> [snip]
>
> Rick, et al,
>
> I call it the Orthogonality Projection Conundrum (OPC).
>
> Students have a basis for thought and generally their questions make sense in their basis and if their basis overlaps a scientific basis, then both the question and answer can have meaning in both bases (student's and teacher's) and information gets transferred to the student. And over time we expand the students basis set.
>
> However some students have a basis sparse to the point that their basis is orthogonal to most any scientific basis. Thus the student's question makes no sense to the teacher and the teacher's answer likewise makes no sense to the student.
>
> Some of the sparse bases are so sparse that they are pretty much othogonal to everything. And we know the empty set is othogonal to everything including itself.
>
> How does one teach the empty set?
>
> Sadly, I find that I'm being presented with this problem with increasing frequency!
>
> Something to think about!
> Clay
>
How to reach the "empty set", salt it with some data.
For example, back when I attempted a BSEE all engineering and
prospective math majors took identical math course sequence (IIRC
it was also the recommended sequence for physical science
majors). 1st semester of calculus was a near disaster. It was
rescued by the first six weeks of 2nd semester physics. The two
curricula had been carefully coordinated, first semester physics
was a "calculus free zone". The labs made the previous semester's
math gel.
There is also the problem (related?) of the student's learning
style. first semester calculus was broken up into section of ~20
students (no large lecture halls). Our section had ~15 engineers
and 3 or 4 math majors taught by a TA who field was pure math.
During the lecture he rigorously "proved" everything. The first
course wide exam gave us a dubious distinction - the lowest
section average. In the next class the TA asked for suggestions
from the class. With one voice the engineers said "Work examples.
Lots of examples." With much trepidation he yielded until the
next exam. Our average was not the highest, but we were above
average.
Reply by glen herrmannsfeldt●July 3, 20132013-07-03
Randy Yates <yates@digitalsignallabs.com> wrote:
(snip)
>> Are you referring to your students at George State?
> Georgia State. Sheesh.
There is a city name George in the state of Washington, but as
far as I know, no state school there yet.
-- glen
Reply by glen herrmannsfeldt●July 3, 20132013-07-03
clay@claysturner.com wrote:
(snip)
> I call it the Orthogonality Projection Conundrum (OPC).
> Students have a basis for thought and generally their questions
> make sense in their basis and if their basis overlaps a scientific
> basis, then both the question and answer can have meaning in both
> bases (student's and teacher's) and information gets transferred
> to the student. And over time we expand the students basis set.
Yes. Continuing the analogy, sometimes one can recognize the
projection, and apply the inverse transform.
I remember hearing the descriptions of problems people had
learning Fortran (in Fortran 66 days) and recognizing the
problem knowing the mistakes beginners make, and the effect
of those mistakes. (Even though I didn't remember doing that.)
Also, as a physics TA asking someone the derivative of 1/x
and getting log(x) as the reply. Learning integrals at the
time, the answer was closer. It wasn't hard to see where
the answer came from, though.
> However some students have a basis sparse to the point that their
> basis is orthogonal to most any scientific basis. Thus the
> student's question makes no sense to the teacher and the
> teacher's answer likewise makes no sense to the student.
Sometimes the inverse transform doesn't work.
> Some of the sparse bases are so sparse that they are pretty
> much othogonal to everything. And we know the empty set
> is othogonal to everything including itself.
-- glen
Reply by Randy Yates●July 3, 20132013-07-03
Randy Yates <yates@digitalsignallabs.com> writes:
> clay@claysturner.com writes:
>
>> On Tuesday, July 2, 2013 9:53:21 PM UTC-4, Rick Lyons wrote:
>>> On Mon, 1 Jul 2013 20:33:01 -0700 (PDT), dvsarwate
>>>
>>>
>>>
>>>
>>>
>>> >On Monday, July 1, 2013 11:54:06 AM UTC-5, robert bristow-johnson quoted:
>>>
>>> >
>>>
>>> >> > Sheeeesh!
