One of my main interests is in college-level mathematics. I believe that this is an under-studied part of mathematics education chain. I was intrigued by a discrepancy I saw between the messages I interpreted from my undergraduate education and what part of our secondary mathematics education program was trying to tell our future teachers. One particular issue was regarding technology. Why don&#x2019;t college professors use technology?
Good vs. Bad - Don&#x2019;t want to make this good vs. bad. Not everyone who uses technology is going to use it in good ways. Geometry - Dynamic, Visual, Simultaneous Representations Technology - Any electronic medium used for pedagogical purposes in the geometry classroom. The most immediate examples that fit this definition are graphing calculators, and computer software. However, personal response devices and even slide shows could fit this definition Question - Did I want to describe what was occurring in geometry classrooms, did I want to evaluate and compare student learning in different classrooms. Decided I wanted to come to a better understanding of professor decisions, and what affects and goes into their decisions.
There was no existing framework of university mathematics professors decision-making Becker, 2000 - Characteristics of Exemplary Technology users across subjects Russell, Bebell, O'Dwyer, & O'Connor, 2003 - Different Uses of Technology in Mass. school districts Ravitz, Wong and Becker (1999)- Instructional practices, teaching philosophies, and uses of computing technologies Thompson, 1992, Ernest 1998 - Three conceptions of mathematics and teacher&#x2019;s conceptions - beliefs, concepts, meaning, rules, mental images, and preferences concerning the discipline of mathematics. Kuhs & Ball, 1986 - &#x2018;at least four dominant and distinctive views of how mathematics should be taught&#x2019; Dick, 2007 - Mathematical Fiedlity of Technology (Zbiek, Heid, Blume, & Dick, 2007) - Pedagogical Fidelity of Technology
Thought that professors who had taught more than once would be more likely to have thought about their instruction Vary in size, degrees granted, public/private status and technology initiatives
A way of comparing data across cases so that a theory can emerge from the data. Used in Grounded Theory
A mathematics professor at a... What I&#x2019;m not doing, trying to make connections between types of institutions and the data. Couldn&#x2019;t anyway because there isn&#x2019;t enough data. All professors did use technology in their classroom
Talk about the results here, but also include some discussion of these results as well.
Originally was number of years they taught the course. Most professors had not only taught this course more than once, but had taught it almost every year. How are professors coming this conclusion, either to intentional change, or solidiy content?
Is it a limit that prevents, or a challenge to adapt to?
Separation of Internal and External Forces. External Forces seemed to divide themselves into two categories, those that were related to specifically the course, and those that were external and related explicitly to the institution. I don&#x2019;t know how these interact with each other, or how they interact with each other.
Apprenticeship of Observation, surprised there wasn&#x2019;t any connection to the similarities or differences in how they were taught geometry
Forces Affecting University Mathematics
Professors' Use of Technology in Their
Mathematics Learning Research Group
Michigan State University
Narrowing my Focus
Good vs. Bad, Geometry, Technology, Question
Creating a Framework
Teacher’s Use of Technology in K-12 Schools
(Becker, 2000), (Russell, Bebell, O'Dwyer, &
O'Connor, 2003), (Ravitz, Wong and Becker, 1999)
Teacher Beliefs (Thompson, 1992), (Ernest, 1998),
(Kuhs & Ball, 1986)
Beliefs about Technology in Mathematics Classrooms
(Dick, 2007), (Zbiek, Heid, Blume, & Dick, 2007)
Initial framework of forces affecting university mathematics professors’
decisions about using technology in their geometry classroom
What is a framework that can help describe the
forces affecting college professors’ decisions to
use (or not use) technology in their classroom?
who had taught their
class more than once
Vary institution type
from within Michigan
No more than 8
(Glaser & Strauss, 1967)
1. Comparing and contrasting incidents to create
categories into which the data can ﬁt
2. Integrating categories and their properties into
3. Delimiting the theory to focus it
4. Writing the theory that has emerged out of the
I. Asks professors about the course as a whole, structure
of individual lessons, and class preparation
II. Asks professors about any technology use in their
lessons, how they came to decide upon technology,
and thoughts on technology and geometry
III.Asks professors about training and support for
technology at their institutions,
Dr. Herb Williams – Small private liberal arts college. He has
previously taught an axiomatic geometry course.
Dr. Christine Lauer – Large public research university. She has
previously taught a course in Euclidean geometry.
Dr. Samantha Gooding – Private technical institute. She has
previously taught a course focusing on the intersection of
geometry and the arts.
Dr. Karl Quinn – Small, private liberal arts college. He has
previously taught a course axiomatic geometry course.
Dr. Ursula Nichols – Medium-sized, public research institution.
