Bravo Math News

Homework Brain Dump

Here are a bunch of my thoughts on homework. Converting them into operations and policies may be a bit of a separate beast. Here goes.

The Problem

On each date, Timmy the student, has just arrived for his math tutoring lesson.

January 8, 2019

“I’m happy you’re my tutor now. I totally get that I’m behind in math and doing lots of homework is crucial to catching up. I promise to do it all and if I get stuck I’ll contact you right away for help! I’ll get this new year started out right.”

January 15, 2019

“I totally did all the homework on decimals. I’m so sorry, though, that my sister cleaned the kitchen after I did homework on the kitchen table. She didn’t know that it wasn’t just scrap paper and put it in the recycling bin. But I did it all, I did!”

January 22, 2019

“So, I looked at the decimals homework last night… I just didn’t get it. And, no, I’m sorry, I didn’t ask you for help. It was so late last night.”

January 29, 2019

“This week was just so busy. I went away for the weekend then my friend had a birthday party and then I had a hockey game, plus school gave me so much homework, and I had a science test! I didn’t have time to do the decimals homework.”

February 5, 2019

“Decimals homework? I never got the email for it. I know you sent it to me, my mom, and my dad in the email. They got it but I didn’t. I don’t know why. They didn’t tell me about it either. I don’t know what happened!”

February 12, 2019

“The decimals homework is done. All the right answers are there. See? I did it with my mom/dad/friend/brother/sister. I don’t know why I can’t do exercise 1a of the exact same worksheet now. I’m just blanking.I totally got it last night. Math just doesn’t stick in my brain.”

February 19, 2019

10:30am: “Ok, this time I did the decimals homework. I actually submitted it on Google Classroom two days ago like you mentioned. I got all the right answers so I totally totally get it!”

10:45am: “Five point two seven million dollars… that’s five million dollars and twenty seven cents… Right?”

February 26, 2019

“I didn’t really do the homework because I don’t think this tutoring is working out. It has been almost two months and we’re still on decimals. And we’re doing percentage word problems in class, which is completely unrelated, so my grades aren’t improving. That sucks! Math sucks!”

The Need

From elementary educators to billionaire CEOs, everyone has dealt with people who do not do their homework and stagnate. The themes are common and Peter Liljedahl has tracked many root causes. Timmy:

  • Doesn’t have time
  • Doesn’t make time
  • Cheated or got someone else to do all the real work for him
  • Made up excuses or pretended to have done it
  • Didn’t understand the instructions or pretended not to
  • Did the homework, but completely missed the point of it
  • Ends up even farther behind

Homework Done Right

On each date, Rhonda, the student, has just arrived for tutoring and is speaking as she unpacks her things.

January 15, 2019

“Here’s all the fraction and decimal conversion stuff. I am pretty fluent in all the methods now, but I didn’t understand the ‘Estimate or Exact?’ section. How am I supposed to know which conversions I should just know quickly vs when I need to estimate? Or just use a calculator? Is it OK if I just always use a calculator?”

January 22, 2019

“Two nights ago, I submitted all my decimals homework over Google Classroom. I know that the ‘.27’ in ‘$5.27 million” means ‘$270,000’ because you provided a similar example, but I don’t know why. Doesn’t ‘$5.27’ mean 5 dollars and 27 cents?”

How do we convert Timmy into Rhonda?

The Big Picture Solution 

  • Early involvement and early buy-in for both the student and parent.
  • As a tutor, I have to set a much better example of doing my own “homework”.
  • Start with quick homework wins, then gradually increase homework load.
  • Making homework useful and satisfying.
  • Create a support system around the student, such as fixed scheduling and electronic reminders.

Tool 1: Early Involvement Buy-In

Among the first few times I meet a student and their parents is the right time to discuss how homework is going to work. How should that discussion go?

