Summer2021 Part 2

Summer 2021 Part 2 [non sibi]

Welcome to the mad, mad world of math education. 😎

What has happened to math education in the U.S?

We need to teach the right math, the right way, to advance achievement, but we don't! Progress has stalled in both math and reading for over a decade. Instead of basic arithmetic, students get reform math--not enough memorizing, practicing, or teaching fundamentals. Understanding is over-emphasized and does not produce mastery; practice does! Also, being able to solve an equation is practical understanding! Dr. W. Stephen Wilson, a mathematician, establishes the priorities. 

Note: BackToSchool-1 is now available.

IQ is not fixed for life, says Sanjay Sarma. Schooling increases IQ.  

✓  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 

In addition to dumbing down the math curriculum, using ineffective instructional methods (i.e., group work), and adhering to the "false equivalence between literacy and math skills," our classrooms have become battlegrounds for challenging issues, especially critical race theory, mask mandates, gender, and equity math. These issues and others have derailed education off course and stalled learning in math and reading. Parents are angry! 8-12-21

Children in elementary school should learn "as much knowledge as possible as quickly and efficiently as possible," writes Natalie Wexler (The Knowledge Gap, 2019). That's not happening! For decades and decades, educators "have vastly underestimated [and undersold] what their students were capable of." Consequently, by the 4th or 5th grade, U.S. students in math are at least two years behind their peers in top-performing nations. 

In the name of equity, Oregon has shelved its requirement that students demonstrate competency in math, reading, and writing to graduate. It is dumbing down the curriculum and part of the woke movement to end testing for graduation, rendering a high school diploma meaningless. It happens when liberal buffoons run the state and department of education. Equity means no student gets ahead. All students get the same instruction regardless of achievement. Equity is based on equal outcomes, a radical idea. Consequently, some parents are fleeing public schools for private schools or homeschool. 8-10-21

Math reforms like Common Core have not worked. Dr. W. Stephen Wilson has established priorities for basic arithmetic. He argues against popular reform math programs like TERC, Everyday Mathematics (EM), and others based on reform math and minimal guidance methods. In math, teachers should not be facilitators. They should explain examples explicitly and make sure kids practice enough. 8-11-21 

✓  Understanding does not produce mastery; practice does! 

"To learn something is to remember it." If you can't retrieve the fundamentals from long-term memory, what have your learned? Your mind is an empty set. 8-11-21

Face it: Common Core has failed.

After a decade, the Common Core math standards have had minimal effect on student achievement, including State Standards built on CC. They were another flawed, top-down theory. So why are many states clinging to them in one form or another? A new assemblage of standards is not going to change things. Get out those old, dusty math textbooks and workbooks and put "group work" to rest. Teach arithmetic by explaining examples and practicing for automation. 

There are workbooks available at stores like Barnes & Noble: e.g., Spectrum, Harcourt, Kumon, etc. 

FlashCards work! (Stanislas Dehaene, How We Learn, 2020) Memorization of certain fundamentals such as math facts and efficient procedures is good for kids. Furthermore, the standard algorithms must be automated. Students should practice-practice-practice! 8-11-21

Kids need to memorize math facts and practice-practice-practice to make fundamentals, such as the standard algorithms, stick in long-term memory and be remembered for problem-solving. Students also need to recognize routine problem types and be able to solve them. They are beginners, not experts, so they need to practice a lot!. You can't solve problems in math without knowing how to calculate well. Kids should first learn standard algorithms for calculating, even in the 1st grade. Standard algorithms require the memorization of single-digit math facts. 8-11-21 

Students are novices and should not use calculators or be required to invent their own algorithms, as claimed by Everyday Mathematics (EM). Also, in EM students learn "focus algorithms" for each operation, which are substantially more complex and different from the standard algorithms that must be automated for problem-solving. The so-called focus algorithms, which are claimed to promote conceptual understanding, are rubbish. They confuse kids and hold them back. Instead of teaching basic arithmetic operations (i,e, standard algorithms) that kids must know for problem-solving, EM teaches pretend math. 8-11-21

Teachers tell me that they teach 5 or 6 different ways for multiplication and don't have time for the standard algorithm, which they never get to. Teachers do not realize that the standard multiplication algorithm is essential for problem-solving and should be given top priority. All these alternative, unconventional, or invented algorithms are not that important.    

Excuses

I teach for understanding.

I believe in group work. 

It's not on the state test. 

One teacher told me that children don't understand long-division, so she doesn't teach it. I replied, "And your kids understand the lattice method for multiplication that I see on your bulletin board?" 8-11-21

Comment: Even 1st graders have an intuitive understanding of division. Also, Singapore starts multiplication in 1st grade as repeated addition: 3 x 4 = 4 + 4 + 4  or 12.  What do all the standard algorithms require? Automation of single-digit math facts. 8-11-21

 

All this reform math stuff has ruined U.S. math education, in my opinion. The reform leader has been Jo Boaler, who, at one time, stated that kids don't need to memorize the multiplication table that supports the standard algorithms and that teachers should be facilitators. The reform math idea is that kids should invent their own mathematics. Really? How many kid experts like Newton are out there? 8-11-21

***** Hung-Hsi Wu explains ("What's Sophisticated about Elementary Mathematics?"), "In other words, students' ultimate understanding of these [standard] algorithms must transcend place value to arrive at the recognition that all whole number computations are nothing but a sequence of single-digit computations artfully put together." 

