In other words, the teaching of remedial (high school level) algebra courses at community colleges is just as poor as the teaching of algebra in high schools. Apparently, using calculators doesn't help much. Indeed, they are "absolutely unnecessary," writes W. Stephen Wilson.
Keith Devlin says that with all the cheap gadgets available today, the need for mastery of arithmetic has lessened considerably. I think he is wrong. Being able to do arithmetic well--especially fractions--is needed for Algebra. Kids are not little mathematicians or junior scientists. They are novices. They do not think like adults.
Note: If there is no need to learn the mechanics (procedures) of algebra because technology does the procedures faster, as Wagner & Dintersmith (Most Likely to Succeed) argue, then, using the same argument, there is no need to learn the mechanics of arithmetic such as standard algorithms because calculators can do the operations faster. But, oddly, Wagner & Dintersmith don't think that about arithmetic. They claim, arithmetic is useful and algebra and high school math are not. They also claim that "most college courses require only K-8 school mathematics, "especially arithmetic, ratio, proportion, expressions, and simple equations."
According to Wagner & Dintersmith, arithmetic is needed because it is used in everyday life. Really? When was the last time you did long division, a decimal multiplication problem, fractions, proportions, percentages, arithmetic mean, or a financial calculation without a calculator?
According to the National Math Panel, "To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills."
They are interwoven! You have to teach more than just concepts. Students need to know foundational knowledge, both factual and procedural (mechanics).
"By the nature of algebra, the most important foundational skill is proficiency with fractions (including decimals, percent, and negative fractions)." We do not teach fractions well. "The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in Algebra can be expected." (Source: Math Panel, Critical Foundations of Algebra)
In many K-8 schools, we seem to have a "steady diet of test prep." Is that a good thing? Wagner & Dintersmith (Most Likely to Succeed) think test prep is bad for kids because it hinders creativity and curiosity, but there is little evidence to support the claim. Rather, I think test prep is a poor substitute for a math curriculum and a waste of time. In my view, test prep is not the same as learning core arithmetic fundamentals in long-term memory.
Wagner & Dintersmith write, "Clearly we want every child by a certain grade level to be an adept and passionate reader, to be proficient (without a calculator) at core math operations (e.g., division, fractions, estimation, and financial literacy), and be able to communicate well. Mastering these foundational building blocks requires repetition and practice."
I agree. Kids need to master basic arithmetic. But...
Wagner & Dintersmith also conclude that the mechanics of algebra and much of high school math is outdated and unnecessary. They explain, "Don't get us wrong about the need to drill on lower-level math operations. Any young adult needs to be facile with core operations (+, -. x ÷, %, fractions, and decimals," which are K-8 math. But, we also know "they will never have to solve a quadratic equation by hand."
Today's college entrance tests, they say, "require students to master skills that are obsolete. Indeed, "80% of U.S. adults never use any math beyond decimals, fractions, and percentages." Wagner & Dintersmith assert that "the math needed for college courses does not require high school math (algebra, trig, or calculus)--except for STEM students. Most college courses require only K-8 school mathematics, "especially arithmetic, ratio, proportion, expressions, and simple equations."
Comment: The problem I see is that the core basics are not taught well in our K-8 schools, which seem to focus more on test prep than on learning core fundamentals. (By core, I do not mean Common Core.)
Wagner & Dintersmith want to toss out much of high school math as obsolete, especially the paper-pencil techniques, procedures or mechanics of algebra, trig, and calculus, replacing them with calculators, tablets, computers, and smartphones. While calculus concepts are useful, they say, the "mechanics [of calculus] belong to smartphones." They imply the same for algebra and trig. Kids should learn just the concepts, not the mechanics.
I think they are wrong!
Comment: In the real world, students still need to pass the admission and math placement tests at colleges and universities. Unfortunately, a massive number of high school graduates have been placed in remedial Algebra courses at community colleges because they didn't learn the mechanics and weren't able to apply concepts.
Wagner & Dintersmith think that students should drill the procedures of arithmetic, but there is no need to drill the procedures of algebra, trig, or calculus because they are old-fashioned and nonessential. They argue that high school kids should use the latest technology such as WolframAlpha on their smartphone, tablet, or computer. Their main argument has been that no one will ever need to solve a quadratic equation or an integral on paper.
According to Wagner & Dintersmith, arithmetic is needed because it is used in everyday life. Really? When was the last time you did long division, a multiplication problem, or a financial calculation without a calculator? Algebra and Calculus are not needed because they are not used, but neither is arithmetic. Notice the inconsistency! The lack of numeracy among students and adults has been a perplexing problem for decades. Today, only 3% of adults can ace a math quiz without reaching for a calculator. The questions on the quiz featured multiplication, subtraction, percentages, and division.
Comment: What do Wagner & Dintersmith and many others have against algebra mechanics and quadratic equations? Physics is loaded with quadratic equations. To understand physics well requires a calculus background, but most beginning physics courses in high school and college are algebra-based. Kids need to know algebra, but many don't know it well enough. So, they struggle in the hard sciences, if they get that far.
Also, I guess no one will quote Shakespeare either, so his plays should be eliminated from the high school curriculum. Latin is gone too. Gee, I thought the mechanics of algebra were embedded in the understanding of algebra concepts. "If you can't do it, then you don't understand it," says mathematician W. Stephen Wilson.
If there is no need to learn the mechanics (procedures) of algebra because technology does the procedures faster, then, by the same argument, there is no need to learn the mechanics of arithmetic such as standard algorithms because calculators can do them faster.
I don't buy it!!!
In the real world, kids need to learn the concepts, but they also need to learn the mechanics (e.g., standard algorithms, distributive property, etc.) and solving routine problems. Most of the concepts in arithmetic and algebra are easy. Even 1st-grade students can learn some of the fundamental concepts of algebra via arithmetic. By 3rd grade, well-prepared students can learn the mechanics (technique) for solving simple addition or subtraction equations using inverses.
© 2017 LT/ThinkAlgebra
