This webinar was held on the Elluminate web site and the featured speaker was Adam Bellow. Mr. Bellow is the creator of the EduTecher web site. This site is described by Mr. Bellow as a “repository for web 2.0 links”. The site contains 1100 links and the links provide a vast array of free tools for educators. During the course of his discussion Mr. Bellow introduced his audience to several useful web tools that can be found on EduTecher. Some of the ones highlighted were; http://www.Printwhatyoulike.com., http://www.Sumopaint.com, http://www.Wall.FM, http://www.edmodo.com, http://www.only2clicks.com, and many more. The Printwhatyoulike.com site is a very nice tool for editing text or pictures from web sources. This tool allows you to take any URL and edit the content to suit your particular needs. Sumopaint.com has some really cool graphics tools that enable the user to create interesting designs and use them in presentations. Only2clicks.com is a bit like Diigo but with a few more bells and whistles.

The presentation really opened my eyes to the amount of cool stuff that is available on the web for free. I will definitely spend some time exploring the site and I know I will download a bunch of useful web tools. Adam Bellow is a very interesting and creative guy. Since launching EduTecher in 2007 he has revised and up-dated the site several times. The site also contains a tool to add links and there are about 5-7 links added each week. This amazing resource is a must see for teachers.

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If there were lows they were insignificant. Like a computer that chose to rebel or a piece of technology that was particularly confusing. For the most part things went well and I amazed myself with my ability to actually make things work and complete assignments.

As far as changes are concerned I believe that the course must meet the needs of the students. Sometimes it’s hard to know just what those needs are and the direction you start with must be adjusted. The beauty of this course was that student input lead to change. That was nice to see and I think everyone appreciated the flexibility of our very special instructor. Again I want to express my gratitude for all the work that went into the creation of the course and I am sure that students who are lucky enough to enroll in this course in the future will also find it to be one of the highlights of their on-line education.

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Unit 6 – assignment 6.7

Robert Stock

For this assignment I chose to participate in the discussion at EduBlogs Serendipity ,Thursday 7pm, August 19. The discussion at this bi-weekly webinar centered on the use of 2.0 web tools and personal learning networks. There were a number of web resources that were described and demonstrated. Some of the sites were unfamiliar, others were not. The bulk of the discussion dealt the merits of using web tools in education. My contribution to the discussion was the introduction of the wetpaint wiki tool which I had used to create a web quest activity in an earlier technology class. Other tools that were discussed included Jing, Twitter, Tumblr, Ning, Elluminate, Google, Wikipedia, Skype, and several others.

There was also a brief discussion about the creation of personal learning networks. These networks are really the web tools and internet groups that are of interest to the user. Social networks and focus groups form the basis of the personal learning network. These networks are designed by the individual and provide a link to the larger community of educators. They function as a resource for study and professional development. Any topic of interest can be investigated and the strength of such a network is the ability to concentrate a wide body of information in an effective and useful fashion.

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Unit 6 – Assignment 6.1

Robert Stock

1. **Knowledge **

** **Tasks at this level will require the student to remember information or to recognize concepts. Students could be asked to describe the difference between rational numbers an irrational numbers. An assessment for this level of understanding could be to provide students with a list of numbers and have them place the number in the correct category. A second assessment could require the students to memorize the order of operations and then create a quiz to test their knowledge.

2. **Comprehension**

At the comprehension level of understanding students are able to work with facts and procedures. They can convert units of measure from one system to another. They should also be able to determine the classification of geometric figures. A task that could be used at this level might be to convert temperature readings from Celsius to Fahrenheit. An assessment for this level could be to provide students with graphic representations of data and have them answer questions based upon the information contained in the graph. Another assessment would require students to put a list of numbers in order from least to greatest.

3**. Application**

** **At the application level students can use formulas and solve equations. They can apply their understanding to problems and calculate solutions. An example of a task at this level might be to have students plot two points on a coordinate plane and then use the slope formula to calculate the slope of the line containing the given points. An assessment for this level might be to have students find the areas of different geometric figures. Another assessment could involve the use of several quadratic equations where students would have to employ the quadratic formula to find the roots of the given equations.

