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This study examines the mathematics behind hair weaving. The observation is conducted in a small salon in Decatur, Georgia. The stylist uses math on a daily basis. The scope of the mathematics in this study is only focused on a small aspect that occurs daily in a salon. The mathematics that is involved includes: fractals, transformation, circumference, counting, estimation, prediction, measurement, ratios, angles, and addition. In addition, the study demonstrates the importance of using culture in the classroom, and literature that has successfully implemented activities involving hair braiding and other African contributions.
Context of the Study
Integrating culture into classrooms is very important. One practice that is common in the African American culture is hair braiding and hair weaving, where hair braiding is a very important step in the hair weaving process. These particular styles are evident in all classrooms across the nation. Since the hairstyles are prevalent in schools, linking hair weaving to curriculums will motivate the students (Gilmer, 2004). The students can serve as models. Making the students a part of the lesson will foster peer interaction and build self esteem (Gilmer, 2004). In addition, hair weaving will provide a connection to history. This connection will provide the opportunity to learn mathematics in a contextual form that African American students are familiar with. In addition, since hair braiding and hair weaves are a current fashion trend, this trend can introduce the historical contributions of the African culture to students as well, redesigning the current delivery of mathematical instruction (Weiger, 2000). The investigative procedures involved in using conceptual mathematics will strengthen the African American student's critical thinking, problem solving, and communication skills because the students are using and discussing the mathematics.
Through the literate review and the analysis of data, the following questions will be answered at the end of this ethnographic study :
What is the relationship between hair weaving (sew- in) and mathematics?
How do you utilize the historical fashion contributions of ancient Africans to prompt motivation amongst African American youth?
How do you use the culture of hair to motivate African American youths?
Why is it important to integrate culture and education?
How do you identify the mathematical concepts in hair braiding and hair weaving?
Concise Literature Review
African Americans take pride in their hair and their appearance. This is evident in the billion dollar hair industry with women, men and children contributing to the profits (Chris Rock's Good Hair, 2009). The billion dollar industry contains weaves, hair care products, and hair care tools. African American women can spend thousands of dollars on one weave session. Since so much emphasis is placed on hair, the research of classroom usage by Gloria Gilmer (1998) is important to African Americans. During Gloria Gilmer's investigating into hair styles of African American women, geometric designs and patterns were discovered in the braiding process (Gilmer, 1998). After further investigation, the concepts of tessellations were identified in the braiding patterns of the participants. The tessellations were easily visible in the photographs provided in the study. Another researcher connected the patterns of hair braiding to the transformations also (Eglash, 2004). On the website provide by Ron Eglash cornrow braids translate, reflect, rotate, and dilate y patterns in which the y resembles a braid stitch (2004). Pamela Frost discovered that African fractals are not limited to hair braiding, but can be extended to compute graphics, genetics, and biology (1999).
Since hair braiding contains common taught mathematical concepts, implementing the concepts is an easy task. Teachers do not have to purchase additional products to implement the concept, since paper and pencils can be utilized to investigate fractals. It is noted that "students can still learn about fractals using common school supplies" (Frost, 1999). Teachers do not have to research a lot of information about hair braiding and hair weaving. African American students come with prior knowledge about hair braiding and hair weaving, linking their prior knowledge to geometry and fractals can assist in "constructing their own identities" (Frost, 1999). Also teachers can be provided with pre-written activities about the connection of hair braiding and mathematics (Frost, 1999).
An important aspect of using hair braiding in the classroom is to aid in the development of African American students and other minorities. It has been noted that Ethnomathematics such as patterns in hair braiding "respond to the needs of increasing numbers of students who feel like failures for not understanding" (Gilmer, 2004). African American students will experience small success by contributing information that they are familiar with. In the current educational systems mathematics is used to boost test scores, so student can achieve a certain status (Gilmer, 2004). Often in this process minority students are left behind in mathematics. In other to level the playing field in mathematics, using Ethnomathematics that involves cultural concepts such as hair braiding and hair weaving will give the students the power to "discern and investigate" which engages students (Gilmer, 2004). Student engagement assists with processing information into memory (Woolfolk, 2004). With engagement, comes learning. African American students will have the opportunity to learn mathematics and transfer the learning to tests and other learning activities (Gilmer, 2004).
This assignment provided an opportunity to observe an African American stylist with over eighteen years of experience in the cosmetology business. The stylist works in a small upscale salon with two other stylists. The observed stylist received her training from a local cosmetology school and a business degree from Bowie State University in Maryland. The stylist stated her craft was mastered through on the job training and that school only prepared her with the theory.
The client is a professional educator that receives hair weaves every six to eight weeks. The client has chemically damaged hair and receives hair weaves to relieve the everyday stress on her hair. Permission was given to only record the back of the head.
Since hair is a part of the African American culture, an ethnographic approach was taken. Culture cannot be examined with creating a hypothesis, formal testing, and statistical analysis of data.
Data Collection Instruments:
During the study, a FLIP video camera was used to record snippets of the hair weaving process. In addition, notes were written to record the atmosphere, the conversations, and the actions of the stylist. An informal interview was used to gain knowledge about the client and the stylist techniques.
Initial Entry: In order to complete this study, assistance from the stylist was requested during a weekly salon visit. During the solicitation, the stylist was given a copy of the project requirements and a brief explanation about the videotaping. The stylist was concerned with the publication of the recorded techniques. She was assured that the technique was for a class project with no public viewings. The stylist agreed and requested a copy of the video once the project was completed.
