November 27-28-29-30, 2021

**Musings of an Education Contrarian: A Divergent View**

I am an education contrarian. My views often diverge from mainstream education "group think" and orthodoxy. For example, I teach 4th graders real algebra. By 1st and 2nd grade, students are working with expressions, evaluating expressions, solving addition and subtraction equations (functions) using guess and check, and later inverses (3rd grade). Given an equation, the student builds a table of values and extracts number pairs from the table to plot points in Q-I.

**When I was in elementary school**, grades 1 to 5, there were no adults on duty before school, during morning recess, or at lunchtime. Students walked to school, and many walked home for lunch. Again, no adult supervision. Lunch was one hour long. Parents did not drive kids to school. No buses. I could run to the school in 5 minutes. The school bell was heard for blocks. Desks were bolted to the floor. Every K-5 elementary school teacher I had could play the piano. Also, for the last half-hour of the school day, the teacher would read to the class. There was a morning milk break. We were graded on deportment (behavior and manners) on the report card. Beginning in the 3rd grade, we wrote in cursive.

**Three Passions**

**Photography**

**Visit MathPage1**

**need competent teaching**, not graphing calculators or manipulatives (e.g., Cuisenaire rods, Algebra Tiles, etc., yet they seem commonplace in some

**reform math**programs. Calculator use was just one of the bad ideas advocated by the National Council of Teachers of Mathematics or NCTM. Another was "minimal guidance" during instruction such as popular discovery/inquiry or project learning, and so on, i.e., group work.

**If you want to teach, don't major in education. Avoid easy APs.**

**major in a regular academic subject**such as history, literature, chemistry, mathematics, finance, physics, computer science, etc. In other words, get an

**excellent liberal arts education**first.

**presumption**is that American teachers know best how to teach math and reading; however, national and international test scores don't support the conjecture. Many of today's teachers are products of liberal education schools.

*Future teachers should not major in education but a regular academic discipline. Along with the humanities, prospective teachers should pass college-level precalculus, chemistry, physics, history, and literature, even those college students who want to teach 1st grade. A methods course is not the same as a rigorous freshman chemistry course in qualitative analysis.*

**Note:**"

**Correlation is not equivalent to cause**for one major reason. Correlation is well defined in terms of a mathematical formula. Cause is not well defined," explains David Salsburg,

*Errors, Blunders, and Lies*, 2017.

**You can't jump from correlation to cause.**Yet, that's what many journalists, the media, policymakers, politicians, writers, and so-called experts often do, thinking their opinion is valid, consequential, and factual.

**Even the most careful scientific investigations can be afflicted by uncertainty and bias.**Every measurement has a degree of error, a "cloud of uncertainty." Over time, new observations often forge changes in physical laws and scientific theories. For example, the idea that mass is conserved was wrong. Energy, not mass, is conserved in reactions. Moreover,

**e**

**xtrapolating**beyond the observed data is

**pseudo-science**and reckless practice. Science is not absolute like mathematics. Things can change in science, but in arithmetic, 2 + 3 still is 5 in our regular number system, and it has been the way for centuries.

**Insert:** Have we gone nuts?* I don't want boys, thinking they are girls, entering the girl's locker or restrooms, much less participating in girls' sports. *However, I believe some girls can play boys' sports, but that's on athletic merit and skill, not a girl pretending to be a boy.

**Note:**My

**algebra program**for grades 1 to 5 is

**Teach Kids Algebra (TKA)**, which started in January 2011. The lessons for algebraic thinking introduce true/false statements (=), variables, and the algebraic rule for substitution. Then, it quickly expands to the three representations of a function: equation-table-graph.

*TKA is*

**STEM mathematics**for very young children. Most students learned most of the algebra content.

**TKA 4th Grade: Finding slopes of lines and**

**writing the equations in y =mx+b form.**

**Joanne Jacobs**education blog: Pre-K doesn't lead to lasting gains in academic skills, but Pre-K grads may be

**more likely**to complete high school and avoid repeating grades. "Most studies suggest a benefit in social-emotional skills such as self-control," writes Claire Cain Miller in the

*New York Times.*"The effects are larger for children whose parents are poor; Black or Hispanic; or did not finish high school" and for boys." (11-16-21)

**Note:**** **Academic gains don't last. We have known it since **Head Start**. What does **more likely** mean? It is an **estimate**, and estimates always come with **error**, a probability distribution. Many estimates or judgments by experts are often shown to be dead wrong.

