
GF:

Research in Undergraduate Math Education

Location:

SS Ballroom DE 
Date:

Wednesday, Aug.03 
Time:

1:00PM  3:00PM

Presider:

John Thompson,

CoPresiders(s):

None

Equipment:

N/A



GF01:

Seeing Through Symbols: Personal and Cultural Semiotic Systems in Algebra

Location:

SS Ballroom DE 
Date:

Wednesday, Aug.03 
Time:

1:00PM  1:30PM

Author:

Aaron Weinberg, Ithaca College
6072747081, aweinberg@ithaca.edu

CoAuthor(s):

None

Abstract:

Algebraic symbolism plays a prominent role in mathematics. We try to teach our students to "see through the symbols" to focus on the underlying meaning of variables, functions, systems of equations, and other algebraic notation. Despite our best efforts, students frequently struggle to use algebraic notation meaningfully. The idea of personal and cultural semiotic systems gives us a new way of understanding how students work with algebraic symbols. Previous research on algebraic representation has attempted to describe either the ways students interpret symbols or the ways they produce symbols. In contrast, viewing students' work as part of a semiotic system unifies these perspectives, enabling us to describe the interaction between symbol production and interpretation. This presentation will introduce the idea of semiotic systems and look at examples of student work to illustrate the concept and show how it can be used to understand students' mathematical activity.

Footnotes:

Sponsored by John Thompson



GF02:

The Functions of Examples in Instruction

Location:

SS Ballroom DE 
Date:

Wednesday, Aug.03 
Time:

1:30PM  2:00PM

Author:

Tim FukawaConnelly, University of New Hampshire
6038623705, tim.fc@unh.edu

CoAuthor(s):

None

Abstract:

Examples are an important part of our teaching of mathematics and physics. Some of the ways that we might use examples in our teaching are to show how to use a formula, perform an algorithm, illustrate a theory, or help understand concepts. While these are relatively common, there are less common uses to which we might put examples that include having students recreate the fundamental ideas of our disciplines, develop their own original ideas, and develop ways of reasoning that support innovative thinking. In this presentation I will show examples of teachers in mathematics and physics drawing on different scientific functions that examples might serve in teaching at the university level. I will then suggest how instructor's uses of examples can communicate to students what it means to be a scientist, and, perhaps convey the wrong message about our respective disciplines. Or, good teaching may be leading to bad results?

Footnotes:

AAPT is sponsoring my presentation if that's what this box means.



GF03:

How I Learned to Stop Worrying and Love the Applications

Location:

SS Ballroom DE 
Date:

Wednesday, Aug.03 
Time:

2:00PM  2:30PM

Author:

Michael C. Oehrtman, University of Northern Colorado
9703512344, michael.oehrtman@unco.edu

CoAuthor(s):

None

Abstract:

Subtitle: Confessions of a Mathematician.
In this talk I present findings from my design research using numerical methods and error analyses to establish a strong conceptual foundation for an introductory calculus and differential equations sequence. I will intersperse this discussion with reflections on my own experiences as a student of both mathematics and physics, as a mathematics faculty, and as an education researcher that led me to this approach. I will present results indicating that properly developed, an applied approach to calculus and differential equations can 1) be based on natural language and ideas directly accessible to students, 2) provide a coherent approach to the range of topics covered in the entire sequence, 3) be coherent in meaning and structure across multiple representations, and 4) establish a foundation for subsequent formal mathematical development. A natural hypothesis is that such an approach should also support modeling in science and engineering.

Footnotes:

Sponsored by John Thompson.



GF04:

Learning for Transfer: How Much Does Context Matter?

Location:

SS Ballroom DE 
Date:

Wednesday, Aug.03 
Time:

2:30PM  3:00PM

Author:

Joseph F. Wagner
Xavier University, Department of Mathematics & Computer Science
5137453834, wagner@xavier.edu

CoAuthor(s):

None

Abstract:

“Transfer in pieces” is a theory of knowledge transfer that stands in contrast to longstanding theories of “transfer by abstraction.” It seems almost selfevident that knowledge of mathematics or science should be applicable across different contexts by virtue of its abstractness or distance from the contexts in which it was learned. Surely this has served as a basis for traditional instructional practices in mathematics and science. A transferinpieces approach, however, suggests that the utility of abstract knowledge is somewhat illusory, and that the cognitive mechanisms of transfer are much more attuned to specific features of the contexts in which knowledge is applied. For learning theorists, this presentation offers an introductory tour of the basic tenets of a transferinpieces consideration of the problem of transfer. For teachers, it suggests that the role of learning contexts and initial applications of knowledge may be both more significant and more limiting than we think.

Footnotes:

Sponsored by John R. Thompson, University of Maine


