剑桥学习科学手册英文版.pdf

Figure 5.1. A screen shot of a problem-solving activity within Cognitive Tutor Algebra. Students are
presented a problem situation and use various tools, like the Worksheet, Grapher, and Solver shown
here, to analyze and model the problem situation. As they work, “model tracing” is used to provide
just-in-time feedback or on-demand solution-sensitive hints through the Messages window. The
results of “knowledge tracing” are displayed in the skills chart in the top center.
activities to help students develop a deep
understanding of domain knowledge. In the
final section of the chapter, we describe
the learning sciences principles and meth-
ods that we have employed to address these
instructional design questions.
Cognitive Tutor Algebra: A Brief Example
A screen shot of a unit in Cognitive Tutor
Algebra is shown in Figure 5.1. Cognitive
Tutors tend to have relatively rich graphi-
cal user interfaces that provide a workspace
in which students can demonstrate a wide
variety of problem solving behavior. The
workspace changes as students progress
through units. The workspace in Figure 5.1
includes a problem scenario window in the
upperleftwherestudentsarepresentedwith
a problem situation, often with real facts
or data, that they are expected to analyze
and model using the tools in the workspace.
The tools illustrated in Figure 5.1 are the
Worksheet,Grapher,andSolver.Inthisunit,
the Worksheet has automated features like a
spreadsheet. Once students write the alge-
braic expression for the height “67+2.5T”
given the time, then the worksheet com-
putes a height value (e.g., 117) when a time
value is entered (e.g., 20). In earlier units,
the worksheet does not have these auto-
mated features, but is more like a table
representation on paper and students must
demonstrate they can perform the steps on
their own. Similarly, the Grapher and Solver
tools change as students advance through
tutor units. Initially these behave much like
blank pieces of paper where students do all
the work. Later these tools begin to auto-
mate lower level skills, like plotting points
or performing arithmetic, and let students
focus on acquiring higher-level concepts and
skills, like deciding which symbolic func-
tiontographorwhatalgebraicmanipulation
to perform. As students work, the Cogni-
tive Tutor monitors their performance and
64 the cambridge handbook of the learning sciences
may provide just-in-time feedback or on-
demand solution-sensitive hints in the hint
window. The Cognitive Tutor also monitors
studentlearning,anddisplaystheseresultsin
the Skills chart, shown in the top center of
Figure 5.1.
It is critical to consider the social context
ofuseofanytechnologyoreducationalinno-
vation, and Cognitive Tutors are no excep-
tion. We have tended to create complete
Cognitive Tutor courses whereby we apply
learning sciences theory to develop instruc-
tional materials, like consumable textbooks,
in addition to Cognitive Tutor software. Vir-
tually all schools using our mathematics
Cognitive Tutors also use the curriculum
and text materials. The typical procedure
is to spend two days a week in the com-
puter lab using the Cognitive Tutor soft-
ware and three days a week in the regu-
lar classroom using our text materials. In
the classroom, learning is active, student-
centered, and focused primarily on learn-
ing by doing. Teachers spend less time in
whole-grouplectureandmoretimefacilitat-
ingindividualandcooperativeproblemsolv-
ing and learning. In the classroom, students
often work together in collaborative groups
to solve problems similar to those presented
bythetutor.Teachersplayakeyroleinhelp-
ing students to make connections between
the computer tools and paper and pencil
techniques.
Learning Sciences Theory Behind
Cognitive Tutors
Cognitive Tutors are based on the ACT-R
theory of learning and performance
(Anderson & Lebiere, 1998). The theory
distinguishes between implicit performance
knowledge, called “procedural knowledge,”
and explicit verbal knowledge and visual
images, called “declarative knowledge.”
According to ACT-R, performance knowl-
edge can only be learned by doing, not by
listening or watching. In other words, it is
induced from constructive experiences – it
cannot be directly placed in our heads. Such
performance knowledge is represented in
the notation of if-then production rules
that associate internal goals or external