  1. Participants: Everyone. Student, parent, and tutor.
  2. Homework Empathy table: 
    1. “Tell me about good and bad experiences with homework. This is important enough that I want to get it right and that means not assigning junk for you to do at home. I want the homework I assign to be useful and as enjoyable as possible.” Everything the student says can be recorded in a table.
  1. The student can read Timmy’s statements above and respond. “What do you think of Timmy’s statements above? Does Timmy value homework? Is he right to object to it? How should teachers respond to that? Are teachers responsible for any of this?”
  1. What is the purpose of homework? Rank importance.
    1. Practice
    2. Marks, grades
    3. Check understanding
    4. Get stuck
    5. Generate new questions
    6. Long-term benefits:
      1. Work habits
      2. Opportunities,
      3. attitude…
      4. Job at Bravo Math
  2. Timing
    1. How much homework time do you have?
    2. When do you have this time? Would you like to fix that time?
    3. Would you like automated reminders? Email homework? Google Doc? Google Classroom? [I probably need a better LMS]
  3. My end of the bargain
    1. You will know the purpose of the homework. It’s not answers or repetitions, but mastery and learning.
    2. It will be assigned 70% night of tutoring, 100% by following night
    3. It will not be mindless drills, but involve actual thinking.
    4. You can skip literally anything if you feel like you could ace a quiz on it both during the next tutoring session and again in a month at a surprise time
    5. Homework will be easy to start 90% of the time, probably 100% at the beginning.
  4. Student’s end of the bargain
    1. Do homework in pencil. Mark it in pen. [Show example.]
    2. Submitted at least 2 days in advance, with a prediction on how you’d do on a similar quiz
    3. Tell me before tutoring starts if I’m not holding up my end of the bargain.
  5. Consequences for low effort on homework
    1. This time? Do now instead of tutoring lesson.
    2. Past few times? Cancel lesson, but charge in full.
    3. For a few months? Find a new tutor.
    4. You will stagnate badly and waste your family’s money and everyone’s time. [Show an example tutoring log.]
  6. Consequences for high effort on homework
    1. I guarantee progress that you can feel.
    2. Your work and learning habits will improve.

Tool 2: Good Homework Only!

  • Risk-free. No homework will be marked unless you want it to be.
  • Answers provided, sometimes solutions or exemplars provided.
  • Worked examples for procedural exercises.

Tool 3: Responsibility Ramp

Nobody turns around their habits instantly and nobody should expect that from students. Instead, “homework” assignments will start in an easy way that nearly guarantees initial success.

What does the Responsibility Ramp look like? From easiest to hardest:

  1. Practicing homework during the lesson. “We have 20 minutes left in the tutoring session. I’d like you to show me how you’d get started on this homework assignment. Show me how you’d do it, mark it, generate questions and comments, then submit it on Google Classroom.”
  2. Fun stuff.
    1. Perform this magic trick
    2. Play this game
  3. Administrative work. 
    1. “Please find out what math course and grade you need to apply to Langara Commerce.”
    2. “Obtain a binder and paper. Bring them next day.”
  4. Leveled Drills. “You did Level 1 integers today. You have links to Levels 1-5. Do about a page or so each day and level up when you can.”
  5. Interleaved homework and cumulative review
    1. SSDD Problems
    2. What are the 3-5 main types of problem types you’ve learned recently?
    3. Generative work. “Create and solve three word problems similar to the set you solved before, but use last unit’s math and place everything in the context of managing a donut shop.”
  6. “Prepare for a quiz that will look like this.”
  7. Make a good copy of your notes.
  8. Try this open task and give it a shot. Notice and Wonder.
  9. Read ahead in the next chapter. What are the essential questions and big ideas? How do you think subsequent math will build on this?

Tool 4: Metacognition

Students will write answers to a few of these after every homework session. 5 minutes in note-form or in a Google Doc or email is fine.

