The HG2S Training Blog

(c) 2009 Jeff Parker, Florida Today.

A new study conducted by Dr Clare Wood, of Coventry University, and the British Academy has addressed whether “texting” has a pathological effect on learning to read and write. Dr Wood, who is a specialist in reading development, looked at a group of 8–12 years olds over the course of the school year and has concluded that far from eroding basic reading and writing skills, the activity may be a sign of their mastery. The results come as a surprise to many who assume the practice to be a clear sign of the decay of basic literacy. From the university report on the research:

“We began studying in this area initially to see if there was any evidence of association between text abbreviation use and literacy skills at all, after such a negative portrayal of the activity in the media. We were surprised to learn that not only was the association strong, but that textism use was actually driving the development of phonological awareness and reading skill in children.  Texting also appears to be a valuable form of contact with written English for many children, which enables them to practice reading and spelling on a daily basis.”

The study goes further to suggest that the degree to which a user has mastered texting may be indicative of his or her overall reading ability:

“The research, carried out on a sample of 8-12 year olds over an academic year, revealed that levels of ‘textism’ use could even be used to predict reading ability and phonological awareness in each pupil by the end of the year.”

Dr Wood is hoping that the results of the study change the way people look at texting in relation to phonetic literacy:

“In short, we suggest that children’s use of textisms is far from problematic. If we are seeing a decline in literacy standards among young children, it is in spite of text messaging, not because of it.”

For those unfamiliar with texting, this post is re-written in Lingo below:

A nu stdy conducted by Dr Clare w%d, of Coventry uni, n d brit Academy hs adressed whether “texting” hs a pathological effct on lerning 2 read n wrt. Dr w%d, who’s a specialist n readN dvlopmnt, lOkd @ a grp of 8–12 yrs olds ovr d corZ of d skool yr n hs ended dat fr frm eroding basic readN n ritN skilz, d activity may B a cYn of their mastery. d rslts cum as a surpriz 2 mnE hu aSume d prctic 2B a clr cYn of d DK of basic literacy. frm d uni rprt on d rsrch:

“We began swating n dis area initialy 2C f der wz Ny evidnce of asociatn btw txt abbr uz n literacy skilz @ ll, aftr sucha neg portrayal of d activity n d media. We wr surprisd 2 lern dat nt 1ly wz d asociatn strong, bt dat textism uz wz actuly drivN d dvlopmnt of phonological awareness n readN skill n kids. txtN also appears 2B a valuable 4m of contct W ritN en 4 mnE children, wich enables em 2 prctic readN n sp on a daily basis.”

d stdy goes furthA 2 sugest dat d Dgre 2 wich a user hs mastered txtN may B indicative of hs or her O’all readN ability:

“d rsrch, carried ot on a sampL of 8-12 yr olds ovr an academic yr, revealed dat lvls of ‘textism’ uz cUd evn B uzd 2 4tell readN ability n phonological awareness n ea pUpl by d Nd of d yr.”

Dr w%d S hopin dat d rslts of d stdy chng d wA ppl l%k @ txtN n relation 2 fonetic literacy:

“n short, we sugest dat children’s uz of textisms S fr frm problematic. f w’r seein a ebb n literacy stdz among yung children, itz n spite of txt msgN, nt coz of it.”

References.

Text Messaging Chat Abbreviations

Is texting valuable or vandalism?

For more information about the research, or an interview with Dr Clare Wood, please contact:
Kate Turnbull, Press and PR Manager:  0207 969 5263 / k.turnbull@britac.ac.uk or Ali Bushnell, External Press and Media Relations Officer, Coventry University on 024 7688 8245

According to technology blog CNET, the educational content wing of Apple’s iTunes Music site, iTunes University,  passed a milestone of over 100 million downloads this week. iTunes University is part of a mobile learning and content distribution service available through Apple’s iTunes application. As stated by Apple on their mobile learning site:

“Today’s students expect constant access to information—in the classroom and beyond. Which is why more and more faculty are using iTunes U to distribute digital lessons to their students. And now, with the 3.0 software update for iPhone and iPod touch, iTunes U is directly accessible over both cellular and Wi-Fi networks through the iTunes Store.”

Interestingly, according to CNET, one of the most popular draws on iTunes University’s bandwidth is the much esteemed Open University (OU) in the UK that had earlier tried and failed to launch an American campus in the late 1990s. A brief report of the OU’s foray into the American educational market is provided here.

