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Citizen Maths - powerful ideas in action

ImageForLinkedIn

[Cross posted, with some very minor changes, from LinkedIn.]

Since late 2012 I have been closely involved (as "project director") in the creation of Citizen Maths, a free open online maths course at Level 2. I last wrote about it here just over a year ago. 

Citizen Maths is a free open online maths resource for:
  • self-motivated individuals who want to develop their grasp of maths at Level 2;
  • employers/unions who want to provide staff (or, in the case of trade unions, their members) with a practical and flexible learning and development opportunity in maths;
  • colleges and other learning providers who want to give enrolled learners an additional or alternative route to improving their maths.

To make use of Citizen Maths, learners need access to (and knowledge of how to use) a desktop or laptop computer with a broadband internet connection.

Here's a four-minute screen-cast about Citizen Maths from a learner's point of view:

 

Who is behind Citizen Maths?

Citizen Maths is funded by the Ufi Charitable Trust. It is developed by Calderdale College, with the UCL Institute of Education, OCR, and with advice from the Google Course Builder team.

What does Citizen Maths consist of?

We’ve designed Citizen Maths to involve between five and 10 hours of study for each powerful idea. It it built up from:

  1. short “to camera” videos and explanatory screencasts, by experienced maths tutors Paula Philpott and Noel-Ann Bradshaw; 
  2. activities, tasks and other practical challenges, using
  • applets that provide an onscreen manifestation of a powerful idea
  • the Scratch programming environment
  • standard tools like pencil and paper, and spreadsheets.

There are also frequent “low stakes” quizzes to help users check their understanding.

Why “powerful ideas in action”?

Citizen Maths engages people in familiar activity to reveal the ‘maths inside’, focusing on the way that maths has an immediate relevance to the problems we all of us have to solve every day. These problems could range from comparing deals and prices on groceries and creating a household budget, to understanding a payslip, creating sales forecasts, keeping track of savings and pensions, controlling a production process, or making political judgements. By putting problems in meaningful contexts, learners who do Citizen Maths will begin to grasp the power of mathematical ideas in action.

Which powerful ideas does Citizen Maths cover?

There will be five. During autumn 2014 we ran a proof of concept trial of Citizen Maths based on the powerful idea proportion. From mid October 2015 Citizen Maths will embrace, in addition, representation and uncertainty. From spring 2016 here will be two further powerful ideas: pattern and measurement. Here's a summary of the scope and importance of each.

  1. Proportion is about mixing, sharing, comparing, scaling and trading off. It sits behind many aspects of everyday maths, for example when you are sharing out costs, or altering a mixture, comparing amounts, or scaling something up or down.
  2. Uncertainty includes making decisions, playing, and simulating. It offers a way of thinking about uncertainty in personal and work-related situations, for example when making sense of risks to health, deciding whether to take out an extended warranty, or playing card games.
  3. Representation is about interpreting data and charts, comparing groups. It recognises how much we are influenced by data and the presentation of data, for example in media reports of opinion polls, interpreting stories about health risks, or comparing our own household income to that in the rest of the country.
  4. Pattern is about appreciating structure as in tiling, or knowing how to construct such structure. Pattern focuses on how mathematics can find and describe the regularities in both the natural and the man-made world, for example in the symmetries of animals and plants or in the design of buildings.
  5. Measurement includes reading a scale, converting, estimating, and quantifying. It picks up on the importance of measures and measurement in everyday and working life, for example when dispensing medication, converting currencies or estimating the size of a crowd.

To find out more, go to https://citizenmaths.com/. There is also this Slideshare presentation:

Posted on 28/09/2015 in Moocs, News and comment, Resources | Permalink | Comments (0)

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Video and Online Learning: Critical Reflections and Findings From the Field

A terrific article by Anna Hansch, Lisa Hillers, Katherine McConachie, Christopher Newman, Thomas Schildhauer, and Philipp Schmidt.

Well, I think it is terrific, because if chimes with so much of my experience working on the design and development of Citizen Maths and FutureLearn's Assessment for Learning in STEM Teaching, and as a committed MOOC learner.

Here's the abstract:

Video is an essential component of most Massive Open Online Courses (MOOCs) and other forms of online learning. This exploratory study examines video as an instructional medium and investigates the following research questions:

  • How is video designed, produced, and used in online learning contexts, specifically with regard to pedagogy and cost?
  • What are the benefits and limitations of standardizing the video production process?

