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Bravo Math News

(7) Business Models for World Domination

Previous posts have discussed:

This post will cover the company’s trajectory from my current tutoring services to global domination… or at least a pedagogical revolution.

Model 1: Andrew does 1-on-1 Schoolwork-Based Tutoring. I used to accept any student who needs help with math from school. I’m winding this down. I’ll help my “legacy” students graduate high school but as of August 2021, I will take no more students who just need to “get through” tomorrow’s test. I have already begun transitioning toward…

Model 2: Build V1 of the Best Damn Math Course Ever (BDMCE) for 10 Early Adopters. I’m looking for 10 students who:

  • Need 1-on-1 tutoring in basic number sense and algebra.
  • Are not on a tight schedule or deadline. This could be home schooled students, students in self-paced course, adult learners, students seeking enrichment, etc. But not crammers.
  • Are willing to do all tutoring on camera so my employees and I watch the video and build V1 of The BDMCE.

This is underway already with 2 students, both doing well! Bravo Math needs 8 more as of September 2021 and the equivalent of a full-time employee to help me build lesson resources for them. That position is open, by the way!

When the crude but acceptable V1 is complete, hopefully around June 2022, then it’s time to transition to…

Model 3: Andrew = Super Teacher, Publicly Offered Course. It’s time for expansion and refinement.

  1. Offer the course to the general public. Anybody who wants a life-changing experience in math can sign up.
  2. Drastically increase the rate of testing and iteration of the resources.

When I first started tutoring in 2010, I had no idea what I was doing, yet managed to get fully booked within a year. Word-of-mouth alone drove this.

If this course is even a tenth as good as my dreams, there will be a flood of demand and an army of raving Bravo Math fanatics in Vancouver. That alone will be an earthquake in the local math education scene, but to really change the world, the model must be scalable. I can’t be the one teaching everything.

Model 4: Full Implementation of the Team-Based Rapid Prototyping Model of Pedagogical Development

See Hypothesis 2.

This is how Bravo Math will create learning resources so refined and potent that recent graduates can become excellent peer tutors. This is the path to exponential growth and, hopefully, a template for how any educator can improve their pedagogy.


Any questions?

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Bravo Math News

(6) The Bravo Math “Culture Deck”

Students FirstCourageTruthfulnessMerit

Enron probably had a great values statement but the company ended in criminal disgrace. More often, organizations ignore their purported core values and become overrun with cynics just trying to get through the day.

Inspired by the Netflix Culture Deck, below are examples of how Bravo Math will be unorthodox and how I will ensure the entire organization revolves around its 4 core values.


Students First may be the most systematically ignored cliché in the world of education.

Whose interests are served by a $550 textbook on business ethics or an overpriced and obsolete but mandatory calculator or universities that do not incentivize good teaching? Not the students’.

Which of the following sounds more familiar?

[a] “You’re going to write the test next Thursday then if you pass we’re all done and we’ll never see each other or discuss this ever again.”

or

[b] “You’re going to write the test next Thursday. Also, in 5 years, we’re going to follow up with you to discuss how our pedagogy impacted your life over the long-run since that’s obviously what matters most. Then we’ll use your feedback to improve the course for the next cohort.”

Obviously [a] is the norm and [b] is largely unheard of.

Whose interests does this serve?

Here is how Bravo Math will be different.

