Thursday, January 27, 2011

And Scarecrow's Brains.... as the Tin Man in a local production from 2009....

"The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side." -Scarecrow's version of the Pythagorean Theorem, from The Wizard of Oz

So...was this meant to be an intentional error, or simply a mistake by the scriptwriters? See the Poll on the left to cast your vote!

Wednesday, January 26, 2011

Peer Teaching

One of my favorite, and often most successful, ways in which I conduct a lesson is through peer teaching. In general, I will have formulated a lesson plan that involves the pairing off of my students (slightly different than a true group activity) in such a way as to build on each pairs' particular strengths and weaknesses. For example, if I am planning a Geometer's Sketchpad activity, I will have a bright math student, who may not be technologically savvy, paired with a classmate who knows the software extremely well, but may not be as good a math student. In this way, each member of the pair supports and compliments each other without either participant feeling "lost" in the activity or the concept. After introducing and setting up the parameters of the lesson, I can often just observe without feeling the need to interact with the pairs until they are ready to share their results. I have found this to be a great way to cover material in a teacher-lead, student-run fashion.

Promote Your Blog

Other than fellow math bloggers' sites, this website is one of the best ways I have found to promote my blog; especially as a "newbie" blogger. Signing up is free and, once your site is approved and added to their site, promotion of--and traffic to--your blog is seamless.

Monday, January 24, 2011

Math Portfolios

I came across this site today and was wondering what other math teachers' experiences are who use portfolios for their math students; especially in terms of grade level, pitfalls, and assessment rubrics. Any input would be greatly appreciated, as I am really intrigued and see the many benefits of having students keep a math portfolio....

An excerpt from this site:

"A math portfolio contains samples of a student's work that is collected over a given length of time. A good portfolio offers insights to a student's thinking, understanding, and mathematical problem-solving skills, and thus offers a picture of the student's progress in math. Following are some suggestions on how you can incorporate the use of portfolios in your math classroom:
  • Explain to your students what a portfolio is and how it will be used.
  • Provide students with portfolio envelopes. They should be large enough to hold various kinds of work.
  • Make sure that your students understand that they are to select their best work for their portfolios. Because one of the purposes of the portfolio is to show individual growth, all papers should be dated.
  • Portfolios may be one of two kinds: an assessment portfolio that shows particular growth, or a work portfolio that contains various projects and activities. Generally, papers from the work portfolio are selected to go into the assessment portfolio.
  • While you may guide students in their selection of material for their portfolios, they should be the judges of what actually goes in.
  • The material that goes into a portfolio should help the teacher and others to understand how students see themselves in the learning of math.
  • Many papers, activities, and projects are appropriate for inclusion in a portfolio. Following are some suggestions:
    • A table of contents
    • Solutions to difficult problems that detail problem-solving abilities
    • The use of mathematics in another discipline
    • Problems created by the student
    • An example of the student's group activity
    • A written report on a major topic in math
    • The student's written account of his or her growth in mathematics
    • Responses to challenging questions and problems
    • A written explanation of the contents of the portfolio
Excerpted from The Math Teacher's Book of Lists."

Sunday, January 23, 2011

Current Math Culture

Last spring, my school had a math consultant come in to evaluate our program. Below I post the introductory paragraph of his final report which seems to "hit the nail on the head" regarding our society's current math culture...

"Math teachers face a particularly daunting paradox. Mathematics is an inordinately complex web of logical connectives, whose mastery requires extraordinary powers of concentration, frequent repetition, the emotional stability to live with perplexity, and the self-discipline to accept the need for sequence and continuity; yet many, if not most, of today’s parents are unwilling to see their children struggle with this complexity, and discourage the kind of experimentation and risk-taking that might lead to “failure.” [Students]... everywhere, need to become risk-takers instead of automata obsessed with getting “the right answer.” Learning involves taking risks. This means being willing to “give it a go,” to guess, to estimate, to try a new and different way of doing things. The systematic and formal way in which mathematics is usually presented conveys an image of  the subject which is wildly at odds with the way it actually develops. Mathematical discoveries, conjectures, generalizations, counter-examples, refutations and proofs are all part of what it means to do mathematics. School mathematics needs to show the intuitive and creative nature of the process, and also the false starts and blind alleys, the erroneous conceptions and errors of reasoning which tend to be a part of mathematics. Children need to learn that lack of certitude and comfort with ambiguity are perfectly acceptable in the math classroom. Yet, while teachers rightly decry the lack of risk-taking in the older students, I would suggest that assessment methods themselves often discourage students from taking risks – [students]... may surely be forgiven for feeling that “the right answer” is paramount when their competence and progress is judged solely by graded homework assignments, quizzes, tests and exams."
- R. Michael McNaught

