Tuesday, May 17, 2016


Only a meager 25% of 12th-grade students are proficient in math in a national test, which indicates that math has been taught poorly in K-12. US math has been in trouble for decades! Most top-down, imposed math reforms, mandates, and policies haven't worked well, including reform math, Common Core, state standards-testing-accountability, test prep, inclusion, No Child Left Behind Act (replaced by Every Child Succeeds Act), technology hype, equalizing-downward crusades, self-esteem movement, untested fads (often called innovations), inferior minimal guidance methods (group work), etc. 

My views often challenge conventional thinking in education. 
1. Some say the NAEP (National Assessment of Educational Progress) proficiency levels (4th, 8th, 12th) are set too high when the underlying math problem has been low expectations via a substandard curriculum and inferior instructional methodsStudents are not learning nearly enough background knowledge (prerequisites). 
2The reality is that kids need to learn more math, especially standard arithmetic and algebra, much earlier than previous generations because of high-tech job demands.
3. Our kids are smart enough to do this. Knowledgeable teachers can fuse algebra to standard arithmetic as children learn arithmetic beginning in the 1st grade. 

4. Educators seem to ignore the cognitive science of learning such as the role of working memory and long-term memory, cognitive load, etc. Mathematical thinking and problem-solving come from mathematical knowledge (skills, ideas, uses) automated in long-term memory, not thin air.
5. The perception of parents and the actual performance of students are extremely disconnected, according to the PTA's Parents 2016.
6. Students enrolled at community colleges, sadly, often lack basic arithmetic and algebra knowledge (skills, ideas, uses); consequently, they are placed in remedial math classes to make up for the content they didn't learn in K-12. For example, 74 to 88% of the high school students that applied to Pima Community College from the nine Tucson-area school districts were placed in remedial math (PCC 2014). The remedial students were products of reform math.

7. Most children can succeed in math class when they are given focused, well thought out, achievable learning (performance) objectives within a logical, hierarchical sequence (Gagne); however, the objectives should fit the child's achievement or performance level, such as low, average, and advanced. Instead of a reasonable and flexible levels approach with different materials (curricular learning objectives) and actual math teachers, not reform math educators from schools of education, we have substituted inclusion policies in elementary schools with a generalist who attempts to differentiate instruction, which doesn't work well. Consequently, arithmetic and algebra have been taught poorly. Also, the one-size-fits-all stance of Common Core or state standards has been a flawed practice. Lastly, behavioral learning objectives should be performance-centered (Robert Mager). They must be Specific, Measurable, and Achievable (SMA). 

American math standards are not world-class.
The popular minimal guidance methods during instruction are inferior.
Reform math does not work.

Common Core or state standards are not world-class and put our students at a disadvantage starting in 1st grade. Inferior achievement in math doesn't start in high school or middle school. The difficulty begins in early elementary school. 

All the math results of the 2015 NAEP (National Assessment of Educational Progresstest are now available, including the 12th-grade, and they are not good. Math proficiency for 4th-8th-12th: 40%-33%-25%, respectively. What else do we know?

  1. Math achievement in 2015 was lower than in 2013.
  2. The percentage of weak students (below the Basic level) in math was much larger.
  3. Common Core revived inferior reform math. (JJmom2 writes, "Common Core threw out common sense and made simple calculations into ridiculously difficult problems, which really held kids back from moving on.") 
  4. Common Core standards and state standards are not world-class or for STEM students. They are a stumbling block for many students. (The problems of inadequate content, inferior instructional methods, and low expectations start in the 1st grade.) 
(Quote: JJmom2 comment is from the Answer Sheet, Washington Post blog by V. Strauss, 4-30-16; Nation's Report Card 2015 NAEP) 

We expect too little from elementary, middle, and high school students, and it shows on both national and international tests. A student does not need to be gifted or a genius to learn Algebra-1 with trig in middle school, AP Calculus in high school, or grasp some key algebra ideas in 1st grade. Average kids can learn when they are properly taught the prerequisitesAlgebra-1 with trig is a middle school subject when students are prepared well in elementary school, but most are not. Indeed, Common Core disregarded the recommendations of the National Mathematics Advisory Panel (2008) for getting more kids ready for Algebra-1 by middle school. Common Core intentionally delays Algebra 1 to high school, which is indefensible. It is not for STEM students.

Under Common Core, the 2015 NAEP (National Assessment of Educational Progressmath scores for 4th-, 8th-, and 12th-grade students were lower in 2015 than in 2013. (NAEP scores are often called the Nation's Report Card.) Also, in the PTA's Parents 2016 report, 90% of parents think their child is achieving at or above grade level in mathematics, but only 40% are proficient by the 4th grade (NAEP). The perception of parents and the actual performance of students are extremely disconnected. By the 8th grade, student proficiency drops to 33% in mathematics. [Note. 87% of Hispanic parents think their child is achieving at or above grade level in mathematics when only 26% are proficient in 4th grade. The percentage drops to 19% by the 8th grade. Black students are even lower.] (Sources: Nation's Report Card, 2015; PTA Parents 2016)

The "at or above proficient" math trend (2015 NAEP), from the 4th to 8th to 12th grades, has been a free-fall: 40% to 33% to 25%, respectively. The trajectory is negative, that is, the performance of students is distressingly bad. Ze've Wurman points out, “The only plausible explanation for such an unprecedented broad national decline is the Common Core."

