Class Notes for Math 918: Local Cohomology, Instructor Tom Marley

Topics include: Injective Module, Basic Properties of Local Cohomology Modules, Local Cohomology as a Cech Complex, Long exact sequences on Local Cohomology, Arithmetic Rank, Change of Rings Principle, Local Cohomology as a direct limit of Ext modules, Local Duality, Chevelley’s Theorem, Hartshorne- Lichtenbaum Vanishing Theorem, Falting’s Theorem.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

Germline-Specific MATH-BTB Substrate Adaptor MAB1 Regulates Spindle Length and Nuclei Identity in Maize

Germline and early embryo development constitute ideal model systems to study the establishment of polarity, cell identity, and asymmetric cell divisions (ACDs) in plants. We describe here the function of the MATH-BTB domain protein MAB1 that is exclusively expressed in the germ lineages and the zygote of maize (Zea mays). mab1 (RNA interference [RNAi]) mutant plants display chromosome segregation defects and short spindles during meiosis that cause insufficient separation and migration of nuclei. After the meiosis-to-mitosis transition, two attached nuclei of similar identity are formed in mab1 (RNAi) mutants leading to an arrest of further germline development. Transient expression studies of MAB1 in tobacco (Nicotiana tabacum) Bright Yellow-2 cells revealed a cell cycle-dependent nuclear localization pattern but no direct colocalization with the spindle apparatus. MAB1 is able to form homodimers and interacts with the E3 ubiquitin ligase component Cullin 3a (CUL3a) in the cytoplasm, likely as a substrate-specific adapter protein. The microtubule-severing subunit p60 of katanin was identified as a candidate substrate for MAB1, suggesting that MAB1 resembles the animal key ACD regulator Maternal Effect Lethal 26 (MEL-26). In summary, our findings provide further evidence for the importance of posttranslational regulation for asymmetric divisions and germline progression in plants and identified an unstable key protein that seems to be involved in regulating the stability of a spindle apparatus regulator(s).

Intelligent tutoring system for distance education

This study aims to develop and implement a tool called intelligent tutoring system in an online course to help a formative evaluation in order to improve student learning. According to Bloom et al. (1971,117) formative evaluation is a systematic evaluation to improve the process of teaching and learning. The intelligent tutoring system may provide a timely and high quality feedback that not only informs the correctness of the solution to the problem, but also informs students about the accuracy of the response relative to their current knowledge about the solution. Constructive and supportive feedback should be given to students to reveal the right and wrong answers immediately after taking the test. Feedback about the right answers is a form to reinforce positive behaviors. Identifying possible errors and relating them to the instructional material may help student to strengthen the content under consideration. The remedial suggestion should be given in each answer with detaileddescription with regards the materials and instructional procedures before taking next step. The main idea is to inform students about what they have learned and what they still have to learn. The open-source LMS called Moodle was extended to accomplish the formative evaluation, high-quality feedback, and the communal knowledge presented here with a short online financial math course that is being offered at a large University in Brazil. The preliminary results shows that the intelligent tutoring system using high quality feedback helped students to improve their knowledge about the solution to the problems based on the errors of their past cohorts. The results and suggestion for future work are presented and discussed.

An evaluation of the impact of Inner City Development's Cooperative Home School: An educational alternative program to increase the quality and level of education in San Antonio's West Side community

The research study was intended to evaluate the effectiveness of Inner City Development's (I.C.D.) Cooperative Home School, an educational alternative program to the Title I public schools of San Antonio's West Side community. The study investigated students', parents' and tutors' perception of parental involvement and educational resources. The study also investigated each student's academic achievement. ^ The study found that students progressed toward expected math proficiency at a faster rate than they did in reading proficiency. However, because the target population size was small and a comparison group was not used, the results of this study are only suggestive. This research also indicated that study subjects believed students' quality and level of education increased substantially since program exposure. Study subjects mainly attributed the students' strides in academic performance to the increased amount of individualized attention students received in the small twelve-student class size. Study subjects were more satisfied with the home school's educational resources than those of the Title I public schools. Study subjects also perceived that parental involvement both at home and at school increased since enrollment in the home school program because: (1) there were more opportunities for involvement in the home school; and (2) parents felt closer to the tutors than the teachers in public school. ^ This evaluation also suggested improvements to program operations. With the help of additional volunteers, I.C.D. program operators could improve collection and organization of academic records. Furthermore, as suggested by program participants, science could be added to the curriculum. Lastly, a formal tutor orientation could be implemented to familiarize and train tutors on classroom management procedures. ^

Higher self-control capacity predicts lower anxiety-impaired cognition during math examinations

We assumed that self-control capacity, self-efficacy, and self-esteem would enable students to keep attentional control during tests. Therefore, we hypothesized that the three personality traits would be negatively related to anxiety-impaired cognition during math examinations. Secondary school students (N = 158) completed measures of self-control capacity, self-efficacy, and self-esteem at the beginning of the school year. Five months later, anxiety-impaired cognition during math examinations was assessed. Higher self-control capacity, but neither self-efficacy nor self-esteem, predicted lower anxiety-impaired cognition 5 months later, over and above baseline anxiety-impaired cognition. Moreover, self-control capacity was indirectly related to math grades via anxiety-impaired cognition. The findings suggest that improving self-control capacity may enable students to deal with anxiety-related problems during school tests.

Illinois Standards Achievement Test sample math materials.

