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If you've not heard about Conrad Wolfram, begin with his quick overview on Wikipedia. Then take a few moments to watch the following TED presentation.
- Teaching Kids REAL Math with Computers (17 min)
- Take a few minutes to peruse through his web site titled http://computerbasedmath.org/
- Jot down several scenarios or statements that stirred you up a little, and describe your feelings.
- How might one creatively address the impact that Mr Wolframs' presentation could have on current math curricula, instruction, and student learning?
Posing the right question... How much can I agree with this. We live in a society of Ready, Fire, Aim.
ReplyDeletePeople have a huge problem knowing what we want at an individual level. Math and others get blamed when we don't get what we want. If we don't know ourselves, how can math help us get there.
GIGO - Garbage in garbage out.
So how does this translate to curricula, instruction, and student learning. I would suggest let's spend more time on getting the right questions and then the computers to do the work once we have a shared conscious target.
Application is key, make it real and useful to the user. Find the math in their lives and then teach them the processes so they can better solve their problems/overcome their concerns and get what they want in a sustainable way.
This fits with what I have learned about internal motivation and schema.
There is a process that Nasa used to solve a rather complex problem of putting a person on the moon. It's a 5 step. that begins with know what your objective is. When others are brought in to create a shared vision - that leads to action. Ask them about their step 1, do not impose 1.
Make it fun, call it what is it. Personal Logical Problem solving using measures. (PeoPLe SUM)
I have done this twice and it won't let me post due to willamette...lets try again.
ReplyDeleteAfter watching the video's I feel like Conrad was really stressing getting rid of teaching hand calculations and relying much more heavily on technology to do that work for us. This makes me uneasy. Not to be a science fiction freak, but we have seen the drastic effects of this is Irobot and the Matrix. Yes this is far fetched, but if we can't do them by hand what is the point in teaching that curriculum?
I did like Conrad's exploration of different mediums/methods/paths to follow. My math classes were always direct instruction and never strayed from the board up front. I think that through Conrad's examples we can implement computer examples and real life problems to break up an otherwise static classroom. Furthermore, I really liked that he began his speech with why teach math. I think this would be a great opener to students, so that they hopefully see that math is apart of every subject (art-grid-ding/proportions/perspective, grocery shopping, shopping and calculating percentages off, dining and leaving a tip etc...)So although I fight technology with tooth and nail, I see that incorporating in properly to me specific plan can be vital in keeping students attentions and applying it to real world issues.
One of the things that really resonated with me in the video was that we should reorder how we teach math. Instead of teaching math and ordering from the difficulty of the calculation but instead teaching according to the so-called difficulty of the concept. Conrad Wolfram gave the example of teaching calculus at an early age and that his young daughter understood the concept that the more sides a polygon has the more circular it becomes. The visual of the triangle turning into a circle was really helpful. I really like that idea because it is very practical in the real world which Conrad stresses. I think this can be implemented in the classroom by doing computerized drawings to help visually show what the math problem and concept is indicating. The very common algebra problem with the two trains leaving the station is sometimes very hard to comprehend so possibly having a visual, like a small movie of what is happening can help understand the algebraic concept.
ReplyDeleteTechnology and visuals can help those who do not simply learn by direct instruction. Some students have a difficult time comprehending concepts if the teacher is simply doing demonstrations of problem solving with students copying the examples and then going home to repeat the same sort of process. Technology and visuals can definitely aid the under of math in the classroom.
--Maria David
The impact of Conrad Wolfram’s philosophy of math could alter math curricula, instruction, and student learning. There is an evident struggle between classroom math and real-world math. Since classroom math does not even correlate to applications of real-world math, many students are disengaged and “hate” math.. These days many students say “I’m not going to use algebra in life,” and they ask a valuable question, “Why learn math?”
ReplyDeleteWolfram touches upon several major points as to why we need to “stop teaching calculating, and start teaching math.” The advancing world is becoming more quantitative and more careers need individuals highly skilled in math and science. Wolfram mentions his three reasons to the question “Why teach math?” are technical jobs, everyday living, and logical thinking. Math has several components and in the classroom have been only focused on calculations. Math is more complex than just calculations. We have computers and other means to do the calculations for us, which gives more time for us to do more complex things with math and opens up the door for more people to use math.