Common Core revived constructivist reform math and its inferior minimal-guidance approaches, which had dominated the 90s: problem-solving, project-based, discovery, inquiry-based, etc. The methods were not efficient or effective. Students stumbled over simple arithmetic (Kirschner, Sweller, ClarkWhy Minimal Guidance During Instruction Does Not Work, 2006).

For decades, we have overemphasized pedagogy at the expense of mathematical content. The idea of pedagogy over content traces back to the 1989 NCTM reform math movement, which has been revived through Common Core. Indeed, the Common Core math standards are often interpreted through the lens of reform math, which makes simple calculations complex. Simply, our kids don't know enough math content, which has been confirmed through both international (TIMSS, PISA) and national tests (NAEP).

According to international tests, American kids have lagged behind in mathematics for decades. In fact, most state standards, including Common Core, have not been world-class(One exception was the 1997 California Math Standards. There were others.) Also, the math reforms over the years have not worked well. Indeed, evidence-lacking fads (often advertised and sold as innovations and reforms by special interest groups, as if new means better) have flourished in US education. The truth is that math has been taught badly. 
Our kids are mediocre in math because we made them that way. I agree with Ze'Ve Wurman. Common Core has added to a downward trend in math achievement. State standards are often interpreted as reform math. (NAEP 2013, 2015; Wurman's quote from Breitbart )

NAEP 2015: 12th-Grade Math

Only 25 Percent!
The NAEP 2015 results for 12th-grade mathematics (public + private schools) are not good. Only 25% of 12th-grade students were "proficient or above" in mathematics.

The average score dropped one point since 2013 and is nearly the same as it was in 2005. In short, the math reforms over the years haven't changed the dynamic--not NCTM reform math, not NCLB, not Common Core, not technology, not inclusion and other policies, etc. My conclusion is that there is something terribly wrong with the math reforms. In brief, the math reforms aren't supported by scientific evidence.

Note1. In NAEP math, the percentage of 12th-grade students who scored below the Basic achievement level increased from 35% in 2013 to 38% in 2015. In short, weak students are worse off. Not good!

Note2. Some say that the NAEP math scores for the proficient achievement at the 4th-, 8th-, and 12th-grade levels are set too high; however, I think, American expectations for students in math are often too low. IndeedAmerican students underperform on national and international tests. Furthermore, the underperformance starts in 1st grade when students are not taught standard arithmetic. Our math standards are not at the Asian level.    

NAEP 2015: 12th Grade College Readiness Estimate
The 2015 NAEP's 37-Percent Estimate for College Readiness
Math scores often indicate academic preparedness for college. The NAEP governing board determines that only 37% of the 12th-grade students were "academically prepared for college."

Note. According to a new metric from the NAEP, only 37% of 12th-grade students are college-ready in math and reading. To be college-ready, 12th-grade students should score at least 163 out of 300 in math and 302 out of 500 in reading. Furthermore, the percentages of students academically prepared for college in math and reading (both 37%) were lower than in 2013: 39% math and 38% reading.

Remember: The main selling point of Common Core was that it would make all students college and career ready, a truly extraordinary claim that lacks evidence. 
NoteThe math proficiency level in 12th-grade NAEP is not the same as its college readiness metric, which includes community college and is more in line with ACT, SAT, college outcomes, placement in college-bearing courses (not "admissions" to post-secondary institutions), etc. College readiness means ready for College Algebra, a course that is similar in content to high school Algebra-2. College Algebra is often the only required math course at community colleges.  

 The underlying strength of a math program, I think, can be inferred from the Advanced Benchmark levels of the Trends in International Mathematics and Science Study (TIMSS). 
At the 8th-grade level, 48% of Singapore students reached or exceeded the Advanced Benchmark compared to 7% of US students. At the 4th-grade level, 43% of Singapore students reached or exceeded the Advanced Benchmark compared to 13% of US students. Clearly, a huge number of Singapore students learned content significantly above their grade level. Indeed, grade levels are not always an acceptable gauge of achievement. In state testing, saying a student is at grade level or proficient in mathematics is pointless. What is consequential is the math content (ideas-skills-uses) the student knows and applies.

The TIMSS Advanced Benchmarks show that American math programs are 
weak both in curriculum and instructionAsian students lean toward rote learning and drill for skill. On average, Asian nations rank the highest in math achievement on international tests. Asian students know much more math knowledge (ideas, skills, uses) than American students at all grade levels. Contrary to popular belief, the Asian "rote-leaning" nations also rank the highest in creative problem-solving skills (2014 PISA - Programme for International Student Assessment for 15-year olds). Indeed, there is a strong link between gaining mathematical knowledge in long-term memory over time and solving problems (mathematical thinking). Also, there is a cultural difference. Asian parents regard education, especially mathematics, the highest priority while many American parents do not. American students grossly underperform in math.] Note. Highly-regarded Finland has been displaced by Asian nations in the 2014 PISA Problem Solving Test and the 2015 PISA math and reading tests for 15-year olds. Also, Finnish 4th and 8th graders were about the same as American students (TIMSS).
(Advanced Benchmark: TIMSS 2011; Creative Problem Solving: PISA 2014; NAEP 2013, 2015; Note. The 2015 TIMSS results will be announced in November 2016)