A Response to A Mathematician's Lament
Last week's "Math News" suggested that you read A Mathematician's Lament, and possibly use it as a catalyst for discussion with colleagues. Some took this to heart....Thanks.
Some even replied. For example, please give equal consideration to this response from D.B. (Marysville), which I will call A Mathematics Teacher's Caution.
"Having just finished Paul Lockhart’s essay for the second time I am sitting here...nearly on the point of tears. I am saddened by having a teacher at an elitist school for the gifted in New York who lacks the perspective of teaching in a public school where students are present by requirement not choice and apply his half baked theories into the public sector. I am thinking of my first period class, which has 15 SPED students none of which have passed a math class ever and of the two truly outstanding students, none of which I have the time during my 55 minute period to devote to what they all truly need. It is interesting that in his very first example he is using concepts from arithmetic that my students do not truly understand, ½ and a perpendicular which he just calls a line dropped to the other side. Here he has made an assumption that I will understand the properties of a perpendicular line, and that such a line contained inside a rectangle will form two rectangles the sum of which is equal to the original rectangle and that his line is perpendicular. Another of his math problems leads me into a world of research of why does a negative exponent mean a reciprocal and not a negative answer. 2-2 = -4 not ¼ the negative response makes perfect sense to me so I must just remember the convention. Since this is a convention could not the convention be that when a number is raised to an negative exponent then the number becomes itself times its additive inverse. I agree with the author in that a child’s curiosity should be rewarded with but there are some building blocks to mathematics that are still necessary to the exercise of that curiosity. I am still trying to grasp infinity and know that my continued growth in math is stalled until I can finally see that infinity is. I am still looking for a definition that I can grasp without questioning.
Thanks for your reflections, D.B.....anyone else care to share their view on things?
Teaching in a public school is the most frustrating thing I have ever undertaken. ¼ of the way into my second year at Marysville I am more frustrated than ever with what I am able to give to my students. For the most part my students are unable to perform the most basic of arithmetic operations and have no concept of fractions, multiplication beyond single number nor division. I have listened to the argument for allowing them to use calculators for these basic operations but it is of little help since they have no sense of what a correct number should look like and take whatever is given the calculator as gospel. I started this year with a refresher on basic arithmetic and am just now assessing the first Unit of the CPMP ed. 1 book on number line plots to scatter plots. I have changed the look of the test I have used for the last four years to be more WASL like and am going to use the year to see if familiarity can lesson anxiety when the actual WASL comes around.
The struggle to get disengaged students to re-engage is common to every teacher in public school. I chose to work with all freshmen classes this year so my students are all Integrated 1 whether they are freshmen, sophomores, juniors and seniors. I have all four grade levels in my classes, so there is a vast gulf in ability levels of students. The biggest problem we are facing for next year is as Marysville does away with the Integrated 1 course and requires all incoming students to take at least Integrated 2, how are we going to work with the large number of students that have been passed up through the system but have acquired no real math skills and are disengaged with school in general. Our middle schools have adopted CMP II and our elementary levels have adopted Everyday Math but these are only as good as the teachers that are teaching the classes. The world report has made it very clear that it is not curriculum, it is not mom and dad but it is the teacher that has the greatest impact on the student and during the first three years of schooling this is most apparent. "