If math curricula and instruction focused on computer based math, then it will create numerous amount of possibilities to challenge students’ learning and application of mathematics to everyday life. Maybe more adults will know better not to get that third credit card, or which insurance policy would be the most cost-effective.
Wolfram's ideas were a bit radical for me. If math does not equal calculating, does that mean that Language Arts does not equal reading and writing? What's next Wolfram? Do we stop teaching handwriting and go straight to typing? Do we stop teaching reading, and instead let computer programs read to us? Since calculation is interesting, but unnecessary like Ancient Greek, should we offer it as an elective history class?
ReplyDeleteThe thing that shocked me most was his rather underdeveloped claim that using computers to solve math made math more democratic. How does he account for the unequal distribution of resources? How will the large number of people computers learn math? The way math is taught now is more democratic, because numbers are a universal language that can be taught to people no matter what their SES or native language is.
Wolfram is correct that the society we live in is becoming increasingly quantitative, but I believe he is incorrect in suggesting that we should rely solely on computers to solve our problems for us. I agree that math should be more practical and more relevant to life, and I believe that is the key to increasing interest and performance in math. However, we do not need computers to do this. I also think Wolfram may have been suggesting a bottom-up approach to teaching math rather than the top-down approach most curriculum uses. I think this is a great idea, which I hope to learn to use.
Technology is a useful tool, and I believe it should become integrated into curriculum, but I don't think it should be the foundation of learning.
While I agree with much of what Conrad Wolfram says, I find it to be somewhat removed from the reality that teachers face today. In my experience teaching math at Chemeketa Community College, I was asked “when will I EVER use this?” dozens of times over my three years of teaching. Instead of teaching formulas and calculations, I would have loved to have instead been teaching students how to solve everyday problems with a computer. However, as long as teachers are bound by national standards which stress knowledge of formulas, the ability to do calculations, and while students are being assessed in multiple choice format, I feel that in many cases teachers are forced to teach to these same standards. So, the change (more real life application through the use of computers) needs to come at the curricula level before it can be translated into the classroom.
ReplyDeleteAlso, I’m not sure that computer programming is the way in which we should teach math to students. If we teach all students how to computer program, I think it is a bit like Wolfram’s example of driving a car, I do not feel it is necessary to understand the inner-workings of a computer application in order to be able to use it. Just like in the car example, user-friendly applications must first be designed by computer programmers for use in the classroom.
In watching Mr. Wolfram’s video I felt it hit home with how I see the modern world. Being in the pharmaceutical industry for the past 15 years, I understand that in industry people don’t sit sown and perform calculations to find answers. They use computers to their fullest potential to do the work for them. In this atmosphere, people spend their time discussing difficult ideas/concepts and less time perform calculations that a computer can do.
ReplyDeleteOn the same note, I am now moving into the world of education and I really am unsure how I could translate what I’ve seen of “mathematics” in industry to the classroom. While I love his ideas presented by Mr. Wolfram, I’m truly unsure how this computer-based concept would be taught. I feel that we can understand procedures and processes by using programming, but how and when would we teach this in school? I truly agree that we can make math more practical through the use of computers, but what about the schools that can’t even afford to purchase computers? How will these concepts be taught to these students? We need to teach concepts rather than calculations but the true question is how do we go about doing this?
In watching Mr. Wolfram’s video I felt it hit home with how I see the modern world. Being in the pharmaceutical industry for the past 15 years, I understand that in industry people don’t sit sown and perform calculations to find answers. They use computers to their fullest potential to do the work for them. In this atmosphere, people spend their time discussing difficult ideas/concepts and less time perform calculations that a computer can do.
ReplyDeleteOn the same note, I am now moving into the world of education and I really am unsure how I could translate what I’ve seen of “mathematics” in industry to the classroom. While I love his ideas presented by Mr. Wolfram, I’m truly unsure how this computer-based concept would be taught. I feel that we can understand procedures and processes by using programming, but how and when would we teach this in school? I truly agree that we can make math more practical through the use of computers, but what about the schools that can’t even afford to purchase computers? How will these concepts be taught to these students? We need to teach concepts rather than calculations but the true question is how do we go about doing this?
