Research has shown that students’ beliefs about their own intelligence have a large effect on their behavior in the classroom (Dweck, 1986). In a prior study of low-achieving urban students, I found that students’ who had positive beliefs about themselves as doers of mathematics, showed persistence with challenging problems, whereas those who held negative beliefs, failed to seriously engage in problem solving (2010). Correspondingly, research has found that students’ ability to solve problems is one of the greatest deficits in U.S. students’ mathematical learning (NRC, 2001). This obstacle becomes even more apparent in underachieving urban classrooms.

These findings call for research on the methods teachers in underachieving urban classrooms can use to influence students’ beliefs in ways that support their problem solving engagement and success. This paper reports findings from a case study of one teacher in an urban middle school mathematics classroom implementing pedagogical moves that successfully influenced low-achieving students’ beliefs about their own intelligence and motivated them to engage with challenging mathematics.

Dweck’s (1986) theory on student beliefs of intelligence contends that teachers can influence students’ motivational patterns in ways that affect their persistence on challenging problems. Students who believe their intelligence is malleable, Dweck says, develop learning goals that influence them to choose more challenging tasks that foster learning. Contrastingly, students who believe their intelligence is fixed develop performance goals that hamper their persistence when faced with challenges because in order to tackle a challenge, they must already perceive their ability to be high. Thus, when teachers incorporate challenges within a learning-oriented context where students are praised for effort as opposed to intelligence, students are likely to develop more adaptive motivational patterns (Dweck, 1986).

Given that in traditional mathematics classrooms being smart means getting the right answer, influencing low-achieving students’ beliefs about their malleable intelligence requires broadening what it means to be smart in mathematics. One pedagogical approach developed by Cohen and colleagues (1999), complex instruction (CI), aims to address the multiple ways students are competent in order to increase engagement. In CI, teachers publically recognize the wide range of intellectual skills that are valued and pertinent to the classroom, and publically assign competence by recognizing students’ intellectual contributions (Cohen, 1999). This method has been shown to increase students’ participation and thus, their learning (Cohen, 1999).

The data for this paper come from a classroom where the teacher, Ms. M, implemented instructional methods that merged and built upon these two existing theories for influencing students’ beliefs. Ms. M began with the pedagogical goal of helping students experience themselves as smart in mathematics. Consistent with Dweck’s theory, Ms. M reasoned that if students believe they can increase their intelligence through hard work, they will have more sustained engagement in challenging problem solving tasks. Creating these opportunities to engage with challenging content will thus result in greater learning. The students in the study were all rising 8^th graders with a history of low-achievement enrolled in a five-week summer school mathematics course, in which the primary curricular materials were challenging problem-solving tasks. In light of the teacher’s goals, this paper addresses the following research questions:

1. In what ways did Ms. M provide opportunities for students to feel smart?
2. How did these opportunities result in more sustained engagement on challenging problem-solving tasks?
3. In what ways did this engagement lead to increased learning outcomes?

To capture teacher pedagogical moves and student engagement, field notes and video recordings were collected each day, including pre-lesson and post-lesson teacher interviews. Students were administered pre- and post-assessments at the beginning and end of the program in order to assess learning. To provide additional evidence of student beliefs and engagement as a result of the course, three focal students were interviewed during the last week about their self-efficacy and experience with mathematics both prior to and as a result of the course.

Current analysis of these data includes identifying and characterizing evidence of Ms. M’s affordances for making students feel smart, and of students’ increased engagement in challenging mathematics over time. From this analysis, I draw direct connections between these opportunities and students’ behavior at the level of mechanism and of broader long-term effects, and relate these findings to evidence of increased student learning.

Ms. M’s goal for students’ beliefs of their intelligence became particularly relevant when pre-assessment data showed all twenty students entered the course below grade level, and observations from the first few days showed evidence of early disengagement when faced with challenges. Analysis of Ms. M’s pedagogical moves reveals that, like in CI, she provided many opportunities for the students to feel smart. Most explicitly, Ms. M shared a quotation from Dweck's Mindset (2006) each week, and engaged students in relating the quotes to their own experiences as learners. Similar affordances were made when she and the students co-constructed the notion “tigering-up” when faced with challenging problems, encouraging the idea that students can increase their intelligence by working hard. Additionally, she consistently intentionally assigned competence to low-status students by crediting them for their contributions when solving challenging tasks. Analysis also shows evidence of student engagement on challenging tasks in direct response to these affordances, with increasingly more engagement over time. Accordingly, initial assessment data show an increase in student performance from pre- to post-test, even though the teacher did not specifically teach the mathematical concepts assessed.

These initial findings illustrate a successful case of a teacher in an underachieving urban classroom influencing students’ beliefs about their intelligence in ways that support their problem solving engagement and success. This presentation will provide detailed qualitative analysis of this classroom to elaborate on the mechanisms by which this process occurred, and hypothesize how these conclusions could be applied more broadly.

References 

Cohen, E., Lotan, A., Scarloss, B., Arellano, A. (1999). Complex Instruction: Equity in Cooperative Learning Classrooms. Theory into Practice, 38, 2, 80–86.

Dweck, C. (1986). Motivational Processes Affecting Learning. American Psychologist 41, 10, 1040–1048.

National Research Council. (2001). “Adding it up: helping children learn mathematics.” Washington, DC: National Academy Press.