Austin Scholar #31: Benjamin Bloom and the Two-Sigma Problem
Austin Scholar #31: Benjamin Bloom and the Two-Sigma Problem
& The Great Mastery Debate
Hey, y'all!
In the 1960s, an educational philosopher had a series of amazing breakthroughs in understanding how kids learn. His research unlocked the ability for kids to learn two standard deviations faster than most people thought possible.
But his methods were almost impossible to implement in the traditional classroom.
They got ignored -- most people didn't even know his papers existed.
Technology is only just starting to catch up -- which means this philosopher's ideas are becoming relevant again. Because we can finally implement them, and radically change how kids learn.
But I'm getting ahead of myself.
This week from Austin Scholar...
Austin’s Anecdote: The Great Mastery Debate
Benjamin Bloom and the Two-Sigma Problem
Scholar’s Sources: My Favorite Resources on the Taxonomy of Learning
This week, I’ve actually been extremely organized and have been able to keep up with my work without getting overwhelmed, which is a super awesome change from last week :)
The coolest side effect of the work I did this summer is the amazing thinkers I now have the ability to interact with. I got a text from David Perell this week telling me I should write an article about Benjamin Bloom and his research into education.
Which, honestly, I thought was an amazing idea. So here it is (and credit to David Perell for the idea).
Austin’s Anecdote: The Great Mastery Debate
When I first started to use learning apps (like Khan Academy and ALEKS) as a young, energetic 10-year-old, I wanted to move through them as fast as I could.
Doing sixth and seventh grade math while I’m in fifth grade? Wow, you’re so smart, Austin.
I started trying to race myself through the apps. I zoomed through my 4th through 8th-grade ALEKS pies, just trying to prove that I could.
I’m not going to lie: there were definitely some concepts that I just memorized my way through, without fully understanding what I was learning.
But, I was able to finish 8th-grade math in sixth grade, so I didn’t care.
And then it was time for me to do Algebra. Yeah, I definitely wasn’t ready.
It took me absolutely ages to get through Algebra–and I barely understood what I was doing.
Because I’d sped through my middle school math courses, I didn’t have the fundamentals to understand this next level.
After many tears and crumpled-up papers, I finally finished Algebra. I promised myself that I would make sure to actually learn all of the content in my courses so that my Algebra issue wouldn’t happen again.
Then, I started Geometry, and I forgot all about my promise.
Geometry was absolutely miserable for me. I couldn’t visualize any of the shapes or remember how to make a proof or any of the stupid laws of sine or cosine.
I got bored and frustrated, so I gamed Khan Academy and guessed my way through.
After Geometry came Algebra II, and it didn’t matter that I didn’t know Geometry, because I absolutely knew Algebra I.
And then came PreCalculus, and I was still crushing it because PreCalculus is basically just more Algebra.
By the end of my freshman year of high school, I could factor anything in my sleep.
Then, it was time for Calculus. I had definitely mastered everything to do with Algebra, but I didn’t know any Geometry.
When it came time to use the Unit Circle or solve derivatives in other angle problems, I was completely lost.
I had to spend time learning basic Geometry concepts while I was doing Calculus because I hadn’t mastered them beforehand. It was pretty embarrassing.
Needless to say, I definitely learned my lesson.
Now, to make sure that I continue on my track towards mastery in math, I’m enrolled in the gt.school program. In this program, all students, even high schoolers, have to go back to fifth grade math and complete mastery challenges and work their way up.
I’m completely ensuring that I have mastery over every single math concept, from fifth grade up to Calculus.
The sad thing is: if I had aimed for mastery when I first did these math courses, I wouldn’t have to take the time to go back and re-learn them, and I would’ve had a much easier time in high school math.
So, while it might seem like mastery is too hard and takes too much time, trust me: it’s worth it.
Benjamin Bloom and the Two-Sigma Problem
Benjamin Bloom was an absolutely brilliant educational psychologist from the sixties who published three groundbreaking papers about how students learn best.
Each paper contained a new concept of education, and Bloom’s three concepts working in tandem are guaranteed to produce a high-performing student.
Let me explain.
Bloom’s Taxonomy of Learning is a system that classifies learning objectives into increasing levels of complexity: from basic remembering of facts to an advanced comprehension and evaluation of a concept to, finally, an ability to form new thoughts and insights around a topic.
Most schools keep kids in the first two levels–never letting them reach the higher levels of understanding necessary to truly master a topic. Think of how much human potential is being wasted by never teaching kids how to evaluate and create!
Mastery Learning is the idea that students should achieve mastery of a concept before moving on to the next one. Today’s school system moves kids through all of the content at the same pace. The kid that gets a 70% on the test will move on to the next topic at the same time as the kid that gets a 95%. The first kid clearly doesn’t understand the concept, and so the next, more complex concept will still not make sense. (Like my experience with Calculus after gaming Geometry).
