|
Adults Learning Mathematics - An International Journal |
|
Volume 1 (1), June 2005 |
|
A New
View of Mathematics Will Help Mathematics Teachers |
|
Juergen Maasz |
|
Johannes
Kepler Universität |
| Abstract |
|
For
many people mathematics is something like a very huge and impressive
building. It has a given structure with lots of levels and rooms. For many
people this structure and therefore mathematics itself is independent from
society, culture and history. It exists and mathematicians try to recover
(not: to construct!) new parts of it. From this point of view mathematics
is often seen as a lifeless and strange thing and not as a living
construct of human beings. |
|
Many mathematics teachers argue that they can’t change their way of teaching because they see mathematics from this dominant point of view and think that mathematics will not allow changes. Asking what this means they say that mathematics is something independent from them with a fixed structure. Therefore they have to teach little parts of mathematics (often concentrated on the correct use of algorithms) in a fixed sequence. Changing the sequence or leaving out a part seems to be not allowed. So they are not happy with mathematics but they see no way to change mathematics and therefore no way to change their teaching (perhaps except in some minor important methodical aspects). |
|
I
think there is a “way out” if mathematics is seen as a social
construct. Is this view correct? A new look at the history of mathematics
proves that the history of mathematics in the last 200 years looks like a
very good example of applying a sociological theory to make a new
interpretation of what happens. In more provocative words: If the
sociological theory I apply to make my interpretation of the history of
mathematics had existed 200 years ago one could think that the
mathematicians tried to prove that the sociological theory is correct by
forming the history of mathematics in the way the theory “wants”. If
teachers try to share this view they will be able to recognize that
mathematicians decided what “mathematics” is. I hope this will
motivate teachers to make more individual and pedagogical decisions on
what and how they teach. |
|
Folding
Back and the Growth of Mathematical Understanding |
| & University of British Columbia |
| Department
of Curriculum Studies, University of British Columbia |
| BC
Construction Industry Skills Improvement Council – SkillPlan |
| Abstract |
| This paper presents some initial findings from a multi-year project that is exploring the growth of mathematical understanding in a variety of construction trades training programs. In this paper, we focus on John, an entry-level plumbing trainee. We explore his understandings for multiplication, fractions and units of imperial measure as he attempts to solve a pipefitting problem. We consider the apparently limited nature of his images for these concepts and the role of ‘folding back’ in enabling his growth of understanding. We contend that it cannot be assumed that the images held by adult apprentices for basic mathematical concepts are flexible, deep, or useful in specific workplace contexts. We suggest that folding back to modify or make new images as needed in particular contexts is an essential element in facilitating the growth of mathematical understanding in workplace training, but also offer a note of caution about ensuring that this is genuinely effective in its purpose. |
|
Mathematical
Autobiography Among College Learners |
| Shandy Hauk |
| Assistant Professor, Mathematics |
| School of Mathematical Sciences |
| University of Northern Colorado |
| Abstract |
| This
study examines the K-12 mathematical experiences of
U.S. university students via an expressive writing assignment: a
mathematical autobiography essay. The essays of 67 college students, out
of over 300 enrolled in 16 sections of a college liberal arts mathematics
course, were analyzed using constant-comparative methods. Two categories
of experience connected to aspects of mathematical self-regulation emerged
as significant: (1) locus of control for mathematics knowledge and
learning; (2) self-evaluations of mathematical ability, efficacy, and
potential. Interviews of 18 of the 67 students provided support and
clarification for the analysis. An argument grounded in existing research
for increased mathematical self-regulation as a result of completing the
mathematics autobiography is made. Finally, connections are drawn between
learning and psychological theories to support the assertion that using
the assignment may help build pedagogical content knowledge among novice
college mathematics teachers. |