Pre-K programs do all these other things listed by Miller. **Really? It's a miracle! **The government spends billions and billions on programs without assessing their quality. The alleged benefits are often **anecdotal**. Completing high school and doing well in school are far more influenced by family background than the teachers, according to the **Coleman Report** (1966). Sandra Stotsky (*The Roots of Low Achievement*, 2019) points out, "Low achievement was, as **Coleman** and his colleagues concluded, more a reflection of family background than their schools and teachers--then and presumably now."

Stotsky observed, "Most of the changes during the twentieth century reduced the content of academic coursework and time spent on this coursework." Many of the initiatives, such as gap closing, national standards approach, math reforms, diversity, equity (meaning equal outcomes), Zoom learning, etc., didn't work. **Educators still don't know how to change low-performing kids into high-performing kids**, explains Stotsky. Also, it seems apparent that the **Coleman Report** findings regarding family background have been ignored well into the 21st century.

**✓**"If you can't explain difficult mathematics to little kids, then you don't know it well enough." (Or, you don't know how children learn math or both.) H. Wu, a mathematician at UC-Berkeley, has been teaching workshops and courses for K-8 teachers for decades.

**Wu wrote that many K-8 teachers don't know enough math to teach Common Core math.**(Most state math standards are based on

**Learning more content doesn't always alter the way teachers teach, noted Wu, but, I think, it is a step in the right direction**.

**K-8 t**

**eachers need to know more about mathematics**, at least to the precalculus level, and

**science**, especially chemistry and physics. Unfortunately, for many decades, K-8 teachers have been weak in both math and science. They should be held to higher academic standards, but it's not their fault if they are not. The

**schools of education**are at fault.

**Education should not be a major.**Future teachers should major in a regular academic discipline such as history, English, literature, mathematics, science, philosophy, finance, economics, engineering, classical languages, etc.

*In addition to precalculus, a combination of college algebra and trigonometry, wannabe teachers should take rigorous chemistry and physics courses in college, not watered-down courses. For example, a*methods course in science should not be substituted for a college-level physics or chemistry course. Likewise, a math education course should not be substituted for a real math course such as precalculus or calculus. Furthermore, a statistics course should not be substituted for a precalculus course.

*The Roots of Low Achievement,*2019) points out that schools should spend money on

**improving the curriculum for all students**, not always on struggling students or closing gaps.

**The standards approach has not worked.**

**The late Richard Feynman wrote,**

**✍️****"I would rather have questions that can't be answered than answers that can't be questioned."**It is why I oppose those in education who think they know best how to teach children math, such as Jo Boaler, a so-called math educator. If reformists like Boalerknewn how best to teach math, almost all our kids would learn some algebra skills in the 1st grade and perform the standard long-division algorithm by the 3rd grade. Frankly, when asked how I teach 1st and 2nd graders real algebra, I reply, "

**I don't know**how I explain complex material to children ... But I do know that if I can't explain complex math to young students, then I don't know it well enough." Also, I think in terms of

**prerequisites**(Gagne's Learning Hierarchy), not stages (Piaget), and write coherent "

**worked-out examples**" or

**models**that are performance-based (Mager's behavioral objectives). I often think, i

*s there a more straightforward way to get from A to B?*

**************

**Inadequate Calculating Skills & Deficient Problem-Solving Skills.**

In my opinion, the decline in math and reading, as shown by the disappointing data from the NAEP Long-Term Trends (LTT) *before the pandemic*, roughly matches the advent of Common Core in 2011 through 2020, during which there was a swing toward conceptual understanding using minimal guidance methods, often at the expense of computational fluency. Common Core math and state standards delayed the **standard algorithms** for no good reason.** Students must learn mathematical procedures. Many aren't. They must perform procedures efficiently. Many can't. **

**Note:** I shall always remember a quote from Ian Stewart, "Mathematics happens to require rather a lot of basic knowledge and technique." (*Letters to a Young Mathematician, *Ian Stewart, 2006)

✓ Understanding does not produce mastery; practice does!

