High Schoolacademics

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How to write about a work of art when you don’t know how to begin
Writing about art, especially abstract work, can be intimidating! However, at some point in your life as a student, you will probably have to analyze a painting, a sculpture, an installation, or even a creation that you don’t know how to categorize.
Baking bread with math
Math is relevant to every day life, though it is certainly a language that requires patience to learn and practice to upkeep. While most of my work these days uses a very different kind of math – mostly statistics and regression – my love of baking helps me keep up some of my fundamental algebra skills.
6 tips for overcoming writer’s block
It’s all happened to us—you get a writing prompt or essay assignment, but once faced with the blank page of a document, great ideas vanish like rats fleeing a sinking ship. Watching the cursor blink, writing anxiety and procrastination set in. A week later you’re clicking submit at 11:59 PM. You waited until the last minute to hammer out a text, ...
Selecting quotes for deeper literary analysis
As academic writers, we are often told that quotes are important because we need them as evidence. What we are often not told is that a truly well-selected quote should operate not just as support for your argument but as an essential springboard for analysis.
An intro to neural networks
Are you someone with a burning curiosity for the fascinating world of computer science? Well, you're in for a treat because we're about to embark on a fun, engaging, and totally digestible journey into the captivating realm of neural networks.
Approaching Shakespeare
The first Shakespearean play that I had to read in school was A Midsummer Night’s Dream; I was in eighth grade. I found the kooky language insurmountable, and, truthfully, thought the plays were pretty boring. These challenges continued year after year, as we moved on to Romeo and Juliet, Macbeth, Hamlet, and more. In short, I hated ...
Evolution is mostly random
Competition in nature is relentless. Predation, famine, disease, and disaster all threaten to prevent individuals from reproducing. In this competitive environment, mutations that make survival more likely are more likely to appear in future generations, and mutations that make survival less likely probably won’t stick around in the population for ...
The writer’s palette: color-coding as a revision strategy
Revision is an essential part of the writing process, but it can feel daunting. You’ve toiled over ideas, finally gotten words onto the page, and now you need to revise. This step can seem overwhelming, especially if you’re pressed for time or tired of looking at the same draft.
5 tips for managing writing anxiety
Some writing anxiety is inevitable and even useful. But if your anxiety is keeping you from producing your best work, try the strategies below to improve your writing process.
Solving systems of equations by graphing (even after Algebra 1)
When learning about lines in Algebra 1, you likely learned how to solve a system of (linear) equations, such as the following, by graphing:
Centrifugal force explained
Fictitious forces such as the centrifugal force are fake forces – they don’t really exist! However, fictitious forces are helpful when working in non-inertial reference frames (a fancy term for reference frames that are accelerating, like when we use the rotating Earth as a reference frame). In these frames, F = ma doesn’t hold, and you’ll need to ...
Attempting to become a theoretical physicist: initial steps
If you've clicked on this blog, you must be captivated by the beauty of relativity, quantum mechanics, dark matter, or black holes. Now, you're eager to delve deeper into these subjects. Maybe this moment just happened recently or a few years ago. Regardless, you want to get paid to study nature and attempt to describe it using mathematics. As I ...
How to revise your writing in 3 easy steps
So, you’ve finished the first draft of an essay, paper, short story, or personal statement! You’ve done the first hardest part: sitting down and putting pen to paper. But writing, like any other creative pursuit, is “10% inspiration and 90% perspiration.” In other words, the first draft is just a start. Revising is where the real work happens.
Making mistakes in math class
Learning math often feels like it’s all about right or wrong, like success or failure are the only two possible options and that all of your math expertise is visible as soon as you take a test. What I experienced as a student studying math and now as a math teacher is that this couldn’t be further from the truth. Some of my greatest learning ...
Freewriting: the cure for writer’s block
Writing an essay or term paper can often feel like an uphill battle. We have all been victims, time to time, of the dreaded “writer’s block.” It can be frustrating and overwhelming when you sit down to write but you just don’t know where to start. But fear not! In this blog post, I will describe a helpful technique for overcoming writer’s block: ...
Does reading poetry make you feel grumpy? Lean into it.
