If you have a 5th grade student in PWC, you better make sure he /she has a calculator. Because the PWCS Investigations based curriculum for grade 5 is all about calculators.
The Virginia SOLs suggest that elementary students should be familiar with all technology, including calculators and computers. That suggestion has engendered a bit of controversy and resulted in the rating for Virginia’s SOLs to drop from a B to a C.
Rather than back away from the controversy and ensure that students have a solid foundation in arithmetic and don’t need calculators to perform basic operations, Prince William County has made calculator use an integral component in their math curriculum. That dependence is quite evident in their 5th grade curriculum.
It starts with rounding, a standard you wouldn’t expect to see calculators as integral tools. The VA standard on rounding states:
5.1 The student will:
(a) read, write, and identify the place values of decimals through thousandths;
(b)The student will round decimals to the nearest tenth or hundredth place; and,
(c) The student will compare the value of two decimals through thousandths using
the symbols >, <, or =.
Pretty straightforward, isn’t it? And most of us remember the rounding strategy we learned as kids – if it’s five or more round up. That’s the strategy VA suggests in it’s Curriculum Framework.
But not PWCS. That strategy is missing from the PWCS Curriculum. Instead the PWCS strategy states:
“To round a number means to substitute a “nice” number that is close to the actual number so that computation or comparison may be more easily done. Emphasis should be on understanding the rounding concept, not on memorization of a procedure. Students should develop their own procedures for rounding instead of memorizing a given procedure without understanding. For example, students who have learned rote procedures for rounding whole numbers will have difficulty understanding why 14.638 rounded to the nearest tenth is 14.6 rather than 14.600. Students should pair models with symbolic notation when exploring strategies for rounding. Emphasis should be on understanding the rounding concept as practical real-life application.”
What if the strategy I develop is to always round up? That way if I’m in a store and I’m estimating how much my purchases will cost, I won’t be caught with too little change. In their example 14.638 would round up to 14.7. If the strategy I developed is to always round up, isn’t my answer just as correct as someone who rounded down to 14.6?
And right after PWCS suggests that students develop their own strategies for rounding, we get this:
“Computations on a calculator may provide a context for exploring the rounding of decimals. For example, in investigating the conversion of 1/6 to a decimal fraction, students encounter the repeating decimal 0.16666… (Note: Some calculators will round the final digit of a repeating decimal, while others will truncate it.) Mathematically, a repeating decimal is denoted with a superscript line over the repeating digit(s), technically known as a vinculum. Students may also express the decimal equivalent as a rounded number. Thus, to the nearest hundredth, 1/6 is equivalent to 0.17; to the nearest thousandth it would be 0.167. Students may use calculators to build an understanding of the effects of multiplying or dividing numbers by powers of ten. This understanding is useful for computation and estimation with whole numbers and decimals and for conversions within the metric system of measurement. It also builds a foundation for the future understanding of scientific notation.”
Wonderful! Forget my always round up strategy, my new strategy is to let the calculator do the rounding for me.
It gets better. Students in Grade 5 are expected to be able to fluently add, subtract, multiply, and divide whole numbers and decimals of any magnitude. Computational fluency is one of Investigations largest weakness. That weakness is transferred onto our children with PWC’s strategy for teaching large number arithmetic.
“A certain amount of practice is necessary to develop fluency with computational strategies for multi-digit numbers; however, the practice must be meaningful, engaging and purposeful if students are to develop fluency in computation. Calculators are appropriate tools for solving problems with large numbers. Using calculators during problem solving changes the focus from the steps in the computational algorithm to the process for solving the problem.”
Apparently in the eyes of the PWC school division plugging 143 X 365 into a calculator and seeing the answer teaches students much more than actually solving the problem themselves. It does – it teaches them to be experts at turning their brains off and plugging and chugging numbers into a calculator.
Most amazing of all is the fact that PWCS has denied, repeatedly, that the curriculum overemphasizes the use of calculators. In August 2008 a parent commented to Carol Knight, the head to the PWCS math department, that Investigations overemphasized the use of calculators. Ms Knight responded:
This is not true. There are VERY few lessons in Investigations that use the calculator. In these few times, they are used in a problem solving setting, not to learn or practice basic facts.
Perhaps Knight’s statement is true, if you like playing semantic games, as the setting in which calculators are used is to teach children multi-digit arithmetic, not basic facts.
In PWC, mathematical fluency comes from a calculator.
I can only hope the teachers in PWC use the discretion they’ve been given by the school board and remove calculators from the curriculum the school district requires them to teach.