4. **Analysis**

** **At this level students can interpret results and make deductions. They can sort data and distinguish between various types of information. A task that could be used at the analysis level might be to provide students with sets of data and have them decide how to represent this information using a graph. As an assessment for this level students might be asked to determine the relationship between ordered pair s and to state if the data represents a first or second order relationship. A second assessment could be designed around a linear relationship where students would be given information and the goal would be to develop a verbal model, an algebraic model, and to ultimately calculate a solution to the problem.

**5. Synthesis**

The synthesis level of understanding is reached when students can take information and create new methods of working with the data. At this level students can recognize patterns and make predictions from their observations. A task at this level could be to have students discuss the concept of an asymptote or the value of an inverse function as the independent variable grows beyond all bounds. An assessment at this level could be to have students plan and create a method to study a physical system and to determine the mathematical relationship between the variables in the system. Student projects at this level could involve research of a topic and the creation of a presentation to demonstrate the topic. Another way to assess at this level is to provide student groups with a list of clues to solve a problem and to have the students work through the process of developing a plan to find the solution.

**6. Evaluation**

** **At the evaluation level students are able to make conclusions based upon given information. They can justify their explanations and are capable of appraising the validity of a solution. A task at this level would be to work through a mathematical proof. An assessment might be to have students explain and prove the Pythagorean Theorem. Another method of assessment at this level might be to have students solve a system of linear equations and then defend their solution by showing their work and explaining why the method provided the correct solution.

Reference: http://www.is93.org/blooms_math.htm

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As a high school math teacher who works predominately with ESL students my focus is on trying to convince my students that their education has value. For many of my students the cultural divide poses a significant barrier to embracing the ideals of public education. It is far more important for these students to find a compassionate and encouraging environment than to be overly concerned with their performance on standardized tests.

That being said I firmly believe that good teachers know their students. They mold their instruction to meet their student’s needs. If something is not working they change their approach. Education is not a static enterprise. Teachers for the most part want their students to learn and they are willing to do whatever is necessary to accomplish that goal. It is the function of professional development to keep teachers abreast of the latest information that is emerging from educational research. Teachers will take what they can use from the current research and discard what they can’t use. There is no perfect method nor is there a perfect teacher. We are all works in progress.

http://letsplaymath.net/2009/03/25/how-do-we-learn-math/#comment-19367

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The text is structured in a way that allows differentiation of the material that is being covered. Tasks are provided for most of the levels of understanding. Higher order skills can be developed for many of the topics covered in the text. Students who need reinforcement of lower level thinking skills are also provided with ample opportunity to strengthen their understanding.

The biggest problem I have encountered in the past two years as an ESL teacher is the aversion to any textbook by my students. Although many students can function at a conversational level they struggle when asked to read anything that is written in English. Math textbooks are notoriously difficult for ESL students and as a rule they avoid them like the plague. This makes delivering instruction that is tied to a text an interesting proposition. Although I believe that the McDougal-Littell text is an excellent textbook it is still are resource that is largely ignored by the ESL students at Reading High.

Here is my screen cast for this assignment:

http://screencast.com/t/MDQwNWEx

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Unit 6 – assignment 6.2

Robert Stock

In unit two I created tasks and assignments that were based upon student understanding of the Pythagorean Theorem. Since in this task utilizations of tasks based on this theorem are not recommended I will re-design tasks based on other topics and attempt to complete this assignment using these new tasks.

A basic task for algebra 1 students is to be able to utilize and understand the order of operations.

An activity for this task might be to have students create a rap jingle and present it to the class as a way to reinforce the concept. The creation could be an updated version of the popular “Please Excuse My Dear Aunt Sally”. Students could add their own interpretations and present their final product as a screen-cast or a live group presentation. Some other resources for this topic are:

http://www.funbrain.com/algebra/index.html

http://www.quia.com/jfc/281615.html

http://www.slidermath.com/integer/OrdOps3.shtml

Another concept that may lend itself to this type of creative activity would be the slope of a line. Here students need to find ways to represent this idea in a real world application as well as an algebraic one. They could demonstrate the relative differences between slopes by building a moveable ramp and experiment with this ramp to see how objects move on the ramp when the slope in increased or decreased. Other activities that could reinforce understanding can be found at the following web sites:

http://www.mathwarehouse.com/algebra/linear_equation/interactive-slope.php

http://www.mathwarehouse.com/algebra/linear_equation/slope-of-a-line.php

http://www.coolmath.com/algebra/Algebra1/06Lines/05_whatstheslope.htm

My third concept that could be presented at the creating level for algebra students would be the real number line. For this topic students could create different representations of the number line. These representations could be simple drawings or graphs or they could be real world examples of the number line concept such as numerical scales or measuring devices. Some web resources that may be useful for this topic are:

http://themathworksheetsite.com/numline.html

http://www.abstractmath.org/MM/MMRealNumbers.htm

http://www.educationbug.org/a/number-lines.html

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Unit 5- Assignment 5.7

Robert Stock

In this assignment I chose to take part in the web discussion “It Takes a Village” which was presented by Greg Whitby. The forum was held on the Elluminate web facility at 7:30, 8/12/2010. The topic of discussion was contemporary learning which is based on a variety of unconventional teaching strategies. It is the vision of Mr. Whitby to radically alter the way in which instruction is provided for students in the Australian school system. His belief is that students should be free to choose where, when, and how they acquire knowledge within the framework of the educational system. By shifting the onus for learning from the teacher to the student the hope is that student engagement will improve and learning outcomes will be enhanced. Although I am unfamiliar with the public school system of Australia I believe that there are several caveats to this utopian vision. In this country students do not have a choice whether or not to participate in the educational process. They are required by law to attend school. This fact alone creates a completely different dynamic within the classroom. Certainly for students who appreciate their educational opportunities and who are eager to increase their understanding this pedagogy could prove highly successful.

Changes come slowly to any area of human endeavor and that is not necessarily a bad thing. Ever since the inception of public education there has been ongoing debate as to how this system should be operated. What may work for one group may not meet the needs of another. Cultures vary from school to school and from classroom to classroom. As an employee of a public school system I am obligated to work within the framework of my school district and to uphold the policies and regulations that have been set forth by the powers that be. Change will come, of that I am certain. My hope is that we will be receptive to change when it is in the best interest of our students and that we will resist change when it is motivated by less altruistic motives.

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The following quote describes the differences between formative and summative assessment. Although the quote refers to law students it is applicable to students in any educational setting.

“The difference between formative and summative assessment is often an area of concern for law teachers. The essence of **formative assessment** is that undertaking the assessment constitutes a learning experience in its own right. Writing an essay or undertaking a class presentation, for example, can be valuable formative activities as a means of enhancing substantive knowledge as well as for developing research, communication, intellectual and organizational skills. Formative assessment is not often included in the formal grading of work, and indeed many believe that it should not be.

In contrast, **summative assessment** is not traditionally regarded as having any intrinsic learning value. It is usually undertaken at the end of a period of learning in order to generate a grade that reflects the student’s performance. The traditional unseen end of module examination is often presented as a typical form of summative assessment.”

The use of both of these assessment methods would be included in my instructional protocol. I believe that we must check for understanding as we teach to avoid losing touch with our students. Certainly the summative assessment is necessary when determining student grades.

Reference: http://www.ukcle.ac.uk/resources/assessment-and-feedback/formative/

**2. Neutrality- Objective and Subjective:**

Subjective assessment is described by this reference; “In subjective assessments the teacher’s judgment determines the grade. These include essay tests. Essay tests take longer to answer and they take longer to grade than objective questions and therefore only include a small number of questions, focusing on complex concepts.” Objective assessment can be defined by this quote; “Objective assessments (usually multiple choice, true false, short answer) have correct answers. These are good for testing recall of facts and can be automated. Objective tests assume that there are true answers and assume that all students should learn the same things.” In everyday use the objective assessment is probably the assessment of choice for most educators. The ease of scoring is a big factor in this case and since time is always in short supply this form of assessment will constitute the core of my assessment strategy. The subjective assessment can be used in an open-ended format. Due to the use of this type of problem on standardized tests I would include this type of testing as an alternative assessment technique.

References:

http://vudat.msu.edu/objective_assess/

http://vudat.msu.edu/subjective_assess/

**3. Self Assessment**:

The concept of self-directed assessment is explained by this reference: ” Students need the opportunity to evaluate and reflect on their own scientific understanding and ability. Before students can do this, they need to understand the goals for learning science. The ability to self-assess understanding is an essential tool for self-directed learning. ” The ability to self assess is a function of student maturity. Any self assessment or peer assessment assumes a level of understanding on the part of the students that requires honesty and heart-felt evaluation. In a 9th grade algebra class I am not sure I can utilize this format effectively. Perhaps there will be opportunities to include this assessment type somewhere along the line but I will have to exercise extreme caution when implementing such a strategy.