Poetry can try the patience of even the most willing of readers. John Milton’s extended similes mysteriously belabor seemingly arbitrary comparisons; T.S. Eliot’s famously infuriating footnotes obscure more than they reveal; and Lyn Hejinian’s non-sequitur-fueled “sonnets” boggle the mind, refusing sense and logic at every turn. If you’ve ever ...
IQE: Introduce, Quote, and Explain
Though the arguments in our essays might seem clear to us, that doesn’t always mean our audience is going to find them so easy to follow. This is especially true when it comes to citing textual evidence in essays. Our audiences aren’t there with us in the library or at home poring over our books and papers. They’re not in our heads. We always have ...
4 tips for better papers
There’s nothing quite like the feeling of dread that settles in the pit of your stomach when you sit down in front of yet another blank Google Doc with a paper due at midnight. You might even tell yourself you’re not getting the grades you want because you’re just not good at writing.
5 Tips for writing lab reports
So, you’ve completed the experiment in your high school science class. Now what? After hours in the lab and analyzing your data, it is now time to write a lab report. This can be a hard assignment for students to wrap their heads around. Lab reports are kind of like the essays you have written for English and history, but now it is time to apply ...
Writing advice: know your audience!
Writing, in all forms it takes, can be very scary. This is because writing is hard! If you’re anything like me, you may also worry about what others will think of your writing. It’s inevitable that some people won’t like or agree with what you say, but what you can do is make sure that your writing is as foolproof as possible. You’ve probably ...
The power of Python
Python has gained a reputation over the past decade as an excellent language for beginners to the world of programming. Why is this? It boils down to two primary reasons: it is easy to read and write, and it comes with a great ecosystem of open-source libraries.
Why does chemistry seem so difficult?
I have greeted over 1,000 students to my classroom throughout the 20+ years of teaching AP Chemistry, and the number one question I hear is “Why is chemistry so hard?” I have several responses to that question that I have offered to my students. But first, I want you to read each bullet below and notice which one resonates with you:
How to start writing about a piece of art
One of the things that makes art history such an interesting analytical discipline is that it examines both the anthropological and creative value of an artwork. Artworks are historical objects that can give us insight into the culture of a particular place and time. Yet artworks also transcend their time and place through their creativity, ...
Quantum Mechanics in 5 minutes
I wouldn’t be surprised if you’ve heard the word “quantum” before. It’s a real buzzword: “quantum computing,” “quantum gravity,” “quantum information,” “quantum entanglement”. But what is quantum mechanics, really? My goal in this post is to give you intuition for what quantum mechanics is, where you can find it in real life, and why it’s so ...
How to approximate the value of pi
I always tell my students not to be afraid to ask why. In so many parts of our lives, we are asked to defend our opinions and ideas—to offer evidence and to explain our thinking or reasoning. But sometimes, it feels this is missing from math education, especially in middle school and high school. Math becomes about memorizing formulas rather than ...
Why learn to write? 
In school, we devote time and energy to learning many different skills, in many different subject areas. Some of these skills may feel more relevant than others. A student who dreams of becoming an artist may bemoan the hours spent calculating derivatives in Algebra, while a future chemist might wonder why she should bother with Social Studies’ ...
Decoding and comprehension: the two components of learning how to read
Reading is a fundamental mode of communication and therefore a prerequisite of active participation in today’s world. There are two components to reading: decoding and comprehension. Decoding refers to understanding the relationship between letters and sounds, otherwise known as phonics; comprehension refers to a student’s ability to make sense of ...
The puzzle pieces of an argument
When learning about argumentative writing, my students regularly freeze. The terms claim, reasoning, evidence, and explanation all appear to be the same. They are unsure where to start and where to end. So let’s break it down together.
How to prove the Pythagorean Theorem
The Pythagorean Theorem plays an essential role in many facets of math from Euclidean Geometry to complex numbers to trigonometry. Today we’ll explore one of its many proofs.
How to solve (almost) any math problem
Math is all about problems -- questions for which you don’t currently know the answer -- and problems can be really frustrating. That feeling of being stuck, for me, goes from a scattered confusion to a mind-numbing blankness. It’s really easy to shut down and give up, so the first step to solving any math problem is to persist! Don’t let the ...
How to study for Chinese dictation quizzes
听写 (dictations) have been used to evaluate how much effort students put into learning Chinese. Dictation often tests vocabulary memorization. How do you study/prepare for 听写 effectively? Do you spend hours of writing characters? Have you experienced cramming with flashcards, only found that you forget everything on the day of the quiz?
