Diapositiva 1

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PBL
PBL NASA center on real life problems
Prof. Gloria Faus ITESM, Campus Guadalajara,
México
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Author and Contributing Members

• PBL Author Gloria Elena Faus Landeros
• Academic Advisor of PBL Design Ph. Dr. Jim Botti
• Mathematical Advisor Guadalupe Lomeli

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Noctilucent Clouds

• OLD PBL TIME MODEL SCENARIO
• Polar mesospheric clouds (PMCs), also known as
  noctilucent clouds (NCLs), are bright cloudlike
  atmospheric phenomena visible in a deep twilight.
  The name means roughly "night shining" in Latin.
  Unlike more common clouds that form up to 5
  miles above the surface of the earth, these
  clouds are 50 miles high in a layer of the
  atmosphere called the mesosphere.
• They are most often observed in the summer
  months at latitudes between 50 and 60 north and
  south of the equator. In recent years, however,
  several people have reported seeing NLCs at lower
  latitudes, even as low as 40N in the continental
  United States.

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NASA invites us to find the math model of
limit that shows the time we have to observe
these beautiful clouds. PBL TIME MODEL
SCENARIO Students solutions
Team 1
Team 2
Team 3
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Some Rationale

• I think the new scenario is better because the
  words, "....... to find the math model of limit
  that shows the time may give TOO MUCH direction
  to the learners such as the PBL sun rays math
  model. 
• When I applied this scenario 2 semesters ago the
  students designed different math models but all
  of them were limited to illustrate just
  observation time.

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Some Rationale

• With the new scenario the problem is complex and
  messier because it can cause the students decide
  to investigate not only the observation times of
  the Noctilucent clouds but also they can decide
  to analyze their constitution, and attempt to
  create a different math model that illustrates
  how noctilucent clouds constitution is, and the
  reason of their appearance, why is the electric
  blue color, why is the shinning, why we can see
  them only at night, etc.

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PBL TIME MODEL SCENARIO Polar mesospheric clouds
(PMCs), also known as noctilucent clouds (NCLs),
are bright cloudlike atmospheric phenomena
visible in a deep twilight. The name means
roughly "night shining" in Latin. Unlike more
common clouds that form up to 5 miles above the
surface of the earth, these clouds are 50 miles
high in a layer of the atmosphere called the
mesosphere. They are most often observed in the
summer months at latitudes between 50 and 60
north and south of the equator. In recent years,
however, several people have reported seeing NLCs
at lower latitudes, even as low as 40N in the
continental United States.
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PBL TIME MODEL SCENARIO

• NASA invites us to find the math model that
  shows (illustrates/explains) why (where when)
  it is possible to observe these beautiful
  clouds.

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GOALS AND OBJECTIVES Students will research and
analyze information about Noctilucent clouds to
have a global and clear context about the
elements which are involved in this phenomena, in
order to have a mathematical interpretation with
this information. It is expected that, with
this information, the students will Content
objectives

• Identify the places where the clouds are seen.
• Find the causes of why these clouds can be seen (
  Relationship between the sun rays light and
  noctilucent clouds)
• Obtain the observers angle.
• Obtain when and where the observer can see this
  phenomenon.
• Find the earths circumference, radius, the angle
  cloud-earth-sun, and the angular distance.

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GOALS AND OBJECTIVES
Content objectives
Find the earths arc length (clouds time
observation), and sector area formula.
Physics Find the incidence angle of the sun with
respect of the earth. Understand how the
translational movement of the earth around the
sun is. Analyze if the movement of the earth
around the sun affects the incidence of the sun
rays at the North Pole that make that the
noctilucent clouds can be seen. Understand
summer solstice. Analyze the constitution of the
noctilucent clouds. Why they are in the
mesosphere, why do they have that appearance, the
electric blue color, the shine, why we can see
them only at night, etc.
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GOALS AND OBJECTIVES
Bibliographical investigation objectives Student
s must be capable of making a mathematical model
that includes antecedents, previous
investigation of the problem, hypothesis,
objectives, research fundaments, limitation, and
glossary of terms. Fundamental theoretical for
the problem solution process. The problem
solution process has a logical and coherent
sequence.
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GOALS AND OBJECTIVES

• Math Model objectives
• Recognize the variables that are involved in the
  phenomenon.
• Considered all the relevance variables on the
  math model.
• Make a math model statement coherent with the
  obtained information.
• Make a math model statement completely relevant
  and logic.

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• GOALS AND OBJECTIVES
  Math model objectives
• Included the sufficient and necessary variables
  on the math model.
• Make a math model that shows the information was
  analyzed and comprehensive.
• Make a math model shows the behavior of the
  phenomenon.

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GOALS AND
OBJECTIVES
Math model
objectives

• Make a math model shows the behavior of the
  phenomenon when the variables are changing.
• Make a math model that sustains the presented
  solution of the problem.

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GOALS AND OBJECTIVES

Math model objectives

• Students must be capable of making a mathematical
  model that includes the variables that intervene
  in this phenomena and how modifying these
  variables affect the behavior of the phenomena.
• It is expected that students identify the most
  known variables that intervene in this phenomena.

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GOALS AND OBJECTIVES
Math Model objectives

• Students must be aware that a bibliographical
  research should be complemented with a field
  research.
• Students must be capable of establishing
  conclusions based on the mathematical model.