**I remember ****tutoring**** precalc students who often would say that they understood the concepts but could not work the problems. **So, what I did was reteach the procedures. Kids need practice problems, a lot of practice problems, even precalc students, to hammer in the facts and procedures. And, they need **review**! No matter how good students think they are, they will never come close to matching Richard Feynman's calculating skills. He used to do calculus problems in his head, even at breakfast, which drove his wife crazy.

**Today**, poor problem-solving skills can be attributed to inadequate calculating skills, ineffective instructional methods, a dumbed-down curriculum, and just plain poor teaching. For example, students were handed a calculator rather than a pencil. Of course, both concepts and calculating are essential, but the mix became wrong when concepts pushed aside calculating fluency.

**If you can't calculate it, you don't know it. **

*How can you solve a problem if you can't calculate the solution on paper like Einstein? How can you solve a trig problem if you don't have adequate knowledge of trig in long-term memory and experience solving trig problems? *Knowledge, solving routine problems, and review are needed no matter the level, starting in 1st grade.

**Strong c****alculating skills are needed to solve problems. Fundamentals begin in 1st grade.**

**************** **

**Measuring **is an essential process in **Science--A Process Approach** (SAPA, 1967). It should also be an essential process in 1st grade. In the early 80s, my students measured** mass on old SAPA equal-arm balances** in my self-contained 1st-grade class at a Title-1 urban school. Students used **centimeter cubes** to measure the mass of various objects. Each cm^3 had a mass of **1 gram**. Students also learned to "balance the balance" by adjusting the riders before measuring an object.

**🎯 Measuring gives students opportunities to use numbers and learn parts of the metric system.**

**First-Grade Science Vocabulary**

SAPA (Measuring Lessons)

- centimeter,
~~decimeter~~, meter, horizontal, vertical, between - volume, liter, milliliter, graduated cylinder, pipette, beaker, meniscus
- area (how much space), comparing, ordering, matching, approximate
- mass, gram, kilogram, equal-arm balance, cubic centimeter

**🎯 ****Today**, **how many 1st-grade students are introduced to science vocabulary and ideas like these found in 1st-grade SAPA (1967)?**

The **main weakness** of *Science--A Process Approach* (SAPA) was process at the expense of content knowledge. The expectation was that students would explore an exciting topic more deeply, prompted in a process lesson by finding books and materials at the library. Most children won't do that! There were no SAPA textbooks for students to read and gain deeper information about a topic.

In short, science is not only what scientists do (process); it also is an **accumulation of knowledge or facts**. **Reading** helps kids acquire more profound content knowledge. **Memorizing** facts and definitions in science is essential, too. **Watching** TV science programs can boost a child's interest in science, especially chemistry and physics, topics that are often ignored in elementary school.

**Mathematics is a key part of SAPA. Indeed, "competence in using numbers is essential in science."** The K-6 SAPA science program gives using numbers proper value. SAPA included the **Using Numbers** process "first, to make pupils realize that the ability to use numbers is an essential and fundamental process of science; second, to give pupils an opportunity to use numbers in finding answers to scientific questions in real problem situations." (*SAPA Commentary for Teachers*, AAAS, 1970)

In writing specific performance (behavioral) objectives, the action words are: identify, name, order, describe, distinguish, construct, demonstrate, state, and apply a rule.

**Equations act like a balance.**

The SAPA balances are long gone, but** **today, I use a commercial equal-arm balance (below) to demonstrate the **idea of balance or equal (=) in equations**, that in all equations, the left side equals the right side or visa-versa. In my algebra lessons for grades 1 to 5, students are asked to "Think, Like a Balance."

**Expression = Expression:** **2 + 5 = 10 - 3** is a true statement because 7 = 7. In math, we work from true statements and make equations true given a variable, such as **x**** + 12 = 10 + 7**. (Finding *x** *is called **solving** an equation.) If the right side is 17, then the left side must be 17, too. What number ** x** do we add to 12 to make a true statement, 17 = 17? {5} An equation tells that two calculations have the same answer.

**Stress: A variable like**

*x*is a number.

