Gary Rubinstein, a math teacher, plays the role of the heretic and wonders whether students need more than 5th or 6th grade math unless they plan to be math majors.
His answers: no, maybe, no.
He writes:
“‘No’ because as a Math teacher and a Math lover, I do think that the ‘importance’ of Math is overstated. Like Music and Art, Mathematics is one of the most amazing creations (discoveries?) of mankind and, yes, there are aspects of it — even aspects of the horrible curriculum that has evolved in this country over the past 200 years — which truly expand the mind the way any great piece of Music or Art would.
“But ‘No,’ it isn’t really that ‘important’ in the sense that people could get by in life very well with only knowing up to around 5th grade Math. Come on. Am I the kid who doesn’t know it’s taboo to point out the obvious when the Emperor has no clothes?
“Even for future engineers and even Mathematicians, I think that people who truly love math and who demonstrate an aptitude for it, they should be offered higher math as electives in middle and high school and they would be in great shape to pursue it in college if it were needed for their degree or career.
“But knowing Math, like Algebra, for example, isn’t really something anyone ‘needs’ for college the way that people would ‘need’ to be able to read.”
Or do they?
Watch as Gary debates himself on a matter of great importance.
Diane Ravitch's blog 
Okay but I am gonna play devil’a advocate here: what we “need” to know is what we might fall in love with later, or gain appreciation for later. My Chaucer class seemed extraneous in college, but I am thankful to have been kind of forced to take it: it broadened my sense of what I could tackle academically.
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I’m an attorney, and attorneys are not known for their math skills. I’ve also had a bunch of other jobs that do not “require math.” In all of my jobs, anyone whose best-case math skills topped out at a 5th grade level (and they wouldn’t be that advanced, since people forget so much of what they learn in school) would be regarded as manifestly stupid by every colleague that mattered.
This is not factoring in God knows how many things such a person would have been unable to learn beyond grade 5 in non-math subjects.
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Rubenstein touches on something I’ve been thinking about for quite a while (years). It seems to me that one can say that almost all subjects taught in schools are not necessarily “necessary” for most jobs and day in/day out living in the sense that they aren’t “directly” used on a daily basis.
However, to learn about and comprehend all of the various subject areas does allow one to understand the complexity and variety of human experiences out there that we, most likely, would never know existed. And in learning about them expand our own opportunities for more and different life experiences. Each subject in and of itself may not necessarily be “important” to any one individual but is “important” in the sense that it helps broaden our horizon of human experience which I believe is important in a pluralistic, heterogenous society as is the world today.
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It also helps you understand the world, read the newspaper, participate in important discussions, and generally be smarter.
If Bill Gates’s real goal is to destroy public education and produce a docile workforce for low wage jobs, he should jump on this idea ASAP. Make math courses optional beyond 5th grade. Then we’ll have a whole new kind of “achievement gap” to talk about on blogs.
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Yes, I believe the same as I go on teaching 1st century skills (Latin).
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One of the most valuable courses I took in my junior high-high school career was Latin. 30 years later, I use knowledge gained in that course today. I can help my own teenagers with their grammar and composition because we actually studied it–and they don’t today. I can easily analyze and comprehend new vocabulary not only in English but in related languages by drawing on my understanding of a variety of root terms and vocabulary. I appreciate the structure of language, and was inspired by my study of Latin to take several linguistics courses in college. Linguistics led me to study and explore language in history and social interaction–fast forward to a doctorate in cultural anthropology, and a lifetime fascination with words, language, meaning, social organization, history, the semiotics of power, and the power of semiotics.
To this day I regret, and resent, the school board that voted to discontinue Latin instruction upon the retirement of my teacher. “You don’t need Latin to to buy groceries!” they said. No, but you need it for so much more. Everything I described above was based on two years of study. Imagine what I could have done with three or four or six.
Of course, in a beautiful irony, Latin was brought back into that district about ten years ago, and today it is the most popular, and most heavily enrolled, language course in the high school.
God bless you and all other Latin teachers out there! Thank you!
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I thought we had long ago given up on the myth of Latin (the mind as a muscle) as the root of all learning. I am happy that Latin has served you well, but the evidence is pretty clear that it’s pedagogical worth remains with your enjoyment and application, but not much beyond that. Should add that the evidence on the worth of taking a foreign language –future career success—well, again, better to focus on honing one’s English skills instead of all those years in foreign language classes.
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When my son began learning Chinese in college, he came to me and thanked us for encouraging him to take Latin. He said that it helped more than anything; not that it was in any way similar to Chinese or Japanese, but because it teaches you to see language as a system. He says that if he had it to do all over he wishes he could have studied Greek. He is now a computer programmer. Goethe said that a person cannot know their own language if they have not also studied another language. Our neglect of languages is a national scandal.
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Thanks for the kind words about Latin. My own students can be exasperating at this time of the year, so this is a great morale boost!
Coincidentally, I mentioned that Goethe quote about languages earlier today to a recent graduate: “wer fremde Sprache nicht kennt, weiss nichts von seiner eigenen” (He who isn’t familiar with a foreign language knows nothing of his own).
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And the reason your students are exasperated? Could it be what they are learning is meaningless to them; no motivational technique replaces meaning.
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Learning Latin and Classical studies is not meaningless if you are a participant in Western Civilization who reads, writes, or speaks English or a Romance language.
