I have volunteered to tutor a student in AP statistics at the local high school. Stats: Modeling the World
Have any readers helped a student in this class? If so, what materials were useful? Or has anyone taught himself or herself statistics and found something concise and good?
Separately, the student is quick to say “I can’t do this” or “I don’t know” when in fact a few minutes of thinking would have resulted in the answer or a procedure for getting the answer. My personal theory is that this comes from being given so many trivial problems in the earlier years of K-12. Students who are brighter/quicker than average get the idea that every problem can be solved very quickly and therefore that, if a problem cannot be solved almost instantly, there is no way to solve it. Any ideas for working on patience/persistence with respect to math/stats?
” how to measure anything” might have some useful ideas
Milton, Arnold ‘Intro to Probability and Statistics’ was used for my intro college course. I relied heavily on the book and was pleased with it.
I tend to disagree with your theory of why the student is quick to say ‘I can’t do this.’ Although the student is given many trivial problems, there is always an initial struggle to grasp the concept, which any student should become accustomed to over time. Instead, I would suggest that saying ‘I don’t know’ becomes an instinctual response to get additional instruction from a teacher whose attention span is even shorter because they are trying to divide their time evenly 25 ways.
Also, there seems to be a shared idea that some people ‘get’ math and others ‘don’t’. Students may fear that they fall into the latter category. Lastly, math education requires the student to layer fundamental concepts in order to solve more and more involved problems. If a student barely scrapes by one year in math, they may be doomed to math mediocrity for the rest of their k-12 unless they have a superb teacher who can back-tutor them. Eventually they will get to a liberal arts college where they never need to do another math problem again.
A.L.: The mother of this student agrees with you on the last paragraph, i.e., she believes that something was missed in 8th grade and the student never quite caught up. I’m only about 1.5 hours into this so I don’t know what the missing link might be.
Sounds like the kid may just not be “into” the material (yet). It really surprises me how dry the material is presented in lot of the school/college text books. You’d think the author(s) had no passion for the material they are teaching.
Try something more engaging. I would recommend getting the student this book: http://www.amazon.com/Cartoon-Guide-Statistics-Larry-Gonick/dp/0062731025
It is a great introduction to statistics and probability – don’t let the “Cartoon” part make you think it is not a serious book. And it doesn’t hide the formulas from you. A lot more engaging that the typical text book. See page 4 of the Amazon preview which summarizes what the book will cover. Page 221has more suggestions for books.
Well, what are you trying to do?
As a once AP student, I basically found that, for every single course, the very best way to learn the material was to
1.Buy/Rent/Download the three large AP test prep services
2.Spend a few minutes seeing which chapters corresponded with other.
3. Go through the books, solve about a 4th of the problems from each corresponding textbook
4. Take the practice exam, see which areas had the most missed problems
5. Repeat 3-4 until a score of 5 has been reached.
If you don’t have a strong basis in the prep-textbooks, one can easily go through very advanced material, while forgetting a few test-itself concepts that need to be hounded.
Calico: I used a somewhat similar method for SAT II Chemistry test back in 1998 (ancient history). I bought three different AP Chemistry test prep books / practice tests, read the book, took notes, and then did the exams. I got a perfect score. I also learned, basically, nothing about chemistry — I just hacked the test and was able to pass. So your method is an excellent way for self-motivated, high IQ students to get high scores on standardized tests!
So I suppose the question for Philip is: what’s the goal? To get a high score on the test/class, or to learn something about statistics?
If the goal is to really learn something, then I’d recommend finding an interesting problem the student actually cares about, and then using the math to understand it! Many kids who don’t love math are into sports, for example — a field with a ton of data for those looking to putter around.
Calico, PN: You raise a good question… what is the student’s goal? I am not sure why she is in AP Statistics and didn’t ask. It does seem like an odd thing to want to take, actually, since high schoolers are not conducting experiments and writing papers. I will ask the next time that I see her! Anyway, my goal is to help her truly understand statistics and probability, not just pass the test, because she may have to do other kinds of math in the future.
I rather like the on line stats book from Rice: http://onlinestatbook.com/index.html
My son did this when I was tutoring him in math in high school – drove me crazy.
Kids can sincerely not realize that there is a way of spending more than 30 seconds studying a problem. So they just mentally walk away. I had some success starting with simpler problems and building up to the bigger problem.
Don’t discount the possibility that the kid doesn’t want to be there and figures that if you get mad or frustrated enough, you’ll quit.
Preamble: we take that stats and probability are either a branch of maths of maths for all practical purposes pertaining the student. Thus tell the student that Erdos could not do maths (actually, discover new maths) without amphetamines or that he did not understand the Monty Hall problem — ideally in not such dry form. The point being, if you impress on the student that (1) even people who are considered math geniuses find math hard and (2) their success is predicated on hard work, not god given sudden inspiration, the student might realise that she can actually do stats/probability if she puts the required work in. Also, never give answers, and start from simple problems so that solving them will boost confidence. I had loads of students that did show remarkable improvement when I got into their heads that, yeah, it is hard, that’s why everybody has to work hard at it, but once you work hard you will get your results. It applies to teaching too.
“Preamble: we take that stats and probability are either a branch of maths of maths” should obviously read
“Preamble: we take that stats and probability are either a branch of maths or maths”
Re PN, half of the problem sets in high school math should be about sports. The other half should be about shopping.
I have never been very good at math. I found statistics to be by far the part of math that was most useful in my adult life. I didn’t have any formal instruction in statistics until graduate school (MBA program), though I learned some of it on my own as an undergraduate.
I think the actuarial handbooks have the best mix of theory, explanation and lots of problems/application at all levels. The first exam got split so the one I google now is different (narrower and called Exam P for probability) than what I had but still looks good. Here are some links for notes: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=92250&page=7
The official page with Syllabus: https://www.soa.org/education/exam-req/edu-exam-p-detail.aspx
I found https://www.khanacademy.org/math/probability to be quite helpful.
philg: Calico, PN: You raise a good question… what is the student’s goal? I am not sure why she is in AP Statistics and didn’t ask. It does seem like an odd thing to want to take, actually, since high schoolers are not conducting experiments and writing papers.
At this level of education, there is an argument to be made that it’s not so much what the student wants to get out of it as much as it is the teacher duty to inspire a desire to learn and impart an understanding of the subject at hand? Clearly a goal of the student’s is to enrich her transcript for college applications. The teacher should convince her the usefulness (importance?) of statistics, a la Robin Williams’s Mr. Keating’s teach of poetry in Dead Poet Society? Is that too high-minded and too Hollywood an expectation?