Wu states that carrying is not the main idea of the addition algorithm. "The main idea is to break up any addition into the additions of single-digit numbers...." And with knowledge of place value, "put these simple computations together for the final answer." 8-11-21

 

"If I practice a lot, then arithmetic becomes easier for me, and I learn (remember) more, increasing my storage strength and retrieval strength. I also know that the mastery of fundamentals in long-term memory is essential to advance my STEM goals."

Practice-Practice-Practice
At School & At Home
FlashCards Work!

From The 74, "But a decade after they (Common Core or state standards primarily grounded in Common Core) were first adopted by states, little evidence exists to show that teaching or learning was significantly improved by the vast resources poured into implementing the standards," concludes researcher Tom Loveless (Between the State and the Schoolhouse: Understanding the Failure of Common Core, 2021).

Loveless writes in the book, "This is not a problem that another set of standards can solve. If standards came out tomorrow, and I agreed with every single word in them, I would still give them only a slim chance of being faithfully implemented — and less than that of moving the needle on student achievement. ... It's hard for the top of the system to have a large impact on what happens at the bottom of the system." 8-5-21

-------------------------

Teachers should focus on reading, writing, and doing arithmetic, not critical race theory (CRT), or diversity that excludes Asians, or equity that means equal outcomes by leveling content or "equalizing downward by lowering those at the top, or by lowering or dropping state requirements in math and reading/writing, etc. for graduation." Teachers should not depend on the Common Core reform math curriculum or minimal guidance methods (group work) to improve math achievement. There are workbooks available at stores like Barnes & Noble: e.g., Spectrum, Harcourt, Kumon, etc.

CRT and its many forms, including oppressed vs. oppressors, indoctrinate young children that race drives their future rather than hard work, perseverance, education, and character. If you are white, you are racist or an oppressor. Really? How dumb! Even math is called racist by CRT radicals. It's all wrong! In Arizona and other states, teaching CRT in public schools is illegal. Whiteness should not be described as a form of oppression. According to CRT radicals, in math, getting the right answer or showing your work is racist. No, it's not; it's good pedagogy.

Furthermore, according to the National Math Advisory Panel (2008), teachers should prepare more students for Algebra-1 no later than the 8th grade by stressing factual and procedural knowledge in long-term memory via memorization and practice-practice-practice. Algebra-1 is a middle school subject for average students who are prepared, and preparation begins in 1st grade. (You don't get good in math by not practicing math.) "You know nothing until you have practiced," explains Richard Feynman, Nobel Prize-winner in Physics.

Also, the U.S. mathematics curriculum needs upgrading to match international benchmarks, at the least. (Note: Common Core and almost all state math standards grounded in CC are not world-class. Our kids start behind and stay behind their peers from top-performing nations.) Instruction should be explicit and efficient--not a steady diet of minimal guidance group work. The standard algorithms for multiplication and long-division should be learned by students no later than the 3rd grade. Students must automate math facts in grades 1 to 3. (Credit: equalizing down..., a quote from Thomas Sowell) 8-2-21

Student in 7th-grade Algebra-1

• Algebra-1 is a middle school subject, but not in most U.S. public schools.
• Almost all students get the same dumbed-down reform math, not world-class content. 
• Individual achievement does not count. Merit is pushed aside! It's the wrong approach!
• Advanced kids get grade-level math like other kids. Why?

✓  Children need to do things that don't come easy for them. They should complete tasks and learn persistence in doing so. Also, practice does not cause talent; it improves performance up to a point. "You don't know anything until you have practiced," explains Richard Feynman. 

✓  Merit and learning are not valued enough. Education is no longer merit-based because grade inflation and group work (minimal guidance methods of instruction) squash it. Teachers no longer teach a coherent math curriculum. They facilitate group work. What's that? There has been a slow creep of American Marxism in education, a war against individualism and merit. For decades children have been praised and rewarded for no good reason. It is part of the racist Critical Race Theory, which is not new. 

✓  If students are at risk of algebra failure, then their arithmetic background has been weak. Another cause is the inadequate teaching of algebra. If I can teach 1st, 2nd, and 3rd graders the three representations of functions (equation-table-graph) and have them perform these skills on paper, then why can't teachers teach basic prealgebra math skills for mastery to prepare more students for a solid Algebra-1 course in middle school? I know why, but you won't like the answer. 

Note: Dump the new California math Framework in the waste can and return to the 1997 California math content standards before Common Core reform math replaced them for no good reason. The 1997 document, however, should be upgraded to match the 1st-grade Singapore standards, such as memorizing math facts and learning the standard algorithms. Also, no need for statistics, data analysis, and probability in 1st grade. The old CA standards are a starting point. So start!

