My first day of junior year, our teacher Mr. Shaffer spent some time showing us the important features of our textbook such as how to check our answers in the back (woah!) and where the tables for log and trig values were that we wouldn’t be using (phew!) because we had scientific calculators. Here is that textbook, which I have kept with me since 1984.

But what really got my attention was the REWARD which came at the end of the preface:

At the time I thought it was amazing that I could get PAID if I found an error. (Spoiler alert: I never found an error in that textbook.) But looking back, I realize what seeped deeper into my burgeoning math soul was the admission that there was a possibility that some errors might remain even after they had worked hard to eradicate them AND that I could take it upon myself to tell them about it. How fantastic that two mathematicians were acknowledging that they could have a mistake and soliciting my opinion!

Fast forward 40 years, and somehow I have made a career out of finding people’s math errors. You might be thinking about me correcting my students’ work, and that is of course true. But I have found errors throughout all different kinds of resources… printed and online. Every time I find an error I reach out to the author and almost every time, there is nothing but gratitude on their part.

You’re still reading, so let me share with you what unfolded over the past week…

I was helping a few students with some SAT math practice, filling in on short notice because their teacher had an emergency, and using this book from Vibrant Publishers. I had never used this particular book before and I definitely did not have time to do all the problems. When one student asked me about question 285, I immediately went to solving it using geometry since I knew not everyone in the room would have seen or remembered the identity sin(90 – a) = cos a.

So I grabbed my calculator, put it in degree mode and told the students to do the same. We took the inverse sine of (0.6) and then the tangent of the found angle. The answer was 0.75. But Ms. Cornelius, the back of the book says 2. Immediately I flipped to the back of the book which had not only the answer but the explanation.

Students, this is so exciting! We have just found a mistake in this book! But it wasn’t a mistake in the answer key, since it was an alternate, correct method for finding the solution. So why did the solutions not match? Because it was a mistake on the part of the person writing the question. Because if sin a = 0.6, then sin (90 – a) = cos a = 0.8, not 0.3. Good ole Pythagorean Theorem.

I knew I had to write to Vibrant Publishers. So I emailed them and you know what? They emailed me back the next day! After a few email exchanges, which included them sending me the ChatGPT solution (also 2), I spoke to someone on the phone.

The person I spoke to was very nice. I asked him if he was their math content expert he said no. He asked me how many students I generally tutor in SAT and I said zero. After going back and forth for a bit on the phone, he said he thought he understood the problem and that he would reach out to his math content expert. A little while later I got an email where they said they agreed with me, that sin(90 – a) needed to equal 0.8, not 0.3, and the final answer for the tangent of a needed to be changed to 0.75. He said that they would be updating this for the next printing, which due to the magic of on demand printing, would be next week.

He also sent me another ChatGPT. Once I realized the equal signs look like minus signs, it was easier to read:

It seems like if you ask ChatGPT the right question, it will be better at giving you the correct answer and for this reason, I will continue be suspicious of any solutions wrought by a machine. Humans, we still need to train our brains! LOL

Just this morning I received another email from Vibrant Publishers.

Awesome, thank you so much!

As a goodwill gesture, do you want me to send a paperback of the corrected version of the book to your home address? The updated book should be available through amazon for all customers starting mid of next week.

Thanks again and I look forward to hearing from you!

Well of course I want that free book. So I sent him my home address and look forward to working out if it! It’s not $10 cash money, but it’s something. And more than that, I helped someone. Possibly lots of someones.