Basically, I agree with Conrad’s idea that Math education should focus more on real world problem using computers, which seems a new content of learning. I saw many students who struggled with and did not like Math word problems that related to the real world. They rather preferred calculation. Students may like solving real world problems better with the use of computers. However, not every student likes computers. If they have problems with manipulating computers, they would reach anywhere. I am afraid the use of computers in Math may require more time than just replacing with some parts of existing curricula. The approaches may be successful if students could get enough technological assistance and time.
ReplyDeleteThere is another thing I would like to add. Conrad’s analogy between driving and Math was interesting. Knowing mechanics of cars does not make a person able to drive a car. People do not need to know all mechanics of cars to drive either. However, I think if they know mechanics, they might be able to handle the situation better when they had mechanical problems in their driving. Likewise, the understanding of processes and having computational skills as their mathematical backgrounds may help students better build mathematical higher thinking. They still need to have computational skills by hand to some extent.
Instructor will copy/paste these Comments into a Shared Document for further reflection. Invites will come soon.
ReplyDeleteSo here is my problem with Wolfram...he says that the calculation component is not nearly as important as understanding what is going on, framing the correct question, understanding the answer, etc...he also said that programming is the best practice to understand the mechanics of how a procedure works. Here is my question...how are they going to learn the mechanics to write the program if they can't understand the mechanics in the first place? Honestly, I'm a little fired up about it. I love doing the problems...always have, always will. I love staring down an insane trig identity and showing fifteen or twenty steps. It shows a logical thought process that does appear in computer programming, but must exist before the program can be successfully written.
ReplyDeleteI agree that focusing on application will help alleviate the "when will I ever use this?" question that we all hate. However, I think that understanding how something works is often just as important as understanding why something works.
And another thing to relate to my first general idea. Say we stop teaching the mechanics. Who is going to write all of the nice simulations and algorithms that Wolfram is saying we should be using to teach math? Whew...
"How might one creatively address the impact Conrads' thoughts could have on current math curricula, instruction, and student learning?"
ReplyDeleteRadically at either end of the spectrum I could throw out all the text books and allow computers and calculators in all aspects of math work that I help students identity in projects that they choose to learn bout. This would be based around a pure constructivist model where the entire process is student focused and uses their own internal motivation and schema as the basis for learning. It would embrace technology to allow students to spend less time on computation and more time on critical thinking, higher level Bloom skills.
Or I could reject the idea and repeat with DI until students can complete tasks via repetition so they can the teach the subject. That is the model being used by society at present. It is what those who want to pass the international tests suggest is the way forward.
However when I review the tests what I see is a need for the critical thinkers that are internally motivated by their own passion. As I reflect on my life I have relearned/newly learned many basic processes of science/math, after being inspired by larger, more applied real world high level problem solving including chaos math, and finance and personal problem solving.
First, I'd like to say that I really enjoyed Conrad's presentation overall on this highly important issue in education today.
ReplyDeleteThe most interesting point that will resound with me for the long run is the idea that the use of computers in education should be more of a focal point than to ignore. One of the slides he presented had 4 purposes that the computers can be used for. The area that students are taught to focus on the most is in the area of computations. Conrad argues that computers can do computational work much more efficiently than what we can do by hand, so instead of focusing so much time into computation, schools should focus more on the other 3 areas such as 1)posing the right questions, 2)real world problems, and 3)math formulation.
Towards the end of the presentation, he also reminded his viewers that we should try to make math as enjoyable and practical as possible as well because of the lowered interest in this subject across the country/world. It's interesting to think about; math is one of the highly sought out required subjects in schools today, but is also one of the most "hated" and possibly the most understood subjects out there, but at the same time, schools and teachers are held to high standards in performing well in this area. I believe that overall, educators and students alike must develop a healthy and coping relationship with math in order to be well versed in it.