How to ethically use WolframAlpha, Mathway, and Photomath
As a middle school and high school math teacher, I’ve seen my students try to get out of doing work in all sorts of ways. If you haven’t heard of WolframAlpha, Mathway, or Photomath, you may want to stop reading this article now - the temptation may ruin your hard-work ethic.
The dreaded “P” word
What’s the most dreaded letter that could appear on a transcript? I’ll wager that it’s not a “B,” or, gulp, a “C”, but a “P” as in “plagiarist.” In fact, if Hester Prynne were a 21st century student, instead of the protagonist of Nathaniel Hawthorne’s 19th century novel The Scarlet Letter, she’d probably be less concerned about having the letter ...
Suitcases and schedule scrapes: “packing” more punch into limited study time
In his book, Outliers, Malcolm Gladwell lays out criterion that in some ways has become the anecdotal darling of pop-academic culture. You’ve likely heard of it: the 10,000-hour rule. Mastery, Gladwell purports, is a matter of numbers. Put 10,000 hours of focused practice, and you can achieve mastery of a complex set of skills. Imagine the ...
Good writers start as good readers
Writing is a conversation. Whether you anticipate your audience to be a friend, a panel of scientists, a room full of legislators, the owner of a pizza shop, the divine universe, or oneself, to write is to put forth one’s wish to be heard. By extension, to read is to be in the position of the listener. Just as we learn to speak and to express ...
Where ideas come from
A lot of people who sit down to write a story are worried they don’t have any ideas. They think people who do have ideas are very special, or different in some way to people who don’t. It’s for this reason that authors are so often asked where they get their ideas from. The people asking think that the author will reveal the magical secret of ...
To ask or not to ask? That should NEVER be the question
My family often refers to me as “the questionnaire” because I am constantly peppering people with questions during all of our conversations. What can I say? I spent four years as both an English literature student at Bates College and a reporter/editor for my college newspaper. I simply always have questions to ask of myself and those around me. ...
How to use an outline to your advantage when you’re writing
How often do you start writing an essay with a great idea in mind, only to lose steam—or worse, lose track of your argument—well before you meet the length requirement? Have you ever reread a paper draft only to realize what you’re arguing on the first page isn’t quite the same thing you’re arguing on the last one? These sorts of problems are ...
Introduction to Functions
You’ve made it through algebra: now it is time to start talking about functions. While functions are often used to make upper-level mathematics easier to understand, they can be confusing at first. So – what is a function? How do functions relate to the algebraic equations we have used before? And how do they help us with mathematics and computer ...
Computer science buzzwords explained
Computer science can be intimidating! Especially when people use lingo you aren’t familiar with. The goal of this blog post is to help you start understanding some of the computer science buzzwords.
How to communicate better: unlocking language’s hidden meanings
We all know that language is a powerful tool for communication. Sometimes it can be surprising how much meaning is conveyed in the shortest of sentences. Language is composed not only of the direct meaning of the words used, but also of many additional layers of meaning that arise through prior knowledge, background information, word choice, and ...
5 easy steps to good writing
Great chefs don’t cook wonderful meals on the first try. They’ve been in the kitchen for many sessions trying things out before they put a dish on the table. Writers need to do this too. Plan, practice, and prepare for the writing project you have in front of you. Break it into manageable chunks of about 2-3 hours each. These chunks need to be ...
Why I love teaching English
“I’m not good at writing.” “I don’t really like reading.” “I don’t think of myself as a writer.” “Why do I need to learn how to write? I’m going to study engineering!”
Why I love teaching Spanish
In the spring of 2020, when we were all locked down due to the pandemic and feeling cooped up and anxious, I got an email that lifted my spirits. It was from a former student who wrote to thank me for writing him a letter of recommendation for an internship with his local congresswoman that led to a job after graduation. He revealed something that ...
What I love about psychology
I have always been fascinated by human emotions and behaviors, as well as the unique ways in which we interact with ourselves, others, and the world. I initially learned about a field that addresses these very phenomena—that is, the field of psychology —when I was in high school. However, I didn’t consider it as a possible career path until ...