She has previously taught a course on axiomatic geometry.
Goals for the Course
Each professors’ personal goals for the course
Dr. Williams - students to walk away with an
appreciation of geometry and its importance in history,
and not necessarily facts. Change the disposition of his
students to one favorable towards geometry
Dr. Lauer - “more experiential than content driven”,
wanted students to have different experiences in
Dr. Gooding - wanted her course to change her
students’ perspectives on life, and so they would see
geometry wherever they are.
Perceived Establishment of
Two themes emerged, either solidifying course content,
or intentionally changing content between years
Dr. Quinn - “It’s been a long time since I’ve gone
about…”. He added that he had been teaching this
course since “water was invented”.
Dr. Lauer - tried to change the course content every
year, so that way, she wouldn’t have sat with an idea
Beliefs About What
Technology can do
What was technology’s role within the classroom?
Dr. Williams - geometry is about unpacking and ﬁguring out
what causes, whereas the software package Geometer’s
Sketchpad was a “little black box that won’t let you peer
Dr. Lauer - technology produces an environment and then
the question is, what do you get out of that environment
Beliefs about Technology in
Beliefs about using technology within the geometry
Dr. Nichols - technology’s use in geometry should,
“depend on the content; whether it let’s [students]
look at a problem authentically and does it help them
build their understanding
Dr. Quinn - didn’t believe there was any content
reason to be hesitant about using technology in
Beliefs about Student
Interactions with Technology
Beliefs about how they wanted students to interact with
technology in their classroom
Dr. Williams noted that in his opinion, technology
should be used for discovery by the students, and
not for demonstrations to the students.
Dr. Gooding expressed a desire for students to
experiment more in mathematics as they do in their
arts classes. She described a frustration of students
going right to technology for answers without playing
around with ideas.
How Students will Learn in
Different learning methods to utilized in this course
Dr. Williams & Dr. Gooding expressed the desire that
students would learn by making discoveries
Dr. Lauer & Dr. Nichols expressed the desire that
students would learn by making connections and
constructing their knowledge
Professor’s Preparation to
All professors expressed conﬁdence in their and their
colleagues ability to use technology, however, there
were some on using the technology pedagogically
Dr. Williams - didn’t believe it’s that hard to use
technology, although it might be slightly more
challenging to learn how to use it for teaching
Dr. Nichols - believed that teachers should
technology should be used in meaningful ways to
enhance the learning of a topic.
Goals for the Course
Institution-level goals for the course. Course description
These goals ranged from proof writing (Dr. Williams,
Dr. Lauer, Dr. Quinn, and Dr. Nichols), to better
understanding of Euclidean and Non-Euclidean
geometries (all interviewees), to examining
mathematics in the arts and architecture (Dr.
Gooding and Dr. Quinn).
Population of the Course
Professors were conscience of the different populations
within their courses, and that they had considered
tailoring the content of their courses to ﬁt the
populations enrolled in their courses
Position of Course within the
All these geometry courses were terminal courses, they
were not prerequisites for any other course in their
All professors were aware of the different prerequisites
required for their courses and that seemed to have
effect on course content
Access to Technology
The physical location of technology and access to software
differed among classes.
Dr. Lauer and Dr. Gooding noted that they would have
students bring laptops to the classroom
Dr. Lauer, Dr. Quinn, and Dr. Nichols all described efforts to
utilize one of their institutions’ computer labs during their
Dr. Quinn also described a time his department purchased
a large number of textbooks bundled with software. Went
around to the different computer labs on campus and
installed the software by hand.
Support for Technology
Resources for professors who wanted to use
technology to be successful
Dr. Williams - existed funds for travel for professional
Dr. Nichols’ - institution equipping rooms with
technology carts and built-in data projectors
Dr. Lauer - department and institution’s support in
providing laptop carts for classrooms, support with
setup and storage of technology, and acquiring
Dr. Gooding - institution had formed a working group
with the goal of promoting active learning with
Dr. Lauer - while her university had a position that was
favorable to technology, her department had a position
that was not
Dr. Nichols -classes offered by computing services for
faculty on topics such as podcasting, e-learning, and
developing your website
“Final” framework of forces affecting university mathematics professors’
decisions about using technology in their geometry classroom
External Forces - Course Level and Institution Level
Interactions Among Forces
No relation to their own experiences in geometry
Time was not discussed as affecting decisions
Complexifying College Instruction
Only 5 professors interviewed, all of who used
technology for one of their geometry courses
One analyzer of the data
No discussion on the enactment of these forces
Practicum Committee - Mike Steele, Raven
McCrory, Amanda Hawkins
Writing Group - Lorraine Males, Aaron Mosier,