**Note:** SAPA was the best science curriculum available because *it integrated mathematics into science*. Its downfall was that ordinary teachers were unable to teach SAPA well, not even after extensive training. This is because they didn't have a strong science or math background, to begin with. In addition, SAPA lessons required lots of materials, and when government money ran out, kits were not replenished in the late 70s. As a result, much of the equipment was stored, lost, or discarded.

**🍎 "Children differ a lot in how well they do at school." --**Robert Plomin

*But it doesn't work that way.*"Most of us can be trained in mathematics up to high school level, but few go beyond." (Ian Stewart)

*"*

**Schools matter**in that they teach basic skills such as

**literacy and numeracy**, and they dispense fundamental information about history, science, maths, and culture." Ian Stewart points out, "That's why education is worth the effort."

**✔︎ Here are a few interesting ideas I teach in TKA.**

**1.**

**Equation: Expression = Expression**

**3 + 4 = 8 - 1**or

**7 = 7**by the

**Transitive Property of Equality**, but most teachers never heard of Transitivity. Thus, an equation tells that two calculations have the same answer. Two things equal to the same thing are equal to each other (Transitivity). This is not meant to be formal proof, but it is interesting. I give my

**1st graders**more difficult problems, such as

**5 + 7 =**. Find

*x*+ 5*. If the left side is 12, then the right side must be 12 as well. Well, that is easy for 1st graders who know the commutative property of addition; how about*

**x****5 + 7 = x - 12**? {24} Students at this age use

**guess and check**to solve equations. In 3rd grade, they use inverses.

**2.**

**Division by zero**is not an acceptable operation because it produces a false statement.

**0 x 1 = 0 x 2**(True 0 = 0). Now, divide the original equation (

**0 x 1 = 0 x 2)**by zero on both sides, and cancel the zeros. You end up with

**1 = 2**,

**a false statement**. This is not meant to be formal proof. (Sure, I can divide by zero, but it doesn't work and is not acceptable in regular arithmetic or mathematics.) Yet, it is interesting. An ordinary fraction is a

**quotient of two integers**: a/b,

*but b cannot be zero*.

**3.**-3 x -3 must equal either

**9 or -9**, but which one is it?

**-3 x -3 = 3 x -3**(Does -3 x -3 equal -9?)

**-3 = 3 (False)**, so it cannot be -9. It's a

**counterexample**. Thus, the answer to

**-3 x -3 must be 9**, not -9, which suggests that the

**product of two negatives is always positive**in Real Numbers. This is not meant to be formal proof, but it is interesting.

**Where did I get these ideas?**

**3^2 + 4^2 =**

**x**

**^2**, But

**can either be 5 or (-5). (Just to toss something out for middle school math teachers: solve**

*x***x^2 = -9**. It's complex.)

**-------------**

**The False Narrative of Progressives: & The Fallacy of Fairness**

**If we provide the right environment in school and at home, students will do well academically (equity). "What we need are government preschools," we are told.**

**Really?**Sounds great, but it doesn't work that way. As it turns out, school achievement is more genetics than nurture (Robert Plomin,*blueprint, how DNA makes us who we are*, 2018). Also, poverty is not the root cause of low academic achievement. The root causes have been government policies and**substandard teaching of basics**. A major factor of declining achievement in government schools is**dictating equal outcomes**by intentionally lowering standards and expectations. No child gets ahead.

**Equity as equal outcomes is a "fallacy of fairness,"**writes Thomas Sowell. Equity cannot produce equal outcomes. Kids get better through practice, but practice and memorization have fallen out of favor in progressive schools. Drill is considered old-fashioned, old-school, and poor pedagogy. It's not. It works!

**Children differ a lot in how well they do at school**... How much do differences in children's school achievement depend on which school they go to? "The answer is not much ... Our focus is on individual differences [not schools] ...

**Schools matter in that they teach basic skills such as literacy and numeracy, and they dispense fundamental information about history, science, maths, and culture.**Schools also matter because children spend half of their childhood in school ... This does not mean that the quality of teaching and support offered by schools is unimportant. It matters a lot for the quality of life of students, but it doesn't make a difference in their educational achievement ...

*Some children in the worst schools outperform most children in the best schools."*

**"Equality of opportunity does not translate to equality of outcome."**Thomas Sowell has been saying the same thing for decades.