Saturday, January 22, 2011

The Very First Apple Movie

This sample movie was included on the original Apple Quicktime 1.0 Developer CD-ROM, released in December, 1991.... Enjoy:)

From "In 1988, Apple was eager to show off the graphics power of its Macintosh II line of computers. Using a program called Super3D, a group of talented artists produced "Pencil Test," an animated short created entirely on the Macintosh. Keep in mind that QuickTime did not exist in 1988; the movie was output frame by frame to an imagesetter, and then recorded to film."

Friday, January 21, 2011

Reading Math

One of the most significant challenges teachers face today is tackling their students’ poor reading skills…in math! Too often, students are merely required to do an endless number of “practice problems” that require nothing more than a rote process in order to arrive at an answer. These types of problems have their place, in moderation, but doesn’t it make more sense to challenge our students—regardless of their aptitude and ability—with age-/level-appropriate application (i.e., “word”) problems? Sure these are “harder” to do, and most students do not “like” doing them; especially in our current “eye candy” society that emphasizes instant gratification. If a solution is not easily attained, teachers are afraid that they will lose their students' interest and involvement. However, just the opposite can happen! If well prepared, a teacher can capture his/her student audience by making the concept of the day based upon real world scenarios. When covering a non-basic topic, how many times have we as math teachers heard our students complain, “…when will we ever need to know this?”  Doing more application-based problems, while reinforcing reading skills, not only addresses this common complaint, but it creates a more active learning environment. It’s OK for student not to “get it” right away…it’s OK to struggle with how to go about setting up a word problem!

Students are more apt to retain mathematical concepts over the long-term if they are asked to apply them to application problems rather than simply solve generic equations.

The end result of utilizing more application problems during math classes is two-fold. First, it presents students with real life situations where math is invaluable, and secondly, students are more excited about “getting the answer” when they have to put in some real thought!

Thursday, January 20, 2011

Race to Nowhere - A MUST See

Last night I saw the movie Race to Nowhere at my school. This film by Vicki Abeles, highlights the real pressures placed upon today's over-programed teens by educators and parents alike: the daily pressure to score higher, do better, study harder, complete hours of homework, build the résumé, etc....all at the sacrifice of "down time". This powerful documentary is a must see for anyone involved in the education of a child. It raises serious questions regarding the state of education in this country. From suggesting "radical" changes, to the discussion of student stress, the over-emphasis on homework, and teen suicide (specifically 13-year-old Devon Marvin, pictured above and below), this 85-minute film needs to be seen by everyone who is involved in teaching today's youth--including teachers, administrators, students, parents, and School Board members.

My Philosophy of Teaching

I have been an educator for over 25 years and I truly enjoy working with adolescents—both in the classroom and in the athletic arena as a coach, knowing that sports can be an integral extension of the classroom. I feel that I am able to establish a professional rapport with most, if not all, of the students or athletes in my charge because I make learning fun. Children prefer to take an active role in the learning process, but this only happens when they want to be in your class (or on your team.) By making learning fun (i.e., student-driven and teacher-lead, rather than teacher-driven and student-lead), I am able not only to capture and maintain students’ interest, but also ignite a spark in each of them.

My philosophy and goal each day is to leave class or practice confident that each student has taken away something worthwhile; whether it be some piece of knowledge, an improved understanding of a mathematical concept, or simply more self-confidence. 

The better teachers are those that have not only a mastery of their field of study, but also a way with their students that makes each one of them feel comfortable within their learning environment. 

