Capacity focus, 55f: Using the Bloom mastery learning concept as an approach to renewing education using digital technology in the Caribbean

(Two Sigma/Digital learning transformation series
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 )

As we continue to reflect on how to transform learning effectiveness in our region, I think we now need to make up our minds on a values issue.

For, while it has been thought in some quarters that a mastery-based learning approach can be disruptive to the easy scheduling desired in organising school curricula and timetables (making it seem to be not worth the associated problems . . . ), the differences in potential degree of success bring to bear a justice issue. 

For,

 if we have a cluster of interventions that credibly can reliably convert a C-student into an A-student by changing how learning is delivered,

and if we have digital means to do so cost effectively,

then we owe it to our young people to properly equip them for success,

especially in core areas like Math and English, as well as basic science and computing.

Where, we do have just such, and yes, I am going to use the slide on the two-sigma challenge again, to drive the point home hard:

Just so, we also should recall (courtesy Wikipedia) the component interventions that go into that C- to - A jump:

Effect of selected alterable variables on student achievement.
Adapted from,^[6] Walberg (1984).

Object of change process	Alterable variable	Effect size [+ sigma value]	Percentile equivalent
Teacher	Tutorial instruction	2.00	98
Teacher	Reinforcement	1.2
Learner	Feedback-corrective (Mastery Learning)	1.00	84
Teacher	Cues and explanations	1.00
Teacher, Learner	Student classroom participation	1.00
Learner	Student time on task	1.00
Learner	Improved reading/study skills	1.00
Home environment / peer group	Cooperative learning	0.80	79
Teacher	Homework (graded)	0.80
Teacher	Classroom morale	0.60	73
Learner	Initial cognitive prerequisites	0.60
Home environment / peer group	Home environment intervention	0.50	69

As was previously noted, the highlighted block of key interventions suggests that we can get much of the effect of 1:1 tutoring through a more interactive, rich feedback approach that reinforces learning step by step and provides opportunity for mastering and for remediation as necessary to fill in gaps. Indeed, the logical inference on the effect of 1:1 tutoring is that it is not so much an independent cause of the dramatic improvement, but that it trends naturally to promote several of the factors below it in the table, which leads to a dramatic cumulative effect.

We know that competence or lack of it in the core areas makes a big difference to the potential career options of pupils in school, and that cumulatively, this can make a big difference to development.

So, I now argue that we must try, and must find a way to provide the resources to support educational transformation in these core areas.

First, we need to pause and show a way we can reasonably assess performance in ways that could feed into the sort of statistical scoring scheme above:

A six-point criterion- of- performance based item grading scheme (to be used with multiple items to gain precision*)
Score	Short descriptor	Performance level description
5 or A	Excellent/ Very Good	Nominal or exceptional performance, showing good knowledge base, good solution, good insights with no significant defects
4 or B	Good	Good knowledge, insight and solution strategy, but with minor gaps or defects in the solution
3 or C	Fair	Acceptable knowledge, insight and solution strategy leading to a workable solution, but with significant gaps or defects
2 or D	Poor	Major gaps or defects in knowledge, insights or solution strategy, leading to an unworkable solution, or “on the right track” but too incomplete to be a fair attempt
1 or E	Very Poor	Critical and crippling gaps in knowledge, insights or solution strategy, or utterly wrong approach, or barely attempted and very incomplete
0 or F	No attempt, or disqualified	Not attempted or no significant attempt that moves beyond given information, or disqualified for cause
* If we let +/- 0.5 on the scale be 3 sigma [σ], σ ~ 0.2 or variance, σ2 ~ 0.04. Thus, since variances add in a chain, it can be shown that for n assessed items the actual error range will go like +/-[10%/ sqrt(n)]. For five items, that is +/- 4 – 5%, for ten, +/- 3%. In cases where 0 to 5 in steps of 1 is too coarse, this can be used as a first ranking then finer points can be inserted within the bands. Of course, the scores and criteria assigned are scaled so that acceptable but significantly flawed performance will get a 3. The implied pass-point is 2.5, the inferred margin between fair and poor performance. The scheme can be adapted to cases where the bands for grades should be unequal, e.g. where we can justify and want to make fine distinctions in any given band.

