New formula for Maths Education?
A couple of my cousins who are in class 10th are smart kids and are doing very well in their grades. Still, they find Maths a tedious subject – a difficult mountain to be climbed. One of them, when she was in class 8th, had devised the sum of an arithmetic progression in the same manner as the Prince of mathematics did in his childhood. To put things in perspective, its something that I learnt in class 11th. Every time I meet them, I’m stunned at how much smarter they are than me. At the same time, I could never understand why they find Maths so tedious. It should be very easy for kids that smart!
I recently discovered a good answer when I chanced up on Paul Lockhart’s “A Mathematician’s Lament” Its a moving argument which is 25 pages long and worth reading many times over. Paul argues that maths education is broken.
Everyone knows that something is wrong. The politicians say, “we need higher standards.” The schools say, “we need more money and equipment.” Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right.
Paul says that Maths is really an art; an art at par with music or painting. It is to be enjoyed and taught much the same way as other arts rather than rote learning. He supports his arguments with quotations from mathematicians and anecdotes of his teaching experience. He contrasts this fun filled view of mathematics with ” a completely honest maths catalog”. He also engages in a dialog reminiscent of the Greek classics. All of these show how creativity and fun are the foundation stones of maths and that kids get it; only if they are allowed to.
In all, Paul makes a very passionate and convincing argument against the present methods of maths education. The current methods favor the formalism and the rigor of maths to an extent that the art is lost. All that the kids are left with is the drudgery and they don’t see any point to it. No wonder its a mountain to climb.
While I agree a 100% with Paul, its also difficult to see how schools alone can change things. There is a lot of material to cover and class sizes are only getting bigger. The personalized attention demanded by Paul’s methods cannot scale up to the demands of syllabus and class sizes. I’m not sure if schools and Boards such as CBSE can do anything more than switching to the grades instead of marks. This they have already done.
Paul’s methods have to be adopted by parents and others who have a one-on-one with the kids rather than one-on-many as teachers do. I would recommend every such person to read Paul’s lament. It will connect with many of childhood experiences and convince that kids deserve the fun rather than the drudgery.
I would also recommend patience to all such people because such methods demand a lot more. For example, I’ve gifted a maths problem book to my cousins. At first, the book was not opened because it was seen as “high level maths”. But once we solved one problem together and they realised that it takes only logic and no formula, we had big trouble at hand. First, they are hooked. Food, sleep, TV – everything is given a pass. Second, neither is willing to give the book to the other. So I get a lot of protests. Third and the most difficult, they think that I and other elders can solve the problems they can’t. Its a little difficult to say “I don’t know” to kids but I realized that it doesn’t matter in the end.
Image Courtesy: i’m going to fail… by raquell
The most thought provoking talk from TEDx Mumbai
I had the good fortune of attending the TEDx Mumbai earlier this month. The organisers did a fantastic job of curating the show. So much so that some people commented that TEDx Mumbai outdid the TED India at Mysore! While I wasn’t at the TED, I absolutely loved some of the talks at TEDx. Here is the video of the talk I found most thought provoking. Dhanashree raises a few deep questions and then moves on to demystify music in a way that made me feel that even I could understand music.
I came back with the following questions/thoughts:
- Why do we all across different cultures, ages, religions, regions etc love music and dancing?
- What makes each music different? Dhanashree asks this questions herself and responds that “its the treatment”. I wonder “the treatment” is completely explained by languages and philosophies or is there more to it?
- Music is universal but languages different. Why?
- Reminds me also of the Tower of Babel and Neal Stephenson’s Snowcrash
These questions and thoughts are also interlinked with another great talk at TEDx Mumbai by Prof Ganesh Devy. He says a way of life dies with the death of a language.
Thank you TEDx Mumbai for thoughts worth spreading.
RAMClouds – an evolutionary concept in Cloud Computing
If you ask an architect or a performance engineer for ways to speed up any application, caching is most likely to be the first response. In this, an application in its entirety or at least the most frequently executed part is cached in the RAM of a server leading to faster response and hence faster throughput. This of course becomes difficult as applications become large and loads increase. RAMCloud, a concept promoted in this paper by Stanford Computer Science Dept, offers an evolutionary solution. Essentially it argues for putting together large number of DRAM units and using cloud computing techniques to provide scalability and reliability in spite of failures. The performance gain is revolutionary at 100 – 1000x. All large websites would benefit substantially from such an approach. However, as costs also go up 50 – 100x, the overall impact is only evolutionary.
To put things in perspective, let’s consider Facebook which has been repeatedly cited in the paper. Would the users like to have the pages load 10x faster – maybe yes but would it be discernible from 1000x? My guess is No. Furthermore, speedup at the server doesn’t always translate to better experience for the user due to network issues. So the gains in user experience seem doubtful. Facebook would certainly also gain from the increased throughput but that needs to be compared with the cost. This is where the argument for RAMCloud comes apart. A RAMCloud is 50 – 100X costlier on a per bit served basis. This means that the cost increases even after taking into account the throughput jump. On the whole Facebook would probably stick with its disks.
So why do I call this evolutionary? Using caching to speed up performance is a standard technique and more of it would happen as DRAM sizes increases and costs drop. Disks would still be relevant but increasingly the load would shift towards RAM. This means that cloud computing providers have to offer more RAM per computing unit. This has already been happening – look at the Large instance from Amazon. This trend is likely to continue and sooner or later, an Amazon service may start offering just RAM – a RAMCloud.
Image courtesy Chrisdag