. This type of learning is sticky. But it also takes more time to plan and more skill to execute. That is why most teachers stick to lectures and most tutors simply do lowlevel homework help. Creating a good active learning environment is really hard.
We also follow what is known as the peerassisted learning approach. This approach is built upon research showing that students make the largest learning gains when they actively teach another individual how to complete or solve a problem. We, therefore, implement that into our tutoring. Once we have sufficiently taught a skill to one of our students through active learning strategies. We then employ peerassisted strategies and have our students teach *us* the material. This does a number of things. First, it challenges the student because they have to become the teacher for a few minutes. Second, it shows us how much the student truly understands and where they might be falling short. And lastly, this strategy leads to the biggest learning gains.
What is active learning?
Most teachers and tutors believe that their learning environment is inherently an “active” one. But that is far from always being true. Active learning environments do not generally arise spontaneously or from chance. They need to be built, crafted, composed. Essentially, courses or tutoring sessions in which students only listen are the worst teaching methods possible. These lead to the lowest learning gains. Research shows that students need to think, discuss, write, and engage. They need to perform higherlevel thinking: synthesis and analysis. Interestingly, students actually prefer to be more engaged—and they learn more when they are. That’s why we take an active learning approach with our inhome math tutoring.
August 22, 2019
Portland Math Tutors
What are Portland math tutors?
When your child starts to struggle in mathematics, complain, and bring home poor report card grades, the last thing in the world you want to have to focus on is relearning mathematics and trying to teach them. Having the best Portland Math Tutors available at your door within hours can be a massive relief. Whether your child scored and B+ on a recent exam, or whether they have been struggling with and failing math all year long, Tutor Portland is there to cover for you and help your child start earning A’s again.
In a world that is increasingly being dominated by science and mathematics, the best thing your child can do is master those subjects, and we can help with that.
How do Portland math tutors work?
Math tutoring is simple with Tutor Portland. You pay a monthly membership fee in order to have access to a top handpicked math tutor who comes out to your home for sessions at a time that is most convenient to you.
If your child is wanting help with homework, preparing for a quiz, or learning conceptual math problems, just give us a call and we can set up tutoring. With our monthly memberships, you can rest assured knowing that a math tutor is always available for you. Most families to choose to pick one tutor and stick with them. Together, they find a weekly time and meet every week to work on homework, higherlevel thinking, and general study strategies.
You are only responsible for making sure your child is fed, ready, and prepared for the tutoring session. We will cover everything else! We know how challenging it is for parents and family members to try and tutor each other. We have heard countless stories about this not working out. That’s why many families choose to leave their tutoring up to us!
What topics do Portland math tutors cover?
Portland math tutors cover a variety of topics. This includes algebra, geometry, calculus, and other concepts and courses your child might be taking. We have different membership tiers, which allow you to focus on any of these subjects for a certain number of hours per week. We are proud to offer an unlimited membership, which means that you can do as many tutoring hours as you’d like or as many as you can schedule. With this, there are no limits to the amount of tutoring that we can do. There is also no limit to the concepts or topics we can cover.
What’s Covered:
 Arithmetic
 PreAlgebra
 Algebra
 Functions
 Modeling
 Geometry
 Statistics
 Probability
 PreCalculus
 Calculus
 Trigonometry
How much do math tutors in Portland cost?
Hiring math tutors in Portland can range in price depending on your location, zip code, travel distance, subject, and more. Usually, tutors who teach more challenging subjects charge more than those who teach foundational material. Some organizations offer group tutoring. At Tutor Portland, we focus on individualized personal tutoring. We charge a monthly membership fee based on the number of sessions (hours) that you want to use per month. We believe this makes tutoring simply and more accessible because the rate is standardized regardless of where you live or what subject you need to learn. This allows you to efficiently budget for your children over the course of their academic career. To look up more information about our pricing, you can visit our membership page to see what each different membership tier costs.
When should I get math tutoring for my child?
This really depends on you, your situation, and your goals. We recommend math tutoring first and foremost if your child is struggling with math or if they don’t enjoy math. These two things often go handinhand. People don’t like math because they are bad at it! Normally, once students start tutoring they get better at math and start to really enjoy it.
