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
Learning and Mathematics
The Math Forum is a research and educational enterprise of the Drexel School of Education.