Next, let us sum up the mastery-based learning approach, to clarify what we are talking about.

Laura Candler has a neat, teacher's perspective, summary (that of a Math teacher):

Mastery Learning is an instructional philosophy based on the idea of giving students more than one chance to demonstrate mastery of content and skills. In a Mastery Learning classroom, as in a traditional classroom, students receive instruction on a topic and then take a test to determine their level of understanding. But that's where the similarity ends. In a Mastery Learning classroom, the teacher scores that assessment and determines who has mastered the content and who needs more help. Students who have mastered the material are given "enrichment" opportunities, while those who have not mastered it receive additional instruction on the topic. The new instruction is presented in a different way, perhaps using manipulatives or other hands-on approaches. After a day or two, a retest is administered to the group who did not demonstrate mastery. In my experience, most of the students who didn't master it the first time are able to achieve mastery on the second test. There are many benefits of using his model, but the most important one is that all students can learn and grow, and no one is left behind. Every time you begin a new unit of instruction, you can feel confident that your students have mastered the concepts needed to embark on new learning.  [NB: It is well worth looking at Ms Candler's "Math Facts" workbook sampler here. Want of sound knowledge of addition/subtraction and multiplication/division tables often has a significant role in breakdown of Math capacity.]

 We have already seen a simple flowchart:

However, it will be useful to go into a bit more details (integrating other key points), and to address what happens with those who seem to have major problems:

 

Here, we see that at intake to a unit a student should be profiled to identify his/her knowledge state. This may show that a student is ready to learn, or may show that a student is in need of significant specialist attention. Perhaps enrichment is indicated. It may also show that the student is beyond the learning scope for the unit in question and should go on to something else.

Already, we are seeing a place for individualisation of learning emerging.

Similarly, it would be advantageous to have the diagnostic assessment being explicitly based on an identified knowledge space that defines the scope and ordering of learning states; as was discussed previously.

We then see the significance of the IDEAS approach to presentation, and the significance of the learning activities spiral approach, in light of key case studies and themes that incrementally build capacity:

 Another useful idea is the concept of the CPA approach to inducing concept formation:

C -- Concrete hands-on activities and interactions first

P -- Pictorial representations to help form concepts based on the concrete exposure

A -- Abstract procedures, processes and symbols that build on the pictorial representations

(I suspect that the use of good pictures can help provide scaffolding for those struggling with algebraic representations or the like extremely abstract topics. Indeed, the algebra tiles representations mentioned here -- home made version here (software, here) -- may be helpful even with Algebra!)

The reader will notice that I also stress the use of projects as ways to individualise learning as well; which are dandy for enrichment too. When you have to do something significant and for preference practical with learning, it can teach more, more powerfully than anything else. It is also a major confidence booster, and to have a project as part of a portfolio of learning achievements is also very helpful. Nothing proves that you can do X better than having demonstrably done it!

You will also see that I am stressing the presence of back-up where people who have major learning problems can get help. That too, as a justice matter, should be part of our curriculum planning.

But, where does digital technology fit in?

Everywhere.

A well laid out course should incorporate all of these elements in structured learning frames that embed a case structure designed in light of the structure of the knowledge space identified with expert inputs, frames that also access powerful multimedia learning resources. If we do the job right, no tutor will be better able to more patiently help a struggling child, meanwhile flagging that child for assistance from the teacher -- now more a learning coach and facilitator than a sage on stage to do chalk and talk games and to wield the magical red ink pen for marking.

So, why should we not use digital course organisation and presentation technologies such as Moodle, Xerte, eXe and so forth?  Would not that allow us to use our best, most effective teachers as presenters accessible on demand as needed by students anywhere, anytime? Doesn't that release the teacher to be a coach and facilitator who manages learning and helps adapt to the individual needs of students? And, so forth?

Couldn't we argue that our universities and partner institutions including poverty relief development agencies, as well as private enterprise, civil society and government all have a vested interest in solving this major area of problems with education in our region?