Students should never feel intimidated by the course material. The “old-school” lecture-from-the-textbook approach is an antiquated and usually ineffective method of teaching. It is vital to be able to reach each student in each class everyday, regardless of his/her comfort level within a given discipline. To accomplish this, I incorporate technology, visual aids, peer teaching, and an overall hands-on approach to my classes. The use of multiple aids not only helps to maintain a fresh feel to the classroom, but it also allows me to make connections with students of varied learning styles. Through my teaching, I challenge my students to be the best scholars and well-rounded people they can be, while instilling in them a life-long love of learning.

As educators in the 21st century, it is vitally important that we adapt our individual teaching styles to best address the needs of our students’ diverse learning styles. 

We are here for our students, not the other way around. Utilizing the humanistic approach in my classroom helps me to effectively address this need. This positive and optimistic view contributes to the idea that people need to take responsibility for their own lives through intelligent choices and decision making. In order for students to realize their full potential, they need to believe in themselves. Ultimately, this humanistic concept promotes the necessity of addressing the needs of the individual student in order for that student’s growth and development to be fully realized. As more and more research is conducted on how best to meet the needs of our students, we will need to be flexible in our classrooms. We must be willing to keep up with the times and address future challenges so that we may be effective educators. We need to be as well equipped as possible to meet the educational needs of our students. After all, they represent our future society.

Tuesday, January 18, 2011

Self-Assessment and Reflection

As an experienced and veteran teacher, it is necessary for me to periodically reflect and re-evaluate my effectiveness as an educator. This should be the case for all teachers! The better I understand my professional strengths and opportunities for growth, the better prepared I am to address the diverse learning styles of my math students. Through self-assessment, I reaffirm that learning is a never-ending process. As times change, so do effective methodologies and students' learning styles. Through self-evaluation, I can understand in greater depth my own individual learning and teaching styles, as well as recognize the need to keep up with the evolving times and technologies. A teacher's strengths as an educator are paralleled by his/her strengths as a student. Ultimately, this reflection process leads to the development of various strategies that help me become a more effective educator.

Monday, January 17, 2011

Evaluation and Assessment of Curriculum

An effective curriculum integrates content, processes, and habits of mind (i.e., behaviors that are characteristic of effective learners) taught in meaningful contexts that are relevant and interesting to students. The curriculum should address multicultural issues and perspectives and be accessible to all students. Interdisciplinary connections are also critical. Curriculum should connect the information, skills, processes, and perspectives of various disciplines.

Teachers who evaluate curriculum need to consider whether it has purpose and function, and if it is enriching, stimulating, and transforming for both teachers and students. In addition, curriculum evaluation and assessment must be cylindrical in nature. As one evaluation ends and recommendations are implemented, another cycle should begin anew.

Sunday, January 16, 2011

Curriculum vs. Instruction

Even the best math curriculum cannot make up for poor instruction. Some teachers simply do not have the commitment others do when it pertains to "required" curriculum. It is frequently apparent in their instruction and delivery of content, and often they have lessons that fall flat...or worse. Unfortunately, these teachers feel they can blame the curriculum, their students (or a combination of the two) for the failure of their lesson(s). However, curriculum is simply the what of teaching, while instruction--which is much more in the control of the teacher--is the how. With regards to any curriculum, teachers are presented with a grade-appropriate plan, a text and some materials, and a time frame in which to impart this knowledge. In terms of instruction, teachers make decisions and plans as to the way in which information is best imparted to the learners.

We, as educators, must provide an active role in the structuring, mapping, and planning of curriculum if we are to be successful in the presentation and instruction of the material.... Curriculum and instruction cannot be viewed in mutual isolation.

  • What are your thoughts and experiences as they pertain to curriculum vs. instruction in your school?
  • How would you define curriculum?
  • Who should be involved in curriculum decisions (students, teachers, parents, administrators, etc.?)

Wednesday, January 12, 2011

One of My Favorites

This answer follows the directions, so shouldn't it be awarded full credit? I would have marked this correct; full credit for thinking outside the box (or in this case, the triangle!) To avoid such an answer, the question should have asked for the value of x...!