This report presents an overview of current video practice: the widespread use of video and its costs, the relevance of production value for learning, the pedagogical considerations of teaching online, and the challenges of standardizing production. Findings are based on a literature review, our observation of online courses, and the results of 12 semi-structured interviews with practitioners in the field of educational video production. Based on these findings, we have developed a set of recommendations designed to raise awareness and stimulate critical reflection on video’s role in online learning. Additionally, we discuss some need for further research on the effectiveness of video as a pedagogical tool and highlight under-explored uses of the medium, such as live video.

You can access the full paper from http://goo.gl/MvXXCs. There is also this shorter version by Katherine McConachie and Philipp Schmidt on Medium.

Posted on 24/06/2015 in Moocs, Resources | Permalink | Comments (1)

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New research on how MOOC video production affects student engagement

Just at the point where we are "going firm" on video production for the first phase of Citizen Maths, [25/8/2014 - Citizen Maths is now live and open for registrations], I come across this 10 page research report [PDF] which substantially develops some earlier findings, and which reinforces nearly all my mainly experience-based knowledge of what kinds of instructional video are most effective. (The report is oddly silent on whether there is a relationship between audio quality and learner engagement, which has always struck me as being also of crucial importance.)

The list of seven main findings:

  1. Shorter videos are much more engaging - engagement drops sharply after 6 minutes
  2. Videos that intersperse an instructor’s talking head with PowerPoint slides are more engaging than showing only slides
  3. Videos produced with a more personal feel could be more engaging than high-fidelity studio recordings
  4. Khan-style tablet drawing tutorials are more engaging than PowerPoint slides or code screencasts
  5. Even high-quality prerecorded classroom lectures are not as engaging when chopped up into short segments for a MOOC
  6. Videos where instructors speak fairly fast and with high enthusiasm are more engaging
  7. Students engage differently with lecture and tutorial videos

and seven main recommendations:

  1. Invest heavily in pre-production lesson planning to segment videos into chunks shorter than 6 minutes
  2. Invest in post-production editing to display the instructor’s head at opportune times in the video
  3. Try filming in an informal setting; it might not be necessary to invest in big-budget studio productions
  4. Introduce motion and continuous visual flow into tutorials, along with extemporaneous speaking
  5. If instructors insist on recording classroom lectures they should still plan with the MOOC format in mind
  6. Coach instructors to bring out their enthusiasm and reassure that they do not need to purposely slow down
  7. For lectures, focus more on the first-watch experience; for tutorials, add support for rewatching and skimming

are not a substitute for the report itself. Hats off to Philip J. Guo (developer of the particularly impressive pythontutor.com), Juho Kim, and Rob Rubin for doing the research, and to edX for publicising it through this short summary.

Posted on 13/03/2014 in Moocs, Resources | Permalink | Comments (0)

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Up to six minutes: optimal MOOC video length for student engagement?

Updated on 21/12/2015

Interesting brief post on the edX blog by Philip Guo about video usage, obtained from initial analyses of some edX maths and science courses. The chart below shows "median engagement times versus video length, aggregated over several million video watching sessions". What is not clear from the analysis is whether viewers of long videos may be watching them to completion in short segments. If they are, then the "up to six minutes" point is not so strong. Philip-guo-edx-first-blog-figure

 

Posted on 31/10/2013 in Moocs, Resources | Permalink | Comments (0)

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Links for two talks at ICTP and one for ETUI about MOOCs

Small edits made 16 February 2014. Small changes made to first presentation 9 October 2013

On 30 September and 1 October I gave two talks during "Science Dissemination and On-line Certification for All" at the International Centre for Theoretical Physics in Trieste. On 20 February 2014 I will do a variant of one of these talks in Brussels at a meeting of the European Trade Union Institute's Pedagocical Committee. Below are some links that are (loosely) relevant to the presentations, two of which are:  An introduction to massive open online courses [0.5 MB PDF]; and What I learned from being a MOOC learner [0.5 MB PDF].

Luis von Ahn - "Duolingo: The Next Chapter in Human Computation: Luis von Ahn at TEDxCMU 2011" - a 17 minute video about the origins of Duolingo in reCaptcha.

ALT - "Lecture capture: doing it well and at scale" - presentations, including by ICTP's Marco Zennaro and Enrique Canessa, from a conference in 2011.

JD Bernal - "Anticipating the Web - information available 'in amplitude in proportion to its degree of relevance'" - extraordinary 1939 foresight.

BIS - "The maturing of the MOOC" [PDF] - a literature review for the Department of Business Innovation and Skills (a UK Government Department).

Carnegie Mellon University - "Principals of Teaching and Learning" - a highly structured web site about learning and learning.

Donald Clark

  • "MOOCs: taxonomy of 8 types of MOOC" - 16/4/2013.
  • "Report on 6 MOOCs turns up 10 surprises" - 21/5/2013. Parsing Edinburgh University's report on its six Coursera MOOCs.

