Traditional math student, "integrated" siblings

Scholar received this e-mail in December from a Wayzata High School graduate:
I am a senior here at the University Of Minnesota Institute Of Technology majoring in Mechanical Engineering. I was fortunate enough to go through the Wayzata schools while they were still on the traditional math curriculum.

I took algebra I and II, geometry, trigonometry, pre-calculus, and calculus. I found it odd to hear that my siblings (currently enrolled in Wayzata schools) were not taking these courses; instead, they were taking integrated math 1, 2, 3, 4. While in college, I have taken Calculus 1 through 4 so my siblings are constantly asking me for math help whenever I come home for the weekend or the holidays. What I found while helping them on their homework was that the topics that they were learning in their integrated math courses were very obscure and, in my opinion, not preparing them for college mathematics.

When in college, especially in the Institute Of Technology, the instructors of the Calculus courses expect you to know how to think logically, critically and know basic algebra, geometry and trigonometry. I feel that these "Integrated Mathematics" do not teach students the fundamental basics of mathematics and are not straightforward in their teachings.

I find myself having to look back into my siblings' math books (which, in my opinion, are not very good either) to find out what exactly a problem is asking for. Now, once I figure out what the problem is asking for, I can explain it to my brother or sister, but someone who has completed college mathematics courses should be able to know what a problem is asking for without looking back in the book. If I cannot understand a problem is asking right away, how can the students who are learning the subject for the first time be expected to understand it?