**-----------**

**Stalled Achievement: It's the Teaching!**

**Kids are not learning the fundamentals of arithmetic or algebra well enough**.

*It's not the teaching we are told, but what else could it be?*Frankly, many teachers aren't teaching fundamentals effectively. Either the curriculum is wrong, or the instructional methods are wrong, or both. A steady diet of group work, discovery learning, project learning, or other minimal guidance methods doesn't work in math. There is little explicit instruction using examples (models) in today's classrooms. Kids must master facts and learn procedural knowledge to advance. Sadly, memorizing facts and practicing standard algorithms have been pushed aside as poor pedagogy.

**Really?**

**e**

**quity has come to mean equal outcomes.**Not possible, a liberal pipe dream! The only way to close gaps is to significantly lower standards and expectations, a

**dumbing down of curriculum**, which Thomas Sowell calls a "

**fallacy of fairness**." Common Core or state math standards were shaped so that all students get the same math curriculum. No student gets ahead. The idea of

**sameness**in the name of equity doesn't fit the real world or the science of learning.

**Some kids are better at math than others.**That's DNA, instruction, and practice.

**Some kids are better at the violin.**That's DNA, instruction, and practice.

*Almost all kids can get better in math through practice-practice-practice and better teaching.*

**Nearly all students can learn arithmetic at an acceptable level**to prepare for a rigorous

**pre-algebra**course in 6th or 7th grade that prepares students for

**Algebra-1**in 8th grade. It happens when expectations are high. But, the teaching must get significantly better in the lower grades.

**Therefore, the pathway is conditional on**

**K-6 teachers teaching arithmetic well starting in 1st grade.**

*Hence, part of the answer is for schools to train teachers better in arithmetic and teaching math. Reform math and minimal guidance methods have not worked.*

**0-20 number line**, then use flashcards.

**First graders**should memorize math facts from the start, not count on their fingers to figure out a fact each time needed.

*Bad habits are hard to break.*Also, they should

**not**use calculators! Still, I see exercises in 1st-grade math textbooks that use calculators.

**✓ Elementary School Mathematics Priorities** ( Dr. W. Stephen Wilson)

**The five building blocks** for higher mathematics:

1. Numbers

2. Place value system

**3. Whole number operations (i.e., The Standard Algorithms)**

4. Fractions and decimals

5. Problem solving

**Most teachers are unaware of the content very young children can learn given the proper instruction.**

**Note1:** 2nd-Grade kids learned to do **sums** of integers (-10 to 10), plotted (x, y) points, and identified ordered pairs of numbers, all were part of the 2nd Grade **Science A Process Approach** (SAPA), the Using Numbers process (SAPA **1967**). Moreover, 1st-grade students were introduced to integers (-10 to 10) in SAPA. These exercises were thoroughly tested in classrooms and not optional. **In short, SAPA taught the mathematics needed to understand and do the science. **

**Note2:** In my algebra curriculum (**Teach Kids Algebra**, TKA), 40 1st graders at an urban Title-1 school, after 7 hours of instruction, used a linear equation (e.g., y = x + x + 1), made an x-y table of values given the x values, and plotted the corresponding number pairs (x, y) in Quadrant I (TKA, **2011**). The TKA lessons were for all students--almost all were minority students. Below is one of my 1st-Grade TKA Students (TKA, Spring 2011).

**TKA was a stark response against Common Core reform math, minimal guidance instructional methods, calculator use, the dumbing down of math, grade inflation, and other inane policies.**In 1989, for example, the National Council of Teachers of Mathematics (

**NCTM**) reforms included calculators in 1st grade. Is it any wonder that achievement in arithmetic and mathematics, in general, went downhill? In my opinion, the NCTM lost all credibility.

**Higher-level thinking skills, without substantial knowledge in long-term memory supporting them, are at best superficial if that.**

**Declining Achievement**

Bummer: Declining Achievement! |

**Pre-pandemic Data (The Nations Report Card)**

NAEP Long-Term Trends (2012 - 2020)

Since 2012, our kids are not getting better in math or reading, according to pre-pandemic data (NAEP Long-Term Trends **LTT**, 2020). Betsy DeVos writes, "Not even high-performing students recorded any measurable achievement gains. There wasn't a single bright spot to be found anywhere in the data. No student, of any age, of any subgroup, saw their performance improve since 2012. Most saw declines." (Note: NAEP Long Term assessments are different from the regular NAEP assessments.)

