Calculating the benefits of Common Core
Editor of the Reformer:
Compute: (1-2i)/(3+4i), and give your answer in a +bi form (answer at the end of this letter).
In the article "Common Core critics: educational folly" (Dec. 3), we read that many are not overly positive about the CCSS implementation. Without repeating the objections noted in that article, suffice it to say that one criticism is "too much, too quickly." Curriculum change takes time and these changes all the more so as the high school curriculum in mathematics reflects those changes made at the middle school and elementary levels. Clearly they will not this year, or for some years down the road. Implementation takes time.
A second question is just what is being expected and why? Under CCSS Number and Quantity HSN.CN.A.2 we find: Use the commutative, associative and distributive properties to add, subtract and multiply complex numbers. HSN.CN.A.3(+), it is required to: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. HSN.CN.C.7: Solve quadratic equations with real coefficients that have complex solutions. The (+) after A.3 indicates that this standard is not expected to be taught until a fourth high school course. Will it be included on the test? If so, Brattleboro Union High School will have to require four courses in mathematics for graduation, up from the present three. If not, one wonders just what good it will to for a student to be able to add, subtract and multiply complex numbers, but not divide them.
Students have always asked: "When will I ever use this?" Teachers have given answers to this question, explaining the use of basic mathematics in everyday life and also applications in various careers. With the inclusion of the above mentioned CCSS, teachers are in for a struggle. Complex numbers are an integral part of advanced mathematics, but for everyone?
In her column, "Rescuing the rescuer" (Dec. 3), Becca Balint notes that "... history and social studies have been deemed ‘not critical’ for students today," having been pushed aside by the emphasis on literacy and mathematics, at the elementary level. I have been told that some elementary teachers locally have indicated on report cards "Taught no science this quarter." I have read elsewhere that art and music have been downplayed, and recess curtailed, apparently so that one can compute at some later time with complex numbers. Such is not good. Science, social studies, art, music and recess are an important part of our students’ education.
Finally, students and parents are advised to keep careful watch as to just what use test scores will be used regarding the individual student. So far, overall results have mostly been used to designate a school as in need of assistance; will individual students now be penalized for poor performance on a test for which they were not properly prepared?
The answer to the header questions is: (-.2) + (-.4)i. Aren’t you glad to know that? Just how will you use that information today?
Brattleboro, Dec. 5
More trash talk
Editor of the Reformer:
Joseph Kowalski writes from Florida ("A waste?" Dec. 7) that putting all our garbage into one bin and having someone separate the recyclables from the trash is the inevitable way of the future. I would be more likely to accept the view from Florida if I had not recently seen the president of Waste Management on television saying the exact opposite.
The view from the business end of the garbage line is that tossing everything into a single stream wears on the equipment and increases processing costs 15 to 20 percent. Not exactly a prescription for financial health.
Brattleboro, Dec. 8
A safety hazard
Editor of the Reformer:
I am writing to share my sadness and frustration upon learning of another pedestrian dead, this time at the infamously dangerous intersection of Union Street, Cedar Street and Western Avenue.
What will it finally take for the town to construct four-way stop signs at this intersection? One death? Two? Four or five? How many accidents, from fender-benders to total losses?
If the town installed a camera at this location, a single 24-hour viewing would reveal the incredible numbers of risks drivers take in order to make a turn, from any direction and toward any direction, at this intersection. There is very little besides roadway chaos ensuing, and each time I approach this intersection, which I do at least twice each day, I feel as if I am taking my life in my hands.
What exacerbates these dismal conditions is the winter removal of the temporary posts on Western Avenue, which are erected to prevent forward moving cars from illegally passing, on the shoulder of the road, cars stopped for a turn. Snow plowing is the reason for their removal; is the ease of the plow more important than a human life? Now place a pedestrian amid these conditions, in the winter, at night, and wait for what will ensue.
Ironically, at the same time that the town is neglecting a major safety issue at this location, let’s take a look at what’s happening one block east, at the fork onto Green Street. Here, the town is so concerned with people speeding east down Western Avenue and onto Green Street in front of the school, that a speed warning device is constantly monitoring drivers’ speeds, and urging us to slow down. The one thing that would absolutely guarantee a slow-down at that point would be a stop sign at Union Hill. Unless one is race-car driving, it would be impossible to make a full stop at Union Hill, then build enough speed to barrel down Green Street.
And I cannot think about this issue without also considering the intersection of Birge Street, Washington Street and Canal Street. Last year, Canal Street saw a death of its own. Drivers on Canal approach this intersection at amazing speeds from north and south. Navigating this intersection as a driver on Birge or Washington streets, or as a pedestrian crossing in any direction, is nearly impossible to accomplish safely.
It is finally time for me to say that the failure of the town to provide reasonable safety mechanisms at these locations, despite mountains of evidence, is nothing short of negligence, for which it should be held accountable in a court of law.
Brattleboro, Dec. 10