Summer 2021 Part 2 [non sibi]
Welcome to the mad, mad world of math education. 😎
✓ Elementary School Mathematics Priorities ( Dr. W. Stephen Wilson)
The five building blocks for higher mathematics:
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.
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?
✓ 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.
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 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."
Inflation is nothing more than a new tax.
©2021 ThinkAlgebra.org, LT