- "One of the biggest differences between school math and university math is proof. At school, we learn
**how**to solve equations or find the area of a triangle; at the university, we learn**why**those methods work and prove that they do." -- Ian Stewart (*Letters to a Young Mathematician*, 2006) *Thus*, teaching children arithmetic and algebra should show**how**to do and apply things, not**why**they work. Factual and procedural knowledge is essential to learning math well.*They don't need to make drawings or write explanations to prove they are correct.*- "In my opinion, the implementation of Common Core reform math and the resurgence of minimal guidance instructional methods seem to coincide with the stagnation of achievement. The stagnation is the result of the poor teaching of fundamentals, starting in grade 1." -- LT
- "Thoughts without content are empty" -- Immanuel Kant
- "It's called remote learning because the chance of a child learning anything is remote." (Cartoon)
- "As for the Biden education agenda, I couldn’t be more disappointed by their emphasis on 'inputs' reminiscent of a pre-Coleman era, when schools were judged by their resources and promises rather than by whether kids learned anything in them." -- Chester E. Finn Jr.
- Most
**gifted programs**do not boost academic achievement**knowledge**sparks critical thinking and problem-solving seems lost in many gifted education programs.**Thinking without sufficient knowledge in long-term memory seems shallow and superficial.**Most gifted programs are not based on the academic standards (math and verbal) established by the**Johns Hopkins Center for Talented Youth**(CTY), which requires the School and College Ability Test (SCAT) two grade levels ahead to identify students eligible for its programs. For example, a 2nd-grade student would take the 4th-grade SCAT. Also, 7th-grade students should score at least 500 on the College Board SAT math or 510 on the verbal part to qualify for CTY courses in math or the humanities. - After
*Brown v. Board of Education*, Thomas Sowell explains, “There was a lot of turmoil, racial polarization, and bitter backlashes, but no general educational improvement from seating black school children next to white school children.” Chief Justice Warren, who claimed that schools were “inherently unequal,”*was wrong*! There were many excellent all-black schools, too, that did the same. But, forced integration ruined these black schools, such as the all-black Dunbar High School in Washington DC, says Thomas Sowell, a graduate of Dunbar. (Thomas Sowell:*Discrimination and Disparities*, 2019) **When you learn something, teach it to someone else.**- I often hear, Follow the Science; however, I think most people don't grasp science.
With new data, scientific ideas often change. It is not absolute like mathematics. Data interpretations can often result in**Science does not prove something correct. Rather, it is a process that eliminates wrong ideas.****divergent inferences**.

✔✔✔✔✔ **Declining Achievement!**

In my opinion, the implementation of Common Core reform math and the resurgence of minimal guidance instructional methods seem to coincide with the stagnation of achievement, which, I believe, is primarily the result of the **poor teaching** of fundamentals, starting in grade 1.

**"It's the teaching**,**" **the late Zig Engelmann would retort. Teaching involves both the curriculum and methods of instruction. For example, you can't teach arithmetic the way you teach social studies because arithmetic is **symbolic, abstract, and hierarchically based**, so that "new mathematical ideas build on older ones" (Ian Stewart, *Letters to a Young Mathematician*), so the **sequence** is critical. *Students who do not master the multiplication table or practice the multiplication and long-division standard algorithms by the 3rd grade will struggle with fractions, proportions, percentages, algebra, higher-level math, etc. *Indeed, the alternative algorithms advocated by many reputed experts, math educators, reformers, and policymakers should never replace the standard algorithms, which are primary.

