tag:blogger.com,1999:blog-6645583842972204443.post9036440317890564762..comments2017-01-25T01:03:18.620-08:00Comments on The Education Scientist: Common Core Math Standards Making You Crazy? Some Things to ConsiderMichael Connellnoreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6645583842972204443.post-84673759866723167352015-07-11T18:44:52.050-07:002015-07-11T18:44:52.050-07:00Hi, Nadda.
Your argument has major problems - thre...Hi, Nadda.<br />Your argument has major problems - three examples:<br />1) You commit the anecdotal fallacy when you treat your own personal experience as if it's representative of the human species - do you have any evidence that it is? <br />2) You commit the naturalistic fallacy when you use your post hoc description of how you think you learned math into a prescription for how we should therefore teach all children math<br />3) You seem to assume that your interpretation of your own learning experience - how the learning happens, that is - must be true ("rote memorization first..."). But there's plenty of evidence that people's folk psychological notions of how they learn are just plain wrong. <br /><br />To your specific points:<br />>I direct you to Whitehead and Russell's 300 page proof of 1+1=2. A level of intuition and understanding you will never find in an elementary classroom. <br /><br />This may be true but it's irrelevant here. I'm talking about elementary understanding of the addition procedure, you're talking about the deep philosophy of mathematics. No one needs to understand Russell and Whitehead's 300-page proof to understand how to add 1+1. In fact, the proof doesn't help with that one bit - no more than understanding the grammatical theory and entire etymology of every word in the sentence "Please pass the potatoes" makes me better able to get what I want for dinner. <br /><br />>Unfortunately, you don't have any extra time in U.S. schools. The time in a math class is the same as it has always been.<br /><br />This is wrong on two counts. First, in well-documented cases learning time has been compressed by ten or a hundred times using what we know about how people learn. It's very much like software design - sometimes simply moving or tweaking one line of code can speed up a program by a factor of ten or more. On the other hand, a math curriculum that I designed for kindergarten was used by some students for 100-200+ hours during the regular school year. The limitation is teacher time, not learning time. Adaptive technologies are a multiplier of effective learning time. <br /><br />>Procedure first...Intuition later.<br /><br />Not according to the evidence. To take one example, understanding that a number is a quantity (and not some arcane symbol with arbitrary meaning) is a central intuition that is not a stretch even for young children, but many children don't develop this understanding as early as they should and that lack of understanding has been shown to lead to problems later. Furthermore, the evidence suggests that math instruction is most effective when skill/procedure and concept/intuition are taught together and used to develop each other. See this excellent review of the research, for example:<br />http://www.nap.edu/openbook.php?record_id=9822<br /><br />>>> The reason why other countries do better in math is because they spend more time on it.<br /><br />Evidence? How much more time? Where are they getting that time? How do you know this? We have clear evidence that changing the curriculum can take the kids from the bottom of the class and put them at the top - in the same amount of time. (See, for example, Chapter 7 in this book: https://books.google.com/books?id=EkCq8P0_ZGAC&pg=PA143&lpg=PA143&dq=gradients+in+math+learning+griffin&source=bl&ots=TAMQd-3yGY&sig=-CPUIlKxVoNpYOIevGFhQIuV5UA&hl=en&sa=X&ei=NMKhVaXHC8nu-AGFxbHYAQ&ved=0CEUQ6AEwCA#v=onepage&q=gradients%20in%20math%20learning%20griffin&f=false)<br /><br />>Kids need to be taught "grit", not some magical math panacea. <br /><br />Kids do need to be taught grit. That’s true but irrelevant here since it's not an either-or. They also need to be taught math in an effective way. <br /><br />>Your position is asinine.<br /><br />And here we find the fallacious "argument from (personal) incredulity." Which is not an argument but the expression of a personal preference. I'm sorry you don't like it, but that has no bearing on the truth of the matter.Michael Connellhttp://www.blogger.com/profile/11351479269650780356noreply@blogger.comtag:blogger.com,1999:blog-6645583842972204443.post-27636162233695475152015-07-10T02:47:43.964-07:002015-07-10T02:47:43.964-07:00Old article and I doubt this will ever be seen, bu...Old article and I doubt this will ever be seen, but I read your position and I was compelled to respond.