Measuring success when doing Math
Keeping track of math success daily and how we're using GPT5.
Happy Friday, Friends!
Today’s Journey includes two reflections: one for everyone, and a bonus one for paid subscribers.
The two reflections are:
Measuring success during Math Time
How We Use ChatGPT During Math Time
Let's start with the first...
Measuring success during Math Time
I. The early days: Number of problems = success
When our math kids started to do more and more math, we were amazed at their appetite for math problems.
We would congratulate them and celebrate the number of problems that they had solved that day.
"Did you tell mom how many math problems you did? I think it was more than 20!"
Big numbers meant big success.
However, that led to a few issues in the short and long term.
In the short term, we found that they started to rush through the problems to get a "high score".
Which was cute at first, until we started thinking about the long-term repercussions and realized that it would lead to them solving only easy problems or not spending enough time on each math problem to understand it fully.
Yes, most competitions in math value speed (and accuracy), but we didn't care about competitions.
So we tried to think of the bigger picture and started to focus on "units" completed.
Think of it like chapters in a book.
II. Learning from our mistakes. Units finished = success
Math Units couldn't be finished in a day, so they got over the "rushing through the problems to score a high score" temptation.
However, this also meant that we didn't have a daily "success criteria" that could be celebrated.
Most weeks, there was at least one unit completed, so there could be a small celebration.
Some weeks, however, there was a tough unit either because of the length of topics that needed to be mastered or the difficulty of problems.
These were tough weeks because, as they were still little kids, it was challenging to keep going, knowing just how much more was left before the unit was completed.
Things came to a head when one of them started checking ahead to see how long a unit would be, and groaning and complaining that it looked too complicated.
Another thing that didn't help was that the material became increasingly complex.
It's easy to complete a unit where you are adding single-digit numbers to various numbers.
It's much harder when you start doing multi-step problems where each step needs mastery of a few different skills.
Eventually, even specific sections of a unit couldn't be completed in a day.
So we couldn't even celebrate the conciliatory "you completed a part of the unit!"
III. Big problems and no neat endings. Did we achieve something?
Eventually, the kids started working on problems that they couldn't solve after 10, 20, 30, 40 minutes.
Some weeks, they might not be able to solve the problem in two days.
And some weeks, they encountered problems they couldn't solve at all.
Which brought up some terrific questions for family discussion:
How do I know I had a “good” math day if nothing got finished?
If I spent an hour on math and didn’t solve any problems, did I fail?
What should I focus on celebrating if I'm past “20 problems a day”?
Is there value in just showing up to think hard, even if there’s no output?
What metrics still feel good to track?
You might be asking yourself the same questions at home.
To answer those questions, we looked at people who do math "professionally," that is, math researchers.
And what we found (and you can guess) is that sometimes professors and researchers think about problems for days, weeks, months, years, and some even decades!
If it takes you years to solve a problem, how do you measure and celebrate daily achievements? What keeps you going?
IV. Showing up and doing math
What we concluded is that the math researchers love thinking about math, and that showing up and doing math was the reward.
Obviously, right?
On Reddit, we found a quote from a math professor describing the advice their Ph.D. math advisor gave them (paraphrasing here because I couldn't find the source) when they first joined graduate school:
If you don't want to do math 8 hours a day, then don't do a math Ph.D.
We're not trying to hit 8 hours of math a day in our house, but it did get us to (re-)evaluate what we cared about and wanted to celebrate as parents of math kids.
We wanted to celebrate them doing the thing they loved: doing math.
And then, it seemed so obvious and simple.
V. Success metric: Minutes of effort, not number of wins
Sure, we had heard all the self-help book bromides: "process over outcome", "process-orientation over goal-orientation", "take care of the little things and the score takes care of itself", etc.
Sometimes it takes a while to actually do the obvious thing.
We got there though, and we realized that the success metric was "how many minutes of math did you do today?"
As long as they want to do math and sit down to do math, then it's a win.
Sure, it's nice to get problems right and solve them, but the bigger win and joy is in seeing them do the thing they enjoy and make time for it during their day.
Sure, the metric is gameable: they could write really slowly and take long breaks, but they have realized that it only hurts themselves.
Now every day we write down how many minutes of math they did that day.
Some days it's a really high number ("highest number in the last 4 months!"), and some days it's a low number (lots of 0-minute days when we travel to see family), and some days it's a prime number, and other days it's the same as the previous three days.
And because there is no artificial goal of "X" minutes per day, every day is a win!
VI. Surprise: The new success criteria made more math time available
Once we started keeping track of the time of the day that math was done and how long the activity took, we began to see patterns.
After dinner math time led to shorter math time.
Sports activity days meant less math time.
Doing math before school means way more math time.
If there were math time on weekend mornings, there would be more math time in the afternoons.
After a few months of keeping track, we were able to change schedules in order to be able to give the kids even more time to do math (with us or on their own).
VII. Where we are now
This is working so far and may change in the future.
We, as parents, like math because it means the kids are thinking and wrestling with problems.
In our book, math time is thinking time, and thinking is enough of a reason to celebrate.
To the free subscribers, thank you so much for being part of this journey. I hope today’s reflection was helpful. If you know someone who might enjoy this too, feel free to forward it!
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Have a wonderful weekend!
All the best,
Sebastian
PS: Want to hear how we’re using ChatGPT (and Claude) during math time, not to get the answer, but to really understand why we got something wrong?
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How We Use ChatGPT During Math Time
We've also been experimenting with using ChatGPT (and Claude) during math time. Not just to get the correct answer, but to really understand what we missed.
In the paid section below, I’ll share exactly how we’re using it, what we’ve learned, and how it’s helped us make wrong answers more useful than right ones.
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