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Instructional
Design
The manner in which
students encounter mathematical ideas can contribute significantly
to
the quality of their learning and the depth of their understanding. Core-Plus
Mathematics units
are designed around multi-day lessons centered on big ideas. Lessons
are organized around cycles of instructional
activities intended primarily for small-group work in the classroom and
for individual work outside of the classroom.
In-Class Activities
| The
four-phase cycle of classroom activities,
is designed
to actively engage students in investigating and making sense of
problem situations, in constructing important mathematical concepts
and methods, in generalizing and proving mathematical relationships,
and in communicating their thinking and the results of their efforts. Many classroom
activities are designed to be completed by students working together
collaboratively in heterogeneous groupings - in pairs or in groups
of three or four. |
  Short clips of classrooms are available at Parent Support: CPMP Classrooms. |
Launch Lessons begin
with a full-class discussion of a problem situation and of related
questions to think about. This discussion sets the context
for the student work to follow and helps to generate student interest;
it also provides an opportunity for the teacher to assess student
knowledge and to clarify directions for the group activities.
Teacher is
director and moderator. Sample launch |
Explore
Classroom activity then shifts to investigating focused problems
and questions related to the launching situation by gathering data,
looking for patterns, constructing models and meanings, and making
and verifying conjectures. As students collaborate in small groups,
the teacher circulates from group to group providing guidance and
support, clarifying or asking questions, giving hints, providing
encouragement, and drawing group members into the discussion to
help groups work more cooperatively. The unit materials and related
questions posed by students drive the learning. Teacher
is facilitator. Sample exploration |
Share and Summarize A full-class
discussion (referred to as a Checkpoint) of concepts and methods
developed by different small groups then provides an opportunity
to share progress and thinking. This discussion leads to
a class summary of important ideas or to further exploration
of a topic if competing perspectives remain. Varying approaches
and differing conclusions that can be justified should be encouraged.
Teacher is moderator. Sample Checkpoint |
Apply
Finally, students are given a task related to lesson objectives
to complete on their own. The teacher circulates in the room
assessing levels of student understanding. Teacher
is intellectual coach. Sample On Your Own |
MORE: Out-of-Class ActivitiesIn addition
to the classroom investigations, Core-Plus Mathematics provides sets of MORE tasks, which are designed to engage
students in
These tasks,
which are central to the learning goals of each lesson, are intended
primarily for individual work outside of class. Several MORE
tasks are provided for each lesson. Selection
of MORE tasks should be based on student performance and the availability
of time and technology. Also, students should exercise some choice
of tasks to pursue, and at times they should be given the opportunity
to pose their own problems and questions to investigate. |
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