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For centuries men and women have used their hair not only as a means of fashions but also to display their culture and levels of sophistication. People may have rarely thought of the mathematics involved in their hair styles. The relationship between mathematics and hair styles may be an excellent way to relate mathematics to students. For young people in the United States, particularly African America students, it would be very significant to use braided hair styles such as cornrows to demonstrate mathematical properties. The purpose of this study is to determine what type of mathematics is involved in hair braiding and if the hair braiders are aware of the mathematics that they are using. Some subtopics of interest would be who may find the relationship between hair braiding and mathematics useful, and at what age should the connection be presented to students.
According to a website constructed by Ron Eglash (n.d) cornrow braids may date back to 500 B.C. and are not limited to Africa alone. These hair styles have ties to the culture of African through "religion, kinship, status, age, ethnicity, and other attributes of identity" (Eglash, year?). Braiding allows for communication between the braider and the person whose hair is getting braided. In many instances this is the way that information about the family and community may be shared, as well as a time to socialize. The styles and patterns of the cornrows may vary from a linear pattern to one that involves more elaborate patterns such as spirals and curves. In this way "mathematics is also a traditional part of African hairstyles" (Eglash, year?).
The traditions associated with hair braiding that originated in Africa were able to come to the United States. This was no small feat sense the heads of the African were shaved prior to entering the New World. The main reason for the hair cutting was sanitary reasons but this was still devastating to the Africans traveling the Middle Passage to the New World. Many of the African that worked inside of the homes of the plantation owners had to wear their hair neatly and in many instances used braids, plaits and cornrows to keep the appearance of their hair neat.
Black people were able to straighten their hair after the civil war when Madam C.J. Walker developed a safer system for hair straightening. African American adults mainly wore their hair straight while children continued to use the cornrows and other braided styles to style their hair. During the 1950 African American began to move away from the straightening techniques and back to more afro centric hair styles. It was at this time that some artists and others began to realize that some of the braiding styles in the United States were also used by women in Africa. "The complex geometric emphasis in new cornrow styleâ€¦ is again an important reminder that math is as much a part of African heritage as Black hair" (Eglash ).
The geometric concepts used by braiders are translations, reflections, rotations and dilations. A braid can be thought of as an iteration of plaits, where each plait is a type of "y" shape (Eglash). As braids get smaller or larger to create a design this is known as dilation. To get the curvy or spiral patterns in the designs of the cornrows, rotations are used. Translations are used to determine the space between each completed braid and iteration.
Patterns can be seen in many aspects of nature and are included in the study of mathematics. Some of these patterns that are in nature can also be recreated by humans in the form of hair braiding. The connections between mathematics and the cultural practices of individuals are a part of a branch of mathematics known as ethnomathematics. By looking into ethnomathematics in this way allows for the educators to make connections to the lives of students to the mathematics that is used in the classroom. To understand ethnomathematics a person must go "into a community, examining its languages and values as well as its experience with mathematical ideasâ€¦" (Gilmer, 1997) .Once a person goes into an African American community they may see the "geometrical designs and patterns commonly used in hair braiding and weaving" (Gilmer, 1997).
In a study conducted by Gloria Gilmer (1997) she wanted to determine "what can the hair braiding enterprise contribute to mathematics education and conversely what can mathematics education contribute to the hair braiding enterprise?" (Gilmer, 1997). After interviewing several hair stylist and their customers, she realized that the "concept of tessellationsâ€¦ is widely used by the hair braiders and weavers but not thought of by them as being related to mathematics" (Gilmer, 1997). The methods used to divide the hair can be seen as tessellations of triangles and squares on the scalps of the customers. The method that was used to divide the hair determines the movement of the hair when braided.
Gilmer and others are trying to relate mathematics to the daily lives of students in a hope to make the mathematics more interesting. It was also mentioned that there was a subconscious efforts of White to make the cornrow styles symmetric. "Most hairstylists have no idea how much mathematics they are using" (Math, 2007). Some of the concepts used in the hair styles are algebra to determine how much false hair to add into weaves and hair extensions. Physics is used to attach hair weaves and of course the geometry is used in the design of the braids.
