January 20, 2021
Studying. Few of us like to do it, but it’s totally necessary for nailing exams and earning awesome grades. If you think you’re a bad test-taker, you might be super smart, but lack some of the best strategies for effective studying. Here are some tips for excelling at studying and doing everything you need to ace your next test.
1. Plan a Study Schedule
You might think you should focus on the hardest subjects first, but that can be a counterproductive study habit. Instead, create a plan that designates extra time to focus on more challenging subjects but still includes time to review everything that’s going to be on the test. That way you’ll be well versed in all the topics you need to know and won’t be thrown off by a test question that references a subject you forgot to study. For example, if you have three hours to study for a test that covers six chapters of your textbook, and you really struggled with chapter three, create a plan like this:
Review Chapter 1 & 2: 30 minutes
Review Chapter 3: 50 minutes
Chapter 4-6: 55 minutes
Re-review Chapter 3: 45 minutes
This schedule prioritizes chapter 3 but still ensures that you review everything else at least once. So instead of assuming that you’ll be able to recall information, you’ll go into the test 100% sure that you’re prepared for anything that could be on it.
2. Create Essay Outlines
When you sit down to write a big essay for an end of semester project, it’s common to experience writer’s block. The weight of it’s importance can stir up so much anxiety that you feel totally out of ideas.
Rather than starting off your writing session with no direction or plan, prepare an outline beforehand. This is a complete breakdown of everything you want to include in your introduction, body paragraphs, and conclusion. In the outline, you’ll want to include everything from clever hooks, transitional phrases, and quotations from outside sources. Outlining helps you determine the order of information you’re presenting and what ideas you want to focus on the most. That way when you sit down to write, all you have to do is transcribe everything into an essay format. If you need help getting started, use Scribbr to help you craft the perfect essay outline.
3. Review Your Notes
This might sound obvious, but reviewing your notes before starting any assignment, even homework, is imperative. Doing a quick re-read not only assures you understand every concept before diving in, it can also prevent you from making critical mistakes, which is especially important for writing assignments. Make sure to read a writing prompt in its entirety so you know exactly how many paragraphs you have to write, what topics you need to discuss, and the format it needs to be written in. Nothing is worse than spending two hours on a 1,200-word essay only to realize it only needed to be 800.
4. Test Yourself!
You don’t have to wait for the big exam to get into test mode. Create weekly quizzes for yourself so you can better absorb what you’ve been learning. Focus on identifying the main topics your teacher highlights, especially points that have been brought up multiple times, because they will be on the test.
To find material for your practice test, use questions from quizzes you’ve already taken as well as review sections located in textbook chapters. You can also use online platforms like Complete Test Preparation to find practice tests for math, science, reading comprehension, and more.
5. Compare with Friends
We’ve all had that one classmate who always seems to have the right answer and aces every test without even trying. Rather than seeing them as your biggest competition, use them as your greatest resource. Gather a group of your most prodigious classmates to do a weekly review of the lessons that’ll be on the test. Studying together helps you discover where you can improve, while you share your strengths to help others improve. This way, you’ll all become better students together!
6. List Your Distractions
Do you ever get distracted when you need to study? Not only by Netflix and phone notifications, but by chores too? Chores that your parents are harping about because they needed to get done yesterday? When other important tasks are competing with your studying duties, don’t ignore them. Instead, write them down and choose a time when you’ll be available to complete them. Set a timer that requires you to put in one hour of intense studying. When it goes off, allow yourself 10-20 minutes to get these chores done.
Let’s be honest—many distractions, like texting your significant other, are far less imperative than chores. Many of us are tempted to check Instagram likes on our latest post or scroll through news stories on Twitter, when we should be focusing on studying for a final. This can lead us to take constant mini-breaks that grow into all-day distractions. Putting off our work all day can lead to feelings of guilt or stress as we run over schedule and fall behind on studies.
The solution is to not deprive ourselves of study breaks. Instead, we can reward ourselves for an hour’s worth of intense studying with 10 minutes of free time. This way, we give our minds a break and can indulge in our favorite pastimes, guilt-free.
7. Study Offline
While we highly recommend using online platforms for study tips, time away from the computer allows you to purely focus on studying and not get distracted by the internet. Find a screen-free environment to study in, like the kitchen table, a comfy chair, or outdoors. This’ll give you a nice change of scenery and your eyes a break from the screen.
