The expert’s problem seems to be with the first stage of working out a decimal for that measurement 3 and 3/16 inches (though if he’s so poor at that, I wonder whether he’d be much good at anything else).

It makes me wonder, what kind of materials he would have back at the office that would help him out? Is there a table of conversion from fractional measurements to decimal? That doesn’t seem very likely. Or does he have a 3/16 key on his computer keyboard? I wouldn’t think so. Is there some kind of formula sheet for this? Or did he Google it or ask someone else in the office?

A few thoughts here:

The expert likely uses software to make calculations without understanding how they are calculated. This would be akin to me using an Excel mortgage calculator. I could find your monthly mortgage payments for you but I would need “my formula sheets” for that. I’m not making excuses for him, but certainly there is a line where it becomes socially unacceptable to not understand how a formula works. I think mortgage calculators are on one side and converting distance units is on the other.

This was certainly a high pressure and unsafe environment. It reminds me of times where I have to introduce people to one another and even though I’ve known everyone for years, under the pressure sometimes I will blank out on someone’s name and feel foolish. So, maybe there was an off chance he could have figured it out, but under those circumstances where anything short of perfection would be a huge issue, he decided to do nothing.

That sounds quite plausible, Alex. I’d not thought of calculators with fractions.

I think the context is crucial here.
It reminds me of the times when a politician is asked an arithmetic problem e.g. 6 x 8. Quite often they refuse to answer. I honestly don’t think this is down to them not knowing but it isn’t worth the risk.

Also the calculator is very different tool to the spreadsheet.
If he wasn’t able to recreate it using the same tools he did in the first place, and without the legal teams breathing down his neck, that would concern me.
Though estimating is a great idea, it probably wouldn’t have caught the situation where he mis-typed and ended up with 75 ft. Would 7ft matter, possibly very much.

It reminds me a little of teachers who want their students to divide 987654.123 by 17 by hand.

I get the sense there’s more at play here than what this purports to show. I know we’re supposed to walk away from this with the lesson that we shouldn’t rely on black-box formulas without knowing how to work out solutions from fist principles. But I think what is happening is that the expert witness does not want to set any precedent whatsoever that he’ll do any calculations on the witness stand which could result in errors while performing them under the pressure of a jury proceeding. He’s obviously being very careful in how he answers the questions from the lawyer which leads me to believe he understands the implications of that line of questioning.

A majority of my students use calculators that allow you to input mixed numbers, so they rarely think about what 3 and 3/16 even means, sadly. That is a battle we’re all fighting, no doubt.

This is why I always emphasize to my students that they should estimate the answer before using the calculator, so they can check if they’ve keyed something in wrong. I’d suggest to them to think of 3 and 3/16 as 3 and 4/16, which is therefore 3 and 1/4. 3*20 + 1/4*20 = 60 + 5 = 65. Therefore they know their answer has to be less than 65 and would recognize that their answer of approximately 68 must not be correct.

Thinking in teacher mode, I was struck by the fact that the defense attorney kept asking the question in the same way. He was really focused on turning 3/16 into a decimal, which in my mind is the least efficient way to handle most problems. Everyone wants decimals all the time but fractions are actually so much easier to work with, intuitively. I can’t turn 3/16 into a decimal in my head, and I also can’t multiply the resulting answer by 20 in my head, but I can really simply multiply 3/16 by 20! 3/16 * 20/1 = 3*20/16*1 = 3*5/4*1 = 15/4 = 4 and 1/4. Likewise, if I am tasked with taking the square root of 4/9, turning it into 0.4444444 totally obscures the answer of 2/3 (what?? the square root of 0.44444 is 0.66666??? I mean, that actually looks crazy!).

The defense attorney could’ve asked that question a lot of other ways that might’ve gotten the witness to recognize his mistake, but instead the tactic he took caused the witness to only dig his heels in and refuse to budge out of pride.

But actually the most disturbing part of this video is the (perhaps naive) realization that expert witnesses are paid for their testimony. Why is that legal? Does that not call into question their legitimacy, objectiveness, scruples, and impartiality?

My guess is the witness measured the line on the print out without checking if it was scaled right. I print out maps for hiking and off-roading trips all the time. Almost never does the reported scale actually match what was printed.