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And the evidence for this claim is…..(or could this be a personal belief that all participants in Western Civilization… should learn latin and the classics). I guess the good news for non participants in Western Civilization is that they do not have to learn Latin or study the classics.
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Yes, I believe the same as I go on teaching 1st century skills (Latin).
Alan, that’s awesome.
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A theory popular with many economists is that acquiring educational certificates and diplomas is mostly a matter of “signaling” one’s intelligence and diligence and that the actual content learned is of minor importance.
Thus in 19th century Britain people studied Classical Greek at say Cambridge and then went to work at the British Admiralty. Knowing how to conjugate a classical Greek verb didn’t really come up in their job very often but their having learned how to do so demonstrated their intelligence and diligence which traits were actully useful in their jobs.
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That is true. One bit of evidence for that is that there is a large premium for students that actually finish a degree over students that get very close to finishing the degree. If wages were all about the knowledge gained, you would not expect to see this premium for finishing just a couple of classes.
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That opinion actually jives with a report issued last year “Community colleges’ academic expectations are “shockingly low,” but students still struggle to meet them, in part because high-school graduation standards are too lax in English and too rigid in mathematics according to a study released on Tuesday by the National Center on Education and the Economy.
Students entering community colleges have poor reading and writing skills and a shaky grasp of advanced math concepts that most of them will never need, the study found.”
Here is link to the full Chronicle of Higher Ed article:
http://chronicle.com/article/High-Schools-Set-Up/139105/
and to the study itself:
http://www.ncee.org/college-and-work-ready/
As a side note, I’ve always wondered if it wouldn’t be better for society as a whole if, instead of focusing on universal algebra skills in HS, there was a focus on statistics as the math most useful to the widest populations. Imagine if your average citizen understood the difference between causation and correlation. Imagine the implication of value-added studies if politicians actually understood statistics.
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My state does require four ELA units and three math units for high school graduation out of a total of 21 units. Would you suggest a change to five ELA units and 2 math units?
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To return to Dewey, when thinking about what knowledge is of most worth, you begin with the concept of intellectual tool box —-from that standpoint, what tools will I need to pursue vocational, civic, and existential goals — to name only a few goals. After that determination, then you would need to determine what level of understanding do I need to effectively use these tools. The catch is effectively using these tools. What students are exposed to in schools are academic renderings of disciplines and the work products of these disciplines —e.g. the term paper or do all the even problems on this page. Unless you have a interest or ability in a certain discipline, school subjects are not intellectual tools, but large catalogs of names, dates, procedures, and contrived school problems. For these disciplines to come alive in the classroom they must apply to real world problems and of course, all real world problems, are interdisciplinary in nature. How many times in a subject centered classroom have teachers, I am in this category, said to students that what we are teaching will make sense at some point in their life (or for college, or to past a test, or take the next meaningless subject)—that is a bad response and the reason our classrooms across the country a vast wastelands of boredom. I do not blame teachers or students or administrators for this state of affairs, we all have become objectives of a machinery of schooling (institutional schooling) whose goal is to systematically (or bureaucratically) strip us of who we are in order to measure some valued trait that correlates with the documentation of an institutional goal. Many years ago, in my introduction to educational psychology course, my professor made a profound comment about state of schooling (education) in America: “who is god’s name invented the high school.”
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Preach!
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Said, as a French teacher, who also teaches English: French is so much more than “where will you speak French in the world?”
It also irks me that people are still so ignorant that they even ask that question: um…Canada, most of North Africa, Madagascar….
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Wish I was preaching to the choir.
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this is a return of the “technology bubble” and the pressure for more STEM grads…. change your major to …. etc which is marketing and hype. We had a technology “bubble” in the 90s which will be much bigger this go around when it crashes. On a personal note, my brother went to Wentworth Tech and got lower grades in math than he did in English when he earned his associate’s degree . When he got a job at IBM he learning computers from the start in the 70s he said to me :” Now I know what that math is that they were trying to teach me at Wentworth”…. It reminds me of yesterday saying the comments that we would soon have a video and an algorithm to measure the baseball skills for the Red Sox, the Marlins , etc. some comments that I enjoyed very much.
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Reblogged this on David R. Taylor-Thoughts on Texas Education.
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Good for him. Daring! 🙂
I liked higher-level math, although I’m not a “natural” I had to work really slowly and hard at it, but honestly a big part of it was how much fawning and worshipful attention you get as a student if you succeed at it. I thought it was a little overblown even at the time, that proficiency in math was valued over proficiency in other things and that was the 1980s and 1990s. I can’t imagine what it’s like for students now, with the math-panic and STEM promotion and all.
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It seems to me that this piece is an argument to expand student choice int much earlier grades than is now the norm. It will be interesting to see just how folks here react to that expansion.
I would add many other majors to the list of majors that require more than fifth grade mathematics. All of the natural sciences for sure, engineering and computer science as well, psychology is becoming an increasingly empirical field so we need to add it, as well as large sections of most other social sciences. Philosophy includes formal logic, so depending on the program of study knowing more than fifth grade math might be important. Oh, and absolutely essential in economics as well.
I am sure I left many out. Feel free to add to my list.
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I agree. I did have an econ major in my beginning abstract algebra class. And a meterology major. And a psych major.
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All of which is a good argument for having a much more varied mathematics curriculum, with many more tracks, TE, than we have now.