There’s also plenty of online tools you can use without internet access like Desmos, which is a website that provides a variety of calculators and graphing tools. Use these tools while your computer is in offline mode. That way you’ll have access to all the helpful resources Desmos offers without being distracted by email or social media alerts.
8. Leave Your Friends on Read
With instant messaging, friends are just a text away. But are group chats more important than grades? If you struggle to avoid text messages and Snapchats when you’re supposed to be studying, hold your friends accountable. Let them know that you have a big test to study for and won’t be reachable for the next few hours. If they know how important this test is, they won’t create unnecessary distractions to prevent you from succeeding. If they’re still hitting you up during studying sessions, put your phone on “Do not Disturb” and update your messaging settings so only emergency contacts can reach you while your studies are in session.
9. Ask Your Teacher
It’s good practice for students to regularly ask questions during class. It not only helps you better understand a subject but can provide clarity to other students who have the same questions. However, asking too lengthy of questions can monopolize your teacher’s ability to help other students, and can make you look inconsiderate of those who want to move on to the next lesson. Instead of disrupting other students’ time, pull your teacher aside after class and ask when they’ll have free time to help you with tougher subjects.
Oftentimes teachers’ have office hours where you can get one-on-one help. Going to office hours demonstrates your intentions to improve your schoolwork and shows that you don’t want to take away from their in-class time. Plus it puts you on their good side—they might even be more willing to boost you to an A- when your end of semester grade is 89.8%.
…And if that Doesn’t Help
Every good teacher should be willing to provide extra help to students that need it. However, you won’t always have the privilege of teachers who are willing to help us during their off-time. If that’s the case, don’t be afraid to seek tutoring in subjects that aren’t your strong suit. Here at Tutor Portland, we provide in-home and online tutoring sessions with first-class tutors throughout the Portland area. Each of our hand-selected tutors will provide you with the specialized attention you need to raise your grades, pass your tests, and get accepted to your dream school. Start your free online introductory session today!
December 31, 2020
When your kid’s classroom is a black square on a Zoom screen, it’s no wonder they struggle to stay engaged. Students lose the personal experience they once had during in-person classes while learning from home creates plenty of new distractions. With the future of education taking a hard turn, the need for quality one-on-one tutoring is greater than ever!
Unfortunately, finding the right tutor can be pretty difficult…there are hundreds of names and websites to scavenge through! It can take forever to find tutoring that’s affordable, accessible, and right for your student. Who in the world has all that time?
Who are the Best Tutors in Portland, Oregon?
To make things a little easier for you and your family, we’ve gathered a list of the best tutoring companies in the Portland area, complete with information about what makes each one unique! This list includes companies that offer in person tutoring or online sessions, or both, so no matter what your preference, we’ve got you covered. Don’t spend hours scrolling through Google; we did the work for you! One quick read and you’ll be ready to get your kid learning in no time.
North Avenue Education
Looking for a personalized, holistic approach to tutoring? North Avenue Education is ready to provide incredibly through and varied tutoring services to your family. Not only do they offer academic tutoring in math and writing, they also provide specific programs for those preparing to take SATs or ACTs.
If someone in your family is applying to college, North Avenue Education can offer them guidance on undergraduate and graduate applications. They also have study skills coaching, which is simply aimed at helping kids develop the right habits to stay focused and organized.
One unique offering from North Avenue is their “learning pods”, groups of students who study together in person (with the appropriate safety precautions, of course), or virtually. This small group approach is aimed at creating personal connections between students during a time when we all feel farther apart than ever.
In this time of uncertainty, you’re probably pretty eager to be certain about something…like whether or not the tutoring service you choose will REALLY help your kid out. Luckily, Tutor Doctor reports a 95% satisfaction rate from their clients. And if you’re not happy with your experience, there’s also a 60 day money back guarantee!
Tutor Doctor offers tutoring on a large variety of subjects, including Spanish, German, Chinese, and English for non-native English speakers. They also emphasize the development of what they call “X skills” for every student. These are skills like planning and self-evaluation that help students achieve not only their short term academic goals but also their lifelong dreams. In doing so, Tutor Doctor encourages kids to become more well rounded individuals with high standards for their own achievements.
If you’re looking for something simple and affordable, Tutor Doctor is definitely a company to consider. You can schedule a free consultation online any time! This consultation allows Tutor Ductor to pair your student with a tutor and a learning plan that’s right for them. Not only that, but you can book sessions quickly and easily online as well, making Tutor Doctor one convenience in this rapidly changing world we live in!