Always being a math guy and learning in the style of computing until your eyes bleed and being successful it was hard to digest the idea that students could use calculators or as he put it computers. He also drove home the point that learning the basics was irrelevant to gaining a complete understanding. Both these ideas are very foreign to the style in which I learned. I am a practice makes perfect and once it becomes second nature then we can explain and relate it to the bigger picture or in this case how it is relevant to life. I do believe that Wolfram does have a point that students and people learning math should use the tools that are provided because they will likely have these tools in the real world. I am still struggling with his point that hours of mindless computing does not allow the student to grow and understand the big picture concepts of math. When I tutor in math my students struggle with very easy concepts (adding, subtracting, multiplying, dividing). Sometimes I wonder if we did a little bit more drilling there would be better base to build on. Many students still haven’t grasped the basics. However, I want to have an open mind about this and as the semester goes on I am excited to see what new ideas have come about in teaching math to our future students.
ReplyDeleteI believe that Conrad’s ideas will have a huge impact on the way that students will learn math. If we had the funding in schools to provide the computers he talks about for computing students would be able to do math at a much higher level. As teachers you could ask the big questions and think more critically on the big ideas of the world. I think student interest and activity would grow in the field of math. The biggest down fall to this whole concept of Conrad’s is that we would be creating minds that only see things from the outside in and not the inside out. I believe the little things are what make the world go round. Once people understand and master the little things then you can take them to the next level and experience the concepts and ideas that they little things add up to make. Conrad and myself are from opposite ends of the teaching realm: Conrad being a whole picture teacher where I see myself as a parts-to-whole teacher.
Part 1
ReplyDeleteThe first question I have is will math/calculations become an elitist enterprise. Where only a few know how to do long division? I do think this is a cool and uncharted direction to move but I am unsure if we are ready for it? We still don't have access for computers for all. What would be the basic level at which students would stop calculating on their own? Conrad is not the only one with this question. http://www.nytimes.com/2011/08/25/opinion/how-to-fix-our-math-education.html?_r=1&ref=opinion is an article on just the same questions. Real life problems are a great way to approach math learning. I have used Pathagoras theorem in construction and If you could bring this into the classroom I think students would have a better sense of how math is relevant. Making this connections is in my opinion way more important than solving some of the problems I have seen in text books.
I am also continually dismayed when a text book thinks it is being more student friendly when it puts a skateboard into a math equation. I don't think this really gets kids to enjoy math.
The Wofram interactive player is awesome and I think that the programs that have been developed are a great way for students to visualize mathematical problems. This sort of interaction really helps Students to internalize and put into a context that is useful for them. The only caution I have is that the calculations behind the programs might not be understood. Maybe we need to work students up to these and I like the thought about teaching the to program.
Part 2
ReplyDeleteI think that that the old and the new should be integrated so that we have a seamless transition between basic calculating and broad overarching understanding. I liken the process to a video game where as you learn and pass certain check points, you unlock tools that will help you on your journey. I have always thought that once student master long division they be granted calculators and maybe when they master basic algebra computers could be used to get students thinking beyond what they learn in school to their futures. I think using this technology and focusing on current quantitative demands from society, such as personal finance, math curricula can evolve into something that is much more culturally relevant.
It would also take a lot of money to get every student a computer and hopefully as the technology becomes more available this will become a reality.
I love this guy’s idea! I wish someone taught me math in a way that I could apply it to the real world. The idea that we are teaching outdated math really hits home with me and I agree with it 100% because we are teaching “the basics” that have no relevance to the real world. The question he posed was “is what we are teaching relevant in the real world today?” With technology of the world today and the application of that technology there is no real reason for students to be doing addition of exponents.
ReplyDeleteI think that we should address it by not calling it a math class for starters and call it an applied technology class. I think it would rework the way we teach because now they are attempting to tackle real world problems but at the same time we as instructors have to stay on top of our game as far as new technology, current events, and overall application of programming. With all new classes or student learning some students will love it and embrace it and on the other end students may reject it or still be lost on understanding. I need to learn more about this applied math!
