Learned Helplessness & Amber Hill

Boaler notes at the beginning of chapter 4, that although there were a few open-ended problems available to students at Amber Hill, “when students encountered these questions the teachers would normally close them down” (Boaler, 2002, p.25).  The teachers focused on mathematical work that involved short, procedural, closed questions, in which they would guide students through their mathematical decision making.  It seemed “the teachers thought students would not or could not” make mathematical decisions when solving problems (p.27).  Students were never given the opportunity to become their own mathematical thinkers and gain confidence in their abilities. 

When discussing the traditional approach to teaching at Amber Hill, Boaler mentions the concept of ‘learned helplessness.’  She makes reference to the fact “students were not encouraged to discuss alternative approaches to problems or try their own methods” (p. 28).  Diener and Dweck (1978) define learned helplessness as students who “do not make much effort to learn, do not persist when mathematics tasks become difficult, often refuse to try, avoid work wherever possible, engage in a variety of off-task behaviours, respond badly to failure, or simply give up”.  Boaler (2002) indicates that as a result of teachers providing an entirely structured learning environment, “the students did not learn to think” (p.27). 

Since many students at Amber Hill did not know how to think for themselves mathematically, they were lost when trying to approach open-end problems which required them to use their mathematical skills.  They had mathematical knowledge; however, they did not know how to apply it.  Students at Amber Hill thought “that mathematics [was] governed by rules and that problems should be able to be solved within a few minutes (McLeod, 1992). These beliefs have detrimental effects on students’ behaviours, particularly when they are confronted with problems for which there are no simple or quick solutions. The net result of these negative attitudes is that when students encounter difficulties in learning mathematics, many attribute their failure to their lack of mathematical ability and consequently decrease their efforts, engage in a variety of work avoidance strategies, or simply give up trying and opt out altogether” (Yates, 2009, p.87).

The teachers’ beliefs at Amber Hill were completely contradicted by their actions.  Although they thought it was important for students to be active in making mathematical decisions, they provided their students with a learning environment that allowed no choice, giving the students short, structured sets of mathematical procedures and problems.  Teachers “did not regard the teaching of procedures different from the development of sense making or understanding, and they did not perceive any need to teach anything other than their own standard or canonical methods” (Boaler, 2002, p.29). Teachers did not ask students to think about what they were learning or encourage them to discover methods to solve problems, but instead “chose to reiterate procedures and provide structure, rather than push for wider meaning” (p.29). This was severely problematic with regards to the development of students’ mathematical understanding.  Some effects of teachers’ methods of instruction are discussed in the latter chapters of the book.  Boaler notes it caused “them to develop a shallow, procedural kind of knowledge and perception that mathematics was all about learning and remembering rules and formulae” (p. 106).  

While reading this chapter I could not stop thinking about the ways in which the teachers at Amber Hill were inhibiting their students from gaining a real understanding and respect for mathematics.  Students did acquire mathematical knowledge; however, they had no understanding of how to use it unless it was explicitly stated.  Students could not combine their knowledge to develop a bank of mathematical concepts and methods they could use at any given time to solve a problem.



References:

Boaler, J.  (2002).  Experiencing School Mathematics.  New York: Routledge.

Diener, C. I., & Dweck, C. S. (1978). An analysis of learned helplessness: Continuous changes in performance, strategy, and achievement cognitions following failure.  Journal of Personality and Social Psychology, 36, 451-462.

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

Yates, S.  (2009).  Teacher Identification of Student Learned Helplessness in Mathematics.  Mathematics Education Research Journal, 21 (3), 86-106.