Northwest Reading Clinic
It can be hard to find the right tutoring for kids who struggle with basic reading, writing and comprehension. Every child is so different, and it’s not easy to create a program that’s tailored to their individual needs. That’s why the Northwest Reading Clinic provides kids with an exceptionally thorough assessment and consultation to discover where exactly they’re having trouble.
The center tests for things like sound/symbol association, receptive and expressive vocabulary, and ability to follow oral directions. Then they pinpoint what specific areas your kid is struggling with, to create an effective approach that helps mend gaps in their reading/comprehension skills. Northwest is here to help everyone, whether your kid has some minor difficulties concentrating on text or shows signs of severe dyslexia.
Northwest Reading Clinic offers generous amounts of tutoring, tending to work with students on a daily basis. It’s important to note that they’re not just limited to the language arts, they also offer services for students who struggle with fundamental math computations or have difficulty with logical and deductive reasoning. They’re open right now for entirely virtual sessions! If your kid needs help grasping the basics, this is the center for you.
Huntington Tutoring Center
When a student doesn’t believe in themself, their academic achievement isn’t the only thing that suffers. Everything from their social capability to their organizational abilities is affected. That’s why Huntington Tutoring Center focuses on creating confident kids. At Huntington, tutoring is about more than just words and numbers–it’s about encouraging kids to believe in themselves and their futures.
Boasting an impressive 40 years working with students and families, Huntington offers tutoring in math, reading, writing, science and more. They also offer summer programs, homework help, and special programs for kids who are diagnosed with ADHD. Not only that, but they work with schools to make sure your student is truly understanding the curriculum they are being graded on.
If you’re concerned or curious about your child’s progress and want consistent updates, Huntington might be a good option for you. They offer regular conferences with parents throughout the student’s tutoring journey to keep you clued in to your kid’s progress. Sound like something you’re interested in? You can call them anytime, or even have them call you! Tutoring plans vary from 2-10 weeks if tutoring, or a total of 30-90 hours.
Stumptown Test Prep
If you’re looking for something much more geared toward standardized test-taking, check out Stumptown Test Prep. Even if your student doesn’t have an SAT or GRE on the horizon, it’s always good to get an early start. This is especially true if your kid has a little too much time on their hands since they’ve been stuck at home.
Stumptown narrows successful test-taking down to three essential areas of learning: core knowledge, test strategies and motivation/anxiety. By looking at these three components as a unit, Stumptown helps students master their psyche instead of just the test material. They boil down most test-taking issues to gaps in knowledge, poor time management skills, and problems with the student’s mindset. Their approach includes a free consultation for your child in which Stumptown staff can get to the bottom of your child’s test taking issues.
Weekly sessions are the norm for Stumptown but their plans are very flexible, so if you’re interested, get in contact with their small staff to work out a schedule that looks best for your family. They also tutor students from middle school to college and beyond, so they’re ready to step in at any point in your child’s educational journey.
Students are living under the pressure of expectations from parents, teachers, counselors…so why would they want a tutor who just tells them what to do? Instead of appointing someone to simply instruct your student, Tutor Portland aims to pair your child with a mentor (we were originally called Mentor Portland!) Tutor Portland aims to establish trust and respect between tutor and student, and provide a positive, kind environment.
The folks at Tutor Portland think there are some serious issues with the way math is taught in schools and adopt a more effective alternative. While most school curriculums emphasize long lectures and monotonous practice, Tutor Portland focuses on teaching math conceptually, often having students verbalize their own mathematical thinking to ensure retention. Tutor Portland knows that every student is different, and that tutors might have to describe things a few different ways before kids understand.
Tutor Portland places the most focus on math and science, but they also offer writing and Spanish tutoring as well. In addition they have a unique program for those applying to medical school, and SAT/ACT prep!
Find a Tutor Near You
While school looks a little different this year, it doesn’t mean that personal, individualized learning isn’t possible. By checking out these local tutoring centers, you can give your kid the chance to beat the stay-at-home blues and get excited about their education again.
December 15, 2020
So your child has completed their college apps and they’ve started to narrow down their higher education choices. Whether they want to attend a junior college, attend school part-time, or are taking the plunge into a four-year university, their big decision will help shape their future. You’ll want to be sure that they’re as prepared as they can be.
Before they even step foot in a classroom, their skills will need to be tested. Math placement tests are a required examination prior to enrolling in specific classes. If they’re worried about what lies ahead for them when it comes to math placement tests and scheduling math classes, there’s no need to worry.
We have the ultimate guide right here for parents and students like you to better understand what math placement tests are all about.