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How many students would have to be in a tract for the school to make it available?
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I believe that increasingly that number could be 1. We now have distance learning alternatives
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True, but I think you will agree that those are often second best. If density allows, having local peers in a class greatly helps learning. Unfortunately for many of my students, density does not allow most schools to offer more than basic classes, so some form of distance education is essential for students to have access to a rich curriculum.
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I agree. Having local peers is definitely something we should strive for. If we can’t have those, we should try to create national peers accessed at a distance. But we should have gotten past, at this point, saying, we can’t offer Japanese or Differential Equations because too few kids will take the class. Give the alternative of going the distance learning route or offering nothing, I would favor the former.
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I agree with you.
The next question though is who gets to decide which student can take which course, will the course count towards graduation and who pays for it.
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I’ve long argued on this blog that every kid should have an IEP and a team that includes a couple of teachers, a guidance person, and the parents or guardians, that meets regularly to guide the student through a very varied set of offerings that can be tailored to the child and his or her proclivities, interests, trajectory, etc. I believe that most of us agree with regard to taxation and redistribution to support making school through GR 12 freely available to all. I think that that should be PreK-16, not just K-12.
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Also, when hasn’t math been pushed? We were told “load up on math and science if you’re going to college” over and over again and that was 25 years ago. I don’t really have any objection to it, but it was everywhere.
I think my daughter deliberately focused on foreign languages because she was proficient at math and she was constantly pushed toward a math focus. She had to actively push back, and I think that’s how she did it, because a foreign language is in the “universally admired” section of skills too 🙂
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The math we teach needs to be deeper and richer, but knowing math is part of being an educated person. No, we don’t factor all that much, but try understanding growth, interest and population without at least Algebra 2. And so on.
We don’t use what we should have learned in history and government either. It shows.
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Students ask “when will I ever use this _______________” (fill in favorite math topic). I tell them that is entirely up to them. Most math we teach in K-12 is concrete and computational, limited to a small slice of the vast body of knowledge lumped under mathematics. I meet parents who show their kids “tricks” they learned to compute sums or solve division problems and tout that as better math. I hear the phrase “I hate math” from not only frustrated students, but parents and other teachers who wear it as a badge of honor.
Math is the language of science, and science describes our world. When people do not understand their world, they fill in the blanks with beliefs. Math and science do not care what people believe, it just is.
Part of the problem is that to truly understand math, a great deal of abstract thought is required. Students are developmentally ready for abstraction early in teen years. We introduce variables and axioms earlier, but that is usually done concretely (variables are placeholders for numbers) or procedurally. I often find a good measure in the HS math curriculum of students ready for more abstraction is the derivation of the quadratic formula. Yes, most people rarely use the formula, but the important lesson is not the formula, but the logic used to derive it. Some “see” the abstraction and eyes light up. Math is unusual in that it can describe our world, or even other universes, before we observe it. For example, Einstein’s equations described the relative slowing of time well before we actually observed it.
I had an excellent and greatly missed math prof in college. His lament was that too many students had such a difficult time with proofs (myself included), that we need to stress logic over computation in K12. Perhaps he is right. Maybe what we need to do is not just say you can’t divide by zero, but show why, as an introduction to limits and infinity. Maybe not just introduce functions, but show the evolution and conflict getting to that point.
I’ve got much math to learn on my own bucket list. I wish I had the money and time to do it.
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MV,
There is a vibrant community of mathematicians on the internet that you can learn from. The website Mathematics Stack Exchange is one that my middle son has been involved with. Here is a link: http://math.stackexchange.com/
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Ever notice what children choose for themselves to eat when they are allowed to do so at a buffet restaurant? Lots of starches and dessert, usually.
Children and teens still need adults to frame choice in a manner that will pay off in the long run– and in the long run, young adults need to have the experience of a variety of school subjects, including those that are less palatable for a student’s natural inclinations or gifts.
Middle-school-age is too young to allow math to become an elective. Perhaps tenth grade–however, even tenth graders might be tempted to forego a challenging course for the sake of immediate relief that they will regret within a couple of years.
When I was in ninth grade, I tried to drop out of high school. Why? Just because. No other reason. I was not allowed to because of my age. I know now that I would have regretted being able to carry out that wish.
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I get an RSS feed to Gary’s blog, so I had read this a while ago. I’d like to weigh in with a few, personal anecdotes. I think he is pointing to a weakness in our system that will only be made worse with the implementation of CCSS. The 5th grade math skills he refers to are the skills you need to do Algebra proficiently. By this I mean things like adding, subtracting, multiplying & dividing fractions and percentages. I think Gary is saying that if most adults truly understood math at that level, they would do fine. However, in the name of higher standards, we push things down the grade levels. I once asked a math teacher in my district why every student had to take Algebra. His response, “That’s what we ask the State.”
Math is poorly taught in many places in the US. From my observation, the people who understand it often aren’t good at explaining it to those who don’t. It is difficult to get and keep good math teachers; many districts have to pay bonuses to do so.
Recently, I got a ride home from an auto repair shop by a kid who had attended my district’s high school. It had a 4-year automotive program and he had attended it as an out-of-district transfer ( I related this story to TE before; he often writes about school choice. A consortium of PUBLIC school districts in Pima Co. offer a joint technical program-JTPA. I have no problem with choice among PUBLIC schools.) The mechanic told me the only Math he took was “Math for Automotive Repair”. I responded that future students in that program probably wouldn’t have that choice anymore.
