Dr. Gilmer is the
first African American Woman to publish a non-Ph.D Thesis Mathematics research
paper. She
was well on her way to being the third African American Woman to earn a Ph.D in
Mathematics but she stopped grad school temporarily for marriage.
She returned to school some time later and earned a Doctorate in
Curriculum Instruction from Marquette University.
She has taught in public schools, colleges and universities.

Dr. Gilmer is
currently involved in an interesting field of study which may very well catch
the interest of various groups of people.
The average person probably would not consider the likelihood of
mathematical figures being present in their every day common practices, but Dr.
Gilmer along with Ubiratan D’Ambrosio and Rick Scott have discovered that
mathematical patterns are very much in twined in and unique to various cultures.
This particular study is called, quite appropriately, Ethnomathematics.
Ethnomathematics is simply the study of mathematical ideas involved in
the cultural practices of a people.
Now this term is not just limited or identifying a society on a
small-scale but “Ethno” can be as broad as to include National Societies,
labor communities, religious traditions, and professional classes.
Dr. Gilmer is the founding president of the International Study Group on
Ethnomathematics, which was established in 1985.

According to Dr.
Gilmer, there is ample evidence to prove that people in all societies have their
own way of doing mathematics, independently of what they learned in school.
In addition to formal symbolic systems, mathematical practices also
include spatial designs, practical construction techniques, calculation methods,
measurement in time and space, specific ways of reasoning and informing, and
other cognitive and material activities.
Since the study of patterns is included in the discipline of mathematics
and patterns are found everywhere in nature, humans often copy these patterns to
enhance their own world.
To see how these patterns are enhancing a group of people, one would need
to go into a community, examine their language, their values and their
experiences with mathematical ideas.
This involvement would be a necessary step to understanding
Ethnomathematics.
Sometimes these ideas are even a part of products produced in that
community.

Dr. Gilmer conducted a study with the hair-braiding professionals within an African American community. Specifically she wanted to answer the question “What can the hair braiding enterprise contribute to mathematics education and conversely what can mathematics education contribute to the hair braiding enterprise.”

Click to read Dr. Gilmer's new paper: Using Technology to Explore Mathematical Patterns in African American Hairstyles

Observing and
interviewing the stylist and their customers answered this question.
These stylists use the mathematical concept of tessellations when
braiding and weaving hair.
A Tessellation is a filling up of a two-dimensional space by congruent or
corresponding copies of a figure that does not overlap.
Now the figure is called the fundamental shape for the Tessellation.
Dr. Gilmer found it interesting to see such an endless range of scalp
designs which were formed by parting the hair lengthwise, crosswise and into
curves. The
two most common geometrical designs seen were the Box Braids and the Triangular
Braids. In
the box braids the shape is like a rectangle and the pattern resembles a brick
wall. The
design starts at the nape of the neck with two boxes and then increases by one
box moving away from the neck.
The hair inside the box is brought to the point of intersection of the
diagonals and then braided.
The scalp is actually hidden from view by the tessellations.
The triangular braids were shaped like equilateral triangles.
The hair inside these figures was drawn to the point of intersection of
the bisectors of the angles of the triangle.
Finally another tessellation was that of a regular hexagon shape.
A regular hexagon is a regular polygon with six sides.

The
whole idea and purpose behind this study is to provide quicker and better access
to the scientific knowledge of humanity as a whole by using related knowledge
inherent in the culture of teachers and students.
One major contribution the hair weaving enterprise can make is to show
forth the diversity of a mathematical practice which will assist in revealing
knowledge for education and development.
Dr. Gilmer explains that this single activity can generate more
mathematic, than the application of a theory to a particular case.

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1. BIO’s of Black Women

2. Using Technology to Explore Mathematical Hair Styles