Rob Garcia
By Dave McKae
ReplyDeleteJust lost 3 paragraphs upon submission. Always write responses in Word first....
I agree with a lot of what Conrad says and feel like his ideas may increase student interest in their math classes. We should let students know that they are first going to learn the basics and the foundations, then we are going to teach them how technology can speed up this process and allow us to solve problems that are much greater in complexity. Most of what students learn in today’s math classes will never come up again in a lifetime, mainly because it is too long and difficult to solve many of these problems. As soon as we take the chapter test, we stop using it and we lose it. Instead, if we teach practical applications using technology, perhaps students would be more inclined to continue using the math beyond the classroom. Solving these difficult problems may not be such a burden anymore. All we have to know how to do is set up the problem properly, which computer programs can help us do.
As a result, we spend less time computing and more time on practical applications that may come up in the real world, which gives us better job skills. The one thing that makes this work is that we teach the basics by hand before showing them how to do it on a computer as a short cut. If they only learn the short cuts, they will never learn the “why” or “how”. There should be a balance between the two. Maybe at the end of each unit, the teacher demonstrates how computers can make the process faster. I like the idea of writing a computer program for a final project to demonstrate comprehension. These can be more complex and require practical applications of many concepts, which is how math in the real world works.
Initially I was very skeptical of Conrad Wolfram's ideas of using computers more in math instruction, however, after seeing his TED conference talk I felt like he had many very practical and useful ideas. I especially connected with his statement that math > computing. The traditional forms of math instruction have not evolved with technology or our society and economy. I believe that Wolfram is correct in asserting that mathematics is the key to competitiveness in the 21'st century. The ability for teachers to light a "spark" as Wolfram states for math is integral to building our country's intellectual capital. I believe that a computer enhanced mathematics curriculum would give students the tools to succeed in math and be able to apply math concepts to their lives.
ReplyDeleteI liked the presentation that Conrad gave with a few reservations. He stoked my interest in using technology in the classroom especially in a math format. His ideas seemed to make sense in regards to using real life scenarios to teach and explain math. His examples of driving vs. knowing the mechanics of cars missed the mark a bit.
ReplyDeleteIn his idea of using computers to perform the computing and calculations, I had some reservations (or mostly questions about). I wondered how much computation would be “taken away” from instruction. How much is too little? How much calculation is too much? I would want some data to support how his ideas and methods actually have students more difficult math at younger ages.
Another reservation or question I would have would be about accessibility. Current budget woes may not support the cost of technology for this type of instruction, at least in some districts.
The impact on current math curricula would be quite dramatic. It would change ideas of the need of calculation in the current curriculum. Without some data, it would be difficult to know how this would effect instruction and learning.
In all, I agree with the idea of having the computer calculations as an assistant, but I also believe that calculation knowledge has some importance in math knowledge.
Chad Barr
Wolfram had many good points that I think are worth critical consideration as I plan on being a teacher. Why do we learn math in a classroom that can easily be done on a computer outside of the classroom? Why are we learning a certain kind of math (outdated at that) then trying to apply it to something substantial in a different discipline later, when it has to be relearned for the circumstance? Overall learning math in a constructive and relatable way is a more appealing choice from a student-teacher relationship standpoint because the student is not working on a math problem based solely on their trust in the teacher that they are doing this all for a reason that will show up somewhere along the line, or perhaps only so they can do the work next week.
ReplyDeleteUpon reflection it seems unfathomable to me that we spend an entire year in a math class learning differentiations on the same core concepts of algebra for example. As I learned it, math was taught in a form of building blocks where one week built off the last week in small almost imperceptible increments. The final destination was often not that noticeably different from the beginning. How can we expect a student to thrive in this situation? Obviously Wolfram does not believe that they can.
Saying all of that. I believe that what he is asking for, curriculum shift and content wise, is going to be difficult and that someone like me, who only has ever taken Calc 2 in a traditional classroom setting is going to need guidance and probably practical knowledge to have the kind of interactive discussions that he was discussing.
