My Education Research Obsession: Bloom's 2-Sigma Problem

Benjamin Bloom is best known for his taxonomy, but I think his most interesting work pivoted around the 2-Sigma Problem.

The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring

I have read this paper at least once a year for the past 12 years.

Bloom found that students who received 1-1 tutoring performed 2 standard deviations (2 sigmas) better than the control group, but he realized that 1-1 tutoring is financially infeasible, so he looked for a combination of scalable strategies that could help teachers with normal class sizes get to the same level of student learning as 1-on-1 tutoring.

Here are a couple things that bug me about how and why people cite or revisit Bloom's paper:

A: Mastery Learning isn't totally free form!

Many people use Bloom's paper to justify ideas for mastery learning that are quite different from what Bloom used. For some, "mastery learning" and "competency-based learning" are synonymous. The idea is that students should move at their own pace based on their ability to demonstrate mastery of the content. Bloom's idea of mastery learning was different. Here is a diagram from Thomas R. Guskey's Closing Achievement Gaps: Revisiting Benjamin S. Bloom’s “Learning for Mastery.”

Bloom's model assumed that all students were studying the same unit (maybe 2-weeks long?) at the same time. The different pathways through the unit were informed by Formative Assessment A. Students who didn't initially master the content would get more instruction on the basic content, while those who did master the unit's content after one attempt at instruction which would get enrichment. Notice that all students would move on to the next unit at the same time.

B: It's not just about Mastery Learning!

Mastery learning showed 1 sigma effect, but was not the whole story. The greatest impact (1.6 sigma) came when he coupled mastery learning with "enhanced prerequisites." Essentially, they figured out what specific skill gaps students had relative to the content they were about to learn and remediated those gaps before having students dive into mastery learning with the on-level content. It's important to note how targeted the enhanced prerequisite instruction was. This wasn't about remediating all of pre-algebra before taking algebra. It was about bridging specific foundational skill gaps that were critical to the content to come.

When I go on about student readiness or using formative assessment to inform instruction while keeping an entire class on the same unit of instruction, I'm basing my ideas on Bloom. I'll save my rants about formative assessment death spirals and catching kids up for another day.

Teach to One: Technology that Kills Learning Relationships

Teach to One Math is an exciting idea. What if computers could help students get a truly personalized learning experience? Their supporters include an amazing list of educational organizations for which I have great admiration and respect, including Gates, Chan Zuckerberg, New Profit, and Oak.

Hechinger Report published an interesting article a few years ago What happens when computers, not teachers, pick what students learn? that paints a picture of how Teach to One Math can look in a classroom. It's certainly innovative, and probably works for some kids and teachers, but I was skeptical.

When Open Culture published Trainwreck: The Teach to One Math Experiment in Mountain View, CA Is a Cautionary Tale About the Perils of Digital Math Education, more people took notice of the downside of Teach to One. Around the time the Open Culture article came out, I spoke with a teacher from a Teach to One school, and her comment was that she felt...

"... cut out of the process and overwhelmed at the same time."

I'm sure that computer-driven adaptivity has its place, but when those algorithms get in the way of effective teacher-student relationships, we have a problem.

Why mention this idea that is a few years old? Artificial Intelligence (AI) is getting more powerful and so people keep coming up ways that computers can improve teaching and learning. For instance, some of TeachThought's 10 Roles For Artificial Intelligence In Education have AI-driven systems re-framing the role of the teacher. Teach to One Math should be a cautionary tale that helps us evaluate huge shifts that could harm relationships between teachers and students.

What an Instructional Designer Can Learn from StudyBass

My wife bought me an electric bass for xmas. I have never played a musical instrument, so this represents a big new challenge.

When I wanted to figure out some of the basics of how to play, I wandered around checking out YouTube videos and sites with music to play, but eventually I found StudyBass.com. This works, and I think it's because it reflects pedagogy I have used and valued for years.

