Identifying False Intuitions in Probability and Laying a Foundation for Teaching It

Intuition is something we rely on in our daily lives as pure, untaught truths that guide and direct us. Simple statements like “the shortest distance between two points is a straight line” are common and self-explanatory. While this simple statement can be proved mathematically, it is instinctive to easily understand this notion and accept its entrance into one\u27s cognitive intuition. However, there are other parts of mathematics that are not intuitive and require thought and proofs to explain their existence. The question then is: how does the mind distinguish between what is intuitive and what is in need of a solid explanation? Current research studies, on the psychological effects of incorrect intuitions on learning, state that false intuitions can cause misconceptions in every mathematics classroom. In particular, these false intuitions can be a detriment to students in the beginning stages of learning the basics of probability. The purpose of this thesis project is twofold - understand and examine current literature on the different intuitions brought by students into the classroom, and develop and present a curriculum unit plan that can avoid student’s false intuitions with regard to learning about probabilities in mathematics. The literature review section discusses the different ways people perceive the subject of probability while acknowledging its complexity. Discussion highlights different faulty approaches to learning probabilities with regard to heuristic methods – outcome, representative, and personal. Through a thorough examination of both heuristics and maxim beliefs it is noted that common misconceptions and intuitions are learned before students begin their secondary education. It is further suggested that probability and statistics be taught at the elementary level to avoid this trend. The curriculum section includes a unit plan on probability that meets the New York State Standards at the Integrated Algebra level. This incorporates a pre-assessment, daily lesson plan, daily classwork activities, daily formative assessments, and a unit test

The effect of baffles on tank sloshing, part i

Testing of cantilevered flexible, hinged, and slamming baffles by subjection to sinusoidal variation in water far from free surface - effect on tank sloshin

High angle canard missile test in the Ames 11-foot transonic wind tunnel

Four blunted ogive-cylinder missile models with a length-to-diameter ratio of 10.4 were tested at transonic speeds and large angles of attack. The configurations are: body, body with tail panels, body with canards, and body with canards and tails. Forces and moments from the entire model and each of the eight fins were measured over the pitch range of 20 deg to 50 deg and 0 deg to 45 deg roll. Canard deflection angles between 0 deg and 15 deg were tested. Exploratory vapor screen flow visualization testing was also performed. Sample force and moment data are reported along with observations from the vapor screen tests

Engineering flight and guest pilot evaluation report, phase 2

Prior to the flight evaluation, the two-segment profile capabilities of the DC-8-61 were evaluated and flight procedures were developed in a flight simulator at the UA Flight Training Center in Denver, Colorado. The flight evaluation reported was conducted to determine the validity of the simulation results, further develop the procedures and use of the area navigation system in the terminal area, certify the system for line operation, and obtain evaluations of the system and procedures by a number of pilots from the industry. The full area navigation capabilities of the special equipment installed were developed to provide terminal area guidance for two-segment approaches. The objectives of this evaluation were: (1) perform an engineering flight evaluation sufficient to certify the two-segment system for the six-month in-service evaluation; (2) evaluate the suitability of a modified RNAV system for flying two-segment approaches; and (3) provide evaluation of the two-segment approach by management and line pilots

Operational flight evaluation of the two-segment approach for use in airline service

United Airlines has developed and evaluated a two-segment noise abatement approach procedure for use on Boeing 727 aircraft in air carrier service. In a flight simulator, the two-segment approach was studied in detail and a profile and procedures were developed. Equipment adaptable to contemporary avionics and navigation systems was designed and manufactured by Collins Radio Company and was installed and evaluated in B-727-200 aircraft. The equipment, profile, and procedures were evaluated out of revenue service by pilots representing government agencies, airlines, airframe manufacturers, and professional pilot associations. A system was then placed into scheduled airline service for six months during which 555 two-segment approaches were flown at three airports by 55 airline pilots. The system was determined to be safe, easy to fly, and compatible with the airline operational environment

Flight evaluation of two-segment approaches using area navigation guidance equipment

A two-segment noise abatement approach procedure for use on DC-8-61 aircraft in air carrier service was developed and evaluated. The approach profile and procedures were developed in a flight simulator. Full guidance is provided throughout the approach by a Collins Radio Company three-dimensional area navigation (RNAV) system which was modified to provide the two-segment approach capabilities. Modifications to the basic RNAV software included safety protection logic considered necessary for an operationally acceptable two-segment system. With an aircraft out of revenue service, the system was refined and extensively flight tested, and the profile and procedures were evaluated by representatives of the airlines, airframe manufacturers, the Air Line Pilots Association, and the Federal Aviation Adminstration. The system was determined to be safe and operationally acceptable. It was then placed into scheduled airline service for an evaluation during which 180 approaches were flown by 48 airline pilots. The approach was determined to be compatible with the airline operational environment, although operation of the RNAV system in the existing terminal area air traffic control environment was difficult

Rolling moments in a trailing vortex flow field

Pressure distributions are presented which were measured on a wing in close proximity to a tip vortex of known structure generated by a larger, upstream semispan wing. Overall loads calculated by integration of these pressures are checked by independent measurements made with an identical model mounted on a force balance. Several conventional methods of wing analysis are used to predict the loads on the following wing. Strip theory is shown to give uniformly poor results for loading distribution, although predictions of overall lift and rolling moment are sometimes acceptable. Good results are obtained for overall coefficients and loading distribution by using linearized pressures in vortex-lattice theory in conjunction with a rectilinear vortex. The equivalent relation from reverse-flow theory that can be used to give economic predictions for overall loads is presented

Assessment of a wake vortex flight test program

A proposed flight test program to measure the characteristics of wake vortices behind a T-33 aircraft was investigated. A number of facets of the flight tests were examined to define the parameters to be measured, the anticipated vortex characteristics, the mutual interference between the probe aircraft and the wake, the response of certain instruments to be used in obtaining measurements, the effect of condensation on the wake vortices, and methods of data reduction. Recommendations made as a result of the investigation are presented

The effects of leading-edge serrations on reducing flow unsteadiness about airfoils, an experimental and analytical investigation

High frequency surface pressure measurements were obtained from wind-tunnel tests over the Reynolds number range 1.2 times one million to 6.2 times one million on a rectangular wing of NACA 63-009 airfoil section. Measurements were also obtained with a wide selection of leading-edge serrations added to the basic airfoil. Under a two-dimensional laminar bubble very close to the leading edge of the basic airfoil there is a large apatial peak in rms pressure. Frequency analysis of the pressure signals in this region show a large, high-frequency energy peak which is interpreted as an oscillation in size and position of the bubble. The serrations divide the bubble into segments and reduce the peak rms pressures. A low Reynolds number flow visualization test on a hydrofoil in water was also conducted. A von Karman vortex street was found trailing from the rear of the foil. Its frequency is at a much lower Strouhal number than in the high Reynolds number experiment, and is related to the trailing-edge and boundary-layer thicknesses