Sunday, January 9, 2011

Redirecting a Personal Domain to Your Google Blog....

Click here for a must-read "heads-up".... In fact, this happened to me (I had an incorrect zip code as part of my credit card information), so I ended up simply registering my domain with GoDaddy instead and then redirecting from there.... Now I'm all set!

Math: "Teaching to Mastery" vs. Curriculum Pacing


Saturday, January 8, 2011

Recommended eBook of the Month: The Super Affiliate Handbook

The Super Affiliate Handbook is currently the industry's #1 authoritative guide to making some extra money on the Internet via affiliate marketing. This is NOT a "get rich quick" scheme, and it is written for both "newbies" and "affiliate pros" alike! Below is just one sample of an unbiased review. Feel free to click on the above link for more information. Personally, after doing my own online research of this 220+ page ebook, I have just started to implement some of its MANY useful guidelines.... I will keep you posted as to my results!

Super Affiliate Handbook Review - the following review was written by Daisy Samuel and was copied--with permission--from

"Using a step-by-step plan to business-building, the Super Affiliate Handbook by Rosalind Gardner answers all of the questions you will have and many, many more. Here are some examples of what you will learn:
  • You get 222 information-packed pages of practical tips and real-life examples of WORKING affiliate sites (Note: Many Affiliate Managers recommend the Super Affiliate Handbook to their affiliates. In fact, Anik Singal makes it required reading for his staff.)
  • How-to strategies to save you money, time, and effort while building your affiliate marketing business.
  • Get an easy-to-understand 5-step overview of the business-building process.
  • Discover the top 25 mistakes that normal affiliates make, and how to AVOID them.
  • How to create a web site that keeps visitors coming back for more.
  • 29 ways to market your affiliate sites online and off.
  • Why you must stay away from the flea market approach to Internet marketing.
  • How to assess a market for profitabilty.
  • Discover which products are actually sold online.
  • Learn which programs to avoid and when to drop others.
  • Where to find free software that will save you both time and money.
  • Learn how to negotiate a raise in your commissions.  
  • Learn how to stop thieves from stealing YOUR commissions.
    ...and there's more... MUCH MORE! You will also learn:
    • Which 6 factors you MUST consider when choosing a domain name.
    • How to Promote Associate Programs and Products with a Newsletter.
    • How to use Signature Files to Gain MORE Visitors.
    • How Forums can bring you more traffic.
    • About software that lets you build a 1,000-page site in mere seconds!
    • Learn which methods bring traffic to your site FAST.
    • 9 Ways to Get Traffic to Your Site for FREE.
    • The TRUTH about reciprocal linking.
    • How writing a simple ezine article can bring more traffic to your site for FREE.
    • How to Get MORE sales from YOUR site even though you are selling the same product as thousands of other affiliates.
    • Learn EXACTLY what Super Affiliates do that other affiliates don't do.
    • The 20 questions that you MUST get answers to BEFORE you join an affiliate program.
    • The Best places to advertise.
    • Which software finds profitable niche topics and saves HOURS, even DAYS, of manual labor.
    • How to write compelling product endorsement.
    • Why you don't want to use the marketing material provided by some affiliate programs.
    • 6 Essential Components that EVERY successful website has in place.
    Click Here to Download The Super Affiliate Handbook

    What is this book basically?

    The Super Affiliate Handbook by Rosalind Gardner is, as the title implies, a handbook for affiliate marketers. The word, "super" in the title, doesn't mean that the book is only meant for "super affiliates". Rather, in
    Super Affiliate Handbook, Rosalind Gardner shows you how you can become a super affiliate. Rosalind Gardner knows what shes talking about.
    On her website, she delivers the proof that she personally earned $436,797 the year prior to the publication of Super Affiliate Handbook. Rosalind Gardner has primarily earned this income by marketing affiliate products and services targeting the current market. But, can you do the same, even if you want to target other markets? The experience of several super affiliates confirms the fact that it can be done. In
    Super Affiliate Handbook, Rosalind Gardner shows you step-by-step how she and several other affiliate marketers have become so successful.