It is true that technology and computers are increasingly becoming a part of everyday life. Whether this is a good thing for our society or not remains to be seen and is a different discussion but is relevant nonetheless. What I understood of Wolfram's discussion was the ideas that we need to spend less time teaching students computations. We need to let computers do the work of the computing and teach the students the relevance of the problem, and the solution, in the real world. This is a concept that I strongly agree with. The application of math definitely deserves a place within the math classroom, yet I don't know if I am ready for the drastic reform that Wolfram is arguing for.
ReplyDeleteHe mentions that there is some practicality to hand calculating. But, if we don't teach hand calculating than how will students know when to apply this knowledge? And if they have learned that they don't have to do hand computations what would be there incentive to learn it? As people and students living in the middle of this hand vs. computer argument we have the ability to see the benefits and pitfalls of both. In the future though, if we teach students to be reliant on computer computations will they be able to see the benefits and practicality of hand/mind computations in their lives, I don’t think so.
There is also the question of resources to be reckoned with when it comes to computer calculations. As our world stands now, not everyone has access to a computer, a smartphone, an iPad etc. etc. So what about those students? Do they get left behind? While I like some of Wolframs ideas, I would definitely have to look into it some more to see exactly where he sees math heading and how he expects us to move all students there together.
I do agree with Conrad’s ideas that math does not equal computing. I believe that teacher’s get caught up teaching kids how to do math and not how to apply it. I experienced this as a student. I disagree however when he proposes switching to a computer based math curriculum alone. Perhaps math should be split in to two separate subjects: mathematics and computing. That was just one thought I had, since I still believe there should be some aspect of pen and paper computing, but maybe that’s because I was taught in that way.
ReplyDeleteI think it is important for students to apply their knowledge. I think computers are a great way to get students interested in math and keep them interested. I think that using a computer based math curriculum could really enhance instruction because it is easier to instruct students who want to learn and are interested in the material. Unfortunately, to so what Conrad suggests and overhaul the entire math curriculum, we will have to retrain teachers, which could be time consuming and expensive. In the long run however, I believe that this method of teaching will benefit students more, as our society and economy are becoming more technology and service based.
I can agree with many of the statements that Conrad had. I think that being able to do some simple arithmetic (addition, subtraction, multiplication, and division) in our heads can be advantageous, it's the practical application that we need to emphasize.
ReplyDeleteI read an article in the New York Times recently. I think Conrad Wolfram would have agreed. The article proposed that instead of Algebra I, Geometry, Algebra II, Pre-Calc, & Calculus, the high school math track would start with "finance, data and engineering." I think this would be very beneficial to our students. The hard part is getting students ready for it by the time they get to the high school.
So far, a very interesting argument. During last fall, I was in a MS classroom for the first time since the day I left it (what, 14 years ago?). As I was volunteering to just be helping out, I didn’t know what to expect. When I discovered that a 13 year-old student didn’t know his times tables, I just about had a heart attack. What? Really? The teacher said to me, “It isn’t important to me that he doesn’t know his times tables right now, because he can always use a calculator to do them. It is more important that he is getting through the work and understanding the rest of it.”
ReplyDeleteNow, almost instantly, I rebelled. Of course he should know his times tables, how could he go on without knowing them? What if he were stuck in a situation where he needed to do some computations but didn’t have a calculator? Okay, granted, the chance that this kid would be caught unawares without a calculator is pretty slim (shipwrecked on a remote island but needs to figure out how big to make his escape raft?) and if he gets a job in the future using math, he’ll probably have tools for doing so (you won’t see accountants without one of those big printing type calculators…), but still, it just seemed to me that he should know it. The more I thought about it, though, the more I realized that in part, I was thinking like an old dog (so to speak). Just because it was beneficial for me to learn my times tables doesn’t mean it will be beneficial to this kid. Indeed, it might simply be that there is little reason for memorizing them, unless, in some freak disaster, all the computers and electric calculators in the world stop working at once. Maybe it is like a slide rule. When I took calculus (years ago), my dad told me (misty-eyed and everything) about the slide rule he used when he was in school. He probably thinks I should know how to use a slide rule (and indeed, I have never even seen one, aside from images on the internet) in the same way that I was thinking that kid needed to know his times tables.
