The Difference Between Ignorance and Willful Ignorance

Ignorance just means you don’t know something. For example, I’m ignorant about the names and accomplishments of many famous athletes and the rules of the sports they play.

At any point, if I want to learn more about these athletes and sports, I can. Ignorance doesn’t have to be permanent. It can change if I want it to, and if I have access to the relevant information.

Willful ignorance is different and worse than regular ignorance. With willful ignorance, I don’t know something, but I act as if I’m knowledgeable. I act as if I know what there is to know. I resist learning anything more, even if that’s what I need to do to share my opinion, teach a topic, or make a decision.

Let’s return to the sports example. If I were willfully ignorant, I would launch into a confident-sounding commentary about a game. I would share some strong opinions about the athletes’ techniques and strategies. If anyone were to tell me, “You don’t know what you’re talking about,” I would argue that what I’m saying is reasonable, valid, relevant, and sufficiently well-informed. Just by watching a sport for five minutes, I can learn what there is to know about it.

Willful ignorance isn’t just the state of not knowing something. It’s an attitude that blocks learning. It undermines intellectual humility and careful thought. If you’re just ignorant, you can become less ignorant. But if you’re willfully ignorant, how will you learn more?

One of the Best Assignments I Ever Got in College

In a development psychology course, the professor told us to find two things:

1) A newspaper article about a research study in child development.
2) The actual study itself (written up in an academic research journal).

We then had to do the following:
– Read both the newspaper article and the research paper.
– Evaluate the strengths and flaws of the study. (Some examples: How did the researchers select the sample, and was the sample size too small? How did the researchers define the concepts, phenomena, or behavior they were studying? What were the weaknesses in the statistical analyses?)
– Note discrepancies between the claims made in the study and the way the newspaper article reported these claims.

This was an eye-opening assignment. It helped show me the profound effects of study design and statistics on research findings. And how newspaper articles can misrepresent these findings, usually in the headline and opening paragraph of the article – the parts needed for grabbing attention through bold claims. Also, the parts people usually don’t read past.

I recommend this as an exercise in critical thinking. Research papers are often behind paywalls, but not always (sometimes, a professor will have a copy on their site). And if you’re already a college or graduate student, you may be able to access journal papers for free using school library privileges.

Another Great Site for Learning Math at Home

For online math learning, I usually recommend Khan Academy. But it’s good to find other resources too. I recently came across, a great site that could be helpful to you or your kids for math studies.

Using the site is free. You don’t even need to log in to access the lessons, though logging in allows you to record your progress. (I haven’t yet set up an account, but I think there are also more opportunities to review material if you’re logged in.)

From what I’ve seen so far, here’s what I like about this site:

– The videos are interactive. During each lesson, the video stops at various points, and you’re asked to solve problems. This means you can’t just listen passively. You need to be able to show that you’re paying attention and can figure out what’s going on.

– The lessons check that you have the relevant background knowledge. For example, at the start of the video on raising numbers to a negative power, you’re tested with a question on dividing exponents and given a chance to review if you’ve forgotten.

– Basic math doesn’t get overlooked. For instance, the algebra unit includes videos on arithmetic principles. This is helpful to students who are starting algebra but may have forgotten certain rules about multiplying negative numbers, for instance.

One drawback to the site is that it’s a little “calculator-heavy” in its approach. If you want to study how to multiply or divide decimals by hand, you may need to look somewhere else for a review.

But overall it’s a useful site that I recommend as a supplement to your math studies.

TwoSet Violin Is So Fun

Two classically trained violinists have been running a YouTube channel full of goofy, geeky humor, music games, and silly reviews, plus genuinely educational content about technique, styles of different composers and performers, etc.

The following are samples of the many videos on their channel (I’ve watched just a small fraction):

Continue reading “TwoSet Violin Is So Fun”

How to Keep Your Day Structured: Inspiration From Two Sources

If you’re currently working or studying from home and aren’t used to it, it may be difficult to adjust and to keep your days from collapsing into an undifferentiated mass of goo.

Someone forwarded me this video from It’s a Southern Thing (a lighthearted YouTube channel on living in the American South), and I’m offering it as the first source of “work from home inspiration”:

At roughly 1:15, you’ll find The Planner, who sets up his desk and writes a schedule on a whiteboard. When that part comes up, pause the video and check out how he’s organized his day. It’s a decent template for a day’s schedule, though obviously you’ll need to adapt it to your own set of obligations.

He sets aside a specific block of time to work on a presentation. Maybe that’s his top work priority of the day, because it needs to get done soon. Usually, on any given day, you’ll have at least one thing that really needs attention more than others.

For other work, he’s set up a general work/catch-up category that may also wind up getting carved up into a few main tasks or maybe just serve as a flexible time to attend to whatever comes up. He also makes room for things like meals and exercise.

Consider how you’ll also take breaks within the times allotted for work tasks. For example, an hour of work can look like 25 minutes of work, a 10-minute break, then 25 more minutes. Even if you don’t get everything done within a certain time slot, at least you’ll have completed some of the work (as opposed to leaving it untouched and forgetting about it until the absolute last minute).

(Yes, this is supposed to just be a funny video, but I’m saying, you can get inspiration from anywhere. Also, I had a quick look through the channel, and found this other funny video portraying a southern fashion show that made me smile.)

The second source of scheduling inspiration I’m sharing with you comes from Khan Academy. Among their parental resources for kids learning at home, there are some schedule templates covering preK to 12th grade. These templates offer ideas for different activities throughout the day with time for play and rest too. You can adapt them for your kids or use them for ideas about how to structure your own day if you’re working and studying. (“Ideally run around and play outside. Have a snack” is potentially good advice for an adult, and may be useful if you have a yard or access to an uncrowded outdoor space.)