So, I’d say I agree with Gary. We push kids in the name of rigor and then condemn our teachers when not all students meet those standards at the same time.
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My middle son took some classes from the local university while in high school. Are you in favor of that kind of choice or does it depend on the local university being a public university?
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I, too, feel that math is not the be all and end all of academic success or intelligence. It has always seemed to me that math is the class that most often causes students to be sorted and labeled in K-12 ed. Other subjects get short-changed. I believe that there is a certain level of math that is essential for being a productive and successful adult, and that that should be the goal for every student. I would say every hs 11th grader should be very proficient through algebra 1, which would allow them to learn basic statistics (to understand advertising and political campaign statements, to name a few things) and basic financial math (check books, credit card rates and payments, mortgages, student loans, etc.) which should be offered in 12th grade. Would I LOVE it if students went higher? Definitely. Should all students have access to a calculus class? Of course! Do all students need calculus? No.
I think US parents and those in higher ed need to worry more about if kids really understand the basics, in all subject areas, and quit pushing harder and higher and faster all the time. I would think non-STEM college professors would be THRILLED if freshman came to them with a very solid conceptual understanding of and facility in using math through algebra 1 and basic statistics. I would think STEM professors would be thrilled if freshman came with a very solid conceptual understanding of and facility in using math through algebra 2…they could teach calculus the way they need it taught and at a real college pace and level.
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Driving most of this reform is the lack of STEM graduates. Years ago when there was a teacher shortage top students were given a free ride to be education majors. They signed a contract to teach in the state for X amount of years after graduation. If there is truly a STEM shortage then offer top STEM high school graduates a full ride. They can sign contracts to work in US STEM jobs for X amount of years. Or they can agree to teach in K-12 or colleges with STEM areas of focus.
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I read a survey of college students recently. It noted that college students in the last few decades were choosing to take study Finance over Engineering because that’s where the jobs/money are. If you haven’t noticed, we’ve outsourced most of the manufacturing in this country. We educate plenty of STEM students here. As Diane has written in the past, we lead the World in Patents. What we don’t have are STEM-educated employees who are willing to work for Chinese wages.
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Fractions, percentages, loan rates and interest are important stuff to know backwards and forwards, which is life skills math. If students don’t get this in high school, many have to take remedial college courses.
So, what type of math courses are being taken for four years of high school, for a quarter or a third of the student population which hasn’t mastered this?
Is more complex math being foisted upon them when they need more basic math?
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“Is more complex math being foisted upon them when they need more basic math?”
This is my point and, I believe, Gary’s too.
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Most of those life skills problems are integrated in typical math courses. For example, compounding interest with exponents. But high school kids aren’t real concerned about loans, present value formulas, or the area of stop signs. That comes with maturity and job demands. If a car dealer quotes a monthly payment, then being able to question their figures is important. I’m not sure reading “Othello” directly helped me later in life. But it made me think in a way I otherwise would have missed.
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Yes, definitely. I was teaching the derivative shortcut rule to my precalculus class today and several students reached for their calculators to multiply 14×4. Yes, I’m concerned that they can’t multiply, but WHY are derivatives part of my PREcalc curriculum? And in my district Honors Precalc is primarily a sophomore class (but at least one-fourth of the class are freshman.). We are pushing these kids way too far, too fast. And we wonder why they aren’t retaining anything.
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Students in the fast track in my local district also do precalculus in the sophomore year. The very strongest end up taking graduate courses by the time they graduate from high school.
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TE,
You have frequently posted that your local district is so small they do not offer AP calc, yes?
But they do offer pre calc to sophomores and graduate courses to seniors?
Sounds as though the lack of AP is not about the size of the school, but rather a different type of advancement program ( presumably with the local university ) already in place.
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My district is one of the largest in the state with 10,000 or so students and two high schools with over 1,200 students each. The high schools offer AB and BC calculus. The median size high school in my state, however, is just under 250 students. Schools that small can offer little more than basic classes.
As I have posted before, I do think that being in a university town limits the need of the local high schools to offer advanced classes. After calculus in the junior year there are no courses in the high school that a senior could take that involve using calculus (the physics class, for example, is not calculus based). The strongest students can enroll in classes at the university if they can afford the tuition and if they do not need the units to graduate from high school as the classes do not count toward high school graduation.
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Even if students don’t need to factor as adults, they do need to develop abstract thinking abilities and to practice logic. I suppose that some of this could be done with games, but mathematics represents human wisdom collected over the centuries, and some of the greatest intellectual challenges that we have faced and solved. There isn’t some other substitute that we have that is as challenging or useful.
Literacy in math doesn’t really happen until students master algebra. I think fifth or sixth grade is too early for anybody to decide to deprive a student of the opportunity to reach that level.
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I love that Gary brought this up, especially as a math teacher. To me, we absolutely should reconsider how and why we teach all types of subject matter. I have never understood the arbitrary teaching of many math classes (ie. Trig or Calculus) totally devoid of context, and pushed on kids without question. I was into languages and foreign cultures as a high school student. With all the talk about “global competitiveness”, you’d think that foreign language would be a given, but alas it’s not. So why favor math over foreign language? What if foreign language was pushed as hard as math?? And why isn’t it? Hmm…and imagine if being bi/multilingual were a tested subject. Suddenly our immigrant populations, ie Latino communities, would soar to the top. We’d have to talk about the multi-lingual “gap”. White, wealthy kids might not be #1, gasp!!