The Open University is incorporated by Royal Charter in the United Kingdom but operates internationally. According to its web site the OU serves over 150,000 undergraduate and 30,000 postgraduate students. 25,000 are outside the UK. It is generally considered “the world’s first successful distance teaching university” and the United Kingdom’s only university dedicated to distance learning.

The iTunes University download service is popular among many other universities as well. Contributors include: Stanford University, Princeton, Yale, MIT, UC Berkeley, and the New Jersey Institute of Technology. A partial (and growing) list of schools providing content can be found here. Given it s recent growth and overall wide acceptance, iTunes University appears to have become a standard tool for distribution of audio and video content among American colleges and universities.

I’m tired of talking. Let me explain. One of the basic rules of thumb for adult learning says that a class should be a little more than half practical application and workshop material to appeal to the audience. That aside, classroom (or instructor-lead) training has become expensive, and managers and consumers have become vocal in letting us know that they want to make sure it’s worth their time and money. To be plain, are we doing all we can to make the trip worthwhile?

I have always been an advocate for lots of hands-on activity in class, probably because it matches my own learning style but also because the majority of the attendees enjoy it. Not surprisingly, in the midst of teaching a class a few years ago, I started to wonder if I could get more time for discussion and activities, and lessen the burden we all felt in getting through the lecture pieces to the workshops. In this particular case the lecture was preparatory to the workshops and provided necessary background required to complete the labs and assignments. Fortunately, in addition to instructor-lead courses, I also work on web-based training and have done many voice over and narration tracks for online and computer-based presentations. Eureka! I found a way to off-load all the passive broadcasting of background material and recoup the time for projects, experiments, discussion and debate–the things that make class interesting and engaging. Although I didn’t have a name for it, I adopted the Inverted Classroom and have since learned that many others have had, either from desire or need, their own Eureka! experiences.

The “Inverted Classroom” as coined by professors Lage, Platt and Treglia in a paper presented to the Journal of Economic Education, Winter 2000, moves away from the traditional lecture. In it they describe how they saw a need to serve a wider variety of learning styles in class:

“Recent evidence has shown that a mismatch between an instructor’s teaching style and a student’s learning style can result in the student learning less and being less interested in the subject matter (Borg and Shapiro 1996; Ziegert forthcoming). This finding implies that either educational administrators should strive to ensure a good match between the instructor’s teaching style and the students’ learning styles (a difficult task) or that concerned instructors should use a portfolio of teaching styles so as to appeal to a variety of student learning types. Unfortunately, a majority of introductory economics courses are taught using only one teaching style–the traditional lecture format (Becker and Watts 1995).”

Lage, Platt and Treglia define the inverted classroom in simple terms:

“Inverting the classroom means that events that have traditionally taken place inside the classroom now take place outside the classroom and vice versa.”

What this means is that the class is designed in such a way that “passive” activities (such as listening to a lecture) are done outside class and what was lecture is replaced by workshops, discussion, and activities that require interaction. In theory this should increase the value of class time and provide more time for new and additional. Educators are still unsure how to optimize the inverted classroom, but what seems clear is that inverted classes will use of a mix of technologies like podcasts, DVDs, PowerPoint, text, video and interactive media in conjunction with hands-on projects and group activities.

Researchers Gerald C. Gannod, Janet E. Burge and Michael T. Helmick of Ohio’s Miami University are carrying out a study to evaluate the design and delivery of inverted classes in computer engineering. In a work-in-progress report delivered to the ASEE/IEEE Frontiers in Education Conference, 2007, Gannod states:

“Based on the SGID analysis performed on the course, student acceptance of the inverted classroom process has been well-received. Over eighty-five-percent of the students (in a class of twenty) have responded favorably to the inverted classroom structure, while over ninety-percent prefer the short learning activities over more prolonged assignments. In regards to the use of podcasting as a lecturing medium, students have indicated that the ability to use the play, pause, reverse, and fast-forward capabilities of the podcasted videos beneficial to their ability to learn the material.”

From the standpoint of instructor overhead, questions remain concerning the difficulty in designing, deploying and maintaining an inverted class. Certainly, the initial chore of creating podcasts (if they are used) may be considerable. Further, a sufficient number of high-quality projects and activities are required (vapid “busy work” may be less tolerated than boring lectures). Finally, the students must rise to the new class format and, to use an expression from the past, “come to class prepared.” Gannod plans to address issues of faculty overhead, podcast production and course maintenance in an upcoming report.

