This week’s on-line live event that I chose to attend was eduTecher at Classroom 2.0.

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.Wall.FM,,, and many more.  The 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. has some really cool graphics tools that enable the user to create interesting designs and use them in presentations. 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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Parting is Such Sweet Sorrow

Reflecting on the highs and lows of this course is a task that brings a twinge of regret.  As I look ahead to the coming school year I am thankful to have been given the opportunity to participate in many of the wonderful courses that are part of the CIMS program.  I know that I am much better prepared to do battle with the students I will soon encounter.  I know that the training I have received will serve me well in the coming months and I am anxious to put many of the new skills and strategies I now have in my arsenal to the test.  This class was unique.  It challenged me in ways I did not anticipate.  It used technology in a way that brought the meaning of learning in the 21 century into clear focus.  I will take away many new ideas and many new tools from this course.    Perhaps the best part of the course was the way in which it recharged my batteries and made me see afresh why I want to teach math.

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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Edublogs Webinar

ED526b – Learning and Assessment in Secondary Math

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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Tasks and Bloom’s

ED526b Learning and Assessment in Secondary Math

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.


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How Do We Learn Math?

        The debate over the best method for the delivery of math instruction is not likely to be resolved any time soon.   I’m not sure we should ever attempt to declare a winner.   By the time we all agree upon the best practice the state of education will have changed again and we will have to re-think our approach.   There are benefits to the process however and it is important to work toward improving the system. 

     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.

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Algebra 1 Textbook and Bloom’s

     In this assignment I have chosen to look at chapter 2 of the McDougall Littell Algebra 1 textbook that is currently being used at Reading High School.  The text is very well-organized and provides a solid framework for delivering instruction in an algebra 1 course.  Concepts are presented in a straightforward manner and there many examples and exercises that can be used to build student understanding.  The text is also available in an on-line format which is particularly helpful for direct instruction. 

    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:

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Creative Level Tasks

ED526b – Learning and Assessment in Secondary Math

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:

     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:

     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:

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