  • The sad reality is that the vast majority of the math tutoring demand is for cramming, rote memorization, grade-chasing, and even outright cheating. Learning is frequently viewed as an obstacle. (“I don’t care if ‘multiply’ always means ‘increase’ or not. Just show me how to calculate 795(n/14) = ___ for my test tomorrow.”) I’m appalled at how many students, parents, teachers, and administrators commit to this approach, even when they agree that it’s terrible for students in the long-term. In 10 years of trying to change minds on this issue I have succeeded exactly zero times. In 10 years of dozens of math education conferences, I have not even heard of anyone who has succeeded in changing a single family’s mind on this issue. I receive plenty of this demand already and I could make a lot more money by simply selling my time to the highest bidder but that is not in the students’ interest, even if the bidders think it is. Bravo Math will continue to turn away such customers regardless of the money involved. I want to transform the math education ecosystem, not just profit from it.
  • It is very possible that Bravo Math will have to convert to non-profit status, as durable competitive advantages in education businesses are rare, and in our case, they do not serve students. Such advantages in business generally are network effects, IP, scale economies, branding or licensing advantages, etc. We will largely pursue the opposite.
    • Instead of scale and IP advantages, Bravo Math will eat the fixed costs of developing amazing lessons and learning how to improve pedagogy, then we’ll open source it all. Anyone who wants to use our materials can.
    • Instead of the sticky network effects typical educational marketplaces try to build, I will ensure everyone can come and go as they please, but choose to stay. I want employees to stay because the company is awesome to work for. I want students to stay because they have incredible learning experiences with us.
    • Bravo Math will pursue exactly one type of competitive advantage: rate of innovation. We will win not due to a catchy and expensive advertising campaign, not because of copyrights, not because of network effects, not because of scale, not even reputation. We will win by improving our teaching practices faster than anyone else.
  • Expanding the benefits of good 1-on-1 tutoring is expensive. Not everyone can afford it. Furthermore, many need it because the education profession itself is replete with victims of bad math education systems. We will reach exponentially more students if we train teachers to learn and love math. So, all teachers, teachers-in-training, educational support staff, and homeschooling parents can take our courses without financial charge if necessary. Instead of payment, they can participate in improving the lessons and user-testing. This may cost the company a lot of time and money. Maybe it will all but delete Bravo Math’s market for private math tutoring… But that would mean dramatic improvements in the math education field. Students would be much better off and we work for them.

Next up: Courage. Everyone and their mother has a million ideas on how to reform education, yet successful reforms and even variability are nearly unheard of in decades and across continents and cultures. We don’t need to visit Korea or Kansas or Kenya to know how their high school systems are organized. [Credits and grades for course completion, one big building or complex, students moving from room to room with subject-specialist teachers, students organized in age-grade bands, government-granted diplomas, etc.]

Given the historical record, already discussed in (4), the idea of pursuing a radical improvement in education seems hopeless. And I don’t want to BS you – very few math education experts would rate my ideas as worthy.

I don’t care if my ideas are unpopular. I only care if they are true and effective. And I will pursue that truth relentlessly with everything I’ve got.

Speaking of truth…

Truthfulness, honesty, sincerity, integrity, etc. are also popularly stated core values. How, then, have we accepted the following as norms?

  • Typical job interview
    • Interviewer: “What are your biggest weaknesses?”
    • Candidate: “I’m just so slavishly loyal to my employers! What is it like to work here?”
    • Interviewer: “You’ll experience the greatest work environment in the world as a cashier at Burger King!”
  • An automated message tells us for the 36th time “Your call is important to us.”
  • Typical political press conference:
    • Reporter: “Doesn’t that new bill break the core promise of your campaign?”
    • Politician: “I love this country. I serve her faithfully. And I am proud of my record. Next question.”
  • Estimates and forecasts that nobody believes and for which nobody is accountable.
  • The norm of having a meeting after the meeting.
  • Ads that communicate obvious falsehoods, such as McDonalds contributing to athletic greatness.

In the world of math education, truthfulness, especially the painful, predictive, and accountable type, is not a common practice. The result is in plain sight and I call it The Mathematical Blame Chain TM.

  • Elementary math teachers: “Why are parents so inadequate in preparing students for elementary math?”
  • Middle school math teachers: “Why do students get high grades in elementary school math then arrive so unprepared for middle school math?”
  • High school math teachers: “Why do students get high grades in middle school math then arrive so unprepared for high school math?”
  • Undergraduate math teachers: “Why do students get high grades in high school math then arrive so hopelessly unprepared for undergraduate math?”
  • Nobel Prize-winning physicist who hand picks the best physics students in the world: “Why do students get high grades in undergraduate physics then arrive so unprepared for graduate-level physics?”

Here is how Bravo Math will be different.

