Learning and Mathematics

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Classroom Conversation - Nicholls & Hazzard (1993)

In their book Education as Adventure, John Nicholls and Susan Hazzard explore students' understandings of the nature and point of school learning and the idea that students are valuable critics of the classroom curriculum and their own learning. The authors describe the events and experiences of a second grade class, taught by Hazzard and observed by Nicholls, which focused on incorporating students' initiative, collaborative efforts, and innate curiosity and enthusiasm into classroom situations and learning activities. The authors stress the importance of conversation in the classroom as a means of both inviting and responding to students' own thoughts about school learning and education. When students and teachers are involved in dialogue to define and understand learning, Nicholls and Hazzard believe that education becomes an exciting and meaningful journey of discovery.
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Source:

Nicholls, J. and Hazzard, S. (1993) Education as Adventure: Lessons from the Second Grade . New York: Teachers College Press.

Quotes and Comments:

"Few [researchers] contemplate students as collaborators in the formation of the means and ends of education.... Whether or not we acknowledge it, students are curriculum theorists and critics of schooling. If they are drawn into conversation about the purposes and practices of education, we may all learn useful lessons. Education can become an adventure in which teachers, researchers and children together learn new questions as well as answers, so that their lessons are never complete" (p. 8).

Nicholls and Hazzard point out that what may be labeled "trouble-making" or disruptive activity in the classroom involves students "creating activities which involve ingenuity, initiative, humor and social solidarity." In Hazzard's classroom, students asking "why" they had to do something or stopping classroom work to observe a spider weaving a web in the corner of the room was seen as a means of incorporating their enthusiasm for activities that might otherwise be considered disruptive in a classroom setting. The authors stress that the challenge facing schools today is "enlisting in the service of education the initiative, humor and collaborative verve of [students'] little rebellions" (pp. 3-8).

The authors believe that the "power of conversation" is one of the most important means of tapping students' enthusiasm and of harnessing students' intellectual energy and ideas for classroom learning. In Hazzard's classroom, discussions not only became the center of students' learning but the means of negotiating and understanding classroom practice. The authors recall class conversations about classroom rules, the first test, and the daily difficulties facing both students and teacher in the classroom. The emphasis on discussion began from the first day of class, when Hazzard asked her students what the purpose of learning might be, and was followed by important discussions about respecting others and cheating, all of which became the basis for classroom interaction throughout the school year (pp. 24-45).

When a classroom dialogue about the nature and point of what students are learning is created, and students are allowed to be the main participants in that conversation, students are able to bring their own energy, thoughts and initiative to classroom learning (pp. 86-92)

The authors stress that an essential part of this dialogue is establishing how learning will be defined and evaluated in the classroom. Learning is too often seen as a means to the end of grades and test scores, and evaluation focuses on superiority over fellow students. "When school is seen as a test, rather than an adventure in ideas, students can adopt this limited vision of fairness: teachers are fair, if they specify, in list-like fashion, exactly what must be learned to gain a satisfactory grade. With this implicit contract in place,... the result is schooling that is fair in the restricted sense that everyone knows how the teacher will evaluate them. It is, however, unexciting, unenlightening and irrelevant to the students' personal knowledge of the world.... Such schooling is unfair in the wider sense that it prepares students to pass other peoples' tests without strengthening their capacity to set their own assignments in collaboration with their fellows" (p. 77).

The authors believe that incorporating discussion about authentic, controversial topics into classroom learning is an essential part of making school and learning more interesting and exciting for students, as well as focusing students on discussion and individual understanding rather than grades and ability. For Nicholls and Hazzard, conversation about controversial topics is an essential part of learning: "to gain controversial knowledge is to adopt positions that others, including some who are experts, will not agree with. We define our ideas and values by engaging those of others, and in gaining controversial knowledge we define or constitute ourselves" (p. 180). In a study done by Nicholls it was found that most young children expected that if they studied controversial topics, such as the extinction of dinosaurs or freedom of speech, they would be more committed to school learning and take more initiative to participate meaningfully in the classroom. While the second grade may seem like a young age to begin discussing open-ended questions, the authors believe that "controversial topics strike no fear into these would-be scientists with licenses to guess and to travel in exciting mazes without end" (p. 147).

Links to math:

Several other authors whose work has appeared in the Learning and Mathematics Discussions present theories that can help link Nicholls and Hazzard's work to the specific area of mathematics.

Papert (1993) discusses the lack of language and dialogue in traditional mathematics instruction and believes that an essential component in the art of learning mathematics, what he calls 'mathetics', is open and free discussion of learning experiences in the math classroom. According to Papert, 'good discussion promotes learning' and is an inherent part of all intellectual discovery that cannot be disregarded by mathematics instruction (p.89).

Yackel, Cobb and Wood (1991) describe how incorporating problematic situations into mathematics instruction presents children with the challenge of resolving contradictions, accounting for outcomes, articulating their thought process and justifying solutions. The authors believe that making connections between mathematics instruction and real situations that are genuinely puzzling to students encourages students to construct their own solutions and share those solutions with others. This belief links to Nicholls and Hazzard's idea that discussing 'controversial topics' helps to make school learning more relevant to students and engages students in a discussion of diverse ideas.

Ball (1987) addresses the importance of 'intellectual honesty' between teachers and students in the math classroom. For Ball, this means giving students space and freedom to make sense of mathematics, ask questions, connect new experiences with their own knowledge, and listen to others' reasoning. She emphasizes the need for teachers to learn to hear, and carefully listen to, the things children care and think about in the classroom. Just as in Hazzard's classroom, establishing a community through conversation, attention, and response is a crucial part of both classroom learning and instruction.

The implication in these articles is that discussion of authentic and meaningful problems, classroom practices, and the learning process itself, among students and between teacher and students, is an essential part of promoting student interest, investment, and learning in the mathematics classroom.

References:

Ball, D.L. (1987). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal , 93 (4), 373-397.

Papert, S. (1993). The Children's Machine: Rethinking School in the Age of the Computer . New York: Basic Books.

Yackel, E., Cobb, P., & Wood, T. (1991). Small-group interactions as a source of learning opportunities in second- grade mathematics. Journal for Research in Mathematics Education , 22 (5), 390-408.

- summarized by Liza Ewen

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