Why not find some territories willing to be pilot projects then develop, improve and scale-up? Why not have a regional cyber campus that supports primary and secondary studies over the Internet backbone across the region? Why not have a digital lending library and e-textbook and learning resource retailers on the same backbone? Why not do even more than that?

I am also highlighting the potential of the 7" Android tablet in a folio with a built in keyboard, as a key learning device (and such units should be in the US$ 120 or so range within a year -- actually, if we are willing to accept resistive touchscreen -- stylus, not finger -- technology, we are already there):

Of course, this calls for a major development effort.

The logical foci for this are primary and secondary level core subjects:

Maths
English
Basic Science
Computing
Civics

Why not let us do a regional initiative for these, up to and including second chance secondary education efforts?

So, now, let us think on this for now. DV, more later. END

Capacity focus, 55e: Remedial -- and perhaps first time through -- Mathematics in light of the Knowledge Space Theory concept of Jean-Paul Doignon and Jean-Claude Falmagne (A second possible application of the spiral, individualised window of learning opportunity approach)

(Two Sigma/Digital learning transformation series 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 )

 With Tropical Storm Isaac moving on after a side-swipe, let's return to the question of renewing our approach to education. In this case, for Mathematics, this is under the shadow of shocking regional CXC results this year [looks like about 33% overall passes . . . ], which (HT: reader "X") have excited sharp comments in several quarters.

To begin, let us first extend the Vygotsky Zone of Proximal Development -- window of learning opportunity -- concept. We can do this, based on aspects of the pioneering work of Jean-Paul Doignon and Jean-Claude Falmagne who in the mid 1980's introduced the concept of Knowledge Spaces and the linked idea of the knowledge state of a given student identifiable though the concepts and skills he has mastered and/or is ready to now master by building on what s/he already has learned.

For instance:

Or, in more details of the algebra section from a knowledge space map (of 397 problem types) of Arithmetic, and Algebra up to pre-calculus level, where (a) and (b) are from the same table:

{U/d Aug 24} This can be set in the wider context pioneered by Singapore, i.e the Pentagonal Mathematics Knowledge, Attitudes & Skills Framework:

The overall knowledge space (which is a requisite for identifying a learner's knowledge state at any given time, thus also to monitor progress) can be compiled by various techniques. Wikipedia summarises usefully:

there exist several methods to construct knowledge spaces. The most frequently used method is querying experts. There exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions.^[6][7][8]

Another method is to construct the knowledge space by explorative data analysis (for example by Item tree analysis) from data.^[9][10] A third method is to derive the knowledge space from an analysis of the problem solving processes in the corresponding domain.^[11]

 These techniques can get highly mathematical and quite complex (with very interesting bits of applied set theory and even more fascinating possibilities for algorithms), of course. 

But such complexity -- through clever programming and attractive interfaces -- can be hidden behind the interface to a computer application suite that can identify the knowledge state of a given learner, allowing for individualised curricula. (This can obviously be extended to in effect any subject, but it probably makes sense to focus on the "core of cores" in the curriculum where our region is struggling, Math and English.)

For example, we may look at the ALEKS commercial application. (Video preview here. Note tour here and available courses here.) 

I have found a teacher's guide to ALEKS here at Youtube:

(NB: Do, forgive the fuzzy screen-cast. However, the branching or "case" structure slide show with interactions/activities approach should be clear enough, and this is right up XERTE's street. It is also obvious that the sort of screen-capture explanations that the Khan Academy specialises in or video demonstrations or even exercises with teacher-developed "shoebox kits" of hands-on experimental objects with instructions could easily be incorporated (or of course, various Math kits -- I am partial to the Calvert School's store resources), making for a very rich, stimulating and interactive, individualised learning experience. There is plainly a very large base of pre-loaded problems in the program, and maybe a problem-generating engine. BTW, there is a special module for getting what Americans call "Math Facts" -- addition/subtraction and multiplication/ division solidly learned. I suspect, that is one underlying problem. I like the visualisations provided by Autograph for Maths, from the UK.  Boardworks (also from the UK) provides some very useful resources keyed to interactive classroom whiteboards [not as "hot" as the Autograph ones but quite useful], and covers a wide range of GCE type syllabi at O and A levels, but is a bit expensive.)