What is a Math Placement Test?
A math placement test is designed to measure a student’s math skills and gauge the most appropriate math classes they should take for the upcoming semester. Before starting college or university, students must complete a math placement test at home. This happens after a student has been admitted to a school and is a normal part of the enrollment process.
There is no passing or failing a math placement test. The point of these exams is to see how competent the student is in the subject. They are more of an assessment of personal skills rather than an analysis of mastery. A math placement test is not a measure of intelligence, but a measurement of personal experience and how well a student demonstrates that experience.
After the test, the school will tailor a choice of math class to the student’s best strengths. If a student is a top scorer, they’ll be rightly placed in advanced classes that will properly challenge them. If they score lower on the math placement test, then they will be placed in less intense math courses.
What to Expect on a Math Placement Test
Although all schools require students to take a math placement test, there is no universal standard they adhere to. Each university or college will create their own tests that best measure math skills according to their own set of standards.
However, there will be some similarities across the board. Questions will be pulled from a wide variety of math topics such as algebra, geometry, trigonometry, and some precalculus and calculus, but the questions will not dive deeply into each subject. The range of questions will be wide, not deep.
The wide-range of questions about basic concepts is followed by longer word problems. These word problems focus on the application of concepts. Students will apply the previously mentioned concepts to help solve longer story problems. Further, the test will ask students to provide written analysis to test if they can fully understand and demonstrate mathematical concepts.
These tests usually do not have a time limit and are mostly multiple choice. The point of the exam is to measure skill, not speed. They’re usually administered online too, so there is no need to travel to a testing location. The tests are often completed from the comfort of a student’s own home.
What’s The Deal with High Placement Scores?
Preparing for math placement tests can save students and parents time and money down the road. If your university requires payment for classes by the unit, students can save money by testing out of classes that would otherwise be required for their degree.
By scoring well, students can bypass entry-level courses and qualify for more challenging (and more interesting!) math classes. By scoring poorly, the school may place students in lower intensity remedial courses and take time away from more enriching classes.
If a student plans to enter a field that is less math-intensive, they can bypass math classes altogether if they score high enough. By testing out of basic math classes, they free their schedule to take other classes that are more relevant to their field of study. This will save time and money as students will skip a few steps on their way to complete their degree.
How to Prepare for a Math Placement Test
Before taking a placement test, I encourage students to brush up on basic mathematical concepts. A math placement test will have questions about basic arithmetic such as addition, subtraction, multiplication, division, fractions, proportions, averages, decimals, and integers. It sounds like a lot, but it’s nothing students haven’t mastered before!
Here are our tips to maximize your studying habits!
However, it’s important not to put too much weight on the outcome of the test. There is a downside of over-preparing. If students prepare for the test in anticipation to score “well” or “ace” the exam, then they could be setting themselves up for a difficult situation. By studying for hours to ace the exam, students may earn placement in an advanced level math course they are not ready for. They might become overwhelmed by the higher level material because of their inflated placement score.
Remember, there is no passing or failing these placement tests, so over-preparing won’t always pay off. Ending up in a less intense math course might be the perfect situation for a student who isn’t as mathematically gifted as their peers.
Conversely, if a student enters the math placement test completely unprepared, then they could be placed in a math course that is far below their skill set. These students might get stuck paying for a class that is repetitive, boring, and ultimately a waste of their time because they did not demonstrate higher level math skills on the placement test.
Final Thoughts on Math Placement Tests
If a higher education institution accepts you or your child into their program and requires you to take math placement tests, look into hiring a tutor. When you hire a tutor to work one-on-one, you can focus on reviewing the areas that are the best use of your time. Meeting with a tutor to hone math skills could make a positive difference for your future in higher education.
Experts from Tutor Portland or Zoom Tutor can assist in tailoring a plan for you or your child. Having a tutor that understands how the math placement test works will make a huge difference in your educational experience. By fortifying math experience, you will be ready to take a math placement test and best serve your educational career.
November 3, 2020
School can be intense, especially during exam season. You find yourself spending all your free time studying, working on projects, reviewing assignments, pouring over practice tests, and doing everything you can to prepare yourself. But have you really tried everything? What do you listen to when you study––a favorite playlist, a babbling brook, nothing at all? A wealth of scientific research has found a new way for you to boost your academic performance: listening to classical music for studying!