References.

Lage, Maureen, J., Platt, Glenn, J., and Treglia, Michael, “Inverting the Classroom: A Gateway to Creating  an Inclusive Learning Environment”, Jnl of Economic Education, Vol. 31, No. 1 (Winter 2000), pp. 30-43.

Gannod, Gerald, C., Burge, Janet, E., Helmick, Michael, T., “Using the Inverted Classroom to Teach Software Engineering”, Technical Report MU-SEAS-CSA-2007-001, Miami University, Department of Computer Science and Systems Analysis, School of Engineering and Applied Science, 2007.

Gannod, Gerald, C., “Work in Progress – Using Podcasting in an Inverted Classroom”, 37th ASEE/IEEE Frontiers in Education Conference, October 10-13, 2007.

In a note that could have been taken from one of Maria Montessori’s books, researchers in neuroscience, machine learning, education and psychology have convened to show that findings from a joint study suggest that “the prepared environment” might be supported by new scientific data.

“The ‘prepared environment‘ is Maria Montessori’s concept that the environment can be designed to facilitate maximum independent learning and exploration by the child.”

Terrence J. Sejnowski, Ph.D, researcher at the Computational Neurobiology Laboratory at the Salk Institute for Biological Studies and co-director of the Temporal Dynamics of Learning Center (TDLC) at the University of California, San Diego, echoes Montessori in his team’s findings. As quoted in Science Daily:

“To understand how children learn and improve our educational system, we need to understand what all of these fields [neurobiology, psychology, education, machine learning] can contribute. Our brains have evolved to learn and adapt to new environments; if we can create the right environment for a child, magic happens.”

The cross-disciplinary research points to a new science of learning that might influence the way classrooms are organized and run in the future. In particular, three guiding principles (or concurrent processes) emerge from the study:

1. Learning is computational
2. Learning is social
3. Learning is supported by neurological (perception-action) circuits

Research in machine learning and developmental psychology illuminate the computational complexity employed by learners who use statistical patterns and probabilistic models to infer rules of logic, relationships between words, syntax, and causal dependence between objects in the physical world.

Evidence that the three component processes happen concurrently is supported by the fact that learners do not calculate and compile statistical models of the environment indiscriminately but throttle the process using social cues from the people around them. Further, animal studies point to the presence of certain neurosteroids secreted during social interaction that promote learning.

Imitation also comes into play as a key factor:

“Imitation [presumably from others in the environment] accelerates learning and multiplies learning opportunities. It is faster than individual discovery and safer than trial-and-error learning.”

In essence, a social context fosters learning.

Brain circuits that support both actions and perceptions are directly involved with learning. As seen in language learning, for example, there is a complex mix of imitative, computational and articulatory processes that come into play as learning proceeds that might be further facilitated or enhanced at specific developmental periods. In general, neuroscientists have determined that there is considerable overlap in the systems brought into play during learning that support both perception and action. From Science:

“For example, in human adults there is neuronal activation when observing articulatory movements in the cortical areas responsible for producing those articulations. Social learning, imitation, and sensorimotor experience may initially generate, as well as modify and refine, shared neural circuitry for perception and action.”

Finally, experts in machine learning and artificial intelligence are taking advantage of the recent findings in social learning, computational modeling and the plasticity of the brain to design software that monitors and uses social cues and environmental factors to enhance learning. In the future this software may be used in tutorial programs or embedded in instructional robots that are specifically “tuned” to enhance teaching practices in classrooms.

References.

New Science Of Learning Offers Preview Of Tomorrow’s Classroom

Foundations for a New Science of Learning

New science of learning offers preview of tomorrow

From baby scientists to a science of social learning

Dean José Bowen of Southern Methodist University is not only advocating an outrageous pedagogical overhaul that many see as dangerous and ill-conceived, he is in the throes of implementing it as well. His professors at the Meadows School of the Arts are now required to teach primarily without computers or, more precisely, without PowerPoint slides. An short interview with Professor Bowen can be viewed here.

As reported in the Chronicle of Higher Education, Professor Bowen’s technological denuding of the classroom is motivated by several forces he sees eroding the quality of education in American classrooms:

• Lectures are boring and are usually done badly.
• PowerPoint is a terrible educational tool.
• Lectures are not interactive and can be done just as well online.

