People have different learning styles, and for whatever reason the general population is better at 'concrete' thinking than at 'abstract' thinking (research sez).

When I read about that research, I remembered when I first taught a 9th-grade general math class. I tried teaching fractions the way I was taught ... but after several days, a test showed it just wasn't working at all. Frustrating for most too.

One day about a week later I drew a box on the blackboard, and called it one dollar (still worth something at the time.)

I then drew a single vertical line through it, pointed at the left half and asked 'what's this worth?' Slight delay ... '50 cents?' Then I added a horizontal line, pointed at the upper right corner: 'what's this worth?' Soon it was becoming easy! Sixths, eighths... 'take away 3 sevenths, what's left? ... After a couple more hours of this, most of the class easily solved 'simplify 3 sixths' or 'how many quarters to make 2 and a half'. Every few weeks later, we revisited to see what stuck.

Works the same in the sciences, for many anyway.