This simple practice can boost your grades and help you retain information, so give classical music a try and see if it becomes a helpful habit for life! You might find that you finally get the exam scores you’ve been craving, and feel healthier and happier in the process. Here’s why classical music for studying works for so many people:
Scientifically Significant Study Benefits
You may be familiar with the rumored brainpower phenomenon called the “Mozart Effect.” A 1993 linked the effects of listening to Mozart with an increase in IQ, spurring an increase in the popularity of classical music for studying. The study demonstrated that participants who listened to Mozart tended to score higher on subsequent IQ tests. While this specific research is now widely discredited, it has been replaced by a plethora of well-respected studies demonstrating that there are definite academic effects derived from listening to classical music for studying.
Research conducted in a French university found that when students listened to classical music for studying, their academic performance improved. In this study, two groups of students watched a lecture, one with classical music in the background and one without. The students who listened to the music scored higher on a lecture quiz than the other group.
Another study suggests that students are able to focus better and study longer with classical music playing in the background, leading them to perform up to 12% better on exams than their peers. The absence of words in classical music might decrease distractions and could account for the improved focus amongst listeners.
Classical music for studying can boost academic performance in creative classes as well because it increases divergent thinking. Divergent thinking, or the ability to come up with new and innovative concepts, is the backbone of creativity. A 2017 study from Goethe-Universitat in Frankfurt, Germany, tied listening to “happy music” to enhanced divergent thinking, meaning happy music makes you more creative. Classical music is commonly considered both positive and energetic, and thus encourages creativity. Working on a final project for an art or film class? Trying to find a new way to approach a complex calculus question? Or just feeling stuck in general? Find a classical playlist. Classical music for studying gets your creative juices flowing and puts you in a mindset open to innovation and discovery.
Turn on some Mozart, because studying with classical music has also been shown to increase productivity. A UK-based experiment paired a classical radio station with a psychologist to see if British office workers would be more productive while listening to artists such as Beethoven and Bach. They found a 15% increase in productivity when participants completed a task listening to classical music, versus working in silence. By blocking out noises and distractions, classical music can increase your focus, leading to improved productivity. Apply these findings to your own study habits and get more done in less time!
Plus if you find yourself losing sleep due to exam stress, listen to this. Researchers at the University of Toronto found that classical music can combat insomnia and improve sleep. With 60% of college students habitually getting less than 7 hours of sleep, finding ways to improve sleep quality is of paramount importance. Improving sleep quality is a tried and true strategy to increase cognitive performance, paving the way for better understanding of school subjects.
A study conducted by Baylor University found evidence that listening to classical music for studying both during lectures and while sleeping can trigger targeted memory reactivation (TMR). During this process, the music triggers the brain to move the concepts learned during studying to more permanent memory storage. The students exposed to classical music for studying both during lecture and sleep performed 18% better on the test than the control group. So try turning on classical music to help you study and sleep! But that’s not all, listening to classical music for studying offers a number of physical and emotional health benefits too!
When you listen to classical music, it improves your overall health quality by reducing stress. Researchers at the Duke Cancer Institute found that blood pressure actually decreases as individuals enjoy music. However, this effect was only observed in participants who listened to classical music, not jazz, pop, or other genres tested in this study. So, if you like to read with the music in the background, but feel it hasn’t helped you improve exam scores or relax, you may want to try switching to calming classical music for studying.
Music with too many dynamic changes, unpredictable rhythms, lyrics, or jarring instruments will serve to distract rather than calm, so be intentional in your music choices. Classical music has been found to reduce stress as a result of its specific, unique musical qualities: the slow, rhythmic tempo of classical music is similar to the natural pace of the human heartbeat, encouraging your body to calm down, lower your heart rate, and de-stress. Its patterns and textures allow your brain to expand as you listen, without over exciting your body.
Not only do these physical benefits help you study better, but decreased blood pressure and lowered anxiety contribute to a healthier lifestyle for years to come. Making classical music a part of your daily routine, even on the days you take a break from studying, will certainly pay off in the long run.
Listening to classical music for studying produces a wealth of emotional benefits on top of the physical benefits. When the “Mozart Effect” was debunked, researchers replaced it with a new theory. They determined that while listening to Mozart didn’t necessarily cause increases in IQ, it did improve mood. Listening to Mozart’s music causes the brain to release more dopamine, a hormone known for improving mood and producing a ‘feel-good’ effect. These increased dopamine levels were tied to improved feelings of happiness among listeners. Happier participants tended to perform better on evaluations.