What I love about history
It’s not uncommon for people to find history the most boring subject in school. It often gets a bad rap in popular culture, too. In Harry Potter, for example, the History of Magic teacher, Professor Binns, drones on and on and frequently puts his students to sleep with boring lectures about arcane material. When I tell people I study history, they ...
What I love about physics
What if I told you that there’s a way to describe the waves of the ocean, the winds in the skies, the motions of celestial bodies — almost everything around us — and harness that information to create great things? This tool does exist, and it’s a science so fundamental that its principles guide our understanding of everything from microbes to ...
How to streamline a draft
One way to make sure your writing is clear (beyond writing "good sentences") is to take a look at the content of your paragraphs. The technique I'm going to detail in this post is perfect for a first draft, but can be used for final drafts too. I like to use this method when I need to cut some words to make a paper shorter, or before and after a ...
How to plan and organize historical research
Designing and executing historical research for a short essay, seminar paper, or thesis can be daunting. How do you find a primary research question, and how do you know which sources will help you answer this question? How do you read and take notes on sources once you've found them?
Tips for studying biology
I am often asked the question, “Brooke how do you study for biology?” We know to use practice problems to study for physics, or pathway diagrams for chemistry, but biology is different: it is a lot of memorizations!
Working out your brain
My first day in the gym was intimidating. I always thought the gym wasn’t for me, and so I had tried to avoid it as much as I could. I remember feeling slightly embarrassed as I picked up the smallest weights in the gym with my slender arms. However, overtime I was able to pick up heavier weights and noticed that my arms were slowly filling up the ...
A language study routine that actually works
So you're studying a new language, and you've been told that you need to make time to review and study vocabulary regularly. That makes sense. You tell yourself you'll do it. You may even make some flashcards and spend time drilling them two or three times early in the semester when you are full of good intentions. But if you're like me, the ...
Reading is hard. But it doesn’t have to be.
There is no denying it. In the age of the attention economy, bright stimulating screens, and exhausting schedules it is very hard to sit down and read with focus. Whether we are talking about a novel for English class, a source for AP U.S. History, or that dense SAT Reading passage from the Federalist Papers, it is hard to truly dig in and read ...
What makes a good descriptor?
Cliche is natural; originality, not so much. Pre-packaged phrases like “bring to the table,” “at the end of the day,” or “read between the lines” are overused and now lack their meaning, becoming a kind of automatic thinking, according to George Orwell. But why? Because triggering automatic thinking in a listener is helpful to a speaker if he or ...
How to balance redox reactions in acidic and basic solutions
Balancing redox reactions is an essential skill for the Chemical and Physical Foundations section of the MCAT, the GRE Chemistry Subject Test, and the AP Chemistry Exam. Today, we will learn how to use the half-cell method for balancing redox reactions in acidic and basic solutions. We will first balance a redox reaction in acidic solution, then ...
Top grammar errors to avoid
Throughout the years I’ve spent reading and writing, I’ve seen my fair share of grammar errors. But few are peskier, or more pervasive, than the two I’ll discuss in this post. So common are these two grammar errors that I regularly encounter them in professional writing — sometimes even in articles by full-blown professors! These two errors often ...
How to use root words to learn vocabulary
Retaining new English vocabulary is challenging, whether you’re learning English for the first time or studying for standardized tests like the SAT or GRE. The challenge arises, in part, from the sheer volume of words in English. English’s massive lexicon comes from words in several other languages, and learning some of these words—more often ...
The Intermediate Value Theorem explained by everyday life
Calculus can be tough stuff. Calc AB was the first AP class I ever took in high school, and though I love the subject now, I certainly didn’t love it when I was first struggling with limits or with the chain rule for derivatives.
What I learned about the writing process from bread baking
Working from home means I can adapt myself to the capricious schedule of bread making. Dough waits for no one (and it will not rise more quickly if prodded!). I’ve loved baking since childhood, but I discovered bread more recently.
S’more fun: simplifying limiting reactants using chocolate
Stoichiometry: it’s the bane of many chemistry students’ studies. It’s so easy to get tangled up in a jumble of numbers without any idea of what’s actually going on.
