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- Title
- EXAMINING SOCIOMATHEMATICAL NORMS WITHIN THE CONTEXT OF DECIMALS AND FRACTIONS IN A SIXTH GRADE CLASSROOM.
- Creator
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Nardelli, Marino, Dixon, Juli, University of Central Florida
- Abstract / Description
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Social norms are patterns of behavior expected within a particular society in a given situation. Social norms can be shared belief of what is normal and acceptable shapes and enforces the actions of people in a society. In the educational classroom, they are characteristics that constitute the classroom participation structure. Sociomathematical norms are fine-grained aspects of general social norms specifically related to mathematical practices. These can include, but are not limited to, a...
Show moreSocial norms are patterns of behavior expected within a particular society in a given situation. Social norms can be shared belief of what is normal and acceptable shapes and enforces the actions of people in a society. In the educational classroom, they are characteristics that constitute the classroom participation structure. Sociomathematical norms are fine-grained aspects of general social norms specifically related to mathematical practices. These can include, but are not limited to, a student-centered classroom that includes the expectation that the students should present their solution methods by describing actions on mathematical objects rather than simply accounting for calculational manipulations. For this action research study, my goal was to determine if the role of the teacher would influence the social and sociomathematical norms in a mathematics classroom and in what ways are sociomathematical norms reflected in students' written work. I focused specifically on students' mathematics journal writing and taped conversations. I discovered that students tended to not justify their work. Also, I discovered that my idea of justification was not really justification. I learned from this and was able to change my idea of justification. By encouraging the students to socialize in mathematics class, I found that the quality of their dialogue improved. Students readily discussed mathematical concepts within small groups and whole class discussions.
Show less - Date Issued
- 2007
- Identifier
- CFE0001650, ucf:47245
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0001650
- Title
- USING COMMUNICATION TECHNIQUES IN THE LOW-PERFORMING MATHEMATICS CLASSROOM: A STUDY OF FRACTIONS,DECIMALS,PERFORMANCE AND ATTITUDES.
- Creator
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Guyton, Pamela, Ortiz, Enrique, University of Central Florida
- Abstract / Description
-
Within a low-performing seventh grade mathematics classroom, communication techniques including discourse, collaborative groups, listening, reading, and writing were implemented during a six week period. This study shows how the use of these techniques led to the twenty four students' conceptual understanding of fraction and decimal concepts. This research study provides insight to the deep-seeded beliefs of low-performing students. It provides a record of how the teacher used...
Show moreWithin a low-performing seventh grade mathematics classroom, communication techniques including discourse, collaborative groups, listening, reading, and writing were implemented during a six week period. This study shows how the use of these techniques led to the twenty four students' conceptual understanding of fraction and decimal concepts. This research study provides insight to the deep-seeded beliefs of low-performing students. It provides a record of how the teacher used communication techniques in the classroom and had a strong positive impact on the attitudes and performance of these struggling students.
Show less - Date Issued
- 2008
- Identifier
- CFE0002146, ucf:47928
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0002146
- Title
- DESIGN OF POLYNOMIAL-BASED FILTERS FOR CONTINUOUSLY VARIABLE SAMPLE RATE CONVERSION WITH APPLICATIONS IN SYNTHETIC INSTRUMENTATION AND SOFTWARE DEFINED RADIO.
- Creator
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Hunter, Matthew, Mikhael, Wasfy, University of Central Florida
- Abstract / Description
-
In this work, the design and application of Polynomial-Based Filters (PBF) for continuously variable Sample Rate Conversion (SRC) is studied. The major contributions of this work are summarized as follows. First, an explicit formula for the Fourier Transform of both a symmetrical and nonsymmetrical PBF impulse response with variable basis function coefficients is derived. In the literature only one explicit formula is given, and that for a symmetrical even length filter with fixed basis...
Show moreIn this work, the design and application of Polynomial-Based Filters (PBF) for continuously variable Sample Rate Conversion (SRC) is studied. The major contributions of this work are summarized as follows. First, an explicit formula for the Fourier Transform of both a symmetrical and nonsymmetrical PBF impulse response with variable basis function coefficients is derived. In the literature only one explicit formula is given, and that for a symmetrical even length filter with fixed basis function coefficients. The frequency domain optimization of PBFs via linear programming has been proposed in the literature, however, the algorithm was not detailed nor were explicit formulas derived. In this contribution, a minimax optimization procedure is derived for the frequency domain optimization of a PBF with time-domain constraints. Explicit formulas are given for direct input to a linear programming routine. Additionally, accompanying Matlab code implementing this optimization in terms of the derived formulas is given in the appendix. In the literature, it has been pointed out that the frequency response of the Continuous-Time (CT) filter decays as frequency goes to infinity. It has also been observed that when implemented in SRC, the CT filter is sampled resulting in CT frequency response aliasing. Thus, for example, the stopband sidelobes of the Discrete-Time (DT) implementation rise above the CT designed level. Building on these observations, it is shown how the rolloff rate of the frequency response of a PBF can be adjusted by adding continuous derivatives to the impulse response. This is of great advantage, especially when the PBF is used for decimation as the aliasing band attenuation can be made to increase with frequency. It is shown how this technique can be used to dramatically reduce the effect of alias build up in the passband. In addition, it is shown that as the number of continuous derivatives of the PBF increases the resulting DT implementation more closely matches the Continuous-Time (CT) design. When implemented for SRC, samples from a PBF impulse response are computed by evaluating the polynomials using a so-called fractional interval, µ. In the literature, the effect of quantizing µ on the frequency response of the PBF has been studied. Formulas have been derived to determine the number of bits required to keep frequency response distortion below prescribed bounds. Elsewhere, a formula has been given to compute the number of bits required to represent µ to obtain a given SRC accuracy for rational factor SRC. In this contribution, it is shown how these two apparently competing requirements are quite independent. In fact, it is shown that the wordlength required for SRC accuracy need only be kept in the µ generator which is a single accumulator. The output of the µ generator may then be truncated prior to polynomial evaluation. This results in significant computational savings, as polynomial evaluation can require several multiplications and additions. Under the heading of applications, a new Wideband Digital Downconverter (WDDC) for Synthetic Instruments (SI) is introduced. DDCs first tune to a signal's center frequency using a numerically controlled oscillator and mixer, and then zoom-in to the bandwidth of interest using SRC. The SRC is required to produce continuously variable output sample rates from a fixed input sample rate over a large range. Current implementations accomplish this using a pre-filter, an arbitrary factor resampler, and integer decimation filters. In this contribution, the SRC of the WDDC is simplified reducing the computational requirements to a factor of three or more. In addition to this, it is shown how this system can be used to develop a novel computationally efficient FFT-based spectrum analyzer with continuously variable frequency spans. Finally, after giving the theoretical foundation, a real Field Programmable Gate Array (FPGA) implementation of a novel Arbitrary Waveform Generator (AWG) is presented. The new approach uses a fixed Digital-to-Analog Converter (DAC) sample clock in combination with an arbitrary factor interpolator. Waveforms created at any sample rate are interpolated to the fixed DAC sample rate in real-time. As a result, the additional lower performance analog hardware required in current approaches, namely, multiple reconstruction filters and/or additional sample clocks, is avoided. Measured results are given confirming the performance of the system predicted by the theoretical design and simulation.
Show less - Date Issued
- 2008
- Identifier
- CFE0002292, ucf:47844
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0002292
