Bottles and Divers
(Rates of Change)
High School Math Project
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Ideas for Discussion
(Some ideas may apply to more than one standard of the NCTM Professional Standards for Teaching Mathematics.)
Standard 1: Worthwhile Mathematical Tasks
- The NCTM Standards promote the exposure of high school student to the core principles of calculus. How does the content of this lesson address this
standard? How do the activities of the lesson help students understand the
mathematical concepts?
Standard 2: The Teacher’s Role in Discourse
- Discourse refers to ways of representing, thinking, talking, and agreeing and
disagreeing. Teachers send messages about types of knowledge and thinking
that are valued by the ways that they handle discourse. What are some of the
ways that discourse is handled by the teacher is this lesson?
Standard 3: Students’ Role in Discourse
- The students in this lesson are seniors in high school. They have been in a
mathematics program that has encouraged group work and active
participation. What evidence do you see that demonstrates their ability to
work in groups and discuss meaningful mathematics? What do you look for
as you watch and assess the group work of your own students?
Standard 4: Tools for Enhancing Discourse
- The NCTM Standards encourage teachers to use a variety of means for
promoting discussion and reasoning about mathematics. The use of tools
such as calculators and computers is encouraged in addition to the use of
more conventional mathematical symbols and other means such as
drawings, diagrams, invented symbols, and analogies. What tools helped to
promote mathematical thinking and the discussion of mathematical concepts
in the video lesson?
Standard 5: Learning Environment
- One of the key components of the learning environment is the idea that it
supports serious mathematical thinking. Teachers and students have a
genuine respect for ideas and reasoning, and students have time to puzzle
and think. A positive learning environment helps students be successful
mathematical thinkers. What are some of the important ways of creating
such a learning environment?
Standard 6: Analysis of Teaching and Learning
- Part of the reason for analyzing teaching and learning is to ensure that every
student is mastering important mathematics and developing a positive
attitude toward mathematics. How do you assess the attitudes of students?
What suggestions could you give to help other teachers assess the attitudes
their students have about mathematics?
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