Research Experience for Teachers program

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Research Experience for Teachers program
My summer with the

• Andrew Benzing
• RET Fellow

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Points of Discussion

• Introduction to the PRISM Lab
• Bi-axial Stretcher
• Creating a Vision by Giving Meaning to
  Data Curriculum Overview
• Cheerio Lab
• 5. Taking this back home

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A need for Research

• from the PRISM website

• Minimally invasive surgery is a preferred
  treatment to the traditional open procedures as
  it cuts down on infection rates and recovery
  time.
• As these relatively new laparoscopic procedures
  are implemented the need for training becomes
  clear.
• The need for realistic models of soft tissue
  exploration becomes evident. Satisfying this need
  is in fact the work that the PRISM lab conducts
  on a daily basis.

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Efforts of the PRISM Lab to Satisfy this Need

• At any given time, several experiments are
  conducted including stretching, grasping,
  probing, and cutting.
• Once this experimental data is collected a
  mathematical model can be determined that best
  represents the experimental observation of
  force-displacement behavior.

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Haptic Interface

• Experimentally observed force-displacement data
  can be used to provide feedback to the surgeon
  through an information enhanced display.
• In a sense the surgeon will be able to 'feel the
  tissue as in an open procedure.

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My Role in the PRISM Lab

• In order to model the stretching of this tissue
  the biaxial tissue stretcher was created that
  stretches tissue in two directions at a constant
  velocity and measures the forces involved.
• Once we have a measure of the force in relation
  to displacement we can estimate the stress-strain
  relationship of the specimen.

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Measuring Position

• We also felt it important to measure position as
  the resistance in stretching and relaxing the
  tissue would vary over the duration of the
  experiment resulting in the arms to move at
  different rates and in turn be at different
  positions.
• The measuring of the location of the robots was
  achieved through the use of optical encoders
  placed at the end of the motors.

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Measuring Force

• The measurement of force both on the x and y
• axis was taken with load cells that were placed
• on the stationary arms.

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Interface

• All variables involved were monitored using
  an interface where we could set velocity, tare
  force values and program stretch values.

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RESULTS

• Initial Trial Testing with Synthetic Materials
• Rubber (Shown below) - Sorbothan (Latex-Not
  Shown)
• Hysteresis

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Preliminary Test Results with Liver
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Curriculum Plan

• As taken from the standards outline by the
  National Council of Teachers of Mathematics
• Recognize and apply mathematics in contexts
  outside of mathematics.  
• Formulate questions that can be addressed with
  data collect, organize, and display relevant
  data to answer them. 
• Develop and evaluate inferences and predictions
  that are based on data.

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Expectations of Students after PRISM visit

• Given Description of situation provide a graph
• Provide a reasonable extrapolation of situation
  given graph

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Labs in Math?

• SCENARIO Mrs. Al Gebra was sitting down
• on a Sunday morning getting ready to eat
• her daily bowl of Cheerios when she spilled
• some of the dry cereal on the counter. Looks
• like her lovely husband will have to pick up
• after her again. As Mr. Al Gebra began to
• clean up the mess, he considered the area
• of the counter covered by the cereal. After a
• deeper investigation, Mr. Al Gebra
• discovered that a relationship existed
• between the amount of spilled Cheerios and
• the area covered by the cereal.

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Cheerio Lab

• Procedure Each pair should spill the provided
  Cheerios on their bullseye card. The pairs
  task is to rearrange the Cheerios in an attempt
  to determine which circle radius, in centimeters,
  will contain a majority of the cereal spilt. Once
  the largest radius possible has been covered,
  record the data on the red card as an ordered
  pair, relating the area covered in terms of the
  number of cheerios, x, to the radius of a circle
  in centimeters, y.
• NOTE A minimum of half of an O must be within
  the area ring to be considered part of the
  coverage area. You are allowed to remove
  individual pieces of cereal to better fit within
  a circle, but may not add cereal.
• TOUGHIE Derive a formula that relates the
  radius of a circle, R , with the number of
  Cheerios contained in the circle, c, where R is a
  function of c.

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Follow Up

• R (c) __________________
• DISCUSSION QUESTIONS
• 1.) Evaluate and interpret the real-life meaning
  of the following expressions.
• a.) R ( 5 ) b.) R ( c ) 5 c.)
  5 R ( c )
• 2.) Identify the coefficient contained within the
  function that produces a stretch. What do you
  suppose is the real life significance of this
  figure?
• 3.) General Mills has decided that they would
  like to enlarge the Os in their cereal to 1.25
  centimeters. How will this impact the graph? How
  will this impact the function rule?
• 4.) Let us redefine the variables of the
  experiment so that the number of cheerios is
  dependent on the radius that is to say the number
  of Cheerios, C, is a function of the radius r.
• a) Which function that we have studied would
  best resemble C ( r )?
• b) What is the relationship between C ( r ) and
  R (c ) ?
• c) What is the equation for C ( r ) ?

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• In relating the number of Cheerios within the
  circle truthfully
• we are considering area. So students should
  consider the
• relationship between area and radius.
• We will recognize the notation Ao and ro to
  represent the
• area and radius of the bullseye.
• The given area formula provides us with a formula
  where c
• is a function of R however we need a formula
  where R is a
• function of c. Therefore we must consider the
  inverse.
• Now we have R which is a function of A, but not
  of the
• number of Cheerios.

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• In considering the Area of the bullseye in
  terms of
• the number of cheerios we can say
• and we also know the area of 1 Cheerio
• where Ac and rc represents the area and radius of
  1
• cheerio
• therefore we know

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How to take home?

• NSF Grant for Instructional Materials
  Development Program
• Math and Science Department meeting
• Delaware County In-service for Math and Science
  Teachers on November 4th Technology In Action

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A special thank you for special people

• The group of graduate students below each have
  assisted me on
• numerous occasions and have been extremely
  patient in dealing
• with my never-ending questions. Dedicated and
  hardworking, the
• group below is the heart of the PRISM lab.

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I almost forgot one more thank you
Dr. Desai
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