To be honest, many teachers and content developers could learn from StudyBass. Here is the StudyBass instructional model in a nutshell:

1. Theory is presented, but is connected to skills and to well-known songs from various genres so you can do what the theory says and hear how it applies to familiar songs. Hearing the roots and fifths pattern in Under Pressure by Queen is a pretty powerful way to verify how the theory and practice can lead to something great.
2. Each video of how to perform a skill is an animation that shows the finger positions very clearly. This is more helpful than watching someone do it in a live-action video because human instructors usually go too quickly and it's hard to see exactly what they are doing (their hands get in the way of seeing what their fingers are doing).
3. Each practice exercise is supported by various modes. You can a) hear it, b) read it in standard sheet music notation, c) read it in bass tab (which is very simple), and d) see it in alpha tab (which is like a bridge between the over-simplified bass tab and the pure sheet music). All these different modes allow for multiple learning styles, but also allow a student to gradually decrease the scaffolding support. You can start with the alpha tab (using bass tab as a fall-back option when you're stuck), then move to only the sheet music or only the audio.
4. Exercises progress in a logical order for each lesson. Just about every lesson has exercises, and they are great.

The only thing I would do differently is to start each lesson with a YouTube video of a great song that makes use of the upcoming concept. Motivating with the goal can be powerful.

What StudyBass has helped me appreciate even more than before:

• Connecting theory, practice, and real-world applications is a great way to motivate and build deep understanding.
• Students benefit from guided practice that includes scaffolding they can gradually reduce.
• When it comes to visuals, sometimes less is more.
• Small chunks of instruction can lead to larger chunks of guided practice and then unguided practice.

Now to get back to learning chord roots and how they connect to A Hard Days Night by The Beatles.

Blogs Worth Reading: Math Teachers

I have found a group of math teachers who have made a really strong online community. Together, they are questioning, innovating, and making positive change happen and then sharing through blogs and tweets. It's incredibly inspiring.

Honestly, this is the best use of blogs and Twitter I have seen yet. My favorite thing about all of them is that they clearly have a growth mindset when it comes to their craft. They are growing as teachers in a collaborative, sharing way.

Anyone who is a new math or science teacher should read these blogs and follow these folks on Twitter.

That said, here is a list of some of my favorite math teacher bloggers/twitterers.

Kate Nowak (@k8nowak)
Blog: f(t)
Not only does Kate solicit ideas from the twitterverse; she actually puts the ideas into action and shares the results (regardless of how successful they were).

Sam Shah (@samjshah)
Blog: Continuous Everywhere but Differentiable Nowhere
Sam's post on the Blogotwitterversphere is great.

Fawn Nguyen (@fawnpnguyen)
Blog: Finding Ways
Great sharing, especially with the 3Acts.

Geoff Krall (@emergentmath)
Blog: emergent math
A nice mix of real-world application-driven stuff as well as insightful commentary.

Check these people out. I find them all to be informative and inspirational. I know there are others who are really good (my list of a few thought leaders who are not in the classroom will follow in a later post), but these are quite good. If you know of other great ones, please share.

The Wrath of Khan

With his tutorial videos, Khan Academy has made a big splash in the education world. Having Bill Gates sing your praises in a TED Talk is a sure way to get a lot of attention.

Over at Action-Reaction, Frank Noschese has an article Khan Academy: My Final Remarks. I agree with many of his points. Here is a quote from near the end of the post:

Khan Academy is just one tool in a teacher’s arsenal. (If it’s the only tool, that is a HUGE problem.) Khan Academy can be useful for some kids as a vehicle (build skills) to help them get to better places (solving complex problems).

Here are some other bloggers putting KA into some reasonable context:

• On his Quantum Progress blog, John Burk also chimed in with Project Euler vs Khan Academy: The Future of Online Learning.
• Mathalicious's blog has Socrates & C-3PO. 
• On his MAA blog Devlin's Angle, Professor Keith Devlin brings us The Difference Between Teaching and Instruction. 

It's comforting to see that I am not alone in thinking that if Khan is really the future of education, then we are in deep doodoo. Frankly, I would not really call Khan Academy’s stuff “education,” but rather would consider it “instruction.” If we turn education into nothing but a series of activities that a microchip can perform, then we are on a very dangerous path.

I don't mean to be a Khan basher. When using KA as a way to support struggling students, or as a way to help flip a classroom and allow teachers to focus on engaging with students, it can have great value. The Daily Riff has The Flipped Class Manifest, which provides some insights into how and when flipping a classroom can work, as well as a nice set of links to articles that provide more depth.

Back in 2007 (before I ever heard of Khan Academy), I started developing instructional videos that are somewhat similar to Khan’s work. I think they are great tools, but they are not the be-all and end-all of online education. We need to continue to innovate, but shouldn't get too carried away by the latest educational fad and think it will solve all our problems.