Such an application could of course be integrated with the same kind of multimedia seminar room previously discussed:

ALEKS, of course, is keyed to the American educational system, so it is not directly relevant to CXC-type syllabi. And, while the CXC syllabi are not available online (apart from, by purchase of a print copy), the approach is close enough to that of the UK-based Cambridge GCE Math D syllabus 4024 (June 2014) -- notice, one paper is no-calculator, the other permits calculators, a "scientific & trigs calculator" being strongly suggested -- that we can draw close parallels:

CAMBRIDGE GCE MATH D:

1: Number
2: Set language and notation
3: function notation
4: squares, cubes and matching roots
5: Directed numbers (+/- values)
6: Vulgar and decimal fractions and percentages
7: Ordering by magnitude and relationships:  =, ≠, >, <, 
8: Standard (scientific) notation
9: The four basic arithmetic operations with precedents (BOMDAS)
10: Estimation and rounding
11: Limits of accuracy
12: Ratios, proportion, rate
13: Percentages
14: Use of a calculator
15: Measures
16: Time on 12 and 24 hr clocks
17: Money, including conversion
18: Personal and household finance, including tables and charts, profit/loss, simple interest
19: Graphs in practical situations (including kinematics of speed & distance)
20: Graphs of functions
 21: Straight line graphs, y = mx + c etc
22: Algebraic representation and formulae
23: algebraic manipulation
24: Laws of indices
25: Solving equations and inequalities (Linear, fractional and quadratic)
26: Graphing inequalities (Linear programming NOT included)
27: Basic geometrical terms, figures & relationships
28: Geometrical constructions
29: Bearings from 000 to 360 degrees
30: Symmetry
31: Angles
32: Loci
33: Mensuration (esp. for basic figures)
34: Trigonometry (not solution of identities)
35: Basic statistics (Not inferential)
36: Basic probability
37: Basic matrices (inversion is of 2 x 2)
38: Transformations in the XY plane (2 x 2 matrices)
39: 2-D vectors (but not extensions to complex nos!)

This isn't Grandpa's maths!

The simple listing of topics shows how complex and hierarchical the modern type of Math syllabus is, and how demanding it is of understanding. 

For instance, you cannot apply matrix transformations without understanding simultaneous linear equations and how one gets to a matrix and matrix operations from such. In addition, one would need understanding of how a matrix applied to a vector transforms it into a different one, thus leading to transformation of a figure in the plane. (This is connected to Computer Graphics. BTW, extending to three dimensions, a 3-d rotation matrix allows us to deduce the look angle for pointing an antenna at a satellite in geostationary orbit 23,000 miles up, over a point on the Equator. As an be imagined, many transformations used in computer graphics are based on matrices. Matrices are also intimately involved in many aspects of science and engineering, e.g. in modelling circuits and -- extending to mathematical operations and transforms, in the state space approach to control systems.)

 The low performance of many students is thus not hard to understand. 

Moreover, given the hierarchical pattern of the knowledge space with ever so many dependencies from one capacity to the next and onward, once a child falls behind, it is easy for the child to be run over, and left ever further behind, lying and bleeding in the rear view mirror.

We have to break this cycle, and worse this needs to be in a situation where we have to recognise -- per Piaget and others -- that not all students mature to a level of mental capacity that they can handle abstract mental concepts and formal operations at the same general time. The point that this may well be in part biologically linked, similar to puberty (which obviously happens at different ages for different children) then introduces a justice issue. 

Yes, a JUSTICE issue.

Mathematics capacity is not only critical to access many of the professions that are critical to national and regional progress, but also to access careers that have high upward social mobility.

So, it is simply not good enough to use correctable gaps in Math knowledge as socially loaded filters that lock out people who will disproportionately come from and be relegated to lower social strata, and of course, girls.  

That is, as a matter of justice, we need to think out ways to help our children master and credibly document mastery of a critical core of mathematics for development, especially at secondary level  -- including second chance secondary level . . . that flunked out 60 - 70% should not be simply written off -- and to open gateways for extending the "mastery of Math" knowledge base across time as people who were hampered by their previous level of development gain enough capacity to master abstract concepts and skills. 