In Bowen’s impassioned view there is little reason for students to pay extra for the privilege of residential college tuition given the deplorable state of the antiquated lecture system. Bowen suggests that it can be done cheaper and perhaps better by the online colleges.  Secondly, students have the option of going to open courseware educational sites (like MIT and Stanford) to see lectures delivered in a way that are “really top notch.” In essence, as Bowen sees it, students will vote with their fingers as it were and take their lectures at a cheaper and better online resource if things do not change. “They will pay less for better.”

Bowen’s call to reform the lecture hall starts by asking what role the class meeting serves in light of modern media like podcasts and online presentations? His answer, make the lecture worth attending by using it as a venue for exploration of ideas, spontaneous questions and answers, group projects and debates. Use technology outside the classroom to prepare for the classroom.

Not surprisingly the Chronicle sites problems from both sides of the lecture hall:

“The biggest resistance to Mr. Bowen’s ideas has come from students, some of whom have groused about taking a more active role during those 50-minute class periods. The lecture model is pretty comfortable for both students and professors, after all, and so fundamental change may be even harder than it initially seems, whether or not laptops, iPods, or other cool gadgets are thrown into the mix.”

A previous foray into “inverting the classroom” at Miami University in Ohio evoked similar reactions from the students:

“‘Initial response is generally negative until students start to understand and see how they learn under this new system,’ says Glenn Platt, a professor of marketing at Miami who has published academic papers about the approach, which he calls the ‘inverted classroom.”’The first response from students is typically, ‘I paid for a college education and you’re not going to lecture?””

Both Bowen’s and Platt’s views converge on one nagging conclusion: We have to create good reasons for students to come to lectures. If not they will tune out, turn off, and probably go elsewhere. It seems ironic that in an age of mobile computing, electronic media and information at the speed of light that the lecture hall may only survive if it returns as a low-tech 21st Century edition of the classical academy. Time will tell which particular approaches favor this revitalization of the classroom but it is hard to deny that it is desperately needed.

Further Information.

Teach Naked: Dean Urges Tech-Free Classes (NPR)

Teaching Naked: Why Removing Technology from your Classroom Will Improve Student Learning

Julie Evans of Project Tomorrow delivered a talk at The Future of Education web site on the findings of Speak Up, an annual national research project sponsored by her organization. Titled Top Ten Things We Learned from K-12 Students About Educational Technology in 2008, the report is a real eye-opener and should be of great interest not only to high school and college instructors but also corporate, government and military trainers who need to prepare for the educational tsunami that is forming. A table of findings from the survey are presented below. Many of the issues reported in the summary are already being seen in adult training venues. Others, no doubt, are just over the horizon and will certainly become standard topics of sundry research reports, conference talks, and blogs like this in the near future.

A Word file of the top ten findings can be downloaded here.

A PowerPoint file of Julie Evans’ talk at the Future of Education web site can be gotten here.

An audio recording of Ms. Evans’ talk can be found here.

Teaching College Courses Online vs Face-to-Face

A recent report by the US Department of Education will no doubt add fuel to an already raging debate over the virtues and deficiencies of online education. Evaluation of Evidence-Based Practices in Online Learning – A Meta-Analysis and Review of Online Learning Studies provides an extensive meta-analysis of data that compare the effectiveness of online versus traditional classroom approaches to instruction.

Designed to review over 1,000 empirical studies published from 1996 to 2008, the report focuses on studies that:

(a) contrasted an online to a face-to-face condition,

(b) measured student learning outcomes,

(c) used a rigorous research design, and

(d) provided adequate information to calculate an effect size.

The meta-analysis echoes results reported earlier, namely,

“… on average, students in online learning conditions performed better than those receiving face-to-face instruction.”

The authors of the report explain their findings by noting that:

“The difference between student outcomes for online and face-to-face classes—measured as the difference between treatment and control means, divided by the pooled standard deviation—was larger in those studies contrasting conditions that blended elements of online and face-to-face instruction with conditions taught entirely face-to-face. Analysts noted that these blended conditions often included additional learning time and instructional elements not received by students in control conditions. This finding suggests that the positive effects associated with blended learning should not be attributed to the media, per se.”

A paucity of data for K-12 is noted in the findings, leading the authors to caution readers about generalizing the results to that population.

A copy of the full report in PDF format can be downloaded here.

I think it was from Marshall McLuhan that I first heard:

“We shape our tools and thereafter our tools shape us.”

