08/11/2008 Discrete Math in Middle/Secondary School Competencies Met:
- MATH 9a. Demonstrate knowledge of counting techniques, sets, logic and reasoning, patterning including iteration and recursion, algorithms, and induction, networks, graph theory, social decision-making, efficiency, and binomial series.
- MATH 9b. Demonstrate the capacity to use combinations and permutations to solve probability problems.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
08/11/2008 Probability Competencies Met:
- MATH 7. In the subject are of probability and statistics, the candidate shall have the ability to:
- MATH 7a. Demonstrate an understanding of basic concepts of probability and statistics, including discrete and continuous probability distributions, descriptive and inferential statistics, and exploratory data analysis.
- MATH 7b. Design and experiment, collect appropriate data, analyze the data, and construct a valid statistical argument comparing the experimental and theoretical probabilities.
- MATH 7c. Explore the connections between statistics and probability by making the connections between statistics and probability by making use of various concepts that include hypothesis testing, correlation, regression, and analysis of variance and applying these concepts to everyday situations, such as games and lotteries.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
08/11/2008 Learning Math: Geometry Competencies Met:
- MATH 5. In the subject area of geometry and measurement, the candidate shall have the ability to:
- MATH 5a. Employ common geometric ideas such as Pythagorean theorem, similar triangles, and trigonometry to solve problems involving direct and indirect measurement.
- MATH 5b. Use a variety of tools such as compass and straightedge, physical models, and dynamic geometric software to explore geometric construction and relationships.
- MATH 5c. Demonstrate knowledge of the axiomatic development of Euclidean geometry, and transformational geometry.
- MATH 5d. Solve problems and construct proofs in two-dimensional geometry and three-dimensional geometry that involve parallelism, perpendicularity, congruence, similarity, and symmetry.
- MATH 5e. Demonstrate relational understanding of important geometric concepts associated with visualization, description, measurement, and classification of geometric figures.
02/19/2008 Electronic Portfolio Assessment & Design Competencies Met:
- NH Ed 306.42
- 5.A. through 5.g. [The professional shall consider how the school will:]
- (5) Create digital portfolios which address the following components:
- a. basic operations and concepts;
- b. social, ethical, and human issues;
- c. technology productivity tools;
- d. technology communications tools;
- e. technology research tools; and
- f. technology problem solving and decision-making tools.
- NH Ed 507.22
- 2.A. Ability to evaluate, and use computer and technology resources including applications, tools, educational software and associated documentation.
- 3.E. Ability to integrate computer and related technology resources to facilitate lifelong learning and emerging roles of the learner and the educator.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
02/18/2008 Logic, Proofs, & Axiomatic Systems Competencies Met:
- MATH 3. In the area of knowledge of professional practices, the candidate shall have the ability to:
- MATH 3b. Demonstrate the capacity to construct proofs and logical arguments using an axiomatic approach to verify hypotheses in mathematics.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
02/18/2008 Masters of Education in 7-12 Mathematics & Computer Technology Education (Summer 2009) Competencies Met:
- ED 1h. The applicant demonstrates proficient oral, written, and nonverbal communication and promotes the development of these skills in students.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
- MATH 3. In the area of knowledge of professional practices, the candidate shall have the ability to:
- MATH 3a. Demonstrate the capacity to learn mathematics independently.
- MATH 3c. Demonstrate the capacity to communicate about mathematics and mathematics education in both written and oral ways that includes informal and professional formats.
- MATH 3d. Articulate how the use of formal language and notation increases in importance as mathematical concepts are developed in the K-12 Mathematics curriculum.
- MATH 3f. Provide current examples of mathematical practices and notation within various cultures.
- MATH 3h. Provide examples of how mathematics is practiced in various fields, such as engineering, nursing, carpentry, and the arts.
- MATH 3i. Demonstrate knowledge of state, regional, national and international professional associations and journals, and how to access resources on the Internet.
- MATH 3k. Demonstrate knowledge of current state, national, and international findings and recommendations regarding the teaching and learning of mathematics.
- MATH 3l. Articulate the power of mathematics as an academic discipline, a tool for quantitative reasoning, and a gateway to many career choices
- MATH 4. In the subject area of numbers and numeration, the candidate shall have the ability to:
- MATH 4a. Demonstrate an understanding of the axiomatic development of the real and complex number systems.
- MATH 4c. Use estimation strategies and mental computation techniques to judge the reasonableness of answers and to approximate solutions.
- MATH 4d. Use physical materials and models to explore and explain operations and properties of real numbers and their subsets.
- MATH 4e. Demonstrate a capacity to apply the concepts of proportional reasoning.
02/13/2008 Teaching Standards based Math - "Today’s Math" is not the same as most of us were taught. We didn’t apply lessons to the real world; we just used rote memorization to learn the material. I believe having students, work together helps them learn the different ways to approach the same problem. I keep telling my students there is more than one way to solve a problem. Explain how you got the answer, don’t just give the answer. In reviewing the state test data, our students cannot explain how they arrived at an answer. My goal as a teacher is to make them realize that explaining is more important than the final answer.