<br /><br />Your position is asinine. I direct you to Whitehead and Russell's 300 page proof of 1+1=2. A level of intuition and understanding you will never find in an elementary classroom. Your example of 325-38=287 may not seem so simple... even for a mathematician.<br /><br />Intuition and understanding require experience. Experience requires time. Unfortunately, you don't have any extra time in U.S. schools. The time in a math class is the same as it has always been. You're just introducing a new convoluted algorithm (here the counting up subtraction method) or many algorithms for solving subtraction that replaces the traditional algorithm. Or rather, you're replacing the universal manual with a stack of manuals with pretty pictures and cumbersome math manipulations hoping that magically the child "gains intuition."<br /><br />Procedure first... Intuition later.<br /><br />This concept doesn't change at any level in life. Rote memorization happens first, whether it’s a math model, a foreign language alphabet, a sound, or a pronoun. Intuition comes later. For example, I've returned back to school in my early 30s to earn a second degree, this one in Electrical Engineering. I'm currently learning techniques for solving first and second order ordinary differential equations. I'm not entirely sure I understand it fully, but I can follow the procedures to solve math problems. I expect to acquire intuition slowly after taking more classes that utilize these techniques. This has been the trend for every complex topic I've learned for 30 years.<br /><br />More time... Less crap<br /><br />The problem isn't how math has been historically taught. The problem is a long summer and short school hours. The reason why other countries do better in math is because they spend more time on it. Further, South Korea, for example, requires kids to have basic reading skills “before” attending school, illustrating a level of parental dedication to education you won’t find in a lot of U.S. homes.<br /><br />Math frustration and embarrassment...<br /><br />Kids need to be taught "grit", not some magical math panacea. You see that in the video with the second grader. The lesson isn't "we need to fix math teaching", the lesson is "math is hard, let's learn to tackle hard problems and not give up." The most important lesson you will ever learn is to pick yourself up and try again.Naddahttp://www.blogger.com/profile/04125897927642173536noreply@blogger.comtag:blogger.com,1999:blog-6645583842972204443.post-81101576667707873352014-12-08T19:07:12.526-08:002014-12-08T19:07:12.526-08:00Hi, Jeremy.
Thanks for joining the conversation....Hi, Jeremy. <br /><br />Thanks for joining the conversation. <br /><br />> Needing to do something different implies that what was being done was wrong, which is scary and threatening.<br /><br />I agree this is part of it. Also, change itself can be threatening. There seems to be something particularly challenging about making change in education, though. I think a large part of it is that historically we have not had a scientific framework that could help people understand the relationship between teaching and learning. Without that explanatory framework, people do not have confidence that proposed changes in educational practices would make things better instead of worse. Part of what is puzzling to me about education is what happens next, though. Instead of recognizing or admitting they don't understand and that that creates angst for them, many people seem to get adamant that their point of view is correct and opposing views are obviously wrong. They also seem to become more susceptible to the fallacy of "appeal to an illegitimate authority" in an attempt to back up their claims. The whole system seizes up. It's very counter-productive.Michael Connellhttp://www.blogger.com/profile/11351479269650780356noreply@blogger.comtag:blogger.com,1999:blog-6645583842972204443.post-572010700939008742014-12-03T00:43:28.104-08:002014-12-03T00:43:28.104-08:00 I’m not sure what is most troubling, the mindless... I’m not sure what is most troubling, the mindless allegiance to outdated thinking or the adamant refusal to acknowledge the evidence of concern. <br /> First, I am not defending Common Core, simply the evolution of our mathematics education. Second, the math components would not receive as much criticism if it weren’t packaged with Common Core. It carries with it all the political biases that inhibit rational, productive conversations.<br /> That being said, I’m tempted to just say that our society would rather continue its stagnant performance in education because it’s familiar and predictable. Anytime an adult relies on the phrase, “That’s not how I did it when…”, they concede that they have nothing better to say.