What if kids were taught math only as it’s needed for science or engineering or statistics courses? You need calculus for Physics, then you learn that math as needed. Learn statistics in a social studies or psychology course as you analyze real data from actual research.
I agree with Gary. Make math an elective-I’d say starting in high school-and incorporate authentic math across the curriculum.
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I agree with your world language comment. But the problem is, we are trying to condense 5,000 or so years of math knowledge into 12 years, and really 4 years considering the development of children.
When people do not understand something, they need to resolve that dissonance. Either they support their position through distain (“I hate math”) and rejection, or they expand their knowledge. So we have people rejecting science filling in their non-understanding with belief or irrational reasoning. The Earth is 6,000 years old, for example.
What you suggest is a just-in-time approach to math. In the same way most people cannot become fluent in French one week before a vacation, math builds on skills learned slowly and with effort.
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What we decide to focus on in school is arbitrary and based on all kinds of cultural, socio-economic, and historical assumptions. Pouring 5,000 years of math is nothing more than Freire’s banking method, something progressive educators have tried to get away from for a hundred years. Building math into interdisciplinary curriculum designed with real-world projects still teaches “math”, but in authentic and useful ways. Part of why so many kids hate math is that it’s taught completely disconnected from real life and in rote/inauthentic ways, ie “learn this formula and plug it in.” I’d argue that this disconnect is true for math more than any other subject.
Let’s rethink how we do all the subjects (why have separate subjects period?), but especially math. I have never in my life, ever come close to needing trig or calculus (classes I technically excelled in at the time), but man of man do I wish I’d taken more Spanish classes. I would use that every day. EVERY day. Higher math classes should be electives.
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In my state, trigonometry and calculus are electives in high school. Calculus is an elective at the university where I teach as well.
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I just really like this idea of questioning something so ingrained in us–you have to know Algebra!–or what have you. I like thinking outside the box, asking “why”, and imagining different possibilities. The hyper-focus on math at the expense of many other subjects in schools is weird. I’m glad Gary is calling out our butt-naked math-worshiping emperor!
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All I know is, anything we teach in math should make sense to the student. It should never be seen as magic or a game to figure out what the teacher wants us to say. Math is a wonderfully human endeavor to make sense out of the world around us and to communicate that to others. Students in a math class should always be led to that point where something doesn’t make sense, or that there isn’t a way to deal with a certain situation (yet), or that there has got to be an easier way to do something. 1st grade or high school math can be taught with this in mind….sort of a retracing of the development of mathematics. It takes a little longer in the early years, but would pay off in later years in terms of confidence in math as a way to solve problems, answer questions and communicate.
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I am dismayed by your judgement of math. Because you see no need for it or criticize how it is taught, we should abandon the effort?
My 5,000 year comment is partly humor, partly serious. What you see as math in K-12 is more mathlite. Math is a discipline that takes years to just get to the point where students can even begin to understand the application and theory. The other problem, frankly, is that it is pure thought, very structured, and abstract. There are no exploding experiments, no dramatic novel climaxes, no war films, no cultural food days. Anybody that says math is easy or fun is lying or not working hard enough. Math is hard work even for PhDs. Math is trying to describe the world as axiomatic, sparse, rigid, concise, and provable. Try making that entertaining.
Yes, we can make math more of an applied approach. Even Euclidean geometry, though, is a simplified view of the real world. I did not appreciate math till I began studying the more abstract forms of algebra, analysis, and logic. True math, as my excellent professors demonstrated, was not interest rates or fractions. Rather, it was disciplined thought based on logic and proofs, conjectures and reason. There is SO much more to learn than the small sliver taught in K-12. I try to bring a glimpse of that into the classroom and students love it.
We seem to be arguing a kind of reverse enlightment. Why would we want to limit knowledge and reason? We need to encourage kids to take as many classes as they can. Math and science describe our world. They are important to give an understanding based on reason and thought. When people do not understand something, they fill in the gaps with belief and myth with real consequences.
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I would say that what you see in K-14 is computation and symbol manipulation, not what mathematicians see as actual mathematics. As a result, many students come to college thinking they are good at mathematics only to discover they are not good at actual mathematics, they are just good at imitating Wolfram Alpha. Even worse, some who are actually good at mathematics but do not want to be sophisticated calculators leave mathematics thinking that calculation is what it is all about. That is why we got our middle son out of K-12 math as soon as we could and sent him to be taught mathematics at the local university.
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In Finland they push foreign languages as hard as math.
And by the way, students enjoy Latin, especially boys, because you don’t have to worry about pronunciation. And the culture that comes with it, a lot of which has to do with war and fighting, is attractive to boys.
Latin was by far my favorite course in high school. I opens the door to understanding — by showing you the models — of all of European and English poetry, prose, and speeches for over two thousand years — so that was why they wrote like that, you think! Not only the vocabulary — the skeleton key for all the romance language — but also the periodic sentence and paragraph structure, in Slavic and Germanic as well as Romance. The subjunctives and subordinate clauses. I can’t see how anyone can consider it “not relevant”.
