As mathematics teachers we have a language all our own. First there is the mathematics vocabulary: pi, perimeter, area, table, mean, etc. Then there is the mathematics education/teaching vocabulary: manipulatives, representations, lesson launch, closure, equity, opportunity to learn, diversity, etc. A new term of importance to add to our dictionary is mathematical identity. In this brief primer we will look at what the term means, why the concept is important in mathematics, and how we can influence identity in the classroom.

**What is mathematical identity? **

**Â Â Â Â **â€śIâ€™m just not that good at math.â€ť

â€śEveryone thinks Iâ€™m dumb in math.â€ť

â€śIâ€™m good at fractions.â€ť

â€śMath is hard.â€ť

â€śI like solving problems.â€ť

We have all heard these or similar phrases in our classrooms from students who feel good about themselves in math and others who do not. These phrases give us a glimpse at each studentâ€™s identity in mathematics. While many definitions of identity exist, one that relates closest to classroom practice is my favorite, adapted from Bishop (2012): Identity is a personâ€™s changing view of him/herself in a given social context influenced by their experiences, personal history, and other events. Studentsâ€™ mathematical identity is how and who they see themselves as in the mathematics classroom, in their relationship with the subject of mathematics and mathematical activities. Examples of history and events that can affect identity vary widely.

Two examples include:

- A student who repeatedly receives poor grades in mathematics can feel defeated and think, â€śI am just not good at math.â€ť
- When students who are more mathematically enthusiastic repeatedly dismiss or ignore input from another student, those episodes can translate into an identity that says, â€śMy ideas in math are not worthwhile.â€ť

A studentâ€™s mathematical identity shows itself not only through what they say, but by how they act and position themselves in mathematical situations. For example, a quiet student who is reluctant to take part in group problem-solving activities sends us a different message about his mathematical identity than the quiet student who shows great enthusiasm for such activities.

**Why is mathematical identity important?**

There is a positive link between attitudes about mathematics and mathematics achievement (Ma and Kishor, 1997; Ma, 1999; Schoenfeld, 1989). We can see evidence of this in our own classrooms where students who engage in mathematical activities are more successful. A positive mathematical identity is a major goal for any mathematics programs. NCTMâ€™s goal of students becoming active problem solvers who willing to engage in productive struggle and who value mathematics are traits of positive mathematical identities.

Identity goes beyond attitudes about ability for and disposition about mathematics. Students pick up ideas about mathematics from the way we teach, which can have far-reaching implications. For example, Schoenfeld (1989) found that in traditional classrooms where teachers lecture, demonstrate, and then give students assignments where they repeat what they were just shown how to do, students develop a sense that mathematics is a repetitive exercise where they memorize and apply formulas. Even students who think they are good at mathematics are influenced by these experiences. If the students broadly identify themselves as people who want to be problem solvers and have engaging careers, they will not select mathematically dominant fields because they perceive mathematics as non-challenging.

**How can we influence mathematical identity in the classroom?**

Now that we know what mathematical identity involves, and why it is important to have positive identities, there is a wide variety of ways a teacher can influence those identities. Here are 4 suggestions:

**Model positive discourse.**

As the teacher you can set the climate for an environment where discourse is encouraged and student ideas are heard and discussed in a respectful manner. Value student input. Praise positive interactions of student to student discourse. If necessary, model or role play positive interactions that include listening skills and giving feedback respectfully.

**Get to know your studentsâ€™ identities.**

Watch for verbal as well as non-verbal clues. If you vary your classroom teaching format you can observe students in small groups, pairs, cooperative groups, games, whole group discussions, and one-on-one. Students act/react differently in different groupings and reveal more about themselves. If it is helpful and possible, check on a studentâ€™s past history in mathematics classes through grades and talks with prior teachers. You may need to interrupt a cycle of bad experiences in mathematics.

**Help all students to be successful.**

Make use of formative assessment so that you know how students are progressing. You can identify student misconceptions early and prevent them from holding students back. Use tasks that have multiple entry levels so that all students can access the work at their own comfort and ability level. Vary classroom format. Whole group and teams work but sometimes it is necessary to switch the format so that individuals who need one-on-one or small group intervention can get it before they continually fail at a given topic.

**Engage all students.**

In a classroom where students are engaged in doing mathematics, they can make discoveries, test ideas, solve problems and work like mathematicians. This affects how students see mathematics as a discipline. Mathematics goes from being a boring and repetitive activity, from being â€śhardâ€ť to being â€śchallengingâ€ť and â€śsomething I can figure out.â€ť This factor can have lifelong implications for someone whose broader identity includes, â€śI like challengesâ€ť or â€śI need to be involved in solving problems in my work.â€ť

In summary, mathematical identity is a personâ€™s ever changing view of him/herself in a mathematical context such as a classroom influenced by their experiences, personal history, and other events. It is important that we pay attention to the mathematical identities of our students because 1) identity affects student success; 2) Positive identity traits are part of the goals for mathematics programs; and 3) mathematical identity influences life-long decision making. You hold the key to shaping your studentsâ€™ mathematical identities.

**Â ****References**

Bishop, J. (2012). â€śSheâ€™s always been the smart one. Iâ€™ve always been the dumb oneâ€ť: Identities in the mathematics classroom. *Journal for Research in Mathematics Education, 43*(1), 34â€“74.

Boaler, J. (2002). The development of disciplinary relationships: Knowledge, practice and identity in mathematics classrooms. *For the Learning of Mathematics, 22*(1), 42â€“47.

Ma, X., & Kishor, N. (1997). Assessing the relationship between attitude toward mathematics and achievement in mathematics: A meta-analysis. Journal for Research in Mathematics Education, 28, 26â€“47.

Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30, 520â€“240.

National Council of Teachers of Mathematics. Principles and Standards for School Mathematics, 2000. NCTM, Reston, VA.

Schoenfeld, A. H. (1989). Explorations of studentsâ€™ mathematical beliefs and behavior. Journal for Research in Mathematics Education, 20, 338â€“355.