 

Continue reading "Links for two talks at ICTP and one for ETUI about MOOCs" »

Posted on 30/09/2013 in Moocs, Resources | Permalink | Comments (0)

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A well-balanced, cautious yet optimistic view about MOOCs from Keith Devlin

[Small edits made on 21 August]

This Huffington Post piece by Keith Devlin (whose Coursera Introduction to Mathematical Thinking course I completed and reported on - 1st report; 2nd report - earlier this year), hits several nails on the head, though Phil Hill criticises the piece rather bluntly for what he sees as three types of factual error.

This extract gives you a flavour of the article.

"Teaching and learning are complex processes that require considerable expertise to understand well. In particular, education has a significant feature unfamiliar to most legislators and business leaders (as well as some prominent business-leaders-turned-philanthropists), who tend to view it as a process that takes a raw material -- incoming students -- and produces graduates who emerge at the other end with knowledge and skills that society finds of value. (Those outcomes need not be employment skills -- their value is to society, and that can manifest in many different ways.)

Continue reading "A well-balanced, cautious yet optimistic view about MOOCs from Keith Devlin" »

Posted on 20/08/2013 in Moocs, News and comment, Resources | Permalink | Comments (0)

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Second report from Keith Devlin's and Coursera’s Introduction to Mathematical Thinking MOOC

Notes 1. Small post-publication edits made on 14 June to improve flow and clarity. 2. This post has been republished on the London Mathematical Society's De Morgan Forum, and as an Education's Digital Future reading by Stanford's Graduate School of Education.

About a month ago I finished Keith Devlin’s 10 week introduction to mathematical thinking course. This report supplements the one I published in April, which I’d based on my experience and observations during the first six weeks of the course.

In what follows I will not repeat the earlier report's description of the how the course worked.

Comments, questions and corrections welcome.

1. The numbers. With commendable openness, Keith Devlin reported the following data in his 3 June 2013 The MOOC will soon die. Long live the MOOR:

 Total enrolment: 27,930

Continue reading "Second report from Keith Devlin's and Coursera’s Introduction to Mathematical Thinking MOOC " »

Posted on 13/06/2013 in Moocs, News and comment, Resources | Permalink | Comments (3)

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MOOCs - achieving high quality at scale: nice quote from David Wiley

Getting on for 15 years ago I put an "Open Content" licence on the wholly online Learning To Teach Online Course in which I played a role. I'd read about Wiley and the licence in the Economist or possibly in a digital version of Time Magazine. The Open Content licence was the precursor of Creative Commons, and Wiley  is still very active and justifiably influential in this field. This post [via Stephen Downes] has an incisive observation in it about personalisation:

"There is simply no way to scale the centralized creation of educational materials personalized for everyone in the world (cf. the 15 years of learning objects hype and investment, which feels very similar to the current MOOC mania). Perhaps the only way to accomplish the amount of personalization necessary to achieve high quality at scale is to enable decentralized personalization to be performed locally by peers, teachers, parents, and others. And given the absolute madness of international copyright law there is no rights and royalties regime under which this personalization could possibly happen. The only practicable solution is to provide free, universal access to content, assessments, and other resources that includes free 4Rs [link added by Seb] permissions that empower local actors to engage in localization and redistribution."

I agree instinctively with the emphasised section, though:

  • it maybe too focused on content and not enough on the process of learning;
  • there is also a role for software-driven personalisation of various kinds, including a role for software (in a centralised rather than decentralised way) doing background organisation of things like peer-assessment or ranking and filtering of user-contributions.

Some also argue that there is great scope (I'm less confident about this) for software successfully to shape adaptively which content and which learning activities are presented to which learners, when, taking account of their past performance, in a way that gives learners to feel that their learning has been personalised.

[Links to previous posts touching on personalisation.]

 

Posted on 25/05/2013 in Moocs | Permalink | Comments (0)

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A report from Keith Devlin's and Coursera’s Introduction to Mathematical Thinking MOOC

Root2Irrational_20130329
Attempting to prove that the square root of 2 is irrational

I’m six or so weeks into Keith Devlin’s 10 week Introduction to Mathematical Thinking, along with some tens of thousands of others. [NB. I published my second and final report on the course in June.]

Here is a longish thumbnail sketch of the design of the course, followed by two appendices. Appendix 1 concerns peer review. Appendix 2 is what the course web site has to say about grading and certificates of completion.

Comments, questions and corrections would be most welcome.

1. The course is advertised as needing about 10 study hours per week. This is about right: though in my case I had to skimp a lot while I was on holiday, other than wrestling unsuccessfully with a proof that had been set as course work, the non-fruit of which is shown above.