>>>
>>> >
>>>
>>> >Having been a faculty member for my entire professional
>>>
>>> >life (and a son of a faculty member too), I have lived
>>>
>>> >from childhood onwards with the firm conviction that
>>>
>>> >there is no such thing as a stupid question. Now in my
>>>
>>> >golden years, after encountering manishp's questions,
>>>
>>> >I have begun to rethink the issue....
>>>
>>>
>>>
>>>
>>>
>>> Hi Dilip,
>>>
>>> Ha ha. Your post is interesting.
>>>
>>>
>>>
>>> Occasionally I teach a 3-day DSP class. And at
>>>
>>> the beginning of the class, in order to encourage
>>>
>>> questions from my students, I tell them something
>>>
>>> like, "There are no dumb questions regarding DSP,
>>>
>>> so please don't hesitate to ask questions."
>>>
>>>
>>>
>>> But your post, and some of the questions asked
>>>
>>> here, may well prove me wrong. Ha ha.
>>>
>>>
>>>
>>> [-Rick-]
>>
>> Rick, et al,
>>
>> I call it the Orthogonality Projection Conundrum (OPC).
>>
>> Students have a basis for thought and generally their questions make
>> sense in their basis and if their basis overlaps a scientific basis,
>> then both the question and answer can have meaning in both bases
>> (student's and teacher's) and information gets transferred to the
>> student. And over time we expand the students basis set.
>>
>> However some students have a basis sparse to the point that their
>> basis is orthogonal to most any scientific basis. Thus the student's
>> question makes no sense to the teacher and the teacher's answer
>> likewise makes no sense to the student.
>>
>> Some of the sparse bases are so sparse that they are pretty much
>> othogonal to everything. And we know the empty set is othogonal to
>> everything including itself.
>
> Clay, that is a brilliant analogy!
>
>> How does one teach the empty set?
>>
>> Sadly, I find that I'm being presented with this problem with
>> increasing frequency!
>
> Are you referring to your students at George State?
> On Tuesday, July 2, 2013 9:53:21 PM UTC-4, Rick Lyons wrote:
>> On Mon, 1 Jul 2013 20:33:01 -0700 (PDT), dvsarwate
>>
>>
>>
>>
>>
>> >On Monday, July 1, 2013 11:54:06 AM UTC-5, robert bristow-johnson quoted:
>>
>> >
>>
>> >> > Sheeeesh!
>>
>> >
>>
>> >Having been a faculty member for my entire professional
>>
>> >life (and a son of a faculty member too), I have lived
>>
>> >from childhood onwards with the firm conviction that
>>
>> >there is no such thing as a stupid question. Now in my
>>
>> >golden years, after encountering manishp's questions,
>>
>> >I have begun to rethink the issue....
>>
>>
>>
>>
>>
>> Hi Dilip,
>>
>> Ha ha. Your post is interesting.
>>
>>
>>
>> Occasionally I teach a 3-day DSP class. And at
>>
>> the beginning of the class, in order to encourage
>>
>> questions from my students, I tell them something
>>
>> like, "There are no dumb questions regarding DSP,
>>
>> so please don't hesitate to ask questions."
>>
>>
>>
>> But your post, and some of the questions asked
>>
>> here, may well prove me wrong. Ha ha.
>>
>>
>>
>> [-Rick-]
>
> Rick, et al,
>
> I call it the Orthogonality Projection Conundrum (OPC).
>
> Students have a basis for thought and generally their questions make
> sense in their basis and if their basis overlaps a scientific basis,
> then both the question and answer can have meaning in both bases
> (student's and teacher's) and information gets transferred to the
> student. And over time we expand the students basis set.
>
> However some students have a basis sparse to the point that their
> basis is orthogonal to most any scientific basis. Thus the student's
> question makes no sense to the teacher and the teacher's answer
> likewise makes no sense to the student.
>
> Some of the sparse bases are so sparse that they are pretty much
> othogonal to everything. And we know the empty set is othogonal to
> everything including itself.
