I will second Richard Hake's comments. In my school I have physics students who put the following scale on a graph. 0,.5,.1,.2,.3 and then graph points equal to .5 at the lower value. They see a picture of 2 meter sticks lined up to measure a falling ball, and they then proceed to assume that 0 is in the middle with the ultimate y scale looking like
70cm,80,90,0,10,20,30.... Only 1/4 of my regular physics students understand ratio and proportion on Lawson's "Classroom test of Scientific Thinking". They will put the data points on a graph at evenly spaced intervals to produce a straight line, and then adjust the scale so that it is unevenly spaced. The list goes on and on.
They cannot decode a paragraph to give me the relevant quantities. This is not even doing a problem, just asking for the relevant quantities. Even my advanced students have difficulty. They seem to be incapable of understanding vectors if they score below 9/12 on Lawson's test. My statistics show that only 12% of the students in my school score 9 or above. When they leave my class 30% of my students score 9/12 or higher, but outside my class the scores do not seem to rise.
I also have evidence that low scoring students are NOT capable of understanding conceptual physics. Reducing math does NOT increase understanding.
There are some things that can be done in Middle school or early high school. Shayer and Adey "Really Raising Standards" have come up with a program that seems to have very good effects on early teenagers, without completely changing science instruction in MS. Good instruction in HS can help, but there are too many deficits to make up at that point. Feuerstein's "Instrumental Enrichment" also has been shown to be beneficial as an intervention. All of these things require intensive teacher training!