2) How might Mason's ideas about questions in math class be incorporated into your unit planning for your long practicum?
John
Mason in his article Questioning in Mathematics Education
argues the necessity of challenging students in class teaching. Students gain
experience when they are stuck and are able to observe situations like “what to
do when [they] get stuck” and “what to do when they don’t know what to do”. I personally
believe this is a good article demonstrating how to ask an inquiry question in
class.
These
challenging moments usually come with teachers’ in-class questions. Mason
believes there are two different ways of asking question. The first way is asking as telling: “the teacher has
something come to mind and then asks a question which is intended to direct or
focus student attention on what has come to mind”. Students may directly response
by guessing “what is in the teacher’s mind about this problem” but do not
consider what the problem truly is and how to solve the problem. Some examples
of this type of questions may be: “what do we do with our rulers”, “what does
the definition tell”, “what is the next procedure”, etc. Always, a teacher
should realize that a question of this type is asking when students response
with “inappropriate or unexpected [replies]” which are different from an “expected,
even an intended, answer in the teacher’s mind”. The second way is called “asking as enquiring” (inquiring?). It appears when the “[teacher] asking
does not know the answer and is presumably seeking that answer”. Different from
the previous type of asking “listening for an expected response”, this type of
asking emphasizes on listening to what students are saying/doing. The differences
are that the teacher’s responses may be right or wrong in the “asking as
telling” type, while the teacher’s responses can be interested with various
reasons in the “asking as enquiry” type. Through this asking type, students are
encouraged to share and reveal their thinking by being asked “how do you know”,
“will that always be the case”, “what else might that be the case”, etc. Students
are encouraged to see/analyze/rethink/discuss their responses from multiple perspectives
(interesting in this/that way) rather than from the right/wrong perspectives.
Mason
even mentions some other ways that can encourage students to share their
thoughts in class. Instead of asking questions, students can construct
mathematical problems for themselves. They can also construct examples of
mathematical objects meeting various constraints. The goal of these activities
is to force students to think “beyond the first (usually simple) example that
comes to mind” so that they can “enrich their example space while revealing the
dimensions they are aware of that can be changed, and even something about the
range of permissible change in those dimensions”. Mason even thinks that “a
student does not vary something that can be varied or change something in a
particular way does not mean that they did not think of it, only that s/he did
does not reveal it”.
In
practice, I consider both types of asking matter and should be used in class. The
first type of asking is suitable when clarification is needed, while the second
type of asking should become the majority of my asking. All in all, as a
teacher, my responses show my attitude toward students’ responses, and what
help students are my thoughts that can enlighten them in some ways but not a cold
yes/no/right/wrong answer that may limit their feelings of enlightened. Apparently,
as a result, I do not want to eliminate the better results by failing to ask
good questions at the beginning.
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