How to make sure you don’t fall behind during distance learning
Let’s be real: it’s hard to focus on school at home. And as COVID-19 cases persist and online learning remains part of our lives, it is important to not fall behind. Here are some tips to help you stay on top of your work while learning from home:
Explaining eight common Chinese idioms (“chéngyǔ”)
“Chéngyǔ” (成语) are Chinese idioms that usually occur in groups of four characters and often originate from old fables in classical Chinese writing. As a testament to China’s long history and rich culture, chéngyǔ have persisted as a fundamental component of modern Chinese language in both formal writing and in everyday language. There are over ...
Six ways to brainstorm more effectively
At its core, writing is about discovering relationships between words and ideas. Your brainstorming process can and should reflect that central goal from the very beginning of the writing process. Here are a series of investigative approaches to help you expose and explore these relationships:
A beginner’s guide to analyzing historical documents
Most high school and college-level history courses will require that you read, interpret, and analyze a document or set of documents from the past—otherwise known as primary sources. In this post, I will provide five basic questions that you should ask about your document(s) that will kickstart your thinking about the past and serve as a starting ...
Introductory statistics: are my data normal?
Statistics is fun, I promise! But before we can start having all the fun, it is important to describe the distribution of our data. We will need to handle problems differently depending on the distribution.
Studying at home: how to keep up with work while learning online
In the early stages of the COVID-19 pandemic, most of us had to deal with the sudden reality that we could not go to school physically. We might have had have school content posted online or packets of work to complete, but we were likely not allowed to physically be at school with our teachers and classmates. We were, essentially, homeschooling.
Where do Taylor series come from and why do we learn about them?
Taylor series can often seem a bit mysterious the first time that we learn about them. The formula for the Taylor series of a function f(x) around a point x=a is given by
But what is “dx” really? Calculus terms explained
The symbol “dx” comes up everywhere in calculus. For example:
Two common grammatical mistakes to avoid in polished writing
There are no hard and fast rules in writing. But even if an experimental poet or an avant-garde novelist has dispensed with capitalization or written an entire novel without the letter E (yes, a novel like this really exists!), this does not mean that you need to follow suit. Your personal statement, for example, is not the place to defy the ...
The music of Mandarin: learning the five tones of the language
Learning Chinese is challenging but fun! Even the parts that require repetitive practice can be enjoyable with the right framework and point-of-view.
Homonyms
English is one of the languages in which spelling is a big deal. Spelling bees were created in English, and the concept is not present in other languages in which words are more often pronounced just like they look. In English, we have words that are pronounced the same but have different meanings and spellings (homophones). We also have a lot of ...
Grammar: one to 1
When learning a new language, students almost always begin with the alphabet and numbers. We use letters, of course, to form words, which form sentences that express ideas of varying complexity in a form that people who read this written language can understand. Numbers designate a different kind of language, one that conveys equations and ...
Betwixt and between: difficult grammar rules explained
English is not the easiest language to learn. This may be because of the many exceptions to its rules or because the same combinations of letters can be pronounced in many different ways. English also has one of the largest vocabularies of any recorded language, which means English speakers can say what they mean in a lot of different ways, but ...
Checking your answers in physics
Having worked through a long physics problem, you finally have an answer. How do you know if it’s right and all that work wasn’t for naught? In this post, I will cover a few quick strategies that can help rule out wrong answers.
An application of calculus: finding optimal road networks
Suppose that we have many towns spread across the country and we are trying to connect them with a network of roads. If we would like to do so by laying as little road as possible, how do we do it? In this blog post, we will use Calculus to tackle a special case of this optimization problem.
Understanding elasticity of demand in economics
You may have heard in your econ class about a good’s elasticity of demand, or about “elastic” or “inelastic” goods. Consumers’ elasticity of demand is just a fancy way economists talk about how sensitive people are to changes in a good’s price.
High school chemistry: What is it? Can I be good at it?
The word “chemistry” inspires so many emotions. To some, it brings about the excitement of mixing together glowing liquids and crafting the perfect radioactive potion that, when consumed, will turn you into the Incredible Hulk. To others, it’s discombobulated numbers and letters on a piece a paper in a classroom, a concatenation that strikes fear ...
What physics equation sheets can do for you, and what they  can’t
In your time taking physics courses, you will likely run into one that deals with equation sheets. These can be note cards or an entire sheet of paper, and anything that can fit on it is fair game and can be brought into a test. The natural reaction might be to try to cram and squeeze an entire textbook on those sheets using really, really tiny ...