Bloom’s paper on Mastery Learning posed a really important question: why are we setting our high schoolers up for failure by moving them through content at the same pace when we should be prioritizing true understanding and mastery? (The answer is that self-paced learning is hard to replicate in a traditional classroom, but apps are fixing that!)
Bloom’s Two-Sigma Problem summarizes Bloom’s findings: the average student who was tutored by using Mastery Learning techniques performed two standard deviations (A LOT) better than students who were taught in a classroom setting. Read that again: two standard deviations.
You can see how 60 years ago–when these papers were published–it would have been pretty challenging to give every single student a personalized tutor who creates custom content to ensure mastery over all concepts.
But today, we have a solution: Online apps.
Online apps allow each student to learn at their own pace. For those who are able to quickly understand the material, the apps allow the students to advance to the next level, and for those who are confused, the apps allow the students to stay at that level until they learn the foundations they are missing. Online apps give each student their own personalized tutor.
Bloom’s ideas, along with ideas such as spaced repetition, forced recall, and active learning, are core parts of learning science, which is a field that “combines research, data, and practices to help educators teach better and students learn more.”
Now that apps exist (and many are available for free!), your teen can take advantage of the data and science behind how to learn better and faster and incorporate learning science techniques into their normal studying habits.
Here are a few ways how can you help your kid take advantage of Bloom’s ideas and incorporate other learning science practices into their everyday routine:
First, have them make a learning science infographic. For our Alpha Bootcamp (a four-week intensive for Alpha high schoolers to prove we are committed to 2x learning and building a Masterpiece), each student had to create a learning science infographic that highlighted four core learning science concepts and how to apply them.
Here’s mine:
This exercise anchored our belief in the importance of learning science–because we spent all that time explaining what it can do for us.
And then, to further anchor our understanding, we had to participate in a learning science debate, where each team had to explain why their learning science concept was the best.
I’m not going to lie: I completely stand by spaced repetition :)
Once your kid is completely immersed in the world of learning science, you can start implementing Bloom’s concepts.
To start with the Two-Sigma Problem, you can encourage your kid to use online apps, such as Khan Academy, in order to massively improve their understanding of content. Check out Austin Scholar #2: Austin’s App Analysis for more on finding the right app for your kid.
For Mastery Learning, have your kid try online resources, such as gt.school, in order to ensure mastery over concepts. Or, have your kid take practice tests on every chapter or unit until they get above a 90%. Though this seems absolutely terrible and horrible, as I’ve learned (see above Anecdote), it’s worth it.
This is super important, so incentivize your kid however you can to get them to shoot for mastery, not just passing.
To encourage Bloom’s Taxonomy of Learning, have your kid try this exercise:
Every week, find seven sources in a particular topic or field. Spend a few hours compressing and summarizing the sources. Then, edit the summaries so that they are engaging to read and provide a new insight to the content. Finally, publish the summaries online. This last part is extremely important because it will force your kid to have a complex understanding of the topic and to explain their perspective in a unique way, which reaches the higher levels of Bloom’s Taxonomy. (If they don’t show their unique perspective, their summaries will just get lost in the blizzard of information that is the internet.)
Technology makes implementing Bloom’s research incredibly easy. We just have to take advantage of it.
Scholar’s Sources: My Favorite Resources on the Taxonomy of Learning
This video does a great breakdown of the science behind taking effective notes. It starts with a few tips (avoid transcribing, use images or figures when possible, and try the outline method) before going into what types of notes to take for different subjects. That, for me, was the most valuable part of the video.
Basically, for fact-heavy subjects (ex. history), you should try creating synthesis questions (guiding questions) to help you remember the information.
But for concept-heavy subjects (ex. math), you should try creating summary sheets, which would help you make connections and notice patterns that you didn’t during the original learning stage. The video also really emphasizes the importance of active learning and forced recall.
If you want a super in-depth, clear explanation of Bloom’s Taxonomy, check out this video and this video.
The first video goes into crazy detail on how to utilize Bloom’s Taxonomy while studying. The video clearly explains how students should be using this model to improve their grades and study effectively. The video also provides a study method that aligns with Bloom’s Taxonomy to use when learning new content
The second video goes through a simple example of using Bloom’s Taxonomy to learn about a lemon and highlights how to transition from one stage to the next. This video is super short, cute, and easy to understand, while outlining the benefits of learning through Bloom’s Taxonomy.
This video uses learning sciences to explore the following 13 study tips:
Use paced repetition
Find your own style
Get a good night’s sleep
Focus
Try the Pomodoro technique
Do the hard stuff first
Exercise, meditate, and converse
Go new places
Take fun seriously
Space out your studies
30% read, 70% recite
Instant self-test
Don't force it
While some of these seem obvious at first glance, the explanation behind why it’s important to use these tips actually really boosts understanding and motivation to try them.
Thanks for reading. Go crush the week! See y'all on Sunday.