Now, for the first time, neurological evidence is demonstrating that this is literally true. Data published in the June 23rd issue of Current Biology shows that when we use a tool, even for a short time, it actually modifies the brain’s body schema. That is, the brain enhances the area of its map of our body associated with the tool. As reported in Science Daily:

“‘Since the origin of the concept of body schema, the idea of its functional plasticity has always been taken for granted, even if no direct evidence has been provided until now,’ said Alessandro Farnè of INSERM and the Université Claude Bernard Lyon. ‘Our series of experiments provides the first, definitive demonstration that this century-old intuition is true.’”

A report by the British Psychological Society describes the experiment:

“After several minutes using the grasping tool, the participants subsequent reaching movements with their hand were slower to start and stop, making them longer-lasting overall, compared with before the tool use – as if their own arm was now perceived as longer. Moreover, when the participants were subsequently blindfolded and asked to point to where they’d just been touched by the researchers, on the tip of the middle finger and on the elbow, the places the participants pointed to were further apart, compared with before tool use, again suggesting that they now perceived their arm to be longer.”

Interestingly the feedback loop from man-to-tool and back again is observed. From Science Daily:

“After using a mechanical grabber that extended their reach, people behaved as though their arm really was longer, they found. What’s more, study participants perceived touches delivered on the elbow and middle fingertip of their arm as if they were farther apart after their use of the grabbing tool.

People still went on using their arm successfully following after tool use, but they managed tasks differently. That is, they grasped or pointed to object correctly, but they did not move their hand as quickly and overall took longer to complete the tasks.”

The authors of the study go on to say:

“We believe this ability of our body representation to functionally adapt to incorporate tools is the fundamental basis of skillful tool use. Once the tool is incorporated in the body schema, it can be maneuvered and controlled as if it were a body part itself.”

Further information on this study can be found here:

Cardinali, L., Frassinetti, F., Brozzoli, C., Urquizar, C., Roy, A., & Farnè, A. (2009). Tool-use induces morphological updating of the body schema. Current Biology, 19 (12) DOI: 10.1016/j.cub.2009.05.009

Recent talks and presentations by Google engineers on Google Wave stirred up quite a bit of anxious chatter in training and education circles. Google Wave is a novel and thought-provoking development project that addresses the question “what would email be if it were invented today?” Naturally, the Google answer is a web-based application that (maybe not so naturally) resembles a chat server on caffeinated steroids. Its strengths at threaded media-rich multi-user communication is so impressive that comments on education sites started popping almost immediately on whether the LMS is doomed and if Blackboard and Moodle have finally met their matches.

Frankly, not being a big fan of the LMS, I proffer a view more like that of Godrey Parkin:

“To corporate decision-makers, the treasure map of e-learning has an island in the centre, seductively illuminated by those clever marketing folks of the learning software industry, with a big X over the Learning Management System (LMS) right in the middle. Outside of that island is blank space populated only by ‘here be dragons’ warnings.”

And Parkin continues:

“… an LMS, as available today, is not a universal solution for a corporation’s e-learning problems. In fact, an LMS is often the albatross around the neck of progress in technology-enhanced learning.”

Indeed, the biggest problem confronted by many teachers, instructional designers and trainers is how to work within the confines of the LMS. It’s a classic tale of man serving technology rather than the other way around. Parkin feels the pain as well:

“When your concept of learning is LMS-centric, you look for opportunities to implement ‘a solution’ that conforms to that concept, and ignore or marginalize all else. An LMS is, of course, a relevant tool for certain applications. If you want to track learner activities, you need some kind of system. And if you want to make use of much of the available e-course content, you have no choice but to use an LMS – not because the learning requires it, but because the established architecture of the ‘learning supply chain’ requires it.”

When all you have is a hammer, you treat everything like it’s a nail.

George Siemens at elearnspace.org puts it another way:

“Learning Management Systems (LMS) are often viewed as being the starting point (or critical component) of any elearning or blended learning program. This perspective is valid from a management and control standpoint, but antithetical to the way in which most people learn today.”

I would add that not only is it “antithetical to the way in which most people learn today” but also antithetical to the way in which most people teach. Neither side of the educational equation is true.