Clay, that is a brilliant analogy!
> How does one teach the empty set?
>
> Sadly, I find that I'm being presented with this problem with
> increasing frequency!
Are you referring to your students at George State?
On Tuesday, July 2, 2013 9:53:21 PM UTC-4, Rick Lyons wrote:
> On Mon, 1 Jul 2013 20:33:01 -0700 (PDT), dvsarwate
>
>
>
>
>
> >On Monday, July 1, 2013 11:54:06 AM UTC-5, robert bristow-johnson quoted:
>
> >
>
> >> > Sheeeesh!
>
> >
>
> >Having been a faculty member for my entire professional
>
> >life (and a son of a faculty member too), I have lived
>
> >from childhood onwards with the firm conviction that
>
> >there is no such thing as a stupid question. Now in my
>
> >golden years, after encountering manishp's questions,
>
> >I have begun to rethink the issue....
>
>
>
>
>
> Hi Dilip,
>
> Ha ha. Your post is interesting.
>
>
>
> Occasionally I teach a 3-day DSP class. And at
>
> the beginning of the class, in order to encourage
>
> questions from my students, I tell them something
>
> like, "There are no dumb questions regarding DSP,
>
> so please don't hesitate to ask questions."
>
>
>
> But your post, and some of the questions asked
>
> here, may well prove me wrong. Ha ha.
>
>
>
> [-Rick-]
Rick, et al,
I call it the Orthogonality Projection Conundrum (OPC).
Students have a basis for thought and generally their questions make sense in their basis and if their basis overlaps a scientific basis, then both the question and answer can have meaning in both bases (student's and teacher's) and information gets transferred to the student. And over time we expand the students basis set.
However some students have a basis sparse to the point that their basis is orthogonal to most any scientific basis. Thus the student's question makes no sense to the teacher and the teacher's answer likewise makes no sense to the student.
Some of the sparse bases are so sparse that they are pretty much othogonal to everything. And we know the empty set is othogonal to everything including itself.
How does one teach the empty set?
Sadly, I find that I'm being presented with this problem with increasing frequency!
Something to think about!
Clay
>On Monday, July 1, 2013 11:54:06 AM UTC-5, robert bristow-johnson quoted:
>
>> > Sheeeesh!
>
>Having been a faculty member for my entire professional
>life (and a son of a faculty member too), I have lived
>from childhood onwards with the firm conviction that
>there is no such thing as a stupid question. Now in my
>golden years, after encountering manishp's questions,
>I have begun to rethink the issue....
Hi Dilip,
Ha ha. Your post is interesting.
Occasionally I teach a 3-day DSP class. And at
the beginning of the class, in order to encourage
questions from my students, I tell them something
like, "There are no dumb questions regarding DSP,
so please don't hesitate to ask questions."
But your post, and some of the questions asked
here, may well prove me wrong. Ha ha.
[-Rick-]
Reply by Randy Yates●July 2, 20132013-07-02
dvsarwate <dvsarwate@yahoo.com> writes:
> On Monday, July 1, 2013 11:54:06 AM UTC-5, robert bristow-johnson quoted:
>
>> > Sheeeesh!
>
> Having been a faculty member for my entire professional
> life (and a son of a faculty member too), I have lived
> from childhood onwards with the firm conviction that
> there is no such thing as a stupid question. Now in my
> golden years, after encountering manishp's questions,
> I have begun to rethink the issue....
On Monday, July 1, 2013 11:54:06 AM UTC-5, robert bristow-johnson quoted:
> > Sheeeesh!
Having been a faculty member for my entire professional
life (and a son of a faculty member too), I have lived
from childhood onwards with the firm conviction that
there is no such thing as a stupid question. Now in my
golden years, after encountering manishp's questions,
I have begun to rethink the issue....
Reply by robert bristow-johnson●July 1, 20132013-07-01
sentiments shared (to some extent) but i dunno if i wanna so *two*
Vlad's posting here.
> Sheeeesh!
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."