We also recommend tutoring for students who want to stay ahead of the curve. Many families today realize that college is getting more and more competitive. They are also discovering and reading about how the best careers often involve science, technology, and mathematics. Therefore, we’ve worked with many families that want to simply keep their kids ahead of the curve—and ensure that they are really mastering the material.
Some families even ask for tutoring for their kids who are very gifted at math. Often times they will ask for help preparing for an AP or IB examination. Other families have asked us to help prepare their kids for the SAT, SSAT, or ACT.
Why are math tutors important?
Math tutors are becoming more important for several reasons.
 With the increase in technology, students today are having trouble focusing. This is hindering their ability to learn mathematics. Some research has found that calculators and other technology are reducing children’s mathematical reasoning ability and conceptual understanding. Research has found that hightech classrooms equipped with “interactive whiteboards” actually decrease a student’s math performance. In addition, mathematics learning software has been shown to have no benefit on student’s standardized test scores. One thing is clear: learning math the old fashioned way is what works. Learning math should be hard. It requires hours of sitting in front of a math textbook and working on it. Tutors can help explain some of these difficult ideas and get students working in the right direction.
 Colleges are getting more competitive. It takes higher math, science, and SAT scores to get into the top colleges these days. We can feel the rising stress among families even just since 2015 when we were started our local tutoring company. Acceptance rates are falling across the nation. Standardized test scores are inching higher and higher. Colleges such as Harvard reject students with perfect SAT scores year after year. Many students are now using the common application, which lets them hedge their bets and apply to more and more schools. In order to boost their children’s grades and mathematical understanding, many families are hiring tutors.
 All of the top students are working with tutors. This is causing the best students to pull further and further ahead from the pack. That’s one reason why it’s becoming more and more difficult for average good and great students to make it into great colleges. Top students are highly adept at mathematics. In addition to this, they are highly skilled in writing and English. This shows that they are wellrounded. This is why many parents are hiring subject tutors for various subjects.
What math courses do colleges expect you to have taken?
The majority of colleges expect students to have taken at least 3 years of math in high school. Many expect four years. At Tutor Portland, we highly highly highly recommend that students take four years of high school math. Colleges officially say that they don’t require it. But four years of math is largely accepted—and three years are often frowned upon by the admissions team.
Top schools also expect advanced courses such as Honors, IB, or AP mathematics. For students who want to become doctors or pursue other STEM degrees or programs in college, it is highly recommended that these students complete 4 years of advanced high school math with excellent marks in those courses. This will help set your child apart.
There are three different AP math courses offered to high school students: AP Calculus AB, AP Calculus BC, and AP Statistics. You can learn more about AP Exams and how they are graded here.
However, across the board, geometry and algebra are the bare minimum courses that need to be completed in order to graduate from high school. The vast majority of states have adopted the common core curriculum and standards, which were discussed earlier in this article.
Most high schools follow this progression of courses:
 Algebra 1
 Geometry
 Algebra 2/Trigonometry
 PreCalculus
 Calculus
Many students will commonly stop at precalculus. And this order is not the same at every school. There are some schools in Portland that teach geometry first and then algebra 1 and 2 following that.
Many students believe they will never need to use mathematics, so why bother studying it? And, at first glance, that appears to be true for people studying the humanities. Why do English majors need to know algebra? But these days colleges are realizing the value of having strong interdisciplinary students on their campuses.
Why should I choose Tutor Portland?
Tutor Portland is a local tutoring company that time and time again has gotten results for students. We take our clients very seriously and want to ensure that they have an incredible experience with us. And we will do whatever it takes to make that happen!
What makes Tutor Portland unique is our focus on active tutoring. We believe in having engaging tutoring sessions. Learning should be dynamic. That’s why we focus on active learning strategies which are based on research and have been proven to drive learning results. There is a lot of recent research on math and science education. The data clearly shows that students learn mathematics when they attempt to verbalize their mathematical reasoning and thinking. This helps them realize what they know, think through challenging concepts, and fill in gaps in their own mental models. That’s why we take an active approach. We ask questions which get students thinking and which nudge them to explain their mathematical reasoning.