Competencies Met -
- MATH 1a. Takes into consideration gender, socioeconomic status, culture, and ethnicity.
- MATH 1b. Takes into consideration learning styles, concrete and abstract thought process, deductive and inductive reasoning, and auditory, visual, tactile, and kinesthetic modalities.
- MATH 1c. Builds upon the varied prior experiences and knowledge, which all students bring to the classroom.
- 1d. Meets the needs of students with differing talents, interests, and development, including mathematically talented students and students with various educational disabilities.
- 2. In the area of instructional strategies, the candidate shall have the ability to plan and conduct units and lessons which:
- MATH 2a. Enable students to construct new concepts through active participation in mathematical investigations.
- MATH 2b. Proceed from concrete representation to symbolic representations in ways that make sense for each learner.
- MATH 2c. Provide multiple representations of concepts being learned, alternate explanations, and intuitive as well as formal arguments.
- MATH 2d. Provide opportunities for students to demonstrate their understanding of mathematical concepts in writing, and orally with both other learners and the teacher, and through various means of creative expression.
- MATH 2e. Model and nurture within the context of mathematics important habits of mind including curiosity, perseverance, risk taking, making conjectures, and logical reasoning.
- MATH 3e. Demonstrate the capacity to solve non-standard, real-world problems.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
02/03/2008 Leadership in Educational Technology - For me, this course returned me to my days as Network administrator. The course work updated what I already knew about technology and making proposals for enhancing networks.
Computer Technology Education Competencies Met -
- 1. Relative to the knowledge of technology tools and resources, the following shall apply to the area of proficient computer and technology operations and concepts across platforms:
- 1c. Ability to access and use telecommunications tools and resources, including email, listserv, and other distance learning tools.
- 1d. Ability to practice responsible, ethical, legal, and equitable access to technology, information, and software resources.
- 1e. Ability to practice responsible, ethical, legal, and equitable use of technology, information, and software resources.
- 1f. Ability to develop plans to organize computer and technology systems and related peripherals in a variety of settings.
- 2. Relative to the integration of technology across instructional settings, the following shall apply to the area of general teaching strategies:
- 2a. Ability to evaluate, and use computer and technology resources including applications, tools, educational software and associated documentation.
- 2b. Ability to design and implement integrated technology classroom activities that involve a variety of student grouping strategies, curricular areas, and diverse student populations.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
02/03/2008 Teaching & Learning in a Networked Environment - I renamed this course Web 2.0 because we learned how to use the Internet to get our students engaged. Our students all use Myspace, video games and blogging - why not show them all the possibilities and the correct way to use these tools?
Competencies met:
- ED 1a.The applicant believes that each student can achieve at the highest level possible for that student, shows respect for students’ varied talents and perspectives, and persists in helping all students achieve success.
- ED 1e. The applicant understands and identifies differences in students’ approaches to learning and designs instruction that is responsive to their diverse needs.
- ED 1f. The applicant values and is fluent in a variety of instructional strategies and chooses appropriately from them to encourage and enhance students’ thinking, learning, and skilled use of knowledge.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
- 2. Relative to the integration of technology across instructional settings, the following shall apply to the area of general teaching strategies:
- 2a. Ability to evaluate, and use computer and technology resources including applications, tools, educational software and associated documentation.
- 2b. Ability to design and implement integrated technology classroom activities that involve a variety of student grouping strategies, curricular areas, and diverse student populations.
- 2c. Ability to design and practice methods and strategies for teaching computer and technology literacy concepts and skills.
- 2d. Ability to design and practice methods and strategies for teaching concepts and skills for applying keyboarding, productivity and information access tools, including word processing, spreadsheet, database, presentation, classroom management software.
- 3. Relative to the integration of technology across instructional settings, the following shall apply to the area of curriculum design:
- 3a. Ability to apply basic principles of instructional design associated with the development and use of multimedia and hypermedia learning materials.
- 3b. Ability to develop instructional units that involve using technology to support critical thinking skills of:
- 1. Researching;
- 2. Compiling;
- 3. Organizing;
- 4. Analyzing;
- 5. Synthesizing; and
- 6. Problem solving;
- 3c. Ability to research and evaluate on-line and other sources of information that support and enhance the curriculum, including distance education.
- 3d. Ability to identify and support implementation and revision of curriculum to reflect on-going changes in technology.
- 3e. Ability to integrate computer and related technology resources to facilitate lifelong learning and emerging roles of the learner and the educator.
- 4. Relative to the application of technology in instructional settings, the candidate shall have the ability to provide professional support related to the instructional integration of technology into the curriculum in accordance with the following:
- 4a. Ability to apply computer and technology applications and use technology to support other content areas.