Comment: We know that the best way to teach arithmetic or math is via explicit instruction when the teacher explains carefully selected worked examples. After that, the students need to recognize problem types and practice-practice-practice.

The math curriculum, which was built on Common-Core-like state standards, is not world-class math. Common Core ignored many of the well-established, international benchmarks in arithmetic and pushed algebra to high school. I wonder why states adopted Common Core so quickly, knowing this? (It was all about the money, money!) The gap between the content that Singapore 1st-grade students routinely learn and the content that U.S. 1st-grade students learn widens up the grades. Thus, by the 4th or 5th grade, our students, on average, are about two years behind their peers from top-performing nations, but no one seems to care that our kids are being out-educated. We are told that it is not that bad, but it is. 

TKA

My Teach Kids Algebra (TKA) project is STEM math for young elementary school students from the 1st grade on up. It started in 2011. I would often give 1st and 2nd graders equations such as x + x + 2 = 18 to solve. Find x. Students solved the equations by guess and check (i.e., trial and error), applied the equality idea (LeftSide=RightSide), and the algebraic rule for substitution: x must be the same number (e.g., x + x = 8, x can only be equal to 4). In the equation x + x + 2 = 18, x = 8. Thus, 8 + 8 + 2 = 18 and 18 = 18 (True Statement by Definition of Equal Sign). Solving an equation is critical thinking, starting with the idea that if the right side is 18, then the left side must make 18. Students must follow the substitution rule.  

The Baltimore Problem

The teacher writes in a blog, "I can teach math, but I can't pass the math test for full certification." The 3rd-grade "teacher" wrote that she had two master's degrees and gets excellent reports from her principal, parents, and students. Really? I wonder how she got into graduate school. How can you get a master's degree without knowing some college-level math? 

She works at a PreK-5 Baltimore elementary school where almost all students in grades 3 to 5 scored far below the state average--less than 50% proficiency in math (26%) and even less in reading (19%). It is terrible education with ineffective teaching. In my opinion, some teachers don't know how to teach kids basic reading, writing, and arithmetic. 

The "I can teach math" 3rd-grade teacher doesn't realize that her lack of content knowledge contributes to the innumeracy and illiteracy of students at the school. Like some other teachers, she has no business being in the classroom. 

At this school, almost all students are significantly below grade level. I can only think that most of the school's teachers have low expectations for these black students. Content knowledge is essential in math. Teachers in the lower grades need to know how to prepare students for Algebra-1 in middle school and above, but they don't.  

If teachers knew how to teach arithmetic, reading, and writing well, the scores would be significantly better, at least at the state averages, which, to begin with, aren't high quality. The K-8 teachers lack factual and procedural knowledge in math because education schools that train wannabe teachers don't require it. Instead, pedagogy is often substituted for math content. Also, getting two master's degrees in education does not make you a better teacher. It shows how weak the degrees in education and some other subjects have become. Many online degrees are not valid in my mind. The content and rigor are not there for many so-called degrees. Smart 12-year-olds (6th graders) could pass some of the "degree" courses. 

Advice: When tutoring high school students, I would often hear, "I understand the concept, but I can't work the problems," which is double talk. As a precalc tutor, I would help the student grasp how to do a procedure, step by step. Practicing the steps is important. "You don't know anything until you have practiced," explains Richard Feynman. Also, if the student can teach other students how to do the procedure, their knowledge is more profound.

Tutors must prepare, too. 

For example, I would work out all the precalc homework problems ahead of the tutoring session to guide the student to avoid mistakes. The tutoring was efficient and worked. If an answer didn't correspond to an answer in the back of the pre-calculus textbook, my tutoring students knew where they were mistake-prone, but more importantly, they also knew how to correct the errors without my help.

I kept getting the wrong answer to a complicated trig problem. The angle measurement could not be negative. The solution involved several calculations. My steps were right, but I kept getting the wrong answer. What's wrong? I rounded answers. When I didn't round and stored lengthy intermediate answers for use in other calculations, and so on, I ended up with the correct answer. Now you know why I always work the homework problems ahead of time. As it turned out, the student's math teacher ran into the same problem.

In a tutoring session, a 7th-grade pre-algebra student told me that his calculator kept giving the wrong answers in the trig problems and that his teacher said to get a new calculator. I took one look at the calculator and noticed it was set to radians, not degrees. I reset the calculator to degrees and tested tan (45) = 1. "You don't need a new calculator; you need a new teacher."

Idea: "If you really want to learn something, learn it with the view to explaining it to somebody else." (Sarah Flannery (In Code)

In short, you not only need to perform a skill correctly but be able to teach it, too. Teaching something complex is not easy. "You don't know anything until you have practiced," explains Richard Feynman, Nobel Prize-winner in Physics. If you can't calculate it, then you don't know it. In short, to learn something is to know it well enough to teach it to someone else.

Inflation is nothing more than a new tax.

 

  

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