# Promoting Mathematical Agency

The behavioral aspect of mathematical identity, i.e., the ability of students to see themselves as mathematical problem solvers and to participate in mathematical problem-solving, is referred to as “mathematical agency” (Aguirre et al., 2013). Learners either use procedural knowledge in problemsolving or thought processes to understand procedures conceptually. The former is called a disciplinary agency and the latter is called a conceptual agency (Gresalfi, Martin, Hand, & Greena, 2009). A mathematical agency can be used by students while working individually or working with classmates. Teachers must create opportunities inside and outside the classroom to assist students to develop their own mathematical agency. Aguirre and colleagues (2013) discuss that mathematical agency can also be *collective *when teachers and their students in a classroom are engaged in mathematical problem-solving. A collective mathematical agency can come in a variety of forms—some students can bring initial thoughts to solve a problem, some can bring strategies to solve the problem, some can engage in conversation about the problem in small groups and later feel comfortable contributing to the whole-class discussion, and some can ask clarifying questions in their small groups or during whole-class discussions (Aguirre et al., 2013). During this process, children must be comfortable sharing their developing ideas. Therefore, teachers must provide a safe space so children can feel welcomed to share ideas, reason, and argue professionally with each other. A positive mathematical agency fosters a positive identity in children and through proper teaching practices, teachers can help children to develop as competent problem solvers.

Box 5.4 Promoting Social and Emotional Competence

**Strategies to Promote Collective Mathematical Agency**

Below are some strategies that teachers can use in the classroom to promote collective mathematical agency:

Strategy 1: Establish classroom norms to create a safe space for everyone to participate and communicate respectfully with one another (Aguirre et al.,

2013).

Strategy 2: Allow students to work in small groups to express themselves.

Strategy 3: Teach children to argue and reason professionally using statements such as *I agree with* ...; *Because I disagree with* ...; *Can you restate that for me?, *etc.

Strategy 4: Allow thinking time before letting students do group work.

Strategy 5: Create group norms for active participation and involve children in creating their own group norms as well.

Strategy 6: Assign talk times to each member of the group.

Strategy 7: Assign roles for each member of the group; one student can be the scriber, one student can be the spokesperson for the group, one student can restate the problems and the strategies discussed in the whole group, and one student can be the translator for English as a second language learners (Aguirre et al., 2013).

Strategy 8: Teach students to listen to mathematical arguments.

Strategy 9: Promote positive support and collaboration among peers.

**Strategy 10: Allow students’ mistakes for a richer discussion in the classroom.**

# Fostering Mathematical Problem Solving

Parents and teachers can teach children, from a very early age, appropriate problem-solving strategies so that children grow with the skills needed for making appropriate decisions, and can reason with valid and logical arguments. Also, children’s development of mathematical understanding and skills can benefit from social interactions between peers as well as with the teacher in the classroom. Walker and Henderson (2012) argue that social interactions are very important for children’s academic and social experiences. Children learn to think and apply their experiences and build new knowledge in the process.

Infants and young children acquire knowledge through their senses (Rowan & Bourne, 2001), then they progress through hands-on learning experiences and apply prior knowledge. Mathematical problem-solving is key to promoting such learning experiences in early childhood ( Lopes, Grando, & D’Ambrosio, 2017). Mathematical problem-solving involves understanding the problem, planning, devising a plan, and making sense of the solution in the context of the problem (Polya, 1957). Teachers can use games and various classroom activities to develop children’s mathematical problem-solving skills. Playful conditions help develop children’s metacognitive and self-regulatory skills, which is critical for children’s development of academic skills (Whitebread, Coltman, Jameson, & Lander, 2009).

Schwartz (2013) discusses six major contexts that promote mathematical problem-solving during children’s developmental period. These contexts include channeling children’s intuition towards formal mathematics as they follow their interests and promote curiosity about a problem. For example, a teacher can ask a child, who is drawing a square roof of a house, “is there a reason you chose a square over a triangle roof?" This question guides children to think about the features of the shapes and brings more consciousness to their choices and properties of shapes (Schwartz, 2013). The other contexts involve engaging children in planning playful activities, creating real models or crafts, or engaging them in realistic projects.

In summary, choosing activities or tasks that spark curiosity and interest and that guide children from informal intuitions to understanding formal mathematics can help children to be competent mathematical problem solvers, and thereby can promote positive mathematical identity and mathematical agency.

Putting it into Practice

*Reflection'.* Genevi should believe in her own abilities to learn and teach mathematics. She needs to start thinking of herself as a mathematical problem solver and promote the idea of growth mindsets to her students. Genevi needs to tell her students about the importance of mathematics in the real world. She must pick activities or tasks that engage students and make them curious to learn more. She can involve students in planning for events so that they can take responsibility and learn by doing. She should develop a classroom environment that encourages thinking rather than quick mathematical calculations.