I suggest, first, that this is possible on a modular stage by stage spiral basis that allows for individualisation of learning paths and styles based on the power of modern digital technology:

Clearly, units of instruction should have a heavy diagnostic component, and should then address individual cases through targetted skills building. The knowledge space and knowledge state concepts above are perfect for this. 

Also, the approach offers an obvious shift: FROM grading relative competence on a standard one-size-fits-all syllabus, TO a cluster of learning modules, where what is developed, assessed and put in the portfolio of learning is a growing list of demonstrated, mastered content and skills. That way, students move away from a one-point grade assessment to a profile of competencies that are linked to important areas of achievement.

Computer technology allows this to be done, and thresholds can be identified and listed as a sequence of grades of achievement relevant to onward studies or job requisites.

Where also, we need to remind ourselves of the statistics that say that even in advanced societies, only about 30 - 35% of adults are fully capable of abstract operations:

There is a body of evidence that even in advanced countries only about 1/3 of adults achieve abstract operations capability

It is helpful to give an idea of what the identified Formal Operations are about. Saul McLeod of Simply Psychology gives a good clip:

The formal operational stage begins at about age 11. As adolescents enter this stage, they gain the ability to think in an abstract manner, the ability to combine and classify items in a more sophisticated way, and the capacity for higher-order reasoning.

At about age 11+ years, the child begins to manipulate ideas in its head, without any dependence on concrete manipulation; it has entered the formal operational stage. It can do mathematical calculations, think creatively, use abstract reasoning, and imagine the outcome of particular actions.

An example of the distinction between concrete and formal operational stages is the answer to the question “If Kelly is taller than Ali and Ali is taller than Jo, who is tallest?”  This is an example of inferential reasoning, which is the ability to think about things which the child has not actually experienced and to draw conclusions from its thinking.  The child who needs to draw a picture or use objects is still in the concrete operational stage, whereas children who can reason the answer in their heads are using formal operational thinking.

For instance, a child in the formal operations stage can "easily" design a systematically structured simple experiment (such as to explore the parameters that govern the back-forth swinging of weights suspended from a hook using a string of adjustable length -- pendulums) without detailed step by step concrete instructions. That is because such a child can think abstractly about scientific methods, laws, possible consequences, and the like. But, without step by step "scaffolding," probably detailed sketches and maybe a live demonstration, a child not yet at that level will be likely to flounder.

Indeed, I suspect that for many children in our region, doing math boils down to learning by concrete example how to do a Type X1 problem, then an X2 and an X3 etc. Throw in a similar Type Y that if the underlying principle is understood it can be solved easily enough (but is not directly comparable to the Type X's), and they will flounder and likely get stuck.  And maybe that is where Skemp's contrast of instrumental and relational understanding as raised earlier in this series comes in:

It was brought to my attention  some years ago by Stieg Mellin-Olsen, of Bergen University, that there are in current  use  two  meanings  of  this  word.  These  he  distinguishes  by calling  them  ‘relational  understanding’  and  ‘instrumental  understand-ing’. By the former is meant what I have always meant by  understand-ing, and probably most readers of this article: knowing both what to do and why.  Instrumental understanding I  would  until  recently  not  have regarded as understanding at all. It is what I have in the past  described as ‘rules without  reasons’, without  realising that  for many pupils  and their teachers the possession  of such a rule, and ability to use it,  was why they meant by ‘understanding’ . . .

 So even words like "understanding" may have pitfalls in them.

However, it is worth following McLeod to the next step on possibilities for helping those who are ready make the leap:

Robert Siegler (1979) gave children a balance beam task in which some discs were placed either side of the center of balance. The researcher changed the number of discs or moved them along the beam, each time asking the child to predict which way the balance would go.

He studied the answers given by children from five years upwards, concluding that they apply rules which develop in the same sequence as, and thus reflect, Piaget's findings. Like Piaget, he found that eventually the children were able to take into account the interaction between the weight of the discs and the distance from the center, and so successfully predict balance. However, this did not happen until participants were between 13 and 17 years of age. He concluded that children's cognitive development is based on acquiring and using rules in increasingly more complex situations, rather than in stages.