Data Collection: The researcher began the observation process around nine thirty a.m. The observation process consisted of notes, informal interviews and videotaping. The researcher became an active part of the process by assisting with the threading of the needles. In addition, the researcher interacted with all the other stylists and clients by providing information about the study and participating in the gossip in the salon.
Data Analysis & Synthesis
In examining the data received during the observation, several mathematical operations were revealed. The first mathematical concept that was revealed was fractals. Fractals are defined as the geometric patterns that are repeated, which include dilations (Frost, 1999). In hair weaving, the first process is hair braiding. The stylist sections off small parts of the hair, and then braid the hair. The braids consist of repeated patterns that resemble a "v". The braid begins small towards the edge of the hair and gets larger as the braid reaches the crown of the heard.
The next mathematical concept that was revealed is transformations which include translations and vertical reflections. As mentioned before, the braids resemble several small v's. The translation occurs when the shape of the v travels towards the crown of the head. The shape of the v's is very close together so the braids are tight. This tightness assists with the hair weave lasting eight weeks. Another transformation that is present is a vertical reflection. The stylist begins with a braid on the right side of the heard and ends at the crown of the head. She then begins with the left side of the head and ends at the same spot. The braids on each side of the head are exact opposite of each other. The reflection line is in the center of the head. The vertical refection ends at the middle of the ears.
In addition, the mathematical concept of counting was revealed. In several instances, the stylist was observed counting the number of braids on the client's head. She stated it was important to have the same quantity of braids on both sides of the head. In addition, the stylist the stylist was observed counting the number of weave tracks as she connected the weave.
Another mathematical concept that was observed during the hair weaving process involves measurement and estimation. The stylist used estimation to measure the length of the weaving thread. She removed thread from the spool and used the length of her forearm to determine the length. This process continued until the hair weave was completed. In addition, the stylist estimates the quantity of hair and the price of the service. It was revealed that a prior conversation occurred between the client and the stylist. The client shows the stylist a picture and the stylist determines the quantity of hair that is needed. This estimation is important because they stylist do not want the client to purchase excess hair.
The next mathematical concept observed is arc length. Since the measurement of the head utilizes circumference, which is the length of the outermost edge of a circle. The braids that travel from right to left could be considered to be individual circles. The stylist is estimating the length of the weave tracks to attach to the 'arcs" of the imaginary circles, which is the formal mathematical term called arc length.
Another mathematical concept that is utilized is ratios. The stylist discussed the process of adding color to the hair weave. The client purchases a small bundle of colored weave. Next, the stylist uses a razor to split the weave track. Finally, the stylist combines the color weave track to the black track. In addition, the stylist utilized ratios in the process when she mixed the hair dye for another color. The stylist did reveal that sometimes hair weave clients receive color to mask the gray hairs. This particular client did not receive hair color.
After all of the tracks were attached to the head, the stylist used angles to cut the hair. The stylist stated she was using forty-five degree angles. It was difficult to determine the exact measurement of the angles since the stylist cut the hair rapidly. Using forty five degree angles to cut hair is a concept that the stylist learned in beauty school. During the entire process of attaching the weave track to the braids, the stylist created knots to ensure the thread did not detached. Also in the initial threading process, knots were tied at the end of the string as well. The type of knot was not determined.
The final mathematical concept that was revealed was addition and subtraction. The stylist used mental addition to compute the cost of the hair weave service. Once the client paid for the service, the stylist provided change. There was not any evidence of counting change to the client.
Listing the possibilities of mathematics being used in the world is nearly impossible. Mathematics is used in many forms of life such as restaurants, construction, car dealerships, and malls. This usage of mathematics keeps systems in place working. Since mathematics is evident in the lives of students, it is recommended to relate practical experiences such as hair weaving to the curriculum that students must learn. This relationship would make mathematics relevant to the world of students. In addition, providing this experience will experience students to possible careers that they may have had little knowledge about. Learning mathematics through practical experiences will give student the opportunity to learn why and how mathematics is used. This form of learning supports the constructivist theory, where learning is student centered and not teacher centered (Woolfolk, 2004). Another recommendation to using practical experiences such as hair weaving will give the opportunity for students to learn using cross curricular activities. Since hair weaving involves chemicals, designs, and hair, students will have the opportunity to learn chemistry, art and biology in context. Observing and interviewing a stylist will give a student the opportunity to witness the results of chemical process on the hair, to integrate art and fashion, and to learn how the body develops skin, and the proper nutrition to maintain healthy skin. Also it is recommended to give the students the opportunity to learn by doing. The hands on learning experience will promote motivation. Motivation amongst African American students in mathematics is declining (Gilmer, 2004). Using a practice that is familiar to students can provide a gateway to participation in the class. The students will be a part of the class, removing the phobia of failure, resulting in confidence in mathematics (Woolfolk, 2004). This confidence will motivate the student to continue to learn mathematics since the fear of not knowing is removed. It is also recommended that teachers create problem based learning cases using the concepts that relates to culture such as hair weaving. The cases would promote inquiry about the different culture and give answers as to why a particular culture practices certain routines. This window into the lives of others will help the students to understand and appreciate the cultures of others. The inquiry process in the problem based learning will give the students choices about the methods of acquiring knowledge and how important the information is to their personal situation. The learning is navigated by the students with teacher guidance, instead of driven by teacher input only. In addition, the students will have the opportunity to research and participate in instructional conservations from the research about the different cultures. The instructional conversations would promote unity and assist in teaching diversity amongst the students and the teachers.