  • I haven’t figured this out entirely, but I expect to use open books management. That means all major financial reports and an operations manual will be publicly available, as will many other business records.
  • We are all biased, but in education, we take that to a whole new level that we call evidence of learning. $%&@^ that. Evidence of learning, in a practical sense, means seeking confirmation of what we want and believe, i.e. that the student has learned. This guarantees bias. Bravo Math, on the other hand, will organize assessment around falsifying what we expect. How early can we prove that the student hasn’t really learned anything? That their supposed successes are shallower than they appear? That they’re about to forget all the content? That we wasted a lot of time? That the students did not enjoy themselves? That we are contributing to the Mathematical Blame Chain? The search for early indicators of long-term problems will be the number one method we use to assess learning.
  • Given the choice between candor and politeness, we choose candor. That means
    • Telling the truth to students whether they’re thriving or failing, knowing publicly in bad times who is on the chopping block.
    • We will constantly seek criticism.
    • Telling stakeholders to their face what is in the best interest of the student, regardless of what it does to the business.
    • We disagree then commit.
    • General lack of candor will be a firing offense.
  • We will make a routine of pre-mortems before any major endeavor. Employees will be forthright in stating their biggest mistakes and weaknesses. Everything will be discussed candidly and those who do not participate in such candor will be leaving the business.
  • We will keep a prediction log and check up on it regularly. All estimates and forecasts will come with authors’ names and check-in dates.
  • In terms of credentials, we will do long-term follow up and update the credential accordingly. That is, if you’ve forgotten the Fundamental Theorem of Calculus 2 years after we’ve taught it, we’ll remove your credentials from our records. Credentials will be based on the long-term, not the short-term.
  • When at a crossroads or disagreement, we will not sell our own point of view. We will collectively determine what has to be true to make each possibility best.

Merit, if it means anything, must be infused into hiring, firing, and compensation practices. Clearly, this is not what we see in seniority-based layoffs and pay, golden parachutes, promotions based on sucking up to the boss, hiring decisions based on job interviews that consist of BSing each other, and an infinite variety of “This is how we’ve always done things.”

Here is how Bravo Math will be different.

  • Merit-based pay and teacher evaluation are tough problems. Nobody has figured them out. As of now, I intend to offer all new employees a simple hourly rate. As they take on more responsibility, they’ll earn a basic wage plus performance compensation that scales with their contribution to the mission, adjusted for risk. Everyone should be able to out earn their boss, or if they perform poorly, underearn their direct reports. Compensation has to involve carrots and sticks. Compensation will be modeled on long-term effects, such as the way Magna offers 1% of future profits to current business unit managers. If the company thrives, we will pay way-above market rates to strong performers and strongly negative performers will be fined.
  • Everyone should always know:
    • In bad times, who is on the chopping block. No firing and no layoff should ever be a surprise.
    • The conditions under which they’ve earned a raise or pay cut, promotion or demotion.
  • Merit means the best path has to win, regardless of its source.
    • Everyone must be able to prove or disprove a case on the merits, whether it’s a 5-year-old or the owner (me) and “pulling rank” will be a firing offense.
    • We will ignore sunk costs. We will scrap years of work developing materials whenever it benefits students.
  • As we search for evidence that students have not learned and not benefited from our lessons, we will refund money proactively.
  • Diversity in teams is important, but I do not care about race, gender, age, work experience, credentials, etc. per se. Diversity is important with respect to life experiences, skill sets, personalities, etc. In the unlikely case that I find such diversity by building a team of 30-something Asian males like myself, so be it. [It is, of course, much more likely I will find diversity by hiring across ages, genders, cultures, etc.]
  • Border and airport security employees should wait in line with the rest of us, before every shift. Politicians should file their own taxes, with no outside help. Bravo Math employees will see the results of their work, too. Anybody who designs math education resources must test it with a student. Anybody who designs a new hiring process must try it out themselves then tie some of their compensation to the quality of the new hires. [Additional ideas on dog fooding are welcome.]

Merit means that incentives are aligned and best idea wins.


Bravo Math is an abnormal business and always will be. We are Students First fanatics. We pursue bold change relentlessly. We seek and share truths forthrightly, especially the most painful types. And we decide issues not by job title or norms or gut preferences, not by previous plans or beliefs, not even by market behaviors, but on the merits.

Bravo Math is nascent company on a mission to shake up math education. If its vision for culture appeals to you, apply to join the team!

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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.

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.
Falsification.
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.

TimeActivity
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.
12:30pmBreak
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, lgo from grade 6 math to calculus is absolutely possible.

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.