Bravo Math News

“Why do you refuse so many students?”

Short answer: I want to help students transform from remedial and demoralized to math stars, from students who cry over their times tables to success in university engineering. Many say they want this but then insist on racing towards Math Hell while denying they are doing so. I refuse to partake.

Long answer: See below.

A fitness client speaking to their trainer: “I don’t care if I can only bench press 30kg now. I don’t care what you think about vastly excessive weights, bad form, or injuries. Maybe other people should slowly raise the load from 30kg to 200kg, but I am a unique individual. Just teach me to bench press 200kg now!”

Nobody in the world of fitness is this stupid and any trainer hearing this would quit immediately.

So what does this have to do with math? When students are 12 or under, very little. If a student can only count as high as 10, there’s no point in trying to master 43+18, and everyone knows the student should learn how to count no matter what the teacher is doing with the rest of the class. Prerequisite skills and knowledge matter. In most fields, this is generally accepted.

Would any sane person contradict the gist of the above?

Sanity says no.

But reality says yes.

In fact, people say yes, by the millions.

Something about math education makes people go coocoo for Cocoa Puffs.

Example Precalculus 11 student: “I don’t care about equivalent fractions and I don’t want to simplify the square root of 12. I don’t care what exponents mean. Just show me how to simplify this because I have to pass. I’m NOT going to summer school.”

Example Precalculus 12 student: “I don’t care if 5÷3 equals 3÷5 or not. I don’t care about multiplying or dividing with zero. I don’t care about long-term damage of cramming. Just show me how to find vertical asymptotes NOW. My test is tomorrow and I need to maintain a 91% average just to apply to the University of XYZ!”

Whether it’s back flips before standing on skates, lifting 200kg before learning to lift 100kg, or mastering vertical asymptotes before division, these requests are equally stupid and harmful. If this characterizes what you want – and most students and parents do as soon as there’s an imminent test or deadline – then I will refer you to another tutoring service, but I will send you there with a warning: You are paving your way to Math Hell.

Yes. Hell. “Hell” is the right word.

Many students memorize and hack their way through tests for years, yielding good grades, but never mastering or understanding anything. For example, hundreds of thousands of community college students don’t know that 0.03 and 3% are the same. Here is an example from physics education, where students solve 2000+ calculation problems but then appear to say that gravity pushes up.

Eventual consequences include not graduating, failing, mandatory summer school, extreme demoralization, emotional meltdowns, inadmissibility post-secondary programs, dropping out of academic programs or school entirely, career options closing off, financial illiteracy, permanent math hatred so bad that one passes it onto their children, etc.

This is Math Hell.

And I won’t be part of it.

In other subjects in school, issues of prerequisite knowledge matter much less. If you’ve forgotten all about your grade 8 socials studies unit on the Roman Empire, you can still do just fine studying World War II in grade 9. Many students can get away with learning little in English 10 and 11, but if they apply themselves in English 12, they can get the marks they need for university. The idea that buckling down now will improve marks now is sufficiently true in most courses.

But not in math.

In math, there are no shortcuts.

A student who caught a cold in grade 4 math during their division unit might learn nothing related to division for the rest of their lives. They’ll completely miss out on the two meanings of division, that it’s the inverse of multiplication, fraction as division, division with negative numbers, rate as division, etc. But they can fake mastery on assessments by memorizing and cramming reinforcing the idea that shortcuts in math work.

Then when they face conceptual questions about slopes, the student has years of division content to learn before they can even begin to understand slopes and rates of change. Eventually, there is no way to master the content on tomorrow’s quiz and working hard all weekend improves marks from 22% to 24% and leaves students demoralized.

I feel bad for students and parents in these positions. I really do. I feel especially bad for those who can’t even tell they are insisting on harmful cramming. It is terribly painful to hear that hard work won’t be enough to save the next report card, that you need to remediate years worth of content instead, that everything they’ve believed about learning math was wrong, that the marks they’ve earned in the past were not really earned.

But I’ve also learned that it is easier to talk a hungry dog off a meat truck than it is to talk people off the path of Math Hell.

And that’s why I refuse so many students.

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?