Meanwhile back at the issue, it takes quite a bit of effort to slog your way through the one hour twenty minute presentation on Wave and its features. It is impressive nonetheless. As noted on bavatuesdays:

“In fact, it goes a step further and makes online conference/meeting tools like Eluminate, Adobe Connect, etc. all but irrelevant, for live video and voice can’t be far behind the instantaneous chat, document editing, map embedding, video watching, presentation sharing, and on and on and on.”

Is Google to be the next international online University? Maybe. The problem though is that this is all being orchestrated by an advertising agency. The open web, with it potential for open learning, might very well be the Google version of the open web. Jim Groom at bavatuesdays goes on:

“I still have no doubt that David Wiley’s assessment is right on, especially given the API will soon be unleashed upon an open web full of developers. I know that Google didn’t re-invent the LMS quite as I joked, but what they did is actually make it all but irrelevant by re-imagining email and integrating just about every functionality you could possibly need to communicate and manage a series of course conversations through an application as familiar and intimate as email. Genius, horrifying, but genius.”

A glimmer of hope remains however. Google promises to release the software into the public domain so that anyone will be able to operate their own Wave server. The API will also be published for developers to expand upon. And, hopefully, someone will attend to the matter of content which is where all too often the process breaks down anyway.

I think it was Donald Norman in “The Invisible Computer” who pointed out that as technologies get more and more common, and perhaps accepted, they recede into the background of our lives and become invisible. Witness the electric motor in the 19th century and the microprocessor in the 20th. (How many microprocessors do you have in your life today?)

Are we witnessing a similar “technology blindness” to the web browser? Is Internet connectivity and usage so ubiquitous that average users take it for granted? A recent survey by Google, reported at TheNextWeb.com, suggests that the average American (almost 92%) do not know what a web browser is and cannot contrast it to a search engine (like Yahoo, Bing, Cuil). Whether this has ramifications on Web 2.0 and education remains to be seen.

In case you’re wondering, people are spending more time in front of more screens as sources of information and entertainment. Research conducted at Ball State University used a novel combination of technologies to monitor and measure the media Americans are using and for what purposes.

The data followed 476 participants and resulted in 952  observed days of recorded media usage. The study takes an unbiased look at what technologies Americans are using and does not delve into effects of particular media. The Video Consumer Mapping Study, as it is called, noted some surprising findings:

• TV users were exposed to, on average, 72 minutes per day of TV ads and promos—dispelling a commonly held belief that modern consumers are channel-hopping or otherwise avoiding most of the advertising in the programming they view.
• Despite the proliferation of computers, video-capable mobile phones, and similar devices, TV in the home still commands the greatest amount of viewing, even among those ages 18-24; thus, in the eyes of the researchers, appearing to dispute a common belief that Internet video and mobile phone video exposure among that group (and the next one up, ages 25-34) were sizeable in 2008.
• Rather than young people and retirees, consumers in the 45-54 age group average the most daily screen time, just over 9½ hours. The average for all other age groups is strikingly similar at roughly 8½ hours—although the composition and duration of devices used by the groups during the day varied.
• Even in major metropolitan areas where commute times can be long and drive-time radio remains popular, computing has replaced radio as the No. 2 media activity. Radio is now No. 3 and print media fourth.

• Contrary to some recent popular media coverage suggesting that more Americans are rediscovering “free TV” via the Internet, computer video tends to be quite small with an average time of just two minutes (a little more than 0.5 percent) a day.
• Early DVR owners spent much more time with DVR playback than newer DVR owners. At the same time, DVR playback was even more likely than live TV to be the sole medium.
• “Environmental” exposure outside the home, while still relatively small at just 2.8 percent of total video consumption today, could nearly double during the next few years.

A tables of results for “Average Daily Minutes of Media Consumption: Means Including Zero” can be found here.

SAGE is a free open source package designed for symbolic mathematics. It should be useful for instructors and students who need to apply tools and techniques more commonly found in programs like MatLab, MathCAD and Mathematica.

“Sage can be used to study general and advanced, pure and applied mathematics. This includes a huge range of mathematics, including algebra, calculus, elementary to very advanced number theory, cryptography, numerical computation, commutative algebra, group theory, combinatorics, graph theory, exact linear algebra and much more. It combines various software packages and seamlessly integrates their functionality into a common experience. It is well suited for education, studying and research.

The interface is a notebook in a web-browser or the command-line. Using the notebook, Sage connects either locally to your own Sage installation or to a Sage server on the network. Inside the Sage notebook you can create embedded graphics, beautifully typeset mathematical expressions, add and delete input, and share your work across the network.”