The shop was located in an urban area. Inside of the shop there were six stations. Each station had a swivel chair, a mirror, and a set of drawers with a small counter. There were also three stoles, that the workers would positions at the stations when they were working. They also had a couch in the front of the shop for customers to use when they arrived. In the back of the shop there were two shampoo bowls and a small wall dividing what appeared to be a break area. There was also a restroom in that area. The front of the store had glass windows. On the windows there were poster of women and men with braided hair designs. There was also a television with cable. The walls of the shop were painted a green color. On the walls there were a few posters of Africa and a painting with a flower design.
The shop was open seven days a week. The workers would come in as early as 7am and stay as late as 10 pm depending on what the customer was getting done. They would normally take their last customer at 7 pm. The doors of the shop were kept locked. (There were men that would walk into the shop and harass some of the customers was the reason for locking the doors.) . They also had synthetic and human hair for weaving which is different from braiding hair because the weaving hairs is bounded with a track that is used to sew or glue the hair into place.
This study used one female participant as a main focus. She was 29 and had no children. She had 4 brothers and she was the only girl besides her mother in her immediate family. Her mother was not able to braid hair. So her mother would send her to her aunts to get her hair braided to go to school. This was a requirement. Her hair must be neat and her clothes pressed as part of uniform inspection for her to attend school. Eventually she and her friends would braid each other hair for them to go to school. Many times hair braiding was used as a way to exchange gifts. She has been braiding for about 20 years but for 7 years in the United States. She came here to go to school and used her hair braiding techniques as a way to make money for college on a student visa. She stated that it was impossible for her parents to send her money for daily expenses that tuition did not cover and a family friend told her that she could braid hair for extra money.
The money was pretty good and she only had to pay the owner of the shop a set amount for the use of the chair each week. The amount would range from $100 to $150 a week. She would also have to pay for the hair so this would change the weekly amount to about $200 to$250 week. She considered this to be a good price and could bring home over $200 a week while working part time and still going to school. (She didn't state how much she made now or if she had to pay taxes on this income. Also she didn't state how she was able to stay in the country after her student visa ran out.)
Study design/ methods
During this study observation and interview techniques were utilized. During the majority of the visit the participant was observed without interruption and notes were taken on how business was conducted. During the middle of the time in the shop a conversational interviewing technique was used with a few directed questions. These questions were used to open the dialogue and allowed for the conversation to take a natural course. During the end of the time spent observations technique was used again to see how the transaction was finalized.
Data Collect Instrument:
Below are the leading questions that were used during the interview process. Not all questions were directly answered but this allowed for the conversation between the participant and interviewer to begin.
Questions asked during interview:
How long have you been braiding hair?
How did you learn to braid hair?
How do you know how much hair to use?
How do you intertwine the colored hair into the braid in such an intricate pattern?
Are you able to braid a specific number of braids?
Do you consider yourself to be good at mathematics?
This study was conducted on a Wednesday morning around 7am. An appointment was scheduled for cornrows to be done on that Saturday prior. The hair braider had a cell phone that she used to schedule her clients independent of the shop's phone. Observation was used to determine the procedures used in the hair braiding shop for the first hour. During the second hour questions were asked to spark a conversation. During the last hour observations were conducted.
During my visit to the salon there was only one worker there. She opened the door and asked me to take a seat. She then asked me how I wanted my hair to be braided (she has a bit of an accent). I told her that I wanted cornrows. She then showed me a book with pictures of braid styles. In the book they had many women styles. Many of the styles were very intricate. Some had braids that curved around the head and into a pony tail or some type of intricate design on the top. Others had multiple colors. Some had the braids braided all the way till the ends and other styles were left lose. Some of the braids were curly at the ends and others were straight.
Once I selected my styles I was told that I could have small, medium or large braids. I wasn't really sure of the differences in size so I asked for the price difference. The prices were $65 for the large, $85 for the medium, and $105 for the small. I selected the medium. She also asked me which color that I wanted I selected a combination of black and red synthetic hair. She also asked if I wanted two rows or one. I selected two. Then she began the hair braiding process. While braiding the hair she either stood up or used the stool.
She divided my hair into two parts by parting my hair horizontally. For the bottom portion of my hair she proceeded to braid the hair with 10 vertical braids. This took her about 30 minutes to complete. I realized that she did not add in the colors as I requested when she finished the bottom half. She apologized and said that she would add in the colors as requested in the top portions but did not redo the bottom half. She then began to complete the top portion of the hair. She began in the corner of my head near the ear. While she was braiding she talked to me a little about the news that was on and the way that the United States was always going into other countries saying that Muslim women were oppressed because they decided to cover their hair and bodies. She was very passionate about this discussion. She also talked to other workers as they arrived in another language.
