V.5 #1 Mathematics - Understanding Students’ Mathematics Identities: Setting the Stage for Positive

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Mathematics. The mere mention of the word conjures up an array of affective images and responses from students and teachers alike. There are those mathematics aficionados who embrace the subject and approach it with confidence, those on the opposite spectrum who suffer from mathematics anxiety or phobia and shy away from tasks related to this subject or avoid them altogether, to an array of mathematics dispositions in between. Think about where you may fall along the spectrum and how you may have arrived there. Chances are that experiences in your formative years, notably prior school experiences, impacted your mathematics identity—your beliefs about yourself in relation to mathematics.

The Social Context of Mathematics Beliefs

In mathematics education research, it is well documented that beliefs about mathematics are formed as a result of social influences. Theorists generally agree that beliefs are created early in one’s life through a process of enculturation, social construction, and cultural transmission (Pajares, 1992; Seaman, Szydlik, Szydlik, & Beam, 2005). Beliefs are the product of upbringing, reflection of life experiences, and the result of socialization processes in schools (Raths, 2001) which includes the influence of other significant people in that environment (e.g., teachers, peers, and parents), cultural and personal values placed on the learning, and learner-related affective as well as cognitive variables (Leder, 1992).

Although family and culture do play a critical role in influencing beliefs about mathematics, the greatest factor shaping these beliefs appears to be accumulated prior school experiences. Mathematics classrooms are social settings. The social context enables or inhibits what is learned, how it is learned, and which students learn it. It is all too common to hear students say that they do not like mathematics, are not good at it, or just cannot do it. How often is the same said about English Language Arts? It appears to be more readily, even socially, acceptable to not like or be good at mathematics because in the United States there is a tendency to believe that learning mathematics is a question more of ability than effort (Lewin, 2008; McLeod, 1992). Consequently, we are more accepting of poorer performance in mathematics than other subjects. However, this attitude is problematic because it can genuinely hinder students in the future as they go through school and assume careers; it can result in having life-long negative mathematics identities.

Understanding Students’ Mathematics Identities

In order to avoid perpetuating cycles of negative mathematics affect, what can teachers do to potentially set students on positive mathematics journeys? With every school year, teachers have probably given a lot of thought to setting up the physical layout of the classroom and the scope and sequence of the curriculum, but what about building a community of mathematics learners? Given the educational climate of accountability, it would behoove teachers to get to know their students as mathematical beings. Having some sense of their beliefs about themselves in relation to mathematics at the start of each school year can help guide teachers’ practices. Below are some suggestions for formative assessments for how teachers can learn more about their students as mathematical beings at the onset of the school year.

• Grades K-2. Begin with a simple sentence starter in which students can write their responses in a mathematics journal. This prompt might take the form of “I like mathematics because_______.” or “I don’t like mathematics because______.” Given the nascent writing stages of early elementary school students, keep the prompt short and only expect a response of a sentence or two. Those students with pronounced writing difficulties can dictate their responses for someone else to scribe or can even draw a picture to communicate. It is just important that students somehow reveal their mathematics beliefs in a manner which is comfortable to them.

• Grades 3-5. As students’ writing becomes more developed, ask them to write a paragraph or a few paragraphs on “How do you feel about yourself when it comes to mathematics? Please describe.” Perhaps this could be done during a Writers’ Workshop time. Keep the prompt relatively open-ended so that students can respond in a style which is comfortable to them. Stress that you are not grading or judging them, but just want to learn more about them.

• Grades 6-12. As a homework assignment, you can ask students to write mathematics autobiographies in which they respond to the following questions: “What is mathematics? What is your relationship with mathematics? Who or what are your greatest influences on your beliefs about mathematics?” Make sure students use pseudonyms for any real names they might mention particularly when talking about their influences.

The aforementioned suggestions are meant to simulate thinking about students as mathematical beings and is not an exhaustive list by any means. These formative assessments can certainly take other forms, and not necessarily traditional writing assignments. Maybe teachers want to have students write poems, make collages of mathematics images they find on the internet, or act out their beliefs. Whatever form works best in the classroom will depend on the student population. It is just important to get to know students as mathematical beings as early in the year as possible.

The Impact of Students’ Mathematics Identities on Classroom Practices

Once students respond to whatever prompts are used, a teacher will have a good indication of students’ mathematics identities from their perspective. Armed with this critical information, a teacher can then see who to give extra attention/support to or who to provide extra challenges to foster a continued love of mathematics. Save the assessments and repeat the prompts toward the end of the year to see if any changes in mathematics identities have occurred. Provide time for mathematical discourse as to why any changes may have occurred.

In re-reading my own students’ mathematics autobiographies which I have them write at the onset of every semester of my childhood mathematics methods courses, it is amazing how my undergraduate and graduate preservice teachers can pinpoint the time in their life when they began to like/dislike mathematics and the influences on these beliefs. Most often it was a specific teacher who shaped these beliefs. Teachers really do make a difference and have the power to shape students’ mathematic identities. Set your students on more positive journeys by taking the time to get to know them mathematically, encouraging mathematical discourse, and building a community of mathematics learners.

References

Leder, G. C. (1992). Mathematics and gender: Changing perspectives. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 597-622). New York, NY: Macmillan.

Lewin, T. (2008, March 14). Report urges changes in teaching math. The New York Times. Retrieved, March 29, 2008, from

http://www.nytimes.com/2008/03/14/education/14math.html?

_r=1&ex=1206158400&en=29d06356d9d8bb4f&ei=5070&emc=eta1&oref=slogin

McLeod, D. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575-596). New York, NY: Macmillan.

Pajares, M. F. (1992). Teacher's beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(3), 307-332.

Raths, J. (2001). Teachers' beliefs and teaching beliefs. Early Childhood Research & Practice, 3(1), 1-10.

Seaman, C. E., Szydilk, J. E., Szydilk, S. D., & Beam, J. E. (2005). A comparison of preservice elementary teachers' beliefs about mathematics and teaching mathematics: 1968-1998. School Science and Mathematics, 105(4), 197-210.

Joan Gujarati, Ed.D., is an Assistant Professor in the Department of Curriculum and Instruction at Manhattanville College in Purchase, New York where she teaches the childhood mathematics methods courses. She is a former elementary school teacher and Math Teacher Leader. Dr. Gujarati’s research interests include early childhood and elementary mathematics education, teacher beliefs and identity, teacher quality, effectiveness, and retention, and curriculum development. Dr. Gujarati can be reached at Joan.Gujarati@mville.edu