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LESSON RESOURCES Research from different books
of Analytic Geometry, Trigonometry, Physics and
Geography. (Ellipse formula, Angles laws, angular
displacement, arc length, sector, area).
Investigate scientific vocabulary. Research
about ray sun incidence angle. Investigate how
the ray sun incidence angle change with respect
the seasons. Find and obtain information on
Internet and select the reliable and truth
information. Use the GLOBE atmospheric protocols
to collect data online. If appropriate, consider
a multimedia presentation using images, graphics,
or sound, like flash presentation. (For
presenting the solution of the problem). Self
learning. They need to do collaborative work to
discuss the information, elaborate the math
model, and work on the presentation using
technology.
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Rubric for NASA Project Presentation
Rubric
Problem-Solving Model
PBL model
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PBL SUN RAYS MODEL

• Polar mesospheric clouds (PMCs), also known
  as noctilucent clouds (NCLs), are bright cloud
  like atmospheric phenomena visible in a deep
  twilight. The highest clouds in the Earth's
  atmosphere are made of frozen water, or ice
  crystals, just like some of the clouds that
  appear in the sky every day. Unlike more common
  clouds that form up to 5 miles above the surface
  of the earth, these clouds are 50 miles high in a
  layer of the atmosphere called the mesosphere.
• Scientists are attempting to find out why
  they form and why they are changing. In
  particular, they wish to determine if these
  changes are caused by natural variations in the
  earth's atmosphere, or if they are influenced by
  human activities.

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PBL SUN RAYS MODEL
PBL SUN RAYS MODEL
"NASA invited us to create a math model in which
we could show possible relationships between
relatively recent phenomenon of noctilucent
clouds and global warming and climate change.
PBL presentation
Bibliographic investigation
Overview
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(No Transcript)
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• GOALS AND OBJECTIVES
• Students will research and analyze information
  about noctilucent clouds to have a global and
  clear context about the elements which are
  involved in this phenomenon, in order to have a
  mathematical interpretation with this
  information.
• It is expected that, with this information, the
  students will
• Content objectives
• Infer the general composition of the noctilucent
  clouds. ( NASA,
• links).
• Infer the Noctilucent Cloud density ( NASA,
  links).
• Find the altitude of de Clouds.
• Understand the incident sun ray on the earth and
  reflected ray sun on the earth. (Math and
  Physics).
• Find the incidence angle of the sun according to
  the seasons. (Physics, and other science).

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GOALS AND OBJECTIVES
Content objectives

• Understand what the phenomenon of global warming
  is.
• Understand what the relationship between
  noctilucent clouds and global warming is. If
  exist a relation between both.
• Students must be capable to apply the knowledge
  of reflections law to a real world problem.
  (Mathematics).
• Students must be capable to obtain the angles
  noctilucent clouds phenomenon reflection and
  refraction. (Physics).

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GOALS AND OBJECTIVES Bibliographical
investigation objectives

• Students must be capable of making a mathematical
  model
• that includes antecedents, previous
  investigation of the
• problem, hypothesis, objectives, research
  fundaments,
• limitation, and glossary of terms.
• Fundamental theoretical for the problem solution
  process.
• The problem solution process has a logical and
  coherent
• sequence.

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GOALS AND OBJECTIVES

• Math Model objectives
• Recognize the variables that are involved in the
  phenomenon.
• Considered all the relevance variables on the
  math model.
• Make a math model statement coherent with the
  obtained information.
• Make a math model statement completely relevant
  and logic.

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• GOALS AND OBJECTIVES
  Math model objectives
• Included the sufficient and necessary variables
  on the math model.
• Make a math model that shows the information was
  analyzed and comprehensive.
• Make a math model shows the behavior of the
  phenomenon.

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GOALS AND
OBJECTIVES
Math model
objectives

• Make a math model shows the behavior of the
  phenomenon when the variables are changing.
• Make a math model that sustains the presented
  solution of the problem.

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GOALS AND OBJECTIVES

Math model objectives

• Students must be capable of making a mathematical
  model that includes the variables that intervene
  in this phenomena and how modifying these
  variables affect the behavior of the phenomena.
• It is expected that students identify the most
  known variables that intervene in this phenomena.

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GOALS AND OBJECTIVES
Math Model objectives

• Students must be aware that a bibliographical
  research should be complemented with a field
  research.
• Students must be capable of establishing
  conclusions based on the mathematical model.

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LESSON RESOURCES Research about Noctilucent
clouds, like Geographic position, etc. the
objective is they have a general concept of
Noctilucent clouds (Where they are? Why they are
there? Which is the information of the scientist
about this clouds, etc? ) GLOBE DATA COLECCTION.
Research about ray sun incidence angle, global
warming, and climate change. Investigate how
the ray sun incidence angle change with respect
the seasons. ( Differential calculus). Find and
obtain information on Internet and select the
reliable and truth information. They need to
know how to use the flash software. (For
presenting the solution of the problem). Self
learning. They need to do collaborative work to
discuss the information, elaborate the math
model, and work on the presentation using
technology.
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• Analysis of Calculus learning through the
  technique of Problem-Based Learning.
• School year 2006-2007

Research problem
Conclusions