Continue reading "A report from Keith Devlin's and Coursera’s Introduction to Mathematical Thinking MOOC" »

Posted on 14/04/2013 in Moocs, News and comment | Permalink | Comments (2)

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Ian Chowcat reviews (very favourably) Coursera's Modern and Contemporary American Poetry course

[This is a Guest Contribution by Ian Chowcat.]

When I first explored the Web back in the 1990s one of the greatest thrills I found was being able to virtually visit universities and courses across the world. Since then we have been able to download course materials and view lectures – the Open Culture site is currently listing over 700 free online courses. Now in the era of MOOCs more is promised: with unprecedented ease we can actually participate in courses run by universities the other side of the world. But can MOOCs really provide good learning experiences?

To sample MOOCs for myself I signed up for two courses from Coursera last autumn (being optimistic about course loads on top of full time jobs may well be a characteristic of would-be MOOCers). One, on models for making sense of the world, was enjoyable enough, with video lectures delivered in traditional style by a very engaging lecture, but it fell by the wayside as I became absorbed by my second choice: Modern and Contemporary American Poetry led by Professor Al Filreis of the University of Pennsylvania.

This is a cut-down version of an undergraduate course he runs. In ten exciting weeks we sampled key texts, mainly American, in modernist and post-modernist poetry, starting with Emily Dickinson and Walt Whitman and running right through the key movements until arriving at the daunting shores of contemporary language poetry, chance operations, conceptual poetry and the uncreative writing tendency stimulated by the web itself. I have no hesitation in saying that it was one of the greatest learning experiences I have ever had: I haven’t had so much fun, or felt that I learnt so much so quickly, since my BA over thirty years ago.

What made it so great? The huge passion and enthusiasm of Al Filreis himself certainly helped – passion both for the subject matter and for this way of teaching. The teaching method involved helpful short quizzes. There were four assignments, providing the chance to write brief critical essays and to try out some post-modernist poetic techniques for ourselves: these were peer marked so you also got the chance to read and comment on what other students were writing. The course forums were very lively, with 957,000 views of messages from the 36,000 students who enrolled on the course. Although the Coursera forum structure leaves something to be desired, nevertheless students across the world were hazarding their own interpretations of the poems, and passionate debates broke out whenever boundaries were being pushed further than some people could accept. There was also a Facebook page and twitter feed.

But for me what really clinched the course were the videos produced for each course reading – over 80 of them, with running lengths from nine to twenty-seven minutes. These weren’t lectures but guided discussions. In recordings of high technical quality Professor Filreis and a group of student Teaching Assistants conducted collaborative close readings of each of the texts. While the Professor nudged and cajoled, and only rarely rhapsodised, the students showed how sense and meaning could be made of even the most obscure pieces – and there were many of those in this course (Kenneth Goldsmith’s presentation as poetry of a transcription of everything he said for a week provoked the most virulent debates and was the breaking point for many. But then modernism was always meant to be about aesthetic appreciation of the everyday).

I am convinced that this was a course in which co-creation between students and pure peer to peer learning would not have sufficed: the forums and peer assessments were great vehicles for testing out our interpretative abilities, but in themselves would not have provided the grounding that was needed to make progress. Nor would lectures have done the trick. It was the vicarious learning involved in seeing students being guided to fumble their way towards sense-making that gave participants like me the encouragement that the enterprise was possible, and the tools for being able to go on independently both during and, crucially, after the course. Without this I would have been where I started: struggling alongside others in the same position to make any inroads on the seemingly impenetrable. Lectures would have provided guidance from someone who had been down this path over many years, but the real trick was to link the two: to show in practice how beginners could be guided to develop and use the necessary approaches for themselves, and in so doing to become engaged ourselves in interpretative activity.

As a result I feel whole new worlds of literature have opened up to me which were previously literally closed books.

While difficult texts have not become magically easy I can now see a path to understanding. The main downside has been the damage to my bank balance due to the compelling need to invest in several shelves of new books.

In the current ferment of debate over MOOCs many doubts are being expressed about their pedagogical model and their quality. All I can say is that here is one instance in which a MOOC provided the occasion for what I think was a first rate learning experience. Perhaps this model of vicarious collaborative learning is one that others could follow.

The course runs again this September: check it out if you have any interest in the world of experimental contemporary poetry. It’s currently free, of course, though if there had been a donation box on the way out I would gladly have paid. You can find an overview, with links to some other participant views, at https://jacket2.org/commentary/modpo-overview and there is a link there to the course home page where you can sign up.

Posted on 17/03/2013 in Guest contributions, Moocs | Permalink | Comments (0)

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