We do not know the entire picture here. There are models of teaching other
than to demonstrate how to do a procedure, have students go home and
practice the procedure, and start each class with questions about the
homework over the procedure. Sometimes students get more from answers by
being challenged in some form or other to find their own mistakes rather
than the teacher to demonstrate the problem one more time in a lecture
format. Setting up other means (inside or outside of class) to have
students learn from their mistakes does not necessarily mean that a teacher
is cold or unwilling to help students.
Martha
-----Original Message-----
From: DustyGrigg@AOL.COM <DustyGrigg@AOL.COM>
To: hawkins@SUN1.WAYNE.CC.NC.US <hawkins@SUN1.WAYNE.CC.NC.US>;
owner-mathedcc@archives.math.utk.edu <owner-mathedcc@archives.math.utk.edu>;
nmiller@AUSTIN.CC.TX.US <nmiller@AUSTIN.CC.TX.US>
Cc: b.hentges@cctc.cc.mn.us <b.hentges@cctc.cc.mn.us>;
mathedcc@archives.math.utk.edu <mathedcc@archives.math.utk.edu>
Date: Saturday, September 26, 1998 3:53 AM
Subject: Re: [MATHEDCC] Combined Algebra - Time Allotment For Asking
Questions
Hi Annette!
I can understand why your first year students "get a little upset" ... if
you
only give them ten minutes to ask questions about homework! I would venture
to say that most likely they are more than "just a little upset." Most
likely
they are also feeling quite frustrated with you AND with learning math as
well! How open are you to learning something new - when the learning
environment is one which produces frustration, stress and tension??? I'd
venture to guess that unless you felt you had to attend such a class ...
that
you would quickly drop it!
You ask: "How much time is allowed for homework questions, if at all
... "
Your “if at all” worries me, Annette! Imagine trying to learn something new
and the person teaching you does not allow you to ask questions about things
which confuse you. Ask yourself this question: If you were not allowed to
ask questions about those things you didn't understand - would you continue
attending the class? Probably not, because your lack of understanding would
grow deeper with each class session, along with possible feelings of
inadequacies such as feeling stupid. Your "learning receptors" would
quickly
"turn off" and you'd no longer even be trying to understand what is being
taught! Finally, you’d reach a point where you would just stop attending
the
class. Why? Cuz the class wasn’t interesting or fun to you! Having a
“cloud
of confusion” surround you, having the sense of “drowning,” or having the
experience of “frantically trying to stay afloat” ... are not pleasant
experiences. They aren’t experiences that most people readily choose for
themselves!
As far as the actual time allotted for questions regarding homework ... I’d
say it depends on the length of your classes (50 minutes? 85 minutes? 110
minutes?), the topics being covered, how much instructional time you’ve
already provided your students on the topic(s), etc.
If your class sessions are only 50 minutes long, allotting a total
time of 25 minutes for questions (including your work of problems at the
black/white board) is not unreasonable. Don't make it a rule written in
concrete that it's always the first 25 minutes of class, either! Ideally,
the
learning environment created is one in which students hopefully feel free to
ask you questions regarding confusion they may have regarding past or
present
material being presented ... at any time!
If your class sessions are 110 minutes, additional time for questions and
working types of problems on the board should not cause too much additional
stress. If you just began a particular topic the last class session or so -
encourage your students to ask questions regarding the new material! How
else
are you to learn exactly what and where their confusion lies regarding it???
How else are your student to learn that you care and are concerned about
them
and the confusion they are experiencing! Unless you know exactly what your
students' confusion consists of ... you won’t know where to begin to
dispel/dissolve their confusion! And unless your students' have resolved
conflicts in their understanding of material you have previously presented
...
their receptivity to any new material you present to them will be extremely
low or non-existence. This is especially true if students' need to
understand
what you've already presented to them ... in order to understand the new
material you present to them.
You ask: "What questions do you allow? Problems in which they could not
work at all, problems in which they could start but not finish, or
problems that they finished but their answers did not match the
answers in the back of the book.