Reference: http://www.sedl.org/scimath/compass/v02n02/selfdirected.html

**4. Constructed Response- Selected Response:**

From : http://fcit.usf.edu/assessment/constructed/construct.html

“With *selected response* assessment items, the answer is visible, and the student needs only to recognize it. Although selective response items **can** address the higher levels of Bloom’s taxonomy, many of them demand only lower levels of cognition. With *constructed response *assessments (also referred to as subjective assessments), the answer is not visible — the student must recall or construct it. Constructed response assessments are conducive to higher level thinking skills.” Once again I take the easy way out. With ESL students I am happy when they are capable of selected responses. There are those occasions when a constructed response would be nice but that is a rare occurrence.

**5. Ability and Performance: **

Timothy Slater of Montana State University describes the rationale for performance assessment in the following reference; **WHY USE PERFORMANCE ASSESSMENT?**

“Although facts and concepts are fundamental in any undergraduate SMET course, knowledge of methods, procedures and analysis skills that provide context are equally important. Student growth in these latter facets prove somewhat difficult to evaluate, particularly with conventional multiple-choice examinations. Performance assessments, used in concert with more traditional forms of assessment, are designed to provide a more complete picture of student achievement.” A performance assessment in a secondary mathematics class would probably be constructed in a project format. Allowing the students to utilize their creativity would be an interesting and exciting way to measure student achievement. The design of such an assessment could provide a differentiated approach to the curriculum goals. Here the key is student motivation. For the engaged student a performance assessment may well prove to be a rewarding experience.

**6. Authentic and Standardized:**

In *Developing Authentic Assessment: Case Studies of Secondary School Mathematics Teachers’ Experiences* Christine Suurtamm writes,”Since traditional tests often focus only on the answer or the use of a suitable algorithm to reach the answer, authentic assessment techniques need to be employed to provide a broader range of measures. In this article, the term *authentic assessment **is used to describe assessment of this type: assessment* that involves students in tasks that are worthwhile, significant, and meaningful and that resemble learning activities. Such assessment activities also encourage risk taking, allow for mathematical communication, and provide the opportunity to demonstrate the application of knowledge in unfamiliar settings.” This definition of authentic assessment provides the basis for the design of assessment strategies that can have a significant effect on student understanding. By creating assessment tools that have relevance to the world in which our students live we can build bridges that can connect our students to the goals of our curriculum. It is not always easy to accomplish this goal. Mathematics like most subjects demands a level of commitment on the part of the student. However by providing assessment that is challenging and engaging the chance of a successful outcome is certainly increased.

Choosing the appropriate assessment for a particular group of students is a task that requires a thorough understanding of your students. In an ESL classroom it is important to design assessment with realistic goals in mind. Communication is paramount in working with students who are struggling with language as well as content. Often assessment must be modified to meet these challenges.

As a teacher I am acutely aware of the need to assess my students. The entire system of public education revolves around one form of testing or another. Every student wants to know how they are performing and it is the job of the teacher to provide that information. Whether it is a paper and pencil test, an alternative assessment, a performance based evaluation, or any other measure of student knowledge the fundamental purpose is the same. Teachers must deliver instruction that is tied to a specific program. They must then determine how well their students have learned this material and they must do it fairly and reliably. Assessment lies at the heart of the educational process. It is the very art and science of teaching.

Reference:

Suurtamm,C,*Developing Authentic Assessment: Case Studies of Secondary School* *Mathematics Teachers’ Experiences*,Canadian Journal of Science, Mathematics, & Technology Education, Oct2004, Vol. 4 Issue 4, p497-513, 17p; (AN 15400415)

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Included in the site are a number of templates that can be used to create the materials needed for some of the activities. Because the site is geared to an introductory level it is ideal for differentiating the instruction in a mixed ability classroom. For many of the ESL students that I have worked with in the past these types of activities would provide an effective way to gain understanding. The web address is:

http://www2.edc.org/mathpartners/pdfs/6-8%20Statistics%20and%20Probability.pdf

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