Having just shared a concern about how science is being taught, it may be useful to explain what I think would be a better way to teach it.
Here is one of the many ways you can use the layman’s intuition to explain quantum mechanics, for instance the famous double slit experiment:
Imagine a surface of water, like a swimming pool, where some apparatus creates waves. In the middle, you build a wall with two relatively small vertical holes that you can open or close at will. When a hole is open, the wave goes through, otherwise, it does not. If the hole is small enough, it will behave as a “point emitter” for the wave, i.e. the waves will appear to be circles centered on that point.
When the two holes are open, the waves they emit are not totally independent from one another. They are correlated, since they ultimately come from the same source. Consequently, they will interfere in a predictable way. There will be spots where the wave amplitude will appear to be twice as high, spots were the water amplitude will be almost flat. On the other hand, as soon as you close one of the holes, or as soon as you significantly disturb one of the waves, the interference pattern disappears.
You can think of the amplitude of the wave as a “probability of presence” of water molecules: if the wave is high, then it means that there is a higher probability that water molecules will be here, and ultimately, you find more water here. Conversely, if the wave is low, it means that there are less water molecules at that point, so the probability of finding water molecules there is lower.
To predict the interference pattern, i.e. to add the two heights of water, you cannot simply consider the average height of the wave, i.e. the average probability of presence over time. Instead, you need to consider whether the two waves are correlated or not. In our example, they are correlated. The displacement caused by one wave is not independent of the displacement caused by the other. For this reason, there are locations where the two waves always cancel, and other locations where they always add up.
In the case of a photon for example, this probability of presence is not caused by matter like for water waves. But the same general idea applies. The photons arrange themselves according to a probability wave. The most surprising thing is that the wave exists even when there is a single photon, and that even a single photon does not necessarily follow a straight line, but will be found according to this probability of presence. The straight line is a special case of probability distribution, not the most general case.
I may be wrong, but I believe that by explaining something like the above, you have captured the key elements of the experiment without using a single word of math, without asking the person to give up his/her common sense or intuition at any time, and more importantly, remaining pretty faithful to what the math/physics actually says. In other words, you have actually explained, not asked the other guy to have faith.
Ce qui se conçoit bien s’énonce clairement, et les mots pour le dire viennent aisément.