Even so, the original measurements would have been made at full scale with the calculations based on those. And that would have made the printed figure’s dimensions immaterial. Lawyers make mountains out of mole hills and expert witnesses will play ignorant to avoid creating inconsistencies. Not at all uncommon for a deposition.

http://www.youtube.com/watch?v=y2X52rS-ZLE

(I haven’t watched the NYT re-enactment, so I haven’t compared the two.)

Evan Romer
Susquehanna Valley HS
Conklin Ny
(retired)

You folks are so wrapped up in the math I think you’re missing the point.

This expert used his “formula sheets” to drive his testimony. Since he is basing his testimony on the answers provided by the “formula sheets” he *should* consistently refer back to them. If he does not, he could make himself look like an even bigger ass than he does here. If he failed anywhere, it was double and triple checking his work for mistakes.

Lawyers are very much into consistency, which is something I learned in writing software for a group of lawyers many years ago. Same input == same output every time as long as all data otherwise remains the same.

No doubt this particular tragedy has lots of authors. However, “he needed to see more worked examples” and “he shouldn’t have been allowed to use a calculator until the 12th grade” are particularly unsatisfying explanations for me. Neither addresses a crucial failing of this expert’s education:

This expert has come to the conclusion that math is a thing that requires formula sheets to understand and use.

The comment regarding worked examples seems to imply that worked examples can’t convey conceptual knowledge and depth of understanding. The research on process-oriented worked examples shows that examples can be modified to improve conceptual understanding. Read http://bit.ly/1YXiSLP

For those saying, “he’s a peon,” “he doesn’t need to understand,” “he probably hates his job,” comparing it to flipping burgers, etc…

If you watch the actual footage, in the first minute he introduces himself as the president of an accident reconstruction company.

I’ll buy the not needing to know the ins and outs of the math for the average worker, but you’d think in such a litigious industry as accident reconstruction, someone at the firm would be able to explain the math behind the formula sheets. And if not the president, then hire someone.

I’m actually going to show this to my math sections and my business sections. Hiring the right people for the job is as important, if not more, as being able to do the job. Jack of all trades, hire a master.

As I listened to the original deposition, what I heard was a man who made it clear that the formula he worked with not only calculated the distance but also handled any required conversions. As well, during his professional training he’d been given specific tools and set procedures for making this sort of assessment, and he trusted the judgement & choices made by the instructors at that level.

This is not unusual when adults train for new professions. Nursing students often get caught in a similar situation. An instructor makes a decision that a particular method of dosage calculation, for example, is THE way it should be done & accepts nothing else. This may arise because of what the research says about how best to ensure accuracy, or the choice may be rooted in how the instructor herself was taught to do these problems, or it may reflect the selection of a one-size-fits-all method that works across a spectrum of problems and can be picked up by students with a wide variety of math backgrounds in as short a time as possible. Instructors at this level are professionals in their fields and tend not to have the time, skill, knowledge, or will to champion flexibility, connect the dots from middle school math to the problems at hand, or fill in learning gaps that occurred decades before.

Adult learners can be even more reluctant to challenge such decisions than kids, and if their teachers are inflexible, then they learn to live & work inside the boxes chosen for them. Now with pumps pre-programmed to do all the calculations & conversions, nurses are even reluctant to question what they intuitively feel are incorrect results. So what do I think this man’s K-12 math teachers collectively might have taught him that could have helped him avoid this calamity? A predispoistion to expect errors and check results on a different day or in a different way. I think he probably did his steps & used his tools correctly but entered some bit of data incorrectly. If there’d been a policy in that office that no result went out unchecked by a different person because little errors can have big ramifications, the mistake would probably have been found, and the case would have remained focussed on who caused the accident rather than on the expert’s competency.

The “reconstructionist” is earning $900+ per hour for his testimony, as well as this deposition. In boxing terms I think it’s called a rope-a-dope.

A happy story…

I bought a bunch of hardwood yesterday evening. Unlike building lumber, hardwood is sold by the board foot–misleadingly a measure of volume: 12 inches by 12 inches by 1 inch.

Watching the man grind out the numbers for my chosen pieces of lumber was very very cool. Dude brought the full arsenal of tools to bear…tape measure, scrap wood as a notepad, office calculator, intermediate notes on paper, measurements in both inches and feet. Every bit of his work could be checked by the time he was done. Because my expectation and his final number were within about 12% of each other, I haven’t bothered.