Saturday, February 26, 2011

Alternative Assessments

I have always felt that there is too much emphasis placed on grades. In my math classes, I often use alternative methods in order to assess my students' progress and mastery of content. However, the bottom line is that even these assessments must be ultimately translated into percentages or letter grades. Secondary schools, colleges, and universities require such defining "standards" in order to evaluate prospective applicants. Even though these institutions clearly look at the broader, overall picture of each applicant, I still believe that too many students, and parents, are far too concerned about grades--much more so than the actual learning of content.
How can we as educators/schools de-emphasize grades when our students' next schools place such high importance on these impersonal assessments?

Friday, February 18, 2011

Year-Round School

Because I work at a private school, our students do not have to make up Snow Days (6 so far this year, along with a couple of delayed opennings and early dismissals.) However, we are adding some hours to some of the school days (ones that were originally scheduled to be early dismissals), and making up two full days (one was suppose to be an in-school Professional Development Day, and the other a Parent Conference Day.) In any case, I started thinking about those school systems that have school year-round. Can anyone who is a part of such a schedule shed light as to how this works in your district, and how the school calendar is set up? Do you like that system, and does it seem to work? Pros? Cons?

Saturday, February 12, 2011

When Is A Math Track Too Accelerated?

At my PreK-9 school, we are currently in the process of "decelerating" our math program. As the math coordinator, I am convinced that simply because students can handle advanced topics in math does not mean that they should be learning such concepts at an early age. In other words, I believe that a math curriculum needs to be age-appropriate more than it needs to be accelerated. For example, next year will be the last year I teach a full-year Honors Geometry course in the 8th grade, as it is more appropriate to teach such a course no earlier than the 9th grade. What is the purpose of over-accelerating? So students can "max out", or worse, burn out in math by the time they are Juniors in high school?

As long as students (at all levels) are challenged per their ability levels, it is far more developmentally sound to enrich and enhance their math learning rather than simply move fast because they "get it".

Saturday, February 5, 2011

The Role of Athletics at the Middle School Level

Being a former 5th-9th grade Athletic Director of ten years, I have always been concerned about the role of athletics, or rather its overemphasis, in the lives of students; especially at the Middle School level. In general, children are introduced to competitive sports at a young age. Student athletes are often asked to participate simultaneously on interscholastic school teams as well as competitive town (a.k.a. Premier or Travel) teams. Recent research raises a "red flag" as to what the age-appropriate level of competitive sports should be. When a student athlete is involved in both school and town teams at this developmental age, the issue of sports programs being overly competitive as it relates to overuse injuries and "burnout" is common.

The attitude and mentality that a parent exhibits towards sports often dictates the level of competitiveness the child pursues. This sometimes leads to youth sports being overly competitive in scope because they are parent-driven in nature.

Young athletes would feel less stress and anxiety regarding sports if parents would simply support how their son or daughter chooses to pursue his/her athletic endeavors, rather than be overly concerned about the competitive side of sports.

Most parents mean well, but sometimes they get so caught up in the competitive side of things that they overlook the fact that only a very small percentage of student athletes go on to play at the collegiate D1 or professional level. Young student athletes who chose to play competitive sports during their Middle School years should do so more for fun, exercise, and an enjoyment of the sport rather than for purely competitive reasons.

In addition, too often at this age I have witnessed the athlete who "specializes" in one particular sport and ends up either burning out a few short years later, or falling to overuse or growth plate injuries as their bodies are still developing and simply cannot take the repetitive use and strain placed on certain joints and tendons.

As in other areas of life, moderation is key. In terms of sports participation, this tack is more likely to instill a healthier outlook towards athletics; with an emphasis on fun rather than winning, and fitness over competition.

Wednesday, February 2, 2011

Calculators in the Classroom


In my opinion, and based on my experience, calculators have their place in classrooms for any age. However, their appropriate use, like any other valuable skill or piece of technology, must be taught. A calculator is a tool, not a crutch – valuable for crunching numbers and relieving students of the mindless drudgery of endless pencil-and-paper calculations on topics which they already understand; but it should never be a substitute for mental acuity. An older student studying right triangle trigonometry who uses his calculator to find the value of (15 sin 30°) ÷ (25 cos 73°) is using the tool appropriately, whereas the student who uses it to find the product of 57 x 11 is simply being lazy.

The use of calculators, regardless of age level, needs to be accompanied by constant practice in estimating (or what I like to call “guesstimating”.) Estimation is amongst the most important – and too often neglected – math skills in a school’s curriculum. Math students need daily practice and encouragement to develop these skills if they are not to develop into students to whom “the right answer” is paramount. Too many students rely upon their calculators to give them “the right answer,” even when they have given their calculators the wrong input. “Garbage in, garbage out” should be a catch phrase in every math classroom, and students should be encouraged (required?) to come up with an estimate before any calculation. In addition, students should always ask themselves if what is in their calculator’s display makes sense!

Curriculum Mapping


At my school, we are currently in our second year of creating individual curriculum maps. At present, these maps are for “internal” eyes only. Presumably down the road, we will be asked to create departmental maps that will be publicly accessible.

In order for this exercise to prove worthwhile, teachers need to be given time from their busy schedules to devote to their maps, and time to review and discuss the maps of their colleagues. If this can happen, teachers will get a clear picture of content, sequence, assessment practices and resources that are used in the grades before those they are teaching, and see what the teachers in the grades above are “expecting”. This can be an invaluable tool in any school that does not or cannot devote a great deal of time to departmental meetings or formal discussion of math curriculum between teachers of adjacent grade levels.

In any case, one of the inherent dangers of mapping is that in the urgency of completing the mapping tasks, teachers take the first four pages of the assigned textbook and transfer the chapter headings wholesale into the “Contents” section of their maps. This ensures that the curriculum is broadly defined by the selected text(s), rather than having the text(s) support a curriculum devised by the teacher(s) specifically for their own students. The fact is that despite the efforts of teachers and curriculum reformers over the past six decades to find a single “right way” to improve the math performance of their students, there is no definitive approach or style to the teaching of mathematics. The teaching of any particular mathematical concept will be influenced by the nature of the concept itself and by the abilities, attitudes and experiences of the students. In general, teaching should be informed by a thorough understanding of how mathematical learning occurs and of the nature of mathematical activity. This involves a constant search for new texts, materials and approaches which will enhance the mathematical skills and understanding of your students, while hopefully giving them a sense that math is not solely a “school subject,” but something that they will carry with them and use on a daily basis throughout their lives. Agonizing over whether the one text series is “better” than another is relatively unproductive. The regrettable fact is that most mass-market texts are deplorable – as the prices rise annually, the intellectual content is “dumbed-down”, and the size of the volumes increase to mind-boggling proportions. Educators need to keep in mind that, unfortunately, it is the function of textbook publishers to sell textbooks, not to teach mathematics.


Recently, I've taken an educational leadership approach to the curriculum. For example, I often let the students plan for me. I have a rough idea of what they should do mapped out ahead of time, but I walk in on the first day and ask the students to make a list of what they expect to get out of the class and what they hope to ultimately achieve.

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