<br /> In each PISA performance since 2000, the US’s rankings have dropped. In 2012, for the first time, we fell into the lower 50%. Yes, more than half of the 65 countries outperformed us. Sadly, our performance can be traced back to international testing pre-PISA, and that would show an even farther fall. The leading nations have significantly different designs from each other but offer commonalities. This knowledge is not new, but change is expensive.<br /> Our system is designed to pass as many students as possible across a finish line of “minimum basic standard”. For the majority of their career, students are capable of performing successfully enough on math tests by following recipes to get an answer or recognizing some facts; understanding not required. The proof is that we live and die by multiple choice tests. <br />These new expectations causing the tizzy contradict math routines from our society’s schooling experience. Needing to do something different implies that what was being done was wrong, which is scary and threatening. These demands are not just about solving problems different ways or showing more work that a calculator can do. The push is to build flexibility in thinking and deep investigation into relationships. These strengths transcend math tests or math classrooms and more adequately prepare young learners to be young adult learners which we need to become the next generation of adult thinkers. Adult thinkers do not suddenly appear after surviving all their developmental years in “monkey see, monkey do” teaching environments.<br />Jeremy Copelandhttp://www.blogger.com/profile/12215759026780337046noreply@blogger.comtag:blogger.com,1999:blog-6645583842972204443.post-72989982157765651292014-10-17T17:43:41.347-07:002014-10-17T17:43:41.347-07:00Well said.Well said.Michael Connellhttp://www.blogger.com/profile/11351479269650780356noreply@blogger.comtag:blogger.com,1999:blog-6645583842972204443.post-80794395240976580292014-10-17T17:40:25.730-07:002014-10-17T17:40:25.730-07:00If your readers watched all the way through the vi...If your readers watched all the way through the video, they will have noticed not only task avoidance, but her heartbreaking affect. It makes me both sad and angry because I have seen this in far too many students. No child should reach first grade and hate or avoid math. <br /><br />The push back for Common Core, I think, is a push back against what adults don't understand. Like many, I was taught math by memorizing procedures. I had no conceptual understanding of computation. I followed a pattern by way of imitation. Babies do this when they are acquiring and practicing spoken language. In fact, unless we are mute, we can speak without a conceptual understanding of how it is that we put sounds together to produce words, words to produce sentences, and sentences to paragraphs of thoughts/articulated ideas. (Do many of us sit and contemplate how we produce language?). But articulating an idea, an argument, a stance, requires reasoning. Reasoning is not parroting back memorized replies to specific questions. When I lived in another country and was learning this language, I knew how to conjugate verbs, I had a growing vocabulary, I could produce questions and replies in simple conversation; but I was not yet “thinking” in that language. <br /><br />Thinking mathematically, to me, means problem solving by reasoning. I have a saying in my class, “Solve for the unknown: in math and in life.” In order to do that, you must recognize there IS an unknown, you must recognize what you DO know, and then you must experiment and reason through to a solution. When we give our students multiple experiences in reasoning through their solutions, that is a life skill that transcends math. There is not ONE right method for solving a math problem. When students understand why a solution is correct, and have multiple ways of reaching the solution, they are learning to problem solve. I wish life was simple enough that every problem we encounter had one easy solution. Giving students an algorithm to memorize is like learning how to conjugate verbs, throwing in some vocabulary, but never reaching the fluency to converse in a meaningful way. <br /><br />I will agree that in most of our day to day math experiences, using a calculator, relying on an old learned procedure, will help us; but not acquiring the deep reasoning skills required when wrestling with understanding a math (or science, or social studies, or…) problem leads to a very shallow thinking society which is destined to make poor choices for the good of all. Renehttp://www.blogger.com/profile/04141504361234669724noreply@blogger.com