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Use of the Maple System in Math Tuition at Universities

The following article explores the application of educational technologies at a University level and their contribution in enhancing the educational effectiveness. It discusses the capabilities of computer algebra systems, such as Maple. It is integrated in the math tuition of the Technical University (TU) in Varna and is used by its students during laboratory exercises.

Graphical Approach to Teaching Compound Interest in High School Math Classes

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

Reading comprehension and mathematical concept acquisition through the use of math stories with bilingual children

Math storybooks are picture books in which the understanding of mathematical concepts is central to the comprehension of the story. Math stories have provided useful opportunities for children to expand their skills in the language arts area and to talk about mathematical factors that are related to their real lives. The purpose of this study was to examine bilingual children's reading and math comprehension of the math storybooks. ^ The participants were randomly selected from two Korean schools and two public elementary schools in Miami, Florida. The sample consisted of 63 Hispanic American and 43 Korean American children from ages five to seven. A 2 x 3 x (2) mixed-model design with two between- and one within-subjects variable was used to conduct this study. The two between-subjects variables were ethnicity and age, and the within-subjects variable was the subject area of comprehension. Subjects were read the three math stories individually, and then they were asked questions related to reading and math comprehension. ^ The overall ANOVA using multivariate tests was conducted to evaluate the factor of subject area for age and ethnicity. As follow-up tests for a significant main effect and a significant interaction effect, pairwise comparisons and simple main effect tests were conducted, respectively. ^ The results showed that there were significant ethnicity and age differences in total comprehension scores. There were also age differences in reading and math comprehension, but no significant differences were found in reading and math by ethnicity. Korean American children had higher scores in total comprehension than those of Hispanic American children, and they showed greater changes in their comprehension skills at the younger ages, from five to six, whereas Hispanic American children showed greater changes at the older ages, from six to seven. Children at ages five and six showed higher scores in reading than in math, but no significant differences between math and reading comprehension scores were found at age seven. ^ Through schooling with integrated instruction, young bilingual children can move into higher levels of abstraction and concepts. This study highlighted bilingual children's general nature of thinking and showed how they developed reading and mathematics comprehension in an integrated process. ^

The effects of self-monitoring on homework completion and accuracy rates of students with disabilities in an inclusive general education classroom

This study investigated the effects of self-monitoring on the homework completion and accuracy rates of four, fourth-grade students with disabilities in an inclusive general education classroom. A multiple baseline across subjects design was utilized to examine four dependent variables: completion of spelling homework, accuracy of spelling homework, completion of math homework, accuracy of math homework. Data were collected and analyzed during baseline, three phases of intervention, and maintenance. ^ Throughout baseline and all phases, participants followed typical classroom procedures, brought their homework to school each day and gave it to the general education teacher. During Phase I of the intervention, participants self-monitored with a daily sheet at home and on the computer at school in the morning using KidTools (Fitzgerald & Koury, 2003); a student friendly, self-monitoring program. They also participated in brief daily conferences to review their self-monitoring sheets with the investigator, their special education teacher. Phase II followed the same steps except conferencing was reduced to two days a week, which were randomly selected by the researcher and Phase III conferencing was one random day a week. Maintenance data were taken over a two-to-three week period subsequent to the end of the intervention. ^ Results of this study demonstrated self-monitoring substantially improved spelling and math homework completion and accuracy rates of students with disabilities in an inclusive, general education classroom. On average, completion and accuracy rates were highest over baseline in Phase III. Self-monitoring led to higher percentages of completion and accuracy during each phase of the intervention compared to baseline, group percentages also rose slightly during maintenance. Therefore, results suggest self-monitoring leads to short-term maintenance in spelling and math homework completion and accuracy. ^ This study adds to the existing literature by investigating the effects of self-monitoring of homework for students with disabilities included in general education classrooms. Future research should consider selecting participants with other demographic characteristics, using peers for conferencing instead of the teacher, and the use of self-monitoring with other academic subjects (e.g., science, history). Additionally, future research could investigate the effects of each of the two self-monitoring components used alone, with or without the conferencing.^

Illustrating Cognitive Connections between Math and Language in Pre-Service Teachers’ Perceptions of Common or Everyday Terms

This paper introduces a new construct that we term Math Mediated Language (MML) focusing on the notion that common or everyday terms with mathematical meanings are important building blocks for students’ mathematical reasoning. A survey given to 96 pre-service early childhood educators indicated clear patterns of perceptions of these terms.

Changing Parental Perceptions of Math and Science Curriculum Through Hands-on Workshops

Many parents hold negative perceptions of math and science because they have never been taught these domains from a hands-on, constructivist approach. Only 20 - 30% of adults have actually experienced activity-based science inquiry. Instead, these individuals were exposed to didactic science programs that emphasize drill, skill and memorization (Shymanksy, 2000). This has had a negative impact upon their content knowledge in these areas and their perceptions of math and science. Consequently, parents are hesitant to incorporate math and science into their home life. There is a dire need to determine if parental perceptions of math, science, and their content knowledge will be positively effected as a result of participation in hands-on science workshops.

Strategies for Reducing Math Anxiety in Post-Secondary Students

This literature review explores how educators might address adult math anxiety. Curricular, instructional, and non-instructional strategies are reviewed. The suggested approaches emphasize treating the cognitive and physical manifestations of math anxiety.

Adults Learning Math Online: A Surprising Harmony

Adults returning to school face challenges including overcoming math anxiety. Many choose online courses as they balance life and work schedules. Online math courses therefore can be restructured to prevent math anxiety by catering to individual learning styles, providing tools that aid concept attainment, and using problem-based learning strategies.