Bravo Math News

(5) Three Revolutionary Hypotheses

A startup is largely a collection of hypotheses in a founder’s head, a bunch of ideas that, if true, can revolutionize an industry.

Here are mine. They are the path to building the best damn math course ever.

Hypothesis 1: Bottleneck Content

Students, teachers, and parents typically insist I help them with schoolwork. This is quite difficult when they resist learning 6 – 8 = ___ because their schoolwork is 6f(x) – 8f(x) = ___ . In fact, it’s a vicious cycle that ensnares millions and releases virtually none.

I say: to hell with such schoolwork, even if it means refusing the students and parents’ revenue. Forget the student’s age. All students should learn the same bottleneck content first.

  1. Whole number sense: +, −, ×, and ÷, what they mean, when to use them, and place value.
  2. Rational number sense. This is mainly extending whole number sense to fractions, decimals, and percents.
  3. Introductory algebra. This includes algebra’s generality, representing relations, and some solving.

With these bottlenecks relieved, there’s little to stop a grade 5 student from mastering grade 12 math. This would transform almost any kid’s life.

And that’s Hypothesis 1.

If repeated at scale, it would be an earthquake in education.

Disproof of the hypothesis would be students who have mastered rational number sense and introductory algebra, but are still struggling badly in math otherwise. In 10 years in the math education field, I have never met or even heard of such a student, but if you have, please let me know!

Hypothesis 2: How to Engineer Learning 

The next question becomes how to relieve those bottlenecks. My answer:

Rapid Prototyping
User-Experience Testing
Cognitive Science
+Diverse Team
Pedagogical Breakthroughs

Or in more detail:

VariableStatus QuoBravo Math
ContentTeach the student the government’s prescribed learning outcomes, especially what’s being done in school now.Focus on the bottlenecks of K-12 math regardless of student age or current school work. Work on limiting factors only.
WhoTeacher works largely alone, inputting craft knowledge and hard work. Best practices rarely spread. Diverse team of teachers, tutors, students, researchers, parents, etc. design learning activities inputting hard work, craft knowledge, cognitive science, UX, etc.
Data SourcesTeacher’s memory and relatively static student output, such as tests, quizzes, projects, presentations, etc.Use all of that (left) plus videos of the student learning. Use talk-aloud protocols and visible assessment to help track student cognition.Long-term follow up on the lesson.
Radically superior data.
Feedback LoopA teacher administers 1 or 2 versions of a lesson per calendar year.Test and iterate 4 versions of a lesson per day. Accelerate feedback loop at least 500-fold.
AssessmentRigor means seeking evidence of learning.
Confirmation (bias).
Rigor means seeking evidence the student has not learned.Seek early indicators of trouble.
Output, AssetsA teacher produces lessons, materials, craft knowledge, skill sets, etc. for herself.The team produces “Open-and-Go” lesson plans and resources that are so good that anyone who went through the lesson can administer it.

The company is nowhere near ready for this now, but within a few years I hope this is what a typical workday looks like.

9amOne employee administers Version 1 of a lesson.
Rest of the team observes and records on video.
10amEveryone watches the video of Version 1 together.
Everyone collaborates to develop Version 2 of the lesson.
11:30amOne employee administers Version 2 of the lesson.
Rest of the team observes and records on video.
1:00pmEveryone watches the video of Version 2 together.
Everyone collaborates to develop Version 3 of the lesson.
2:30pmOne employee administers Version 3 of the lesson.
Rest of the team observes and records on video.
3:30pmEveryone watches the video of Version 3 together.
Everyone collaborates to develop Version 4 of the lesson.
etc.Continue the above cycle until the lesson and resources are blazingly awesome.

Even a 5% improvement to each version would be a revolutionary advancement in education. In just a few dozen versions, every lesson could leave the students begging for more.

This is how we relieve the bottleneck.

Hypothesis 3: Bravo Math Graduates Will Be Amazing Tutors

To grow exponentially, requires a different format of education: peer-to-peer (P2P) instruction.

Most people teach the way they were taught. If Bravo Math teaches our students well, then when they graduate from the program, they will have excellent teaching instincts, and some will be worthy of hiring. I’ve already begun this by hiring a former student and it’s going great! [That’s why I might hire you.]

And it’s going well without the kind of world-leading math materials I want to build.

If the average Bravo Math Graduate passes on what they’ve learned to two students each year, then 5000 kids doing calculus will be just the beginning.


In summary:

Hypothesis 1: Students who learn basic number sense and algebra are ready for calculus regardless of their age or what’s happening in school.

Hypothesis 2: A team that rapidly tests and iterating learning activities will learn to teach students that number sense and algebra in under a year.

Hypothesis 3: Students who experience that will become excellent peer tutors, growing our impact exponentially.

Those are the hypotheses Bravo Math needs to test.