**Chester E. Finn Jr. on Excellence**

**accelerating everyone to the max. Today’s push for “equity” is surely at war with meritocracy, especially if it leads to things like eliminating “gifted education” in the name of equality rather than augmenting the scope of gifted ed. to serve many more kids. The “war on testing” is ultimately a “shoot the messenger” project that would blind us to the failings, gaps, and shortfalls that beset both equity and excellence. And the**

**distraction of nonacademic mandates**for schools, such as SEL and other “softer” school qualities and pupil attributes, can only deflect us from the pursuit of excellence. Do please bear in mind that “Excellence in Education” was the name of the commission that issued

*A Nation at Risk*!" (Finn's Interview with Rick Hess, Education Week)

**Failed Educational Goal: Gap Closing**

**Sandra Stotsky**explains that the

**primary educational goal**should be

**improving the curriculum and teaching for all students**, not closing gaps. After dumping billions and billions into schools over the years, the gaps aren't closing and, in many cases, increasing. Over the years, the curriculum has been

**dumbed down**, and

**teachers have been using**

**minimal guidance methods**that are ineffective. Gap closing has been a failed educational goal. It has also been the wrong goal, articulates Stotsky (

*The Roots of Low Achievement*, 2019).

**all students**in the class? She can't easily do both at the same time." Educators are obsessed with gap closing. But, Stotsky suggests that educators don't know how to change "massive numbers of low achievers into high achievers," not in math or reading. She points out, "So far, studies have produced

**no useful insights**for K-12 educators to address low achievement."

*In short, what we have tried hasn't worked; e.g., reform math, minimal guidance methods of instruction, mixing achievement groups in the same classroom, group projects, block scheduling, more money, etc.*

**Not Ready for College**

ACT CEO Janet Godwin observes, "We are seeing a number of year-over-year trends that suggest the emergence of a **'lost generation' **that is less likely to succeed academically and in the workplace ... These trends have all been worsened by the COVID-19 pandemic, but it is not the single cause nor excuse for them." The decline started years ago. In my view, it started with NCTM reform math and 1st-grade arithmetic. Common Core or state standards have exacerbated the decline.

Godwin points out, "This is the fourth consecutive year of declining achievement of high school seniors, and too many of our seniors are simply not prepared for college-level work."

The decline didn't start in high school or the Zoom year. We have not been teaching the foundations of arithmetic well enough beginning in elementary school, so a decline is inevitable. On average, our students cannot match their peers in top-performing nations, not in mathematics.

**Justice-Orientated Science**

I read parts of the *Science and Engineering in Preschool Through Elementary Grades *(2021), a Consensus Study Report that focuses on "justice-oriented science and engineering instruction."** Really?** It is just as bad as equity math.

**We need to go back to move forward.**

In the 1960s, **Science--A Process Approach (SAPA K-6)** integrated mathematics as an essential process. In fact, of the six science processes taught in 1st-grade SAPA, four were math (Using Numbers, e.g., Integers, etc.) or math-related, such as Measuring, Communicating (graphs), Using Space/Time Relationships (geometry). Robert M. Gagne laid the foundation for **SAPA's Learning Hierarchy****. **Below is a glimpse of the 2nd-grade Using Numbers. The** sequence** is important, linking a new idea to an old idea. Prerequisites!

**Part C is 2nd Grade**

**Finnish Schools (are not that great!)**

When Finnish schools were proposed as a model the U. S. should follow a few years ago, Dr. Olli Martio, University of Helsinki, found *conspicuous math deficiencies* in Finnish schools. I gave my two 5th-grade classes at a Title-1 Urban school some of the 9th-grade questions out of curiosity. Martio concluded that the **use of calculators** and a **spotty curriculum** have** **kept many students from learning basic arithmetic. (Note: 9th graders are ages 15-16 in Finland; 1st graders start at age 7.)

**Note:**I also found that Finnish

**4th and 8th-grade students**ranked slightly below the US in international testing (

**TIMSS**).

*I concluded that Finnish math education was not superior after all.*In the most recent TIMSS cycle, I also observed that the results of Finland's 8th graders were conspicuously absent. Therefore, we should not imitate Finland.

**below international benchmarks,**we tell our kids they are not smart enough to learn the same math (or science) that kids in many other nations routinely learn. So, for example,

**the fluency of standard algorithms is delayed**

*for no good reason*

**.**

**standard algorithm**I taught 1st graders in the early 80s. It is efficient and the

**best model for place value**. I used the word

**carry**, not renaming or regrouping. Carry makes good sense to beginners: 4 and 8 are 12 ones, or one ten and 2 ones. See the 12. The one ten is carried to the tens position: adding ones to ones, tens to tens, etc.

