# The ball box problem algebra

Accuracy on the cueing questions might also contribute to cueing effectiveness on the critical question. Now it's just a matter of solving the differential equation and apply the conditions above.

So over there my volume is 1, So this is going to be 30 minus 2x. You can imagine this flap right over here, if I were to fold it up like that, it now would look like this. To what extent might reasoners be led to modify their judgement, and, more specifically, is it possible to facilitate problem solution by prompting participants to consider the problem from an algebraic perspective?

And I just randomly picked the number 5. However, we also expected performance to be highest among participants in the algebra plus words condition, because they were cued with the relevant mathematical equations in the context of the question itself. It's sort of like shooting a ball at a target and changing the launch angle and reshooting until we hit the target. So this has got to be greater than 0. So this is going to be 20 minus 2x. And we've seen this before. Well, x can't be less than 0. Now the shooting method won't find the energy level that it did before since it only searches "up. You can't cut more cardboard than there is. Yeah, 20 minus 2 times 5, so that would be 10, and then times 30 minus 2 times 5, which would be If a mathematical problem is expressed in words, then first try to express all the relevant information in the problem in terms of symbols representing unknowns, in the form of equations, inequalities, etc. Scroll down a little bit. When I find a value for the energy that works, I will no longer be searching so searching will be set to False. And that looks about right.

So it looks like my maximum value is around 1, and it happens at around x equals 3. In my code, the energy steps are always the same.

I'm just going to pick some a random x and see what type of a volume I get. So let's think about what the volume of this box is as a function of x. You can imagine this flap right over here, if I were to fold it up like that, it now would look like this. So if we subtract 9 from this equation right there, you get x is equal to negative 9, or if you add 5 to both sides of this equation, here. We have to use different models to explain properties of very very small things. Participants selected a rating on a scale with five levels, ranging from strongly agree to strongly disagree e. It could've been in cubic feet, or cubic meters, or cubic centimeters, or cubic miles. One hundred ninety-seven participants were recruited to investigate the effect of algebraic cueing as a debiasing strategy on variants of the bat-and-ball problem. What the heck is this? So it might look something like that. What is that distance right over there? Now we want our quadratic expression to be equal to 0. We have excellent intuition about the motion of a tennis ball tossed in the air, but what about an electron trapped in a box? So you get x squared plus 4x minus 45 is equal to 0.

So this means that x plus 9 is equal to 0. Convert these values or constraints back into the context and language of the problem to express the solution.

So what would the volume be as a function of x? Participants who were cued to consider the problem algebraically were significantly more likely to answer correctly relative to control participants. So we don't even have to do it by grouping. In all other cueing conditions, the critical question was preceded by a cue. The height of this box is going to be x. That's your quick intro to quantum mechanics. This control allowed us to determine the unique effect of algebraic cueing beyond the effect of simply being asked an initial relevant question. That's a different shade of yellow. So let's see, this was 1,

So let me write this down. However, cueing the algebraic structure of the bat-and-ball problem as a debiasing strategy has not yet been investigated. Following De Neys et al. So let's see, this was 1, Rated 7/10 based on 102 review