What did that have to do with the video? I might have just sounded like a raving lunatic (and I might very well be), but I promise there was some logic behind my “aside.” When Wolfram made that analogy— how ancient Greek might be fun/interesting to know, yet it is not practical to teach everyone in an entire country ancient Greek—as a reason for cutting back on our focus on the mechanics of math (computing), I thought immediately of times tables and my dad’s slide rule. Can we accept that sometimes, the things we learned ourselves are simply “moot”?
Now, as for the second question, “how might one creatively address the impact Conrads’ thoughts could have on current math curricula . . .”, I am going to have to say that I am a bit confused. Am I being asked how I can implement his thoughts (in a creative manner) in a math classroom, or how do I adapt my classroom if his thoughts cause changes in the classroom? So, since I am pretty confused, I’m going to just say, on a personal level, I don’t know that I am currently equipped to teach math in the manner that Conrad suggests. In fact, it sounds like to me as though he is suggesting that math be taught by computer programmers and engineers, etc. The change? That makes the public classroom look more like a college classroom, where the teachers are people who have used the skills they are teaching in a practical manner (outside of the classroom). That is to say, they did not necessarily go to college to become teachers but are now, as proficient persons in their profession, able to teach that math. Frankly, I think it sounds like a wonderful idea, but of course, what do you do with all those teachers who learned “academic math” (calculations) simply for the purpose of teaching it?
P.S. Calculus first? HELL YEAH!
This video was very interesting, and not being a real “math minded” person, I agree with trying to link up school math with the real world. I spend most of my time in a special education classroom, and while it is important for the students to understand what they are doing they often are allowed calculators. I like the idea that the math needs to be more practical; I remember in high school constantly asking my teacher when I would EVER use this “stuff.” While I find myself using some of the tools he gave me, I all too often pull out my cell phone calculator to figure out the unit price per ounce at the store. Increasing students’ interest in math by making it more accessible to them seems like a great way to go about it.
ReplyDeleteI could see this presentation impacting the way we teach math to our students focus more on understanding the concepts and less on worksheet after worksheet of problems. While I visited my friend at GATech, I sat in on a few civil engineering grad classes. While I couldn’t do the calculations they were performing, the concepts were explained in manner that made me, as a visitor, feel like I “got” what they were talking about (too much cement!).
Wolfram’s entire presentation was very interesting to listen to as an aspiring math educator, but also as a student who is studying our current educational situation. I really loved the way he stressed the importance of us not teaching students how to compute simple or even complicated mathematical problems because we now have multiple tools that are easily at our disposal that can do these things for us, in a much more efficient manner. The fact that he finds it much more important to focus on the application of math, in the beginning stages as well as the final product, to real world situations. The part of his lecture that really hit home for me was when he was talking about the need for reform in order for us educators today to be able to start tackling this feat. How can we as educators try and change the way we teach math and the things that we focus on, when our governing bodies are so focused on teaching to the “tests” that bring money to our institutions? How are we supposed to really take advantage of all the ways that math can be taught and learned when our goal as educators is supposed to be to get our students to perform well on the exams that ask them to do just what it is that has made math so methodical in the past? The jist of Wolfram’s message is yes, we need to utilize the tools around us that will open the world of math up infinitely but we first need the permission from our superiors….! So, please break the chains and let us teach! I agree with this in some respect but I also think that education, especially math, needs to be moldable, needs to change to what is important at the time all while keeping a base standard of what needs to be taught and how. The question of how to teach lies in where education is headed. Until we can all get a firm grip on where that is exactly, we are all just going to run around in circles talking about how things can, could, or should be better.
ReplyDelete1. When Conrad showed the picture of his daughter holding the computer drawn on paper, then told her he had never drawn that when he was a child, can she guess why? That was my favorite scenario, because the answer she gave was so innocent and shows what kind of technology age we are living in. It made me smile, but it also really made me think. This is how students relate to their world. Comparing better writing by using a quill as a metaphor for how we currently describe “the basics” in math education is genius and points out a major flaw in that line of thinking!
