9 Mar
2005
9 Mar
'05
4:53 p.m.
Look at them as superordinate categories. As you look at conjecturing
ask where would it fit? Under WHAT IF? with estimating.
Defining fits undetr the WHAT category. What is this?
Generalizing would fit under WHY?
Exploring is definately a WHAT IF?
Properties are a WHAT, but they also explain some WHYs?
The proposed reasoning approach takes students with little or no math
schema to a place where they can at least start a problem.
See if you can apply the system in you instruction first then see how
the students respond. The first thing our instructors noticed was they
spent most of the time writing out HOW and explained WHY orally.
Eldon L. McMurray
Director
Faculty Center for Teaching Excellence
Assistant Professor
College Success & Academic Literacy
Utah Valley State College
800 West University Parkway
Orem, UT 84058
(801) 863-8550
>> sandowda(a)msu.edu 03/08/05 6:43 PM >>>
Dr. McMurray,
I agree that the three things you list are useful in solving math
problems whose solution methods are already known; however, I
wouldn't say they're sufficient for "fully understand[ing]
mathematics." How do you address central mathematical practices like
conjecturing, defining, generalizing, exploring whether different
solution methods yield different insights, etc.? Or are those kinds
of things not goals for you in teaching undergraduates?
Dara Sandow
At 11:30 PM -0700 3/7/05, Eldon McMurray wrote:
The following article is an example of using
predominant learning
styles and Bloom' Taxonomy to teach mathematical reasoning. It is
the model all of our tutors are trained with. This has been very
helpful to our instructors as they mentor adjuncts.
The WHAT, HOW, WHY, and WHAT IF of Mathematics: Teaching
undergraduates to think up Benjamin Blooms cognitive Levels
By Carole Sullivan and Eldon McMurray of Utah Valley State College
To fully understand mathematics, it is important to know three
things:
1. WHAT precisely the problem is asking;
2. HOW to do the problem; and
3. WHY certain steps give you the correct answer.
Then to consider this: WHAT IF the problem were a little different.
...
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11 Mar
11 Mar
11:23 a.m.
New subject: Motivating grad students to teach thinking in Math simply
Dr. McMurray,
I recognize that it's possible to see the practices I listed as
subsets of your categories; however, I don't think of them that way.
(And note that the practices I listed were intended only as examples
of a larger set of mathematical practices one might want students to
have experience with / develop beliefs about.) Consider the practice
of defining, for example. Mathematicians certainly master existing
definitions, but they also encounter the need to define new
constructs, and there may be questions about how best to define
something, and some definitions change over time, etc. If one wants
students to experience any of these things (e.g., to have a felt need
for defining something), then one structures one's teaching in a
different way (e.g., one doesn't define every concept in anticipation
of its need). Also, in this case, defining isn't just a matter of
what, but also of why (e.g., why is this concept useful / worth
naming?) and perhaps other categories as well.
Dara
Look at them as superordinate categories. As you look
at conjecturing
ask where would it fit? Under WHAT IF? with estimating.
Defining fits undetr the WHAT category. What is this?
Generalizing would fit under WHY?
Exploring is definately a WHAT IF?
Properties are a WHAT, but they also explain some WHYs?
The proposed reasoning approach takes students with little or no math
schema to a place where they can at least start a problem.
See if you can apply the system in you instruction first then see how
the students respond. The first thing our instructors noticed was they
spent most of the time writing out HOW and explained WHY orally.
Eldon L. McMurray
Director
Faculty Center for Teaching Excellence
Assistant Professor
College Success & Academic Literacy
Utah Valley State College
800 West University Parkway
Orem, UT 84058
(801) 863-8550
>> sandowda(a)msu.edu 03/08/05 6:43 PM
>>>
Dr. McMurray,
I agree that the three things you list are useful in solving math
problems whose solution methods are already known; however, I
wouldn't say they're sufficient for "fully understand[ing]
mathematics." How do you address central mathematical practices like
conjecturing, defining, generalizing, exploring whether different
solution methods yield different insights, etc.? Or are those kinds
of things not goals for you in teaching undergraduates?
Dara Sandow
At 11:30 PM -0700 3/7/05, Eldon McMurray wrote:
The following article is an example of using
predominant learning
styles and Bloom' Taxonomy to teach mathematical reasoning. It is
the model all of our tutors are trained with. This has been very
helpful to our instructors as they mentor adjuncts.
The WHAT, HOW, WHY, and WHAT IF of Mathematics: Teaching
undergraduates to think up Benjamin Blooms cognitive Levels
By Carole Sullivan and Eldon McMurray of Utah Valley State College
To fully understand mathematics, it is important to know three
things:
1. WHAT precisely the problem is asking;
2. HOW to do the problem; and
3. WHY certain steps give you the correct answer.
Then to consider this: WHAT IF the problem were a little different.
...
_______________________________________________
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1 comments
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Dara Sandow -
Eldon McMurray