10-11-2014, 08:44 PM
Kids just don't have a chance anymore. HP Prime delivers the wrong answer to a simple median problem, and now test-maker Pearson apparently did not check its own test answer key very closely. See here.
Quote:Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).
(10-11-2014 11:15 PM)Tim Wessman Wrote: [ -> ]I've read the entire standard cover to cover and find nothing objectionable.
Quote:Median. A measure of center in a set of numerical data. The median of a list of
values is the value appearing at the center of a sorted version of the list—or the
mean of the two central values, if the list contains an even number of values.
Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.
(10-11-2014 11:15 PM)Tim Wessman Wrote: [ -> ]Quote:Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).
That obviously is crap that needs tossing...
(10-12-2014 03:24 AM)patrice Wrote: [ -> ]Here in France, even if things evolve, they are a little different.
Schools are mainly government (Ministère de l'Education)
On the day by day basis, teachers are free to build their own lessons and tests, the books are mainly for help, books are not automatically the lessons.
For national tests (such as Baccalauréat), they are made by government employees.
I see a few differences with US:
- All the tests/exams are made public after the start of the exam.
- Since France is spread all other the earth (Europe, Latin America, Pacific ...), there are different set of questions for different places for the same exam.
- Students can get back its corrected answers after the exam.
- The tradition is "open" questions for exams: In the exam, the student get only the questions, not the candidate answers.
(10-12-2014 04:35 AM)Don Shepherd Wrote: [ -> ]Private school teachers do not have to be licensed by the state, and these teachers are free to choose whatever curriculum they want (with approval of the school headmaster or principal, of course).
(10-12-2014 12:18 AM)Don Shepherd Wrote: [ -> ]Regrettably (if I am to believe this thread), the Prime calculator would say the median of that data set is 10, not 11. Every middle school math teacher in the United States would tell you that is wrong. Please tell me this will be fixed.
(10-12-2014 08:40 PM)Tim Wessman Wrote: [ -> ](10-12-2014 12:18 AM)Don Shepherd Wrote: [ -> ]Regrettably (if I am to believe this thread), the Prime calculator would say the median of that data set is 10, not 11. Every middle school math teacher in the United States would tell you that is wrong. Please tell me this will be fixed.
The statistics applications and everything students will use calculate exactly that way.
The discussion in that thread revolved around the hidden CAS command 'median' which used a different but still perfectly valid mathematical definition. Median is "generally" defined as the way described in the document, but there are at least 3 ways to do it that I am aware of. All of them are mathematically and statistically valid.
Bernard chooses to use that other definition in his CAS, and since HP licenses the CAS and did not develop it internally... sometimes there have been things that go through of which we are unaware and might disagree with or wish would be changed. In that thread though, he indicates that it will be easy for him to resolve that to use a different behavior and so that will be changing to bring that CAS command into agreement with the rest of the system should there be another update put out.
(10-12-2014 09:19 PM)Don Shepherd Wrote: [ -> ]Thanks Tim, but the original poster in that thread said that the unexpected behavior of median wasn't just in CAS mode, but in home mode too. Not having a Prime, I can't verify that. If it is fixed, fine, but someone should verify that it works as expected in home mode.
Don
(10-12-2014 08:40 PM)Tim Wessman Wrote: [ -> ]but there are at least 3 ways to do it that I am aware of. All of them are mathematically and statistically valid.
(10-13-2014 04:50 PM)Don Shepherd Wrote: [ -> ](10-12-2014 08:40 PM)Tim Wessman Wrote: [ -> ]but there are at least 3 ways to do it that I am aware of. All of them are mathematically and statistically valid.
Tim, two points.
First, I accept that the change to the CAS calculation of median in the Prime will also be effective in the Home mode, when the next update is released. The larger problem is students who have already purchased a Prime calculator and do not upgrade. If they use their Prime to calculate median they will get the wrong answer ("wrong" as defined by their teacher, undoubtedly).
Second, you cannot say that all 3 methods of calculating median are mathematically and statistically valid: they return 3 different answers for the same data set (I am assuming that the 3 methods you refer to are the "correct" one [mean of the two middle values], the one that returns the smaller of the two middle values, and the one that returns the larger of the two middle values). There cannot be 3 valid values for median of the same data set, that is just basic to any discussion of median.
Quote:Given order statistics \( Y_1=min_j X_j, Y_2, ..., Y_{N-1}, Y_N=max_j X_j, \) the statistical median of the random sample is defined by
\[ \begin{cases}
Y_{(N+1)/2} & \text{if \(N\) is odd};\\
\frac{1}{2}(Y_{N/2}+Y_{1+N/2}) & \text{if \(N\) is even}
\end{cases} \]
(10-16-2014 05:11 PM)Han Wrote: [ -> ]If your domain is the set of integers, then a rational median may seem misplaced.
(10-19-2014 03:28 PM)lrdheat Wrote: [ -> ]Concerning the lion in the cage, I saw the probabilistic way to catch a lion stated as: Place an open cage in lion country. There is a non-zero probability of a lion being in the cage at time >0. Wait!
(10-19-2014 03:28 PM)lrdheat Wrote: [ -> ]Concerning the lion in the cage, I saw the probabilistic way to catch a lion stated as: Place an open cage in lion country. There is a non-zero probability of a lion being in the cage at time >0. Wait!