  • How well would I do if I were quizzed on this tomorrow? POOR / OK / GOOD / GREAT. How do I know?
  • Can I find some specific examples of the hardest questions I could successfully be quizzed on now?
  • Did that homework take a reasonable amount of time? Explain.
  • Can I explain this to someone else?
  • How could I have learned this more efficiently? What do I wish I had known at the beginning?
  • What should I do next? And when? Why is this the best option for improving my mathematical future?
    • Relearn building blocks.
    • This is the right level of difficulty. Focus here.
    • I need to consolidate my knowledge for now and pick a time to review it.
    • Level up. Seek a tougher challenge.
    • Other?
  • What did I find easiest? Hardest? Most and least enjoyable? Most and least surprising?
  • How does this compare and contrast with previous math content?
  • Where does this lead in the next month or year?
  • What is the original math headache that this solves?
  • What are the different ways to record my thinking? What other representations are there?
  • How can I check my work? Did I? Should I?
  • How should I track my progress?

Tool 5: Shape the Path

How can we make it easier and more satisfying to do homework?

  • Role Models. Younger students who struggle with homework should interact with peers and older students who regularly do homework thoughtfully and swear by it. This could happen in the form of a “Homework circle”. I.e. Form a group of friends or journey group? Or a peer tutor appointment?
  • “Come to tutoring 30 minutes early. Take out your homework, quiz yourself, and warm yourself up for tutoring.”
  • “After tutoring, go into that other room and get started on your homework. Do that for 30 minutes before you go.”
  • Student & Parent: “On Tuesdays from 6:30-8:00pm, we’ll do any remaining homework and submit that, with questions, well before the Thursday tutoring session.”
  • Automated reminders. E.g. On Tuesdays at 5:00pm, an automated text or email reminds the student about any remaining homework.
  • Rewards and Destination… Some kind of scoreboard that tracks whether or not students responded to their homework productively.
  • Self-assessment.
    • “How productive was your effort with the homework?’
    • “What insight or skill do you have now?”
    • “Are you and I living up to our original homework agreement?”
  • Typical teacher-imposed “rewards”.
    • Descriptive praise. “I noticed you prepared questions for me in writing on your homework. This is very useful.”
    • Choice. “You did your homework, so today’s lesson went very smoothly and quickly. We now have about 20 minutes. Pick a magic trick to do or a game for us to play.”
    • Rewards. “Homework is done and submitted 3 weeks in a row! Pick anything you like from this grab bag of prizes (toys, candy, stationery, etc.).”
    • Smile, high five, arms up to celebrate, touchdown dance, etc.
  • Teacher-imposed reprimands.
    • “You didn’t put in the time into the homework. We’ll be practicing homework instead of the lesson today.”
    • “This is several weeks in a row that you haven’t done homework. That breaks our agreement and I’m disappointed.”
    • “Look at our tutoring log for the past 5 weeks. Why do you think we’ve been tackling exactly the same content every single time?”

Next Steps

That’s a lot of thoughts on homework and it will be a radical departure from what I normally do. During summer 2022, I’ll be converting all of it into checklists in the Bravo Math Operations Manual so I can implement it systematically as of September 2022.

I’ll keep you posted.

If you have any thoughts on this, please share.

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?

Bravo Math News

(6) The Bravo Math “Culture Deck”

Version: 2021 August 2

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 of Students First, Truthfulness, Merit, and Courage.

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.”


[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?

  • A 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: “It’s the greatest work environment in the history of fast food!”
  • 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 the “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 painfully 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
    • Every student and employee knows exactly where they stand and how to improve. Everyone should be able to state explicitly what their #1 priority is, how it relates to the company mission, and how they’ve worked on it recently.
    • We will constantly seek criticism. We hire our smartest critics.
    • Telling stakeholders to their face what is in the best interest of the student, regardless of what it does to the business. Every manager should know their employees’ least favorite parts of the job.
    • 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. Clearly, this is not what we see in seniority-based layoffs and pay, pay-for-failure golden parachutes, promotions based on sucking up to the boss, hiring decisions based on BS-rich job interviews, 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. Clawbacks will be contractual.
  • Everyone should always know:
    • In bad times, who is on the chopping block, and who is up next for promotions. No firing, layoff, or promotion 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.
    • An employee can work 15 minutes per year and earn huge pay as long as they deliver stellar results.
  • 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.]

In summary, 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!