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There are many things — diagramming sentences, literary analysis, foreign languages — that most adults don’t “need” to know. But we teach them in order to introduce concepts, fire the imagination, and teach thinking skills. Plus, there are just certain things educated people should learn. Did I like Moby Dick? No. Did the analysis of it make me a better engineer? No. But it was still a worthwhile exercise, and I understand allusions to it when they are made. If nothing else, I can at least commiserate with others who were tortured with that horrible book in high school English lit — that’s worth at least something.
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I hated Moby Dick in tenth grade. I loved it when I reread it in my 20’s. My earlier encounter at least made me aware of Moby Dick, and the seed planted then eventually germinated.
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Alan, when I read “Silas Marner” in high school, I was bored stiff. When I read it 30 years later, it made me cry.
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Diane, I had the same reaction. A true example of most of us living lives of quiet desperation.
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my reaction as well! I bet that this is a general phenomenon!
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Just because one might not “need” higher level math in their career doesn’t mean that studying mathematics won’t help develop neuronal growth and brain development. Most neurological development occurs during the school age years. Similar to being active in weight bearing activities allows you to build the healty skeleton you will need in your older years. Exercising the brain will help develop the cognitive skills that will carry you through your senior years.
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It has been argued that a knowledge of statistics might be even more important for citizenship than proficiency in algebra. People ought also to be able to calculate interest and understand taxation, including marginal tax rates and understand some geometry and surveying.
My own feeling is that a decent education ought to prepare people for going on in the sciences without feeling that they had been cheated of learning the fundamentals in their early educational career.
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Another view perhaps? I believe that whatever subject is taught, it is the teacher who educates through that subject. The teacher is, should be, the educator. Education in its best sense, at least historically is the search for ultimate values, good, truth, beauty, who am I as a human being, what is most important in my life, can I evaluate, think critically, have empathy for my fellow human beings, the world around me etc etc etc.
I taught music and always wished my choirs to become totally involved in great art For a few minutes at least they were totally involved in something bigger than themselves, some timeless bit of beauty and intellect. Well after 3 decades since teaching them, I still hear from some of them who felt that music was the most important thing they had in school. That could be said about any subject IF the teacher is an educator. I believe there are at least 3 distinctive categories for those working in classrooms: the instructors, the teachers and the educators. There may be few educators but if one has had one their whole life has changed for the better. The “meaning of life” is more than just words. It has real meaning.
Opening one’s mind to beauty to love of life to learning etc etc is what it is all about I believe. The coach, the shop teacher, those on the low end of the spectrum of many people’s scale of importance may very well be the person who “educates” in its best sense. Academics are important but they are not synonymous with education in my belief system.
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CC standards (and “real world” examples) like these for 12 year olds will not fix our innumeracy problem:
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
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Or this.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
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Or this,
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
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The primary applications of practical “real world” math are largely ignored in everyday math instruction.
Quantitative description, comparison,analysis and most importantly as a predictor.
It seems as if most math teachers have insufficient knowledge in the sciences, engineering, economics, or statistics in order to make their subject come alive. Instead it is viewed as a meaningless and utterly pointless activity by the vast majority of students. Just tricks with numbers. As Alan Jones pointed out, meaningful and substantial instruction is the only way to sell our product.
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…”Well after 3 decades since teaching them, I still hear from some of them who felt that music was the most important thing they had in school. That could be said about any subject IF the teacher is an educator. I believe there are at least 3 distinctive categories for those working in classrooms: the instructors, the teachers and the educators. There may be few educators but if one has had one their whole life has changed for the better. The “meaning of life” is more than just words. It has real meaning…”
Thank you very much for Dr. Wilder’s wisdom. Your simple paragraph spells out the magic of being as an educator of all fields or subjects. In short, it is very important to have the real educator in K-12 curriculum, so that children will appreciate their foundation of learning in order to continue with their life long learning in post secondary at any given age, regardless of working condition for their survival needs.
The joy of learning only happens from being taught by the joy of teaching/educating. Teaching and learning should not be fueled by monetary gain, but by the beauty in understanding its purpose/goal/application of science, emotion, physic, psychology, humanity…Back2basic
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Here’s the elephant in the room:
MOST American adults are effectively innumerate. MOST hate mathematics. And ALMOST ALL have been through a remarkably similar sequence of K-12 mathematics instruction that is barely tweaked by the CCSS.
According a study by the National Advisory Board for Mathematics, 78 percent of adult Americans cannot explain how to compute the interest on a loan, 71 percent cannot calculate the miles per gallon for a cross-country trip, and 59 percent cannot calculate a 10 percent tip, even though all one has to do is to move the decimal point over one place!
Back before CCSS, I did a study of mathematics standards around the country. The state standards were remarkably similar. Almost all were riffs on the NCTM standards. And the CCSS in math is another tweak of those. It represents no major change in our conceptualization of learning progressions or approaches in mathematics instruction.
The moment one starts talking about changing how we approach mathematics, people start pulling out these hackneyed defenses of what we’ve been doing forever:
1. If you don’t know mathematics, you won’t be able to understand [fill in the blank]. Yes, this is true for many, many things that you can put into that blank. AND, because MOST American adults, almost all of whom have been through our standard sequence of instruction, don’t know any math beyond about the 5th-grade level, they are not able to understand [fill in the blank].
So, it’s not like doing what we have been doing is achieving THAT end. Or that what we are going to be doing under CCSS will make any difference in the outcomes described above.
