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| Desks in a row may be old fashioned, but it was highly effective. Kids learned and listened to the teacher. |
Photo: 46 students at a Catholic school in 1950. Students sat down, got quiet, and paid attention to the teacher. No Common Core. No federal regulations. No unions. No bureaucracy. Nuns were the teachers and disciplinarians.
Opinion is Not Evidence
Knowledge Supports Thinking
Educators rely too much on opinion or anecdotal claims, which have led to incorrect assumptions, false beliefs, ineffective programs, and bad policies. Education is a road littered with failed policies, questionable programs, and theories that don't work.
Paying attention in class and practicing the fundamentals for mastery promotes better learning (not group work, discovery learning, or tech). Learning is remembering from long-term memory. Knowledge in long-term memory supports thinking, not vice versa. (You can't solve an algebra problem easily unless you know some algebra.)
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| "The more math I know, the more I can learn, the faster I can learn it, and the better I can think, i.e., solve problems." Factual and procedural knowledge in long-term memory enables thinking. In the cognitive science of learning, "knowing and applying" supports problem-solving, which is higher-level thinking. |
In OLD School, teachers were respected, which may no longer be true in some schools today.
Critical Thinking Should Not Replace Knowledge
Chester E. Finn, Jr. thinks that the "emphasis on thinking skills over facts contributes to students' inability to identify disinformation and misleading information." Clear thinking requires the separation of observations from inferences or facts from opinion. Finn says that critical thinking can go awry in at least two ways. One way is when it replaces knowledge. The second is when interpretation is everything, i.e., everyone's opinion is as valid as anyone else's opinion. If you have an opinion, you can make up the facts that support it. It is unfortunate that "thinking gets detached from knowledge."
Disrupting Education: Tossing Out the Old School Stuff (Wrong Approach)
Christian Madsbjerg (Sensemaking) observes, "Everything has become a disruption: a clean break from the past leaning far forward into the future. The [postmodern] culture has upended the way we educate our children." Indeed, reformers have disrupted education by tossing out the Old School stuff for a clean break, including memorization, drill to develop skill, desks in a row, cursive writing, and so on. In short, reformers advocate "out with the old," even if it worked well, and "in the new such as tech, "even if it has no basis in evidence. Reformers seem to ignore scientific evidence and the cognitive science of learning.
Group Work --> Inattentiveness
Walk into elementary school classrooms and notice that the students are seated at tables or in pods (groups) of 3 or 4 desks facing each other. How stupid! I have suggested to teachers not to set up group work pods with desks. It leads to disruptions and inattentiveness. Kids talk. Starting in K, they are conditioned not to pay attention to the teacher and explanations. It is a flawed practice. In contrast, desks in a row worked much better (Old School). The reasons often given for pod seating and group work are that students need to collaborate and do discovery activities. Really? Since when has student collaboration become the primary focus in school? Moreover, the so-called minimal guidance methods such as discovery or inquiry methods are ineffective in learning arithmetic.
Critical Thinking Without Knowledge Is Pointless and Shallow
In a postmodern world, educators have substituted critical thinking for knowledge. We are told that learning facts is not that important. Individual interpretation and opinion are much more critical. Really? First of all, critical thinking is not knowledge; it requires knowledge. Immanuel Kant (1724 - 1804) once wrote that "thought [critical thinking] without content knowledge [facts] is empty." And he was right! It is a basic premise of the cognitive science of learning.
Hard for Humans: Separating Observation From Inference
Guy P. Harrison (Think: Why You Should Question Everything) writes, "The brutal truth is that human brains do a poor job of separating truth from fiction. This leads to many false beliefs." Factual proof (i.e., scientific evidence) should come before opinion, belief, or assumptions, but too often opinion is valued more than the facts. Our brains have difficulty separating observation from inference. We should think like a scientist, but we do not. Also, computers are good at logic, but human brains are not.
Opinion Is Not Fact
The problem has been that opinion is often disguised as fact. One opinion seems as good as another. Opinion and gossip are considered news. Newspapers and the media are packed with opinions. Comments on YouTube, news articles, and social media are packed with opinions. Most of our beliefs are wrong. Belief and anecdotal "evidence," which are often found in education, are not evidence of anything. Still, many educators rely on anecdotal evidence, not scientific proof.
In the U. S., Sorting Has Been Anathema.
In top-performing nations, it is acceptable.
Putting high achievers with low achievers in the same math class has been a recipe for underachievement and mediocrity. Kids need strong teacher guidance, a world-class math curriculum, a grouping that matches their achievement level, lots of practice to master fundamentals, and persistence to get things done right. Homogeneous sectioning by achievement level is not equal coverage of math content, but it is coverage of the math fundamentals. And, it does not equalize downward.
Old School Fundamentals Are Missing From Eureka Reform Math
Fundamentals for 3rd grade, for example, should include the cumulative memorization and continual review of single-digit multiplication facts for instant recall, along with performing the standard multiplication algorithm correctly (1st Semester) and the long-division standard algorithm correctly (2nd Semester). These Old School fundamentals are absent from Eureka Math, which is a typical reform math program. Eureka Math does focus on single-digit areas, such as the area of a 5 by 7 rectangle by counting square units inside the rectangle. Still, students won't be able to compute the space of a 173 cm x 60 cm rectangle as 3rd graders did decades ago using the standard multiplication algorithm. Cumulative and continual fluency practice should be a primary goal of arithmetic in the 3rd grade, but, too often, it is not.
Fluency
In Common Core, fluency does not always mean auto recall of number facts or learning the mechanics of standard algorithms. Instead of memorizing single-digit number facts, reform math advocates want students to calculate them. Instead of standard algorithms, reform math zealots want students to learn many different ways to add or multiply. The alternative methods (i.e., reform math) found in Eureka Math clutter the curriculum, confuse students, and waste instructional time. Here is an example of "calculating" from 1st Grade Eureka Math. Instead of learning the standard algorithm and the place value system of adding ones to ones and tens to tens, students are directed to number bonds. Who adds numbers using cumbersome number bonds?
Say What?
There are Seven Modules in 3rd Grade Eureka Math, a reform math Common Core curriculum. The Teacher Edition of Module 1 is over 300 pages long. The Teacher Edition of Module 7 is over 500 pages long. It's math education run amok!
©2018 LT/ThinkAlgebra
