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To effectively teach CMP2 several instructional shifts must take place:
The teacher becomes a listener, rather than a talker.
The teacher becomes the sorter of information, rather than the giver of information.
Students learn to rely on reasoning and proof, rather than relying on telling and patterns.
The instructional model for CMP2 is called Launch Explore Summarize. These three pieces define a lesson and lead to mathematical understanding.
Launch
The purpose of the launch is for the teacher to
introduce new concepts.
review old concepts.
help students understand the context of the problem.
issue a mathematical challenge to the students.
Suggestions for effective launches:
Tell a story to set up the problem.
Relate the problem to the students lives and their activities.
Create challenges for the students.
Revisit ideas from previous math experiences.
Vary the type of launch from day to day.
Make expectations clear to the students.
Create a clear focus.
Launches are not as effective if
they last half the period.
teachers or students read the book introduction to the launch all the time.
the teacher models how to do the problem.
not enough information is presented.
the teacher questions away the problem.
Explore
The students are active during this phase and should be observed
gathering data.
sharing ideas.
looking for patterns.
making conjectures.
developing strategies.
creating arguments to support their reasoning and their solution.
The teacher becomes a facilitator during this phase and should be
asking questions to encourage thought.
asking questions to redirect.
observing individual differences.
providing extra challenges.
During an effective explore students should be
choosing the tools they need.
solving the problem.
asking questions of each other.
recording solutions in their notes.
preparing a presentation.
During an effective explore teachers should be
asking questions to redirect or extend learning.
taking note of student strategies and solutions.
tracking attempts, struggles, and successes.
mentally orchestrating the summary.
constantly making instructional decisions.
Explorations are not as effective if
the groups are always the same people.
there is no variation in group configuration.
teachers do not trust their students to stay on task when working in groups.
the teacher uses the time to tutor individual students or a few groups.
the teacher uses the time to do desk work.
students are not held responsible for their learning.
Summarize
During the summary, teachers and students work together to resolve the mathematics presented in the problem and lay the groundwork for future study.
As a group, teachers and students will
collect, organize, and analyze data.
observe differences and similarities.
discuss and refine strategies.
develop rules or generalizations.
verify generalizations.
During an effective summary
students present ideas.
conversations involve the whole class.
students debate over the correctness of answers.
students analyze strategies and discuss similarities.
students are encouraged to ask questions.
The mathematics is related to previous concepts.
upcoming mathematical ideas are foreshadowed.
extension questions are asked.
A summary is not as effective if
it is omitted due to time.
everyone presents ideas.
everything is done orally.
every question is answered.
the teacher tells students how it should have been done.
students hear only correct answers.
students speak to the teacher, not to the class.
there is no push to think about the similarity of thoughts and strategies.
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