2. Math is good mental training. Well, yes, I suppose one can argue that. And one can argue that, as well, for learning computer programming or learning Latin or Greek or learning the generative grammar of English or most anything else. But do we really think that we have had successful mental training if almost every person who has been through that training ABHORS the subject and HAS GRATEFULLY PUT EVERYTHING, JUST ABOUT, THAT HE OR SHE LEARNED IN THE SUBJECT OUT OF HIS OR HER MIND?
Inquiring minds want to know.
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Click to access LockhartsLament.pdf
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I would LOVE to see a more mathematically capable citizenry in this country. I would love it if trade book publishers didn’t follow a rule of thumb that ANY USE OF EQUATIONS in a popular book WILL KILL SALES. I would love it if millions of Americans found math fun to do and perused recreational mathematics in their leisure time.
But we are not going to get from where we are now to anything like that by doing what we have always been doing.
I can imagine whole mathematics sequences for middle school and high school built around computer science. or around graphic design. or around woodshop or sailing.
I can imagine elementary school mathematics sequences that are all about building the requisite mental architecture for doing mathematics, later on, via fluid intelligence activities, mostly pattern recognition activities, that don’t seem like mathematics at all but that seem like art and play.
I can imagine making this fun for kids for the first few years and then, when they have developed the requisite mental architecture for mathematics, introducing abstract, formal mathematics instruction. See Richard Nisbett’s important book Intelligence and How to Get It for more information about such activities.
Doing what we have always done obviously does not and will not work FOR MOST STUDENTS. It never has. It never will.
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Read the Lockhart piece, “A Mathematician’s Lament,” that I linked to, above. It’s profound. It is absolutely the best thing I have ever read on this subject.
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I learned more useful math in my shop classes, drafting classes, through my outdoor hobbies, and as a die-hard sports fan than all of my formal math courses combined.
As long as math is taught as an end, not a means, it will forever be the bane of most student’s school experience. Math cannot be just tricks with numbers. The best math students should never be identified at an early age just because they can follow brainless orders of operation and remember simple algorithms.
And if math items continue to look like this one, in the name of higher order thinking, then we are in deeper trouble with CCSS than most can imagine.
HERE’S A 9TH GRADE MATH PROBLEM FROM THE ASPIRE WEBSITE:
A map of Nelson county is laid out in the standard (X, Y) coordinate plane below, where the center of the county is at (0,0). A cell phone tower is at (5,4), and Esteban’s house is at (10,–2). Each coordinate unit represents 1 mile. The tower’s signal range is 10 miles in all directions.
15) The strength of the tower’s signal to Esteban’s house depends on the straight-line distance between his house and the tower. What is the straight-line distance, in miles, between Esteban’s house and the tower?
This typifies the convoluted approach to mathematics seen during the CCSS era. the Duncan revolution if you will.
They start with the math concept (coordinate geometry) and then pretend to search for a real world application to match.
What they find is an out of context example that no one in the real world would ever use.
For locations on a map we actually have an existing coordinate system: LATITUDE AND LONGITUDE.
For finding the straight line distance in miles between two locations we have MAP SCALES AND RULERS.
Now the icing on the CCSS cake of distortion and deception:
Reminder, the test item reads.
“What is the straight-line distance, in miles, between Esteban’s house and the tower?
the correct answer to is . . .
e) The square root of 61
no joke.
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One of my 12 year old grandson’s math problems: 22,8,3,12,8. Write an equation using each of the above numbers once whose combination equals 1.
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I am in the process of finishing writing a book–one I’ve been working on for about three years now–that deals with nonhuman animal consciousness, the deep history of human dietary habits, and the environmental costs of meat consumption. The section of that book deals with the environmental cost of eating meat has a lot of original calculation in it. I crunched a lot of numbers for that section and did a lot of original research. And I know that when I submit the book to agents and publishers, they are going to freak out about that part of the book. The numbers are CENTRAL to the argument of that part of the book. They are the fulcrum and the lever. If I were to leave out the numbers, that part of the book would be just another empty screed.
But those agents and publishers will have a point. And that’s really, really sad.
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They are going to freak out because every trade book publisher knows that the way to kill a book for a general audience is to put any actual math in it.
Now, what does that say about the LOVE AND KNOWLEDGE of mathematics that has been gained by educated Americans–the ones who buy and read books–who have been through our standard sequence?
Hmm.
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It’s the height of idiocy to do continue doing what has never worked and to think that somehow, magically, things are going to be different if you just DEMAND that they be.
Be more gritful!!!!
This will be on the test!!!
Yeah, that’s going to work.
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Yes, yes, You must be more mathful. If you cant do even the most basic math with or without a calculator, the solution must be to make it harder, more convoluted, more abstract, and to push difficult concepts down into earlier grades. And when we test ’em, lets focus on multi-step word problems because those underdeveloped brains need better challenges.
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If you insist on teaching abstract symbol manipulation to students before they have the neurological capabilities to reason in those particular ways, then you might as well be having them do any other tedious, pointless activity like copying random numbers from one spreadsheet into another spreadsheet, day after day, year after year. No wonder kids hate it.
As TE and MathVale have eloquently said, above, math is not computation. Math is a huge set of ways of thinking. Very abstract ways.
You can work with younger kids to build the neurological foundations for doing that kind of thinking and then, later on, when they are mature enough, introduce them to it.
