In the real world, pouring billions into programs without substantial evidence, because they are such good ideas, does not work. Indeed, reducing class size and upgrading tech in the classroom (both, very expensive), and so on, have not boosted achievement or made America into a math superpower. We have been going in the wrong direction. We are told that our kids are doing well in math when, in fact, compared to international achievement, they are not. Top-performing nations are years ahead. Common Core, state standards, and state testing have not been the answer. Math is taught as a version of NCTM reform math that failed in the past. Furthermore, Common Core and state standards based on Common Core are not benchmarked to international math standards.
We should make sure that kids have the calculating skills to do the applications and solve problems. If you cannot calculate it, then you don't know it. Calculating skills should come before applications. We give beginners word problems before they know 5 + 7 = 12. We should first require kids to memorize facts like 5 + 7 = 12 for instant recall before asking them to solve word problems that involve the addition and subtraction facts (i.e., standard algorithms). The same is true for long-division and the other operations with whole numbers, fractions, decimals, and percentages.
NAEP Changes Won't Solve the Problem
In November 2018, the NAEP committee made name changes: NAEP Basic, NAEP Proficient, and NAEP Advanced. The committee stated that the NAEP Proficient achievement level does not mean grade level, even though the tests are given at the 4th-, 8th-, and 12th-grades. The definitions of these levels were altered somewhat to make them more accessible (equitable), but at what cost? Less achievement? The commission now says that NAEP-BASIC is grade level. "See, our kids are doing okay in math! Most kids reach the NAEP-Basic level." I don't buy the committee's argument. Our kids are lousy at math, and everyone seems to know that. But, for decades, American educators and leaders have glossed over the problem and made excuses. The committee, in my mind, has done the same by making the NAEP-Basic grade level.
Another red flag is in your community and elsewhere. For example, in the Tucson area, from the nine school districts that feed into a local community college, 74 to 88% of the students who had applied at Pima Community College were placed in remedial math (PCC 2014).
U.S. math is going down (across the spectrum), not rising, and the state standards, which were strongly influenced by Common Core and reform math enthusiasts, add to the decline.
Notes
1. NAEP (National Assessment of Educational Progress) is The Nation's Report Card.
2. TIMSS (Trends in International Mathematics and Science Study)
I don't think I am misusing the NAEP results because they indicate major problems with U.S. math instruction. Achievement is not getting better. It is flat. The same is true for international math tests such as TIMSS.
NAEP 2017 (Nations Report Card): How well we educate children in math can be inferred by examining the Advanced levels of NAEP and TIMSS. For example, only 8% of 4th graders, 10% of 8th graders, and 3% of 12th graders scored at the Advanced level of math in NAEP government tests.
Latest TIMSS: In TIMSS, only 14% of U.S. 4th graders reached the Advanced Level in math, but Singapore had 50%, Hong-Kong 45%, S. Korea 41%. We are not in the same ball park. The trend continues. Only 10% or U.S. 8th graders reached the Advanced Level of achievement, while 54% of Singapore 8th-grade students reached that level, and so on. The international difference in achievement is stark.
NAEP fails to mention that the most recent ACT math scores are at a 20-year low and that the most recent NAEP math scores are no better than they were a decade ago. On the other hand, students from Asian nations leave U.S. students in the dust. U.S. state math standards are not world class, and it shows up early when only 8% of 4th graders, 10% of 8th graders, and 3% of 12th graders scored at the Advanced level of math in government tests (NAEP).
International: Asian countries dominated the 2015 TIMSS Math results.
U.S. students were not in the same ballpark. The more "rote" East Asian learners, who memorize and drill-to-improve-skill, soared far above U.S. students not only in content knowledge and ability to perform mathematics correctly but also problem-solving at the Advanced levels. WOW! At the 4th-grade TIMSS level, for example, Singapore's scale score was 618 compared to the U.S. scale score of 539, which, incidentally, is slightly better than Finland's 535.
Reform Math
Reform math, which focuses on reasoning and multiple strategies often at the expense of learning content knowledge and standard algorithms, permeates math teaching today. Kids are novices, not experts. They need to memorize stuff for mastery. Proficiency on the state test is the goal, not the mastery of essential content.
Kids Should Master Standard Arithmetic
In contrast to reform math, the traditional approach focused on the mastery of content knowledge and basic calculating skills such as the standard algorithms. It worked for the Asian students who are leaps ahead of U.S. students. Common Core and state standards are not benchmarked to international standards. They are not world-class. To do arithmetic well means to know facts and procedures. It requires memorization and practice-practice-practice. Unfortunately, the trend in U.S. education has been to eschew memorization and the practice of standard (traditional) arithmetic fundamentals.
Kids are not mastering simple arithmetic.
Learning
If you had learned arithmetic in school but can’t remember it, it means you never really learned it in the first place. Learning something is recalling it from long-term memory. It involves mastery, which, in turn, requires practice-practice-practice.
To apply mathematics to solve problems, first, you need to know the building blocks. You don't start with an application; you start with basic arithmetic--numbers and how they behave and relate to each other, the single-digit number facts, and the standard algorithms. These are the building blocks of arithmetic, along with patterns (i.e., rules) such as the Commutative rule.
©2018 LT/ThinkAlgebra