ReplyDelete2. Incorporating technology and real world scenarios will help engage students in the curricula, open doors for creative instruction and limitless real-world scenarios, make the info applicable to many future jobs students will have, and highlight the real process of mathematics, rather than the computation (which is better done by technology anyway).
Conrad's statement about what math 'is', illustrates the point he is trying to make in a very striking way. Of the four phases he describes in performing purposeful math, only one is involved with doing calculations.
ReplyDelete1. Posing the right question
2. Turn it into a math problem
3. Do the math
4. Turn it back into a real world concept
The world, for all practical reasons, has moved beyond doing calculations by hand and the use of a slide ruler or pre calculated tabulation books a very long time ago. I think it is a perfectly valid question to ask, "why do schools spend so much time teaching step 3 only?" Math does not equal calculating alone. If, in the real world math has been liberated from calculating then it makes sense to me that we should be focusing on steps one, two and four.
The practice of taking real world issues, developing an algorithm designed to process data and provide answers, seems to be a much more worthwhile learning goal than being overly proficient at solving differential equations by hand.
In an educational setting I've begun toying with the idea that math should be taught through learning to write computer programs. It seems to me that being able to understand and master the discrete tools required to code for any number of real world problems or tasks would be a much better use of the schools time than teaching hour after hour, lessons on using the quadratic equation.
The takeaway here is that Conrad is simply saying what we in the educational field have always known, and that is, excellent learning is achieved when a stronger sense of relevancy is created for the student. And that in the case of math, relevancy is no longer centered around performing manual calculations. But, it seems the math education community must first acknowledge that 'math' today does not equal computation alone, before change can happen.
Conrad Wolfram's idea of changing the focus of math instruction from an abstract concept heavy on human calculating to a way of solving real world dilemmas is stimulating. He really hits the nail on the head in my opinion when he addresses the true concerns of math curriculum and instruction. Computers and calculators seem to be looked at as a crutch, as something that props up those less skilled in math. But he makes the deduction, that this view is inevitably skewed in its relation to reality. He asks the question as to whether computers have really hindered the mathematical possibilities for those in engineering. Of course they have not. Somehow this idea has been disseminated in math education to equate the slowing down of true mathematical learning.
ReplyDeleteWolfram also spells out the importance of what we focus on in our math classrooms. He suggests that we need to switch our focus from mathematical computation, and start focusing on how to apply mathematical ideas to real world concepts. He outlined the four steps that he sees as crucial to math education. He perceives this process flowing from encouraging our students to really think about what is it we are trying to find out. He suggests that we take this idea of asking the right question, a question that relates to the real world, and then turn it into a mathematical expression. Once we have this expression, we need to turn it into real answer through mathematical computation. This is the step that Wolfram proposes we let computers aid us. Computers will always be able to do this step more quickly than humans can. And this is the step that in my personal experience seems to bog students down the most. And then finally, take the result of this mathematical computation, relate it back to a real world concept, and then prove its validity.
These four steps are math. If we can take out the tedious, sluggish step of human computation, and let computers support us with efficient calculations, we can streamline math learning. Let’s support our students with the skills necessary to take real world problems, convert them into mathematical expressions, solve them with the help of computers, and then substantiate their validity. Wolfram has excellent ideas, and I look forward to applying them in my own teaching.
Let's see if this will finally post...It has been giving me a lot of difficulty and apparently posted anything I have said...
ReplyDeleteI completely agree with an earlier post by Meg. I think that Wolfram's idea's are a little too intense for my liking. I think that technology is a fantastic tool to have in the classroom, but it is simply a tool at that. I do agree that we need to make sure that we are making math practical for our students, however some concepts we need to teach simply for deepening our understanding so that we may understand and apply a more complicated concept later. Furthermore, I think that Wolfram was a bit ridiculous with his comparison of trying to drive or service a car. My argument to that would simply be I cannot build a calculator but I can use one. Overall I think that Wolfram had some great points, but took them a little too far. Yes, technology is a great aid, but we have to make sure that we are still teaching our students valuable math skills so they aren't completely reliant on technology. We need to keep using and stretching our brains.
Now I am testing from personal gmail.
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