Or you can do what we have always done.
Which doesn’t work for ALMOST ALL WHO EXPERIENCE IT.
Think of all the opportunity cost!
Roughly 2,350 hours of instructional and homework time spent doing something that adults don’t remember and about which they know one thing, that they LOATHED IT.
Yeah, more of that. That’s how to get kids really excited about learning.
And while we’re on this subject of the absolute idiocy of much of our instructional program, let’s talk about foreign languages.
We know that humans have an internal mechanism for learning a language automatically based upon immersion in an environment in which that language is used. We also know that this mechanism, having done its duty, pretty much shuts down around the age of 14. That’s what linguistic science teaches us.
And so, in the United States, when we teach languages in school, we typically BEGIN the instruction AROUND THE AGE OF 14, and we don’t use immersion techniques.
Completely backward. Ignorant. Prescientific.
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This is raw and dangerous ignorance. Good math preparation beyond the 6th grade is just about the only thing that correlates with success in college STEM courses (and that includes a wide variety that are needed for health carriers including nursing). Robert Tai at UVa has done a number of major studies on this, and after looking at the dismal results in Gen Chem for the math unprepared, we increased the math co-reqs substantially.
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What does your “this” refer to, Mr. Rabett?
to the fact that 59 percent of American adults who have been through our standard mathematics sequence cannot calculate a 10 percent tip? That 71 percent cannot calculate the miles per gallon used on a trip?
Your point about STEM education simply underscores the stupidity of doing more of the same of what we have always been doing, which clearly does NOT produce graduates prepared for advanced work involving mathematics.
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Clearly, an invariant program like the CCSS, which does not provide for an advanced track for those who will pursue STEM majors, is a mistake
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I read “The Mathematician’s Lament” and it was wonderful. Thank you for introducing it to me, Bob Shepard.
And thank you for stating what I try and tell anyone who will listen to me, that what we have been doing in math education has NOT been working for the vast majority of people, EVER. Most people do not like to be told to do something that makes absolutely no sense to them whatsoever. They play the game for awhile, but eventually tune it out. Most adults do not like anything to do with math…and yet get upset when math is taught differently than the way they “learned” it.
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Your last point demonstrates the problem with innovation in the traditional zoned school structure. There are likely to be enough advocates of better, non-traditional math instruction in a district to warrant a school devoted to this approach, but not enough to convince the district to change its approach to mathematics education for all schools in the district. The key to change will be to allow those interested in a better way to do mathematics education the freedom to create a program without having to convince a majority in the district that it is a good idea before the program can start.
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Exactly, PUBLIC charter schools the way they were intended to be….not as profit centers….
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It sounds like you are in favor of more regulation of charter schools than is being done in some states. That is certainly a good idea.
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“but not enough to convince the district to change its approach to mathematics education for all schools in the district”
TE is pointing, here, to a VERY SERIOUS PROBLEM with our current approach, one that is not addressed by the CCSS and the new national testing regimen
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But it might be addressed by allowing groups of parents from across a district to form a school that takes this approach independently of the politics involved with a local school board. If only there were a name for this kind of school…….
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lol
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The problem being that not enough math educators realize and accept that “the way it has always been taught” hasn’t worked, ever?
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I am saying that the only charter schools that should be supported are those that come from within a school district, with no outside managing company involved, no outside money that is not donated, no profit motive involved….unless we are talking the profit the students get from attending…..that was what (name escaping me right now) intended when he championed the idea of charters back in the 80’s…
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Most charter schools are stand alone schools, not part of any chain. Requiring charter schools to be non-profit certainly seems like a reasonable idea, and I believe New York and Minnesota do have that requirement. There may be other states as well.
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Ah, not “non-profit”, I said “no profit”…HUGE difference these days…..
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TCliff,
How do you operationalize your distinction between non-profit and no profit?
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Math grades degraded my average. I would have been valedictorian had it not been for the fact that I just could not master geometry, trig or calculous, although I and no problem with logic and algebra where I always received 100. Yes, studying math and music has an impact on the brain’s neurology, but this is an important question to ponder. I used math all my life, and have been able to successfully run my home, and my life planning for a financial future, computing taxes, taking loans and using credit, measuring walls and land to accomplish simple geometric tasks. I never needed to understand trig or calculous.
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I question your claim that math helps the brain. We were saying this long before we had the capacity to observe the brain as closely as we can now. But, I will gladly change my view on this with evidence.
The thought occurs to me that making students take long, drawn-out course offerings in math and science than they are forced to do so make little sense. Students who are highly motivated and have a higher than average aptitude will either attempt to master the material or do the minimum to get a good grade. Thus they look successful but couldn’t tell you anything they learned a few months ago.
Students unable or unwilling to play this game get frustrated. In the past, many would grimly hunker down and deal with it. Today, all too many just drop out and give up.
I think the idea of a deep foray into subject matter is a bit heavy for student with low prior knowledge and/or low motivation. Could we instead have more classes in math and science that are a bit more introductory in nature? This course would have more real world application, more problem solving, but a bit less theory. If a student would like to pursue further studies, they can take an advance math or science course of their choosing.
This would ensure that all students have a basic foundational knowledge, but not a knowledge set filled with gaps and misunderstanding of the subject matter. What’s the point of all the work for students forced to take these courses if this is the outcome?
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