    What I like in this book:

    The Super Affiliate Handbook is one of the very best overviews I've ever seen regarding the process of marketing affiliate products. In fact, the only competitor I can think of right now is James Martell's book on the same subject. In opposition to most other books on affiliate marketing, and Internet Marketing in general, in Super Affiliate Handbook, Rosalind Gardner really goes into the details on how you can build you own profitable Internet business. Gardner covers several subjects that most other authors either skip or just mention in passing. For example, one of the most important and helpful parts of Super Affiliate Handbook is the section on how to track your results. Most other Internet marketers underscore the importance of doing this, but they don't tell you how. Rosalind Gardner doesn't just emphasize the importance of doing this, she also tells you how she does it. She shows you the spreadsheets she herself uses to track her number of visitors, buyers, etc. This is a very valuable part of this book. It's just a shame that you don't get the spreadsheet templates themselves, so that you can use them in your business; you just get a screen view of the templates. Regardless, it isn't that difficult to create these templates yourself. If you have Microsoft Excel (or another similar program) installed on your computer, you can easily create these templates yourself. But it would have been easier if you got them together with the book.

    Rosalind Gardner also leads you through the formula for calculating your conversion rate. This formula is of course well known, but it's really fine that she has included it in the book. If you want to track your ad results, this formula is indispensable. As I mentioned above, one of the things I like the most about Super Affiliate Handbook is the degree to which Rosalind Gardner gives you all the details of how to become a super affiliate. She covers how to decide whether you have what it takes to start your own Internet business, along with the importance of making a plan. Gardner includes her own software recommendations and how to filter away bad products in order to find the kind that will earn you a nice income as an affiliate. In addition, she explains how to successfully market affiliate products.

    The Super Affiliate Handbook contains so much valuable information that I'm really impressed. But despite the amount of information, you get enough details to get a grasp of each step in the process, while never losing the general overview."

    Click here to visit The Super Affiliate Handbook Official Website.

    Friday, January 7, 2011

    iPads in Schools

    The school I work at is one of the first K-9 private day schools in the country to implement Apple iPads into a 9th-grade curriculum. We started this pilot program in September 2010.... To date, our progress regarding this exciting initiative has been staggering! Perhaps you can convince your school and/or district to fund and adopt a similar program!

    Sunday, January 2, 2011

    Inability to use Bill Me Later as a Payment Option on eBay....

    Since there has been an incredible amount of recent discussion and frustration surrounding this "snafu", I thought I would share my experience. What I state below is the closest "official" response or "resolution" to certain issues I've encountered--as there has been NO official public statement or policy update from either of the three contenders (eBay, PayPal, or Bill Me Later).... After personally contacting all three, and talking with two different Support Reps from Bill Me Later, here is the verdict:

    (a) you CANNOT link Bill Me Later to your PayPal account if you have either/both a PayPal Buyer Credit line and/or a PayPal MasterCard Debit Card (including PayPal Smart Connect), (b) as of this post, they are STILL working on trying to get Bill Me Later to show up as a payment option on eBay listings, and (c) as a Seller, one has no way to incorporate Bill Me Later as a payment option. BML reviews eBay Sellers' accounts quarterly and then "transparently" decides on their own whether or not to link a Seller's listing to BML.

    I hope this helps to address some of the confusion:)

    Saturday, January 1, 2011


    As an introduction, I want to let new visitors know that I am an educator at a private day school in CT. I currently teach math and coach. In addition, I am an ice hockey ref as well as an amateur musician and actor. Hence, this blog will be an open forum to discuss anything to do with these stated areas of interest. Also, being an avid Beatles fan and collector, I plan to share my insights and knowledge regarding some of their rare vinyl collectibles that I often buy and sell--mainly via my eBay Store.

    As an open forum, I encourage visitors to comment on what I and others write, and to share their own opinions and experiences as they relate to posts in this blog. Please share this blog with others, come back often, and feel free to offer suggestions--not only for topics for discussion, but also on how I can make this site more interesting.

    Thanks for stopping by and have a great day!


    Welcome to my new blog! More to come soon...just starting out.... :)

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