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Authentic performance: Tasks for teachers. We wish to study teachers in
authentic tasks that include: (a) writing high quality instruction/assessment
activities aimed at authentic performance in mathematics; (b) evaluating the
scope and depth of clusters of authentic performance activities (to generate
instruction-relevant interpretations of the results that students produce); (c)
making insightful observations of students' behaviors during videotapes of
the preceding activities; (d) interpreting and evaluating students' responses
when multiple types and levels of correctness are possible; and (e) tutoring
students using concrete materials and nondirective questioning to mold and
shape their sense-making strategies during authentic performance activities.
RICHARD LESH AND ANTHONY E. KELLY
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3.3 Teaching Experiments
The teaching experiments that we emphasize can be characterized as longi-
tudinal development studies in conceptually rich environments (Lesh,
1983). They focus on "real-life" classroom experiences, such as those that
are involved when: (a) teachers use concrete materials to interview students
to identify specific conceptual strengths and weaknesses; (b) teachers ob-
serve groups of students as they work on complex project-based activities;
(c) teachers assess strengths and weaknesses of results that students produce
during realistically complex "authentic" performance activities; or (d) teach-
ers lead discussions and plan other instructional activities that focus on
deeper and higher-order understandings of elementary mathematical ideas
and processes. Thus, classroom activities for students provide contexts for
encouraging the development of teachers' knowledge, beliefs, and abilities.
Throughout the experiments, activities for instruction and assessment are
integrated: (a) Every assessment activity is designed to be a valuable learn-
ing experience for the individuals involved. Therefore, neither students nor
teachers are required to take time away from instruction-focused activities
to document key achievements and improving abilities; (b) Many activities
used for instruction enable the learner automatically to produce documenta-
tion to verify the kind of learning that has occurred; (c) Assessment activi-
ties are aimed at generating information to facilitate wise instructional deci-
sion-making by teachers, students, and others whose primary aims are to
encourage student development; (d) Assessment activities for students form
the basis for instructional activities for teachers. Examples of such activities
include: adapting existing project-based activities to focus on the "real-life"
experiences of targeted groups of students (e.g., young women, specific mi-
nority populations); making insightful observations during the preceding
classroom activities; or conducting follow-up interviews to diagnose the
strengths and weaknesses of individual students. All of the assessment ac-
tivities focus on "authentic performance" in the sense described in Lesh and
Lamon (1992).
The teaching experiments provide us with:
1. Insight about the nature of teachers' knowledge: The teaching experi-
ments enable us simultaneously to facilitate and investigate the development
of teachers' knowledge about: (a) the nature of mathematics, (b) the nature
of realistic problem-solving and decision-making situations in which math-
ematics is useful, and (c) the nature of "talents" that contribute to the pre-
ceding kinds of understandings and capabilities.
2. Knowledge and prototypes to clarify the nature of high-quality authen-
tic performance activities for students: Participating teachers develop
startup kits of field-tested authentic performance activities for students –
while helping us to clarify key characteristics of "excellence" in such activi-
ties.
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ACTION THEORY AND PHENOMENOLOGY

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3. Knowledge and prototypes to clarify the nature of high-quality authen-