Future

Knowing is the Best Preparation for the Future!

A 7th-grade student solves quadratic equations by "completing the square"
from an old, 1970 Dolciani Algebra-1 textbook.

Knowledge has always been the best preparation for the future no matter the epoch, including the booming Atomic (Quantum), Space, Communication, Computer-Internet, and AI eras. Indeed, standard arithmetic and higher-level math (algebra, trig, precalculus, etc.) have endured era after era, that is, their need and impact have soared over time. For decades, the sad truth has been that kids aren't learning nearly enough math, science, and other subjects that make up a liberal education. 

E. D. Hirsch Jr. (The Knowledge Requirement) writes, "The conclusion of cognitive research concerning skills is this: Broad knowledge of many domains is the only foundation for wide-ranging problem-solving and critical-thinking skills." Hirsch points out, "Teaching strategies [such as those used in math and reading] instead of knowledge has only yielded an enormous waste of school time." One strategy for reading is finding the topic sentence. The "so-called" mathematical practices and alternative, nonstandard algorithms are some of the strategies pushed in K-8 math. The strategies clutter the curriculum.  

Kids don't need less mathematical knowledge (factual and procedural) in long-term memory; they need more math knowledge to prepare for the future. Still, many adults bad mouth math because they don't like math or have a practical understanding of it. Many don't see math as a vital problem-solving tool. Math should be valued, not disparaged.  

Furthermore, many teachers are ill-prepared to teach even basic arithmetic. It shows a bias against standard arithmetic and algebra. Many adults boast that they were not good at school math, but you don't hear adults bragging that they were lousy at reading or hated reading. 


In math, knowing facts and procedures (i.e., standard algorithms) in long-term memory builds the foundation for understanding, applying, and reasoning in math. Students cannot use something they don't know well in long-term memory. Indeed, the memorization of essential facts and efficient procedures plays a vital role in performing math at an acceptable level. The learning goal should be the mastery of content in long-term memory, not proficiency on state tests. Learning is remembering from long-term memory. 

Attitude
Most U.S. kids today are more interested in video games, social media, texting, and sports than in academics or schoolwork. The smartphone is their life. What a dull worldview and an example of gadgets and social media dictating lives.

Other Nations Link Education to the Economic Growth: We Don't!

While other nations connect the economy to better education and march forward, we don't seem to "get it" in the U.S.  Our solution has been importing talent for decades. Up to 60% of the STEM students at our top graduate school programs are foreigners.

The idea of student-centered learning failed in the 70s with open classrooms. 

Lack of Number Sense
Many elementary and middle school students lack adequate number sense. You don't get number sense using calculators. You must learn factual and efficient procedural knowledge in long-term memory, which requires memorization and practice-practice-practice. We need to teach basic math for mastery, not test-based proficiency.  

Sorting Kids
When students come into the 1st grade in Singapore, those who are weak in math skills are sorted to another class for intense math help, and those weak in English are sorted to another class to learn more English. The objective of these classes is to catch kids up. The Singapore system makes perfect sense.

In 2015, Siegfried Engelmann wrote that K-8 math "students should be grouped homogeneously, placed in the instructional programs according to their skill level, and taught at a rate that assures they will perform at about 100% by the end of the daily lesson." Read more about Engelmann: click here.

Over the years of advances in math, science, engineering, and technology, sometimes called revolutions, American education had kept up with the technologies of the age, but since the 1970s our students have fallen behind other nations in math and science. We are still a nation at risk. Evgeny Morozov (To Save Everything, Click Here) says that "schools concentrate all their efforts on improving test scores even if children learn much less as a result." Improving test scores (i.e., proficiency) is not the same as mastering essential content in long-term memory, which implies being able to apply the knowledge to solve problems. 

We stopped teaching fundamentals for mastery. Zig Engelmann points out, "Without a firm foundation in number facts [automated in long-term memory], children are held back from further learning." 

While other nations started to prepare more students for Algebra-l in elementary and middle school, in the U.S. only high school students who were going to college took Algebra-1 in 9th grade. Today, just the very best take Algebra-1 in 8th grade. Simply, we are not preparing enough students for algebra in middle school like our economic competitors. We are not keeping up with technological advances that require more math than other revolutions, not less. Unfortunately, there is a strong anti-algebra movement. Unlike high-performing nations, we don't connect education to jobs and economic prosperity or national security like high performing nations. Education matters; it matters a lifetime. 

How should we prepare kids for future jobs? 
We should prepare kids for the future just like we did in past revolutions, but we need to beef up math and science. Knowledge has always been the best preparation for the future, but, today, kids aren't learning nearly enough math, science, and other subjects. 

3rd and 4th-Grade Arithmetic 1877
in One Small Textbook: Ray's New
Intellectual Arithmetic textbook

Perspective
Kids in the 1800s learned much more fundamental arithmetic than students today, according to Ray's New Intellectual Arithmetic book 1877, which "contained exercises on the primary principles, and their applications; together with models of analysis in the shape of solutions [worked examples], including fractions, ratios, and percentages." 
→ Ray's small 140-page book (4.5 x 7) encompassed the entire 3rd and 4th-grade arithmetic curriculum. Here are two easy 4th-grade questions: 

(1) 3/4 of 24 are 6 more than 2/3 of what number?
(2) Find the interest on $50 for 6 months, at 6%.

Today's 3rd and 4th-grade students could perform like the children in the 1800s if they were appropriately trained in arithmetic starting in the 1st grade, which requires memorization, drills to improve skills, and frequent review. Instead of learning single-digit number facts and standard algorithms from the get-go, students are taught reform math via Common Core state standards, which are below world-class benchmarks. In short, the standards tend to clutter the curriculum, increase cognitive load, and impede student achievement. In reform math, scant attention is given to standard algorithms and basic arithmetic. 

Our schools are infused with weak curricula, ineffective instructional methods, and inane education policies at the local, state, and federal levels. Also, unlike high-performing nations, we don't connect education to jobs, economic prosperity or national security like high performing nations. Our solution has been importing talent and setting up shop where the talent is, such as in China, India, Singapore, Korea, etc. Also, up to 60% of the students in our best graduate schools are foreigners. 

Model Credit: Kailey, 7th Grade

©2018 LT/ThinkAlgebra