- 4b. Ability to integrate advanced features of technology tools to support instruction in collaboration with content teachers.
- 4c. Ability to assist staff in the integration of adaptive assistive hardware and software for students with special needs.
- 5. Relative to the evaluation of technology in instructional settings, the following shall apply to the area of student evaluation:
- 5a. Ability to design a set of evaluation strategies and methods to assess student learning.
- 5b. Ability to evaluate, select, and use appropriate measures to assess students’ computer knowledge and skills and compare to district, state and national standards.
- 6. Relative to the evaluation of technology in instructional settings, the following shall apply to the area of process and product evaluation:
- 6a. Ability to evaluate the process and criteria for selection of technology systems.
- 6b. Ability to evaluate the process and criteria for selection of technology related materials.
- 7. Relative to the evaluation of technology in instructional settings, the following shall apply to the area of program evaluation:
- 7a. Ability to evaluate the use of technology in terms of meeting district instructional goals and national trends.
- 7b. Ability to collaborate with staff to design research strategies evaluating the use of technology in the classroom.
02/03/2008 Philosophy, Ethics, & Education - This course forced me to take a look at myself and my view on different people. As teachers, we have to accept every student, parent and school community member for who they are, not how they act or look. Having an open mind requires us to not prejudge. We might just learn from those that are different.
Competencies Met -
- MATH 1a. Takes into consideration gender, socioeconomic status, culture, and ethnicity
- MATH 1b. Takes into consideration learning styles, concrete and abstract thought process, deductive and inductive reasoning, and auditory, visual, tactile, and kinesthetic modalities.
- MATH 1c. Builds upon the varied prior experiences and knowledge, which all students bring to the classroom.
- MATH 1d. Meets the needs of students with differing talents, interests, and development, including mathematically talented students and students with various educational disabilities.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
01/19/2008 Social Psychology & Mythology Across Cultures - This paper finalized a course that made me search into myself to decide why I want to be a teacher, a good parent and community member. This course helped me to realize the reasons behind different people’s behaviors. I have included this paper as proof of participating in one of my required courses.
Competencies Met -
- MATH 1a. Takes into consideration gender, socioeconomic status, culture, and ethnicity
- MATH 1b. Takes into consideration learning styles, concrete and abstract thought process, deductive and inductive reasoning, and auditory, visual, tactile, and kinesthetic modalities.
- MATH 1c. Builds upon the varied prior experiences and knowledge, which all students bring to the classroom.
- MATH 1d. Meets the needs of students with differing talents, interests, and development, including mathematically talented students and students with various educational disabilities.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
01/19/2008 Research and Design - this course is perhaps the toughest course I have taken to date. I had never attempted a research project of this magnitude before, nor did I have any idea what APA style was. I knew I wanted to research the correlation between one-to-one laptops and mathematics test scores. The government is requiring schools to put technology in the hand of our students and our student to do well on the state mandated tests. Neither program is funded, nor are the tests computerized; however, the push for both to be successful continues.
My research paper took me longer than expected because I had a hard time finding the information I needed to start. We were given sheets to fill out to help us with our paper, but I did not find them helpful. Once I found the information necessary to work on the paper, the paper seemed to flow quite nicely. I was able to use my original essay as a guide to check my APA format (I like the fancier reports). The PowerPoint was not only easy to make, but allowed my creativity to flow. I was able to add podcasts and movies to help sell my research proposal.
If I were to do anything differently, I would find APA reports to look at before trying to write this type of paper. I would not have attempted to take this course on-line because it was harder to get questions answered. I am pleased with my outcome and feel like I have learned valuable tools for both my students and myself.
Competencies Met -
- MATH 1a. Takes into consideration gender, socioeconomic status, culture, and ethnicity
- MATH 1b. Takes into consideration learning styles, concrete and abstract thought process, deductive and inductive reasoning, and auditory, visual, tactile, and kinesthetic modalities.
- MATH 1c. Builds upon the varied prior experiences and knowledge, which all students bring to the classroom.
- MATH 1d. Meets the needs of students with differing talents, interests, and development, including mathematically talented students and students with various educational disabilities.
- ED 1k. The applicant uses a variety of resources to enhance his or her professional development as a scholar, teacher, and educational leader.
01/19/2008 My Bachelor of Science degree is required to show that I have taken my two Calculus courses and have obtained my Bachelor’s degree. My computer degree from Bentley and my work experience has allowed me to apply my work experience towards my Masters in Computer Education.
Competency Met:
- MATH 8. In the subject area of calculus, the candidate shall have the ability to:
- MATH 8a. Demonstrate an understanding of both single and multi-variable calculus relating to limits, differentiation, integration, and infinite series.
- MATH 8b. Apply models of change and rates of change to problems within mathematics such as area, volume, and curve length and other disciplines such as physics, biology, and economics.