Matching Items (4)
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- All Subjects: Mathematics Education
- All Subjects: robotics
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
Description
Mathematics is an increasingly critical subject and the achievement of students in mathematics has been the focus of many recent reports and studies. However, few studies exist that both observe and discuss the specific teaching and assessment techniques employed in the classrooms across multiple countries. The focus of this study is to look at classrooms and educators across six high achieving countries to identify and compare teaching strategies being used. In Finland, Hong Kong, Japan, New Zealand, Singapore, and Switzerland, twenty educators were interviewed and fourteen educators were observed teaching. Themes were first identified by comparing individual teacher responses within each country. These themes were then grouped together across countries and eight emerging patterns were identified. These strategies include students active involvement in the classroom, students given written feedback on assessments, students involvement in thoughtful discussion about mathematical concepts, students solving and explaining mathematics problems at the board, students exploring mathematical concepts either before or after being taught the material, students engagement in practical applications, students making connections between concepts, and students having confidence in their ability to understand mathematics. The strategies identified across these six high achieving countries can inform educators in their efforts of increasing student understanding of mathematical concepts and lead to an improvement in mathematics performance.
ContributorsAnglin, Julia Mae (Author) / Middleton, James (Thesis director) / Vicich, James (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-12
Description
This is a report of a study that investigated the thinking of a high-achieving precalculus student when responding to tasks that required him to define linear formulas to relate covarying quantities. Two interviews were conducted for analysis. A team of us in the mathematics education department at Arizona State University initially identified mental actions that we conjectured were needed for constructing meaningful linear formulas. This guided the development of tasks for the sequence of clinical interviews with one high-performing precalculus student. Analysis of the interview data revealed that in instances when the subject engaged in meaning making that led to him imagining and identifying the relevant quantities and how they change together, he was able to give accurate definitions of variables and was usually able to define a formula to relate the two quantities of interest. However, we found that the student sometimes had difficulty imagining how the two quantities of interest were changing together. At other times he exhibited a weak understanding of the operation of subtraction and the idea of constant rate of change. He did not appear to conceptualize subtraction as a quantitative comparison. His inability to conceptualize a constant rate of change as a proportional relationship between the changes in two quantities also presented an obstacle in his developing a meaningful formula that relied on this understanding. The results further stress the need to develop a student's ability to engage in mental operations that involve covarying quantities and a more robust understanding of constant rate of change since these abilities and understanding are critical for student success in future courses in mathematics.
ContributorsKlinger, Tana Paige (Author) / Carlson, Marilyn (Thesis director) / Thompson, Pat (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2014-05
Description
This thesis focused on grasping tasks with the goal of investigating, analyzing, and quantifying human catching trends by way of a mathematical model. The aim of this project was to study human trends in a dynamic grasping task (catching a rolling ball), relate those discovered trends to kinematic characteristics of the object, and use this relation to control a robot hand in real time. As an ultimate goal, it was hoped that this research will aide in furthering the bio-inspiration in robot control methods. To achieve the above goal, firstly a tactile sensing glove was developed. This instrument allowed for in depth study of human reactionary grasping movements when worn by subjects during experimentation. This sensing glove system recorded force data from the palm and motion data from four fingers. From these data sets, temporal trends were established relating to when subjects initiated grasping during each trial. Moreover, optical tracking was implemented to study the kinematics of the moving object during human experiments and also to close the loop during the control of the robot hand. Ultimately, a mathematical bio-inspired model was created. This was embodied in a two-term decreasing power function which related the temporal trend of wait time to the ball initial acceleration. The wait time is defined as the time between when the experimental conductor releases the ball and when the subject begins to initiate grasping by closing their fingers, over a distance of four feet. The initial acceleration is the first acceleration value of the object due to the force provided when the conductor throws the object. The distance over which the ball was thrown was incorporated into the model. This is discussed in depth within the thesis. Overall, the results presented here show promise for bio-inspired control schemes in the successful application of robotic devices. This control methodology will ideally be developed to move robotic prosthesis past discrete tasks and into more complicated activities.
ContributorsCard, Dillon (Co-author) / Mincieli, Jennifer (Co-author) / Artemiadis, Panagiotis (Thesis director) / Santos, Veronica (Committee member) / Middleton, James (Committee member) / Barrett, The Honors College (Contributor) / School of Sustainability (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / W. P. Carey School of Business (Contributor)
Created2014-05
Description
In order to refine autonomous exploratory movement planning schemes, an approach must be developed that accounts for valuable information other than that gained from map filling. To this end, the goal of this thesis is divided into two parts. The first is to develop a technique for categorizing objects detected by an autonomous exploratory robot and assigning them a score based on their interest value. The second is an attempt to develop a method of integrating this technique into a navigation algorithm in order to refine the movements of a robot or robots to maximize the efficiency of information gain. The intention of both of these components is to provide a method of refining the navigation scheme applied to autonomous exploring robots and maximize the amount of information they can gather in deployments where they face significant resource or functionality constraints. To this end this project is divided into two main sections: a shape-matching technique and a simulation in in which to implement this technique. The first section was accomplished by combining concepts from information theory, principal component analysis, and the eigenfaces algorithm to create an effective matching technique. The second was created with inspiration from existing navigation algorithms. Once these components were determined to be functional, a testing regime was applied to determine their capabilities. The testing regime was also divided into two parts. The tests applied to the matching technique were first to demonstrate that it functions under ideal conditions. After testing was conducted under ideal conditions, the technique was tested under non-ideal conditions. Additional tests were run to determine how the system responded to changes in the coefficients and equations that govern its operation. Similarly, the simulation component was initially tested under normal conditions to determine the base effectiveness of the approach. After these tests were conducted, alternative conditions were tested to evaluate the effects of modifying the implementation technique. The results of these tests indicated a few things. The first series of tests confirmed that the matching technique functions as expected under ideal conditions. The second series of tests determined that the matching element is effective for a reasonable range of variations and non-ideal conditions. The third series of tests showed that changing the functional coefficients of the matching technique can help tune the technique to different conditions. The fourth series of tests demonstrated that the basic concept of the implementation technique makes sense. The final series of tests demonstrated that modifying the implementation method is at least somewhat effective and that modifications to it can be used to specifically tailor the implementation to a method. Overall the results indicate that the stated goals of the project were accomplished successfully.
ContributorsFleetwood, Garrett Clark (Author) / Thanga, Jekan (Thesis director) / Berman, Spring (Committee member) / Middleton, James (Committee member) / Economics Program in CLAS (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12