I asked if she counted to know how many braids to do in that bottom sections she stated that she never really counted that part but in most cases it would range from 8 to 12 depending on the size and shape of the clients head. I asked how she was able to keep the hair from unraveling. She stated that she used a technique of making a small almost invisible knot with the hair. She also stated that in some instances clients wanted styles that would not fit their head. I asked what was meant by that and she stated that "the size and shape of a person's head and forehead including their hair line really determines what the style would look like on a client." She stated that "sometimes a client would come in with a picture and I would try to tell them that style wont look the same on them." Many clients would insists on this styles anyway and then be frustrated when they did not come out correctly.
I then asked how she was able to recreate styles from pictures. She said that she basically knew how many braids to do on each section of the hair and that she could simple look at a picture and recreate it. She thought of this ability as a gift not something that was taught but something that you were "blessed" with. She thought that "skills are education"; something that can be taught. She felt that a person could develop the skills to braid hair but that to really be able to do the intricate designs and patterns that she was able to create you had to be gifted. She thought of her skill as "natural". She felt like she was given this "gift from God" to have a service to exchange. She compared this ability to abilities such as sewing, gardening, and carpentry. She said that everyone in her country was given a gift so that they would be able to have a service to exchange to get the things they need. She felt like all of the gifts take "a lot of discipline" to be able to move beyond just a skill.
She also made some comments about being able to recognize the angles of the head to determine how a style would look on a client. She felt like she used a lot of mathematics in creating the designs but she did not do it consciously. She did have an idea of the number of braids that were in each section of a particular style but all of t this depended upon the size of the persons forehead, head and texture of their hair. She did recognize that hair braiding has many patterns.
Once she was done braiding my hair she went thru and "cleaned" the hair by cutting off the stray hairs with a scissors. When then trimmed the ends of the hair to make sure that the hair was even. Then she took the ends of the hair and dipped them into bowling hot water. She used a towel to dry the hair. Then she put mousse on the top of the hair to make sure that any strays would lay down. Then she sprayed the entire head with oil sheen. Then she gave me a mirror to examine her work close up and it was exactly what the picture looked like. In the end of the time there she collected the fee of $85 (I did make sure to give her a tip of $10).
It appears that the hairstylist knew a lot about mathematics and had made several connections but as she stated she was not aware of these mathematical connections. She was able to replicate a hair with only a glance which showed that she had a great memory and spatial sense. She seemed to have a pretty well defined procedure for braiding the hair and conducting business. It was evident in the intricate designs that she used lines and curves when braiding hair. She was also able to intertwine colors into the style. She did not pay much attention to the amount of hair that she was using to braid the hair but she felt that she was pretty consistent in the amount of hair that she used. It was also fairly interesting that she felt that she had a gift for hair braiding that could not have been taught, since there are several hair schools teaching those skills. It could have easy been assumed that the amount of time she spent braiding hair was directly correlated to her abilities in that area and I would assume that the styles that she is able to create now are not the same styles that she was able to create when she was younger. The mathematics that she used was everywhere. She used mathematics in the way that she divided the hair into two sections, in the selections of the amounts of hair to be used to add to each cornrows, in the number of plaits that she used before altering the colors and in making sure that the water was not too hot as to damage the hair of the client. So although the hairstylists may not be aware of the amount of mathematics she use, there is an abundance of mathematics used in the hair braiding process.
The correlation between geometry and hair braiding is very useful in the school setting. This information can be applied to almost any age group. The connections between mathematics and hairstyles are the type of connections that would bring mathematics to the everyday lives of the students. Hair braiding is something that many young people see in their day to day lives or are exposed to themselves as a part of their culture. Topics that could be used are as simple as lines or a complex as fractals. In either case the correlations are there for the students and teachers to explore.
It may also be of interest to let those that are hair braiders know how much mathematically skills they use in their daily work. This information would be of interest to them in a way to build confidence in their mathematical skills that could be transferred to their children. This may decrease the number of people who use mathematics everyday but do not believe that they are good in mathematics because of a school course in which they were not successful in.