Increased dopamine also makes classical music a tool for fighting the symptoms of depression. If you tend to feel discouraged while tackling a difficult class, classical music for studying can help improve your mood and keep you on track for success. And not only that: by improving your emotional state, classical music actually makes your brain more receptive to new information. By getting you into a good headspace, classical music for studying prepares you to tackle any academic challenge.
Ready to pop in your headphones and play some classical music for studying? There is an endless variety of classical music playlists online to choose from! From hours long YouTube videos to specially curated Spotify playlists, your options are inexhaustible. Taking a bit of time to find the perfect blend for you is definitely worth it.
A good general rule to follow is: skip the big orchestral selections! Pieces with huge dynamic changes that range from whispers to crashes are too busy and distracting for your purposes. The 1812 Overture, for instance, will probably have the opposite of the intended effect and increase your heart rate and anxiety.
Try to stick with simple pieces to avoid inadvertently distracting yourself. Classical radio station producer Alan Chapman recommends solo piano pieces by Mozart, Poulenc, Debussy, or Fauré, gentle guitar music, Bach lute suites, and Elizabethan consort music written in the 16th century.
To help you get started, here’s a list of classical pieces to study to that we recommend:
- Goldberg Variations, by Johann Sebastian Bach
- The Four Seasons, by Antonio Vivaldi
- Für Elise, by Beethoven
- Canon in D, by Johann Pachelbel
- Clair De Lune, by Claude Debussy
- Piano Concerto No. 23, by Wolfgang Amadeus Mozart
- Salzburg Symphony No. 1 (‘Divertimento in D major’), by Mozart
- Gymnopédie No. 1, by Erik Satie
- Academic Festival Overture, by Johannes Brahms
- Etudes, by Frédéric Chopin
- The Hours, by Philip Glass
- Moonlight Sonata (I), by Beethoven
- Organ Concertos, by George Frideric Handel
- The Blue Danube Waltz, by Johann Strauss II
Exam season is challenging, exhausting, and stressful, but now you have another tool to get through it. Listening to classical music for studying has been proven to have a wealth of benefits on your mental, physical, and emotional health. It decreases your stress and anxiety, brings down your heart rate and blood pressure, and helps your retention skills by enhancing memory capabilities. Further, it releases dopamine to improve your mood and fight depression, increases your creative capacity, and improves productivity. The scientific studies point to classical music as the perfect study companion, so crack open that textbook and turn up the Bach!
September 12, 2020
Let’s say you were the creator of one of the world’s most useful and life-changing 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 17th 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.
When you think about who invented calculus, you might imagine some pompous aristocrat in a powdered wig. But early traces of calculus-related 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  from the 15th 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 and fundamental human rights. 
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 A-list 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 well-known 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 low-income 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 , 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 calculus-ish mathematics 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?
Gottfried Leibniz was also an ambitious scholar and a passionate thinker in his own right. Born on July 1st, 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, 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 Leibniz-Keks. 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.
Despite the controversy over who invented calculus, there is actually a well-documented 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.
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…
Leibniz started working on his theory of calculus a few years before making a breakthrough in 1675. While he was in Paris on November 11th, 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.
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.
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.
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 all-out 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.
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
 The mean value theorem is a type of formula that calculates the sine, or a specific angle’s dimensions.
 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.
 John Locke argued for the fundamental human rights of “life, liberty, and property” in An Essay Concerning Human Understanding in 1689.
 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
 Barrow pursued the concept of the derivative and linked calculus concepts like differentiation and integration.
 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 10-digit-based 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
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 down-to-earth 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 meta-cognition. Meta-cognition 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 school-related 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 lecture-based-learning 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 “left-behind” or too nervous to seek help when needed. Tutoring puts the learner in the driver’s seat. They are instantly in-charge 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 self-esteem 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 one-on-one 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 school-related 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!
Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
Article Updated April 2020
March 29, 2020
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 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.
👍 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 call us at (503) 347 7102.
Post updated March 2020.
Tutor Portland | Math Tutoring
950 SW 21st Ave #1117
Portland, OR 97205
We offer Math Tutor services in:
- Lake Oswego
- 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
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 multiple-choice problems without using your calculator.
Challenges With General Chemistry In School
Another reason that general chemistry is challenging is that there is often intense time-pressure 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 co-niches. Instead of complete competition, they are able to live side-by-side 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
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September 1, 2019
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 O-chem 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 per-hour 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 O-Chem 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 O-Chem II in the summer, I made a note when the professor said, “the acid-base chapter is the most important content in the whole O-chem 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 O-chem 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.
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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: email@example.com.
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