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I am going to respectfully disagree with both of your points...

Fractions - You are spending too much time on the micro - measures of your analysis, the focus on gender and racial gaps is going to lead you to the conclusion that "Special Programs" need to be developed, more money & time thrown at the question of "why some people just don't get fractions". Analysis of root cause, in this case, is a waste of money. Kids that don't get fractions are having environmental issues with the subject not personal issues.

1 - Culturally there are parents that are not educated themselves and rather than admitting it their children they dismiss the knowledge as unimportant - hey, you even did that with Calculus - this infects their children with a barrier to the knowledge

2 - Education Methods are changing for the wrong reasons. New math teaching concepts are not teaching math very well, in many schools (particularly public schools) there is an over reliance on computer programs and quiz sites to TEACH rather than enforce information. I have experiences with math teachers so checked out that they just write URLs on the board and let the kids fight with the concepts for an hour, that is NOT teaching. Traditional methods from the 70s & 80s were much more effective at insuring kids could handle the subject.

3 - Admission that not all children are created with equal natural talents and abilities. There will always be kids that are better at somethings over others and some kids that will struggle regardless of the methods. Our current system forces all the kids to be placed in the same environment/class with hopes that the smart kids will influence the struggling kids. Studies have shown that this is actually more of a drag on the smart kids than a lift on those struggling and it has also been proven that by isolating those that struggle into classes with more tailored approaches they will lift naturally eventually rejoining the faster tracks -- and those smart kids are allowed to bloom without the distraction of stops and starts when someone in the class cannot keep up.... please note - that this is an academic solution not a social one, so much focus on how a kid feels is also distracting the process.

If you want kids to be better at fractions: Improve teaching methods by getting back to teaching, group the students by ability level and overcome the culture drag coming from home.

Calculus --

I think you were trying to protect yourself from argument by using the phrase "pure calculus" and I find that disingenuous to your statement. Calculus and the skills learned in studying higher math in high school had direct influence on the approach to physics, astronomy, chemistry, computer programming (more so than algebra especially when dealing with distributed systems ), statics, data analysis, and almost every digital space in the modern workforce. While your out might apply when it comes to the actual equations, the study of Calculus in high school is less about the equations and more about learning how to solve complicated problems and quite frankly Calculus is the best higher math for that because it will weed out sloppiness.

From: Rethinking fractions and calculus

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