5 tips to improve your writing
I was recently helping someone with a comparative essay they had to write for school. This person did not like writing—a common enough state of affairs. They felt that they had no talent for it. The process frustrated them. I could see that they were struggling in part because they were trying to do everything at once (come up with ideas, write ...
The key to mastering mathematics? Quit memorizing.
There are many misconceptions when it comes to the subject of mathematics. One of the most common myths I encounter is related to the way one approaches learning math.
What is a thesis statement?
Every paper you write in college should have it. Sometimes professors call this a “thesis statement,” sometimes a “claim,” and sometimes they don’t really specify what it is. But it’s essential — and sometime elusive. But it shouldn’t be!
A guide to limiting reactant problems... using sandwiches
An everyday limiting reactant problem You’re expecting company and totally forgot to go grocery shopping. What on earth will you feed your guests? Sandwiches! You have some ingredients to whip up some sandwiches. So, let’s assume you are going to go through with making these sandwiches. You need 2 slices of bread, 3 slices of meat (can’t be ...
Electron configurations: a must know hack
Imagine this...you’re taking your general chemistry midterm and you’ve decided to shuffle through the exam and complete all the hard things first. You’ve totally underestimated how much time those problems were going to take you and now you have three minutes left to write the electron configuration of 10 elements. Untimed, this would be easy to ...
Formal charge: what they didn’t tell you in your chemistry class
Formal charge is the charge that a bonded atom would have if its bonding electrons were shared equally. Note:
Tips for writing an exam essay in 80 minutes
We've all been there. The teacher is at the front of the classroom with a pile of blue books. She begins handing them out. You scrawl the name and date on the front and wait for her to start the timer. As you open the first page, an overwhelming white page stares back at you. And you panic. Luckily, there are ways to prepare for essay exams that ...
3 ways to better analyze poetry
“Cikgu Tess!” “Pagi.” “Miss. Look lah.” “Alyaa—why?” “Girl’s bathroom,” she says. “Cikgu, you touch?” Our state has the highest concentration of venomous snakes in the region. “Is it poisonous?” I mime the action of being bitten (by my hand) and then dying. “Mm, don’t know.” In 2017, I taught ESL, literature, and political science at a rural ...
An introduction to supply and demand
What is supply and demand? In economics, supply and demand is the relationship between the quantity of a commodity that producers wish to sell at various prices and the quantity that consumers wish to buy. Though it is a seemingly straightforward relationship, in practical application it can become quite complicated. In this blog, we will use an ...
How to make introductory physics exciting (when you're bored out of your mind)
Why do many students find physics so boring? Cutting-edge physics research gets to address amazing, deep questions: "What is all the stuff in the Universe fundamentally made of?” and “Where did all this stuff come from anyway?” Yet college-level introductory physics courses on Newtonian mechanics can feel quite...mechanical. Why does introductory ...
Introduction to physics: the language of the universe
In elementary and middle school, we learn mathematics for the sake of mathematics, we are never told what mathematics can ultimately be used for or why mathematics is useful other than the fact that it can help us make change and do our taxes one day. What they should be telling you is that the laws of the universe are written in a language that ...
How to write a killer essay in 3 easy steps
We’ve all been there: staring at a blank document, practically able to feel the creeping imminence of our paper’s deadline. For so many of us, it’s really hard to sit down and actually channel our thoughts into a coherent form, let alone one that’s structured and based on an argument worthy of praise.
Solving the “I’m not good at math” problem
You’ve heard it before. Or you’ve said it. I’m not good at math. I hear it from seventh graders struggling with fractions, high school students preparing to take the SAT, friends at a restaurant when splitting a check, and even from parents assuring me that their child’s own difficulties are in fact genetic. And while I’ve heard it countless ...
The top 3 reasons you should study Latin
There comes a moment in the careers of most middle- and high-schoolers learning Latin, and also among some college students considering it as a possibility when picking classes; a moment when they ask themselves (or their parents, or their teachers), “Why do I need to study this?” After all, Latin is a dead language; unless you plan to become a ...
How to solve kinematics problems: a guide to vectors
This article is the third chapter in a series on how to understand and approach kinematics problems. The first chapter covered position, velocity, and acceleration. The second chapter covered solving kinematics in one dimension Now we are going to take a quick detour into vectorland so that we’re ready to approach kinematics in two (and even ...
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