**badly failed**... Problem-solving has been overestimated in all levels of the mathematics curriculum," and

**calculators**have been misused. "The use of calculators is overemphasized since nowadays their use is extremely limited in everyday life." You never hear, "Let me pull out my calculator" in everyday life. The bank calculates your balances, loans, interest, mortgages, credit card payments, etc. Stores compute your purchases and tax. The same, for bills, such as your electric or gas bill, insurance, finance, etc. Almost everything is calculated for us.

*In many cases, your calculator collects dust after schooling is finished.*

*(I forgot where I put my slide rule.)*

**0 x 8436 = 0 x 0.536.**In 1981, 79% of Finnish students were correct, but by 2003, the percentage of students who got it correct dropped to 65.6%. Of course,

**multiplying by zero gives zero**, a 3rd-grade concept, even earlier.

**(-3)^2**, 67.8% of Finnish students had "(-3)^2 = 9" correct in 1981, but by 2003 only 47.5% of Finnish students were correct. Not good! What's went wrong? It's the teaching, a spotty curriculum, and the misuse of calculators concluded Dr. Martio!

**comparison**, in my two 5th grade classes a few years ago, 74% of the students in one class gave the correct answer (

*9*) and 54% in the second class. Calculators were not allowed in my Teach Kids Algebra (TKA) lessons. Group work, discovery/inquiry, and project-based learning were not used in TKA. Instead, carefully selected examples were explained and linked to old ideas (explicit teaching) along with practice worksheets where more than half the questions were

**review**questions. (Note: I met students in grades 3 to 5 once a week for 60 minutes and, depending on the scheduling, just twice a month for an hour for the school year. I met with 1st and 2nd graders for 7 hours.)

**(1/6) x (1/2)**. In 1981, 56.5% of Finnish 9th graders were correct (1/12), but in 2003 only 28.3% gave the correct answer, a significant drop. Remember, these are 9th graders. It's shocking! In contrast, 74% and 100% of students were correct in my two fifth grade classes, respectively.

*I do not think my 5th graders were better students than the Finnish 9th graders. I think the Finnish students were not taught fundamentals, starting from the 1st grade.*It's the teaching! Incidentally, I teach my algebra program at a Title-1 city school with about 85% minority population.

*Long Term Effects in Learning Mathematics In Finland--Curriculum Changes and Calculators,*Olli Martio)

If we provide the right environment in school and at home, students will do well academically (equity). "What we need are government preschools."

**Really?**Sounds great, but it doesn't work that way. As it turns out, school achievement is more genetics than nurture (Plomin). Also, poverty is not the root cause of low academic achievement. The root causes have been DNA, government policies, and

**substandard teaching of basics**. A major factor of declining achievement in government schools is

**dictating equal outcomes**by intentionally lowering standards and expectations. No child gets ahead.

**Equity as equal outcomes is a "fallacy of fairness."**It cannot produce equal outcomes (Thomas Sowell). Kids get better through practice, but practice has fallen out of favor in progressive schools. Drill is considered old-fashioned, old-school, and poor pedagogy. It's not. It works!

**A implies B, but B does not imply A.**

**"That's why education is worth the effort."**In the real world, I will never play the violin as well as 9-year-old Himari, who nails Paganini, no matter how much I practice. I don't have the musical ability she has. (Google "Himari violinist")

Himari from Japan has the soul of Paganini.She's not a prodigy; she's way above that. "She is one of a kind, in a class of her own." I was astonished when I watched her play. Paganini lives! |

**But, you should see her at age 7:**

**She is so much better at age 9 with an orchestra.**

**Food for Thought**

*I survived lead paint, asbestos dust from an old furnace, coal dust, and cigarette smoke at home.*My chemistry set was filled with dangerous chemicals, and I lived. I used encyclopedias (World Book) to help with school work. I read high-school chemistry textbooks in 7th grade and did most of the experiments.

**Note:**Science was one semester in 7th grade and one semester in 8th grade.

*Mr. Wizard*, a science show for kids, on NBC. Today, there is nothing like it.

**Circumstances are much different now than in the 1950s.**

**The latest is climate change hype.**

**If we don't do something NOW, the world will come to an end. What rubbish! The radicals and so-called experts told us that over 50 years ago. The sun significantly controls our weather. We can't change the sun or sun spots, etc.**