Allow ALL questions! ENCOURAGE students to ask questions! And you in
return
- be responsive, respectful and non-judgemental towards
the
students and their questions!
The best teacher I know, continuously encourages his students to ask
questions! He tells his students that there is no such thing as a “dumb”
question! He tells them that if someone sitting next to them thinks that
their question is dumb - “Who has the problem?” Not you!” When a student
asks him: "May I ask a question?" His response is: "Please do!" And his
body language totally supports his verbal message to the student 100%! I've
heard this teacher tell his students: "If my job was to give you a lecture
on
math, I would just video-tape my lectures and let you look at them while I'd
be out on the golf course! I'm here to answer your questions ... but I
can't
answer your questions unless you tell me them!"
During the last four years, I have observed this teacher in the classroom
with
students quite often. As I've said, this teacher actively encourages his
students to ask him questions! I have heard his students ask him a whole
array of different questions, some which could easily be labeled as
“stupid.”
And not once has this teacher’s verbal language OR his body language given
any
indication whatsoever ... that he considered a question asked as being
stupid
OR that he considered the person who asked the question as being stupid for
asking it!
I’ve also seen the results of this type of learning environment that this
teacher has cultivated in his classroom, as well. Students quickly relax in
his class, they quickly begin to feel free to ask questions, they quickly
realize that this teacher respects them as individuals ... and just as
quickly
- the students’ “learning receptors” open and their understanding begins to
freely blossom!
When students do not fear being ridiculed for asking what they may feel is a
“dumb” question - they begin to open up. First they become receptive to the
person trying to teach them! Next - they begin to be receptive towards
learning about the subject being taught!
When students are allowed to ask questions - encouraged to ask questions -
and
when their questions are responded to with respect ... students begin to
relax
and trust! And that point marks the beginning of a student's receptivity:
receptiveness to the person trying to teach themAND receptiveness towards
the
subject matter being taught!
Math can be a hard course to teach - especially if it is a required math
course (e.g. for graduation, transfer to a four year educational
institution,
etc.), as then there is a high percentage of students who would not
willingly
choose to take the class in the first place ... if they felt they had the
choice. And trying to teach people something they really don't desire to
learn ... is a very difficult, but not impossible challenge!
Annette, it’s an invaluable skill to be able to answer students’ questions
completely ... yet also quickly! Perhaps before answering a question - ask
the student: “How far did you get?” OR “Where did you get stuck?” Let
the
student tell you how they proceeded up until the place where they got stuck!
You have now engaged the student (and other students as well) ... in their
own
learning!
Another method of answering students’ questions is as follows. Perhaps you
assigned exercises 1-50. The next class session you could ask: “Does
anyone
have a question about homework problems 1 through 18?” Answer those
questions
and then ask: “Any questions about problems 19 through 26?” “27 to 35?”
etc.
By asking for questions in this way, you are grouping the same type of
homework problems together and thus you create a united focus to the
questions
asked at a particular time.
Still another method is to have students - as they enter the classroom - to
write on the board (in a specified place) the specific number of the
homework
problem(s) they found difficult and wish to be further explained by you,
their
teacher. This method gives students a "protective cloak" of being able to
ask
for help anonymously, plus also of giving students at least some control
over
their learning environment. This method also inconspicuously shows students
that other students as well ... also had problems with the same homework
exercise(s) as they themselves!
Say, for example, a student had problems with exercises #3, 8, 16 and 27.
When the student enters the classroom the next class session and sees that
another student has already written exercises #8 and #27 on the board - a
feeling of camaraderie and unity with his/her fellow students is
experienced.
Also, feelings of “being stupid” (for not understanding) begin to dissolve.
That student now knows he/she is not the only person who doesn't understand
the mathematical concepts being taught!
Teachers who are responsive to their students’ confusion ... help
to
create a feeling of camaraderie and unity between their students AND between
themselves and their students as well!
Learning is a partnership between the teacher and each individual student!
I ran across the following quote - exactly where I forget:
"A teacher is an answer ... in search of a question!"
Dusty
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