Note-Taking Skills Video: Cornell Method

To follow up on this list of educational websites, I’m going to recommend another one: Socratica, a YouTube channel that focuses primarily on math and science topics but also has some humanities videos and videos giving advice on study tips.

On the study tips playlist is one video I watched recently about the Cornell Method of taking notes:

A good thing about this video is that she gives an example of the note-taking method during a short chemistry lesson. This method encourages more than just re-reading notes. You’re expected to engage with them even more actively (by fixing errors and creating the cues and summary sections).

School Closed Because of Coronavirus? Check Out These 18 Educational Sites

Many kids around the world are missing out on classes because of coronavirus closures, and in the U.S. the number of closures is expected to increase, both for K-12 institutions and colleges.

Even if your school is still open, these sites are worth checking out. You’ll find content for a variety of levels, and for both kids and adults.

1) Atlas Obscura – Exploring the wonders of the world.

2) Bozeman Science – Excellent videos primarily on AP chemistry, biology, physics, and environmental science.

3) CK-12 – A resource for different topics in science, math, and social studies.

4) Curiosity Machine – Offers challenges involving artificial intelligence, engineering, and other areas of science and technology.

5) edX – Lots of courses geared towards professionals and students in higher ed. However, there are younger students who could also benefit from the site.

6) freeCodeCamp – Check out their YouTube channel too. HTML & CSS, Javascript, Python, an introduction to statistics, and more.

7) GCFLearnFree – Many tutorials on computer programs, job skills, communication skills, critical thinking, and other useful and important topics.

8) Khan Academy – Because a list like this wouldn’t be complete without it. They even posted content about coronavirus school closures and how the site can help.

9) MetKids – The Metropolitan Museum of Art in New York City offers an interactive, kid-friendly feature for exploring the museum. Includes many suggestions for creative activities.

10) OpenStax – Free online textbooks.

11) Physics Girl – YouTube channel exploring topics in the physical sciences, with demonstrations of experiments you can try.

12) Project Gutenberg – Free eBooks. Here are their top 100.

13) Read Theory – For help with reading comprehension skills.

14) Science Friday – Lots of subjects covered in article, audio, and video form. (Just one example: a look at the word quarantine.)

15) Simplilearn – A YouTube channel for building digital skills. Includes tutorials on data science, machine learning, and artificial intelligence.

16) StoryJumper – A fun way for kids to create their own books.

17) We Are Teachers: Free Printables – Search by grade level and subject.

18) Wonderopolis – For exploring different topics, working on reading comprehension, and getting ideas for creative and educational activities.

New Ways to Fail Students

Just a few observations about New York City public schools:

  • There are schools where getting an ‘A’ is really easy, even without competence in a subject. Hand in the assignment, get a checkmark, and you’re good to go. Sometimes, students quickly realize they aren’t learning anything. Other times, realization comes from failing a state exam.
  • There are schools that shove students along from one grade to another, passing them so that they move ahead, and they arrive in high school struggling badly with math and literacy, including concepts and skills they ideally would have learned years earlier. They arrive without various kinds of basic knowledge and without good study habits.
  • The Department of Education inspires no confidence, although it does produce fuzzy, pleasant-sounding words about the supposed nobility of its aims.
  • It’s worth pointing out that there are excellent teachers and schools too. I’m just highlighting the fact that apathy, burnout, and soft expectations are major problems. Poor policies, ineffective educational methods, and large class sizes affect the general student population; however, students from low-socioeconomic status households feel the negative impact most strongly.
  • Kids whose parents can afford private tutors will hire tutors, or they’ll wind up sending their kids to private schools. Other kids will discover new ways of not learning math, reading, or writing, as the city implements various kinds of educational reforms that fail to address pervasive problems.

For now, that’s all I’m going to say on the subject of NYC schools. Until recent years, I didn’t realize just how much contempt there is for children.

Beware of Forced Binaries

One of the most annoying types of arguments to come across (for me, anyway) is the one involving forced binaries. A complex issue gets reduced to two possibilities – like nature or nurture, or the question of whether rape is about sex or power – and these two possibilities get treated as if they’re mutually exclusive. Pick one, and make your stand.

Whether you’re having a classroom discussion or arguing with someone online, here are three steps to take when you’re confronted by a forced binary:

Ask yourself what each choice really means. In the context of the discussion, how are people defining ‘power,’ ‘nature,’ or any other word? Sometimes, you get a disagreement because people are thinking about the same concept in fairly different ways. If you clarify definitions, you may discover a greater degree of agreement than you expected.

Ask yourself if these choices are really mutually exclusive. Just start with, “Why not both?” and think about it from there. The two possibilities you’re forced to choose between may be interacting with each other in interesting ways.

Ask yourself if there are other factors at play. Forced binaries are simpler and tidier. They’re also a great way to create two clear sides and pit people against each other. But the issues you’re discussing often have more complexity.

Good luck!

Recommending Free Code Camp

When looking for a resource I could use to brush up on HTML and learn CSS, I came across Free Code Camp.

So far, I enjoy using it. The lessons include definitions, examples, practical exercises, and the freedom to play around with the code to see the effect of different changes. And it’s a free site. Definitely worth checking out.

Another thing – the site offers opportunities to complete projects and receive certifications. I’m not sure what value these certifications have for professional development, but the experience gained on the site, including the completed projects, may help when you apply for certain jobs.