Mathematical Communication, Conceptual Understanding, and Students' Attitudes Toward Mathematics

This action research study of my 8th grade classroom investigated the use of mathematical communication, through oral homework presentations and written journals entries, and its impact on conceptual understanding of mathematics. This change in expectation and its impact on students’ attitudes towards mathematics was also investigated. Challenging my students to communicate mathematics both orally and in writing deepened the students’ understanding of the mathematics. Levels of understanding deepened when a variety of instructional methods were presented and discussed where students could comprehend the ideas that best suited their learning styles. Increased understanding occurred through probing questions causing students to reflect on their learning and reevaluate their reasoning. This transpired when students were expected to write more than one draft to math journals. By making students aware of their understanding through communicating orally and in writing, students realized that true understanding did not come from mere homework completion, but from evaluating and assessing their own and other’s ideas and reasoning. I discovered that when students were challenged to communicate their reasoning both orally and in writing, students enjoyed math more and thought math was more fun. As a result of this research, I will continue to require students to communicate their thinking and reasoning both orally and in writing.

Mathematical Communication through Written and Oral Expression

In this action research study of my classroom of sixth grade mathematics, I investigated the use of communication of mathematics through both written and oral expression. Giving my students the opportunity to communicate mathematics both in writing and orally helped to deepen the students’ understanding of mathematics. The students’ levels of comprehension were increased when they were presented with a variety of instructional methods. Through discussion and reflection the students were able to find methods that worked best for them and their learning ability. Students’ understanding increased from probing questions that made the students reflect and re-evaluate their solutions. This learning took place when students were made aware of different solutions or ways of doing things from the class discussions that were held. I discovered that when students are challenged to express their thinking both in writing and orally, the students found that they could communicate their thinking in a new way. Some of my students were only comfortable expressing their thoughts in one of the two ways but by the time the project was completed, they all expressed that they enjoyed both ways, and maybe changed the original way they preferred doing mathematics. As a result of this research, I will continue to require students to communicate their thinking and reasoning both in writing and orally.

Rubric Assessment of Mathematical Processes in Homework

In this action research study of my classroom of 11th grade geometry, I investigated the use of rubrics to help me assess my students during homework presentations. I wanted to know more about the processes students went through as they did their homework problems, so homework presentations were implemented with the rubrics being the main form of assessment. I discovered that students are willing to speak about mathematics and can gain more understanding of mathematical processes as a result of homework presentations. The scores of the class improved after they talked about the homework assignments with each other. As a result of this research, I plan to keep on using homework presentations in my classroom to talk about homework, but discontinue the use of rubrics in assessment of students in mathematics. I also found students going to the board to solve problems in small groups are another helpful way to use presentations prior to assessment to help me understand where the students are with a new concept prior to assigning homework or giving an assessment.

Structural and Magnetic Properties of Neodymium - Iron - Boron Clusters

Using inert gas condensation techniques the properties of sputtered neodymium-iron-born clusters were investigated. A D.C. magnetron sputtering source created vaporous Nd-Fe-B which was then condensed into clusters and deposited onto silicon substrates. A composite target of Nd-Fe-B discs on an iron plate and a composite target of Nd-(Fe-Co)-B were utilized to create clusters. The clusters were coated with a carbon layer through R.F. sputtering to prevent oxidation. Samples were investigated in the TEM and showed a size distribution with an average particle diameter of 8.11 nm. The clusters, upon deposition, were amorphous as indicated by diffuse diffraction patterns obtained through SAD. The EDS showed compositionally a direct correlation in the ratio of rare-earth to transition metals between the target and deposited samples. The magnetic properties of the as-deposited clusters showed superparamagnetic properties at high temperatures and ferromagnetic properties at low temperatures; these properties are indicative of rare-earth transition metal amorphous clusters. Annealing of samples showed an initial increase in the coercivity. Samples were annealed in an inert gas atmosphere at 600o C for increasing amounts of time. The samples showed an initial increase in coercivity, but showed no additional increases with additional annealing time. SAD of annealed cluster samples showed the presence of Nd2Fe17 and a bcc-Nd phase. The bcc-Nd is the result of oxidation at high temperatures created during annealing and surface interface energy. The magnetic properties of the annealed samples showed weak coercivity and a saturation magnetization equivalent to that of Nd2Fe17. The annealed clusters showed a slight increase in coercivity at low temperatures. These results indicate a loss of boron during the sputtering process.

Preparation and evaluation of the electrospun chitosan/PEO fibers for potential applications in cartilage tissue engineering

Fibrous materials have morphological similarities to natural cartilage extracellular matrix and have been considered as candidate for bone tissue engineering scaffolds. In this study, we have evaluated a novel electrospun chitosan mat composed of oriented sub-micron fibers for its tensile property and biocompatibility with chondrocytes (cell attachment, proliferation and viability). Scanning electronic microscope images showed the fibers in the electrospun chitosan mats were indeed aligned and there was a slight cross-linking between the parent fibers. The electrospun mats have significantly higher elastic modulus (2.25 MPa) than the cast films (1.19 MPa). Viability of cells on the electrospun mat was 69% of the cells on tissue-culture polystyrene (TCP control) after three days in culture, which was slightly higher than that on the cast films (63% of the TCP control). Cells on the electrospun mat grew slowly the first week but the growth rate increased after that. By day 10, cell number on the electrospun mat was almost 82% that of TCP control, which was higher than that of cast films (56% of TCP). The electrospun chitosan mats have a higher Young’s modulus (P <0.01) than cast films and provide good chondrocyte biocompatibility. The electrospun chitosan mats, thus, have the potential to be further processed into three-dimensional scaffolds for cartilage tissue repair.