 Since we have things like autistic savants that can do astonishing things in a few areas but are otherwise often severely retarded and even very capable and "bright" people have gaps in capability, perhaps, we need to adjust. Perhaps, there is a progress in stages and in particular areas, and as we reach a critical mass, there is a transformational "jump," an aha reaction. Where, a very encouraging and stimulative environment encourages not just assimilating new experiences to old conceptual and operational schemas in our minds, but accommodating to new experiences, promoting transformation of our thinking. Where also hands-on, minds-on activities/exercises and rich visual and verbal stimulation as well as talked- and- walked- through examples led by people who truly understand what they are doing themselves, can obviously make a big difference.

Certainly, for example: for me music is a mystery, one that I deal with in a very concrete way. 

I can understand the physics and the system of harmonics [I keep wanting to pull out an oscilloscope and plotting waveforms and Fast Fourier patterns then 3-d waterfall plots . . . ], but don't ask me to understand the stuff of artistic composition and the difference between styles, much less the technical terms that apply. I suppose, with a major effort and the sort of supportive scaffolding I could learn, but I suspect my time would be better applied elsewhere if this is going to require a major sustained effort to study.

But, if someone could figure out a way to turn learning music into an entertaining and interesting game . . .  

(Hence, the question of the power of entertainment in education, for good or ill. But also, we have to develop the discipline that sees that if something is important enough, "that's boring . . . " is not good enough to walk away or refuse to put in the requisite effort. Learning is often an acquired taste, and we need strong motivation to make the effort and bear with inevitable drudgery and frustrations. Oh, how I remember working through dozens and dozens of math problems per week, set by a Math teacher who believed in homework and "the Hobartian method of self-correction." That is, we were expected to work through solutions with the teacher -- and, often enough, selected students called on to report from their seats or sent to the board to show how they did the exercise -- and do the corrections for our own homework. Sometimes, if memory serves, we were then called up to have a look at our self-grading, one at a time.)

Back to the math issues . . . 

It seems to me that we may be trying to do too much for most children with one common "one size fits all" syllabus, and may be unfairly labelling other syllabi that do not so sharply depend on mastering a large cluster of heavily abstract operations before giving any certification of achievement, as "inferior."

As labels for children who are dismissed and dumped as failures coming out the starting gates, in short. 

It may, then, well be appropriate for us to develop a more modular approach to mathematical competence certification and provision to add in modules as one moves along. 

Surely, that could be more promising than doing an all or none lumped certificate, where also -- given the huge diversity in the topic outline as listed -- modules can be adapted to where children are heading, career-wise. And, maybe we could make provision for students to build up a profile of performance across time, adding further modules to a higher grade of certification?

(Perhaps, too, the modules could be keyed to a half-term length "standard" unit. That would help us do the plug-n-play game that is so helpful with planning and management. )

Why not distinguish numeracy and math, and focus numeracy on hands on, concrete object oriented math for the world of basic "practical" practice, where we work with concrete objects and related quantities that we can measure or observe directly? 

Then, perhaps a core numeracy could be covered up to about 3rd form, and thereafter we have diverse math programmes for different people, with modularity to fill in gaps as required?

But then, I must defer to those whose educational expertise is in Math, in the end.

Having said something about possibilities, we have to deal with the present reality for the time being. 

Remember, 2/3 of those just sent to sit math in our region "failed." After five years of secondary education.

That sort of "rejects" rate is intolerable.

As a first step, we need to move up to a better level of capacity to build understanding and competence, step by step. The first requisite for this would be accurate assessment of knowledge state in knowledge spaces on a regular basis and the creation of well thought through sequences of units of study, using software. (The ALEKS model could be a guide, but there is no reason why we cannot develop our own.)

This could serve in the first- time- through setting, but would obviously be more oriented to the remedial setting.

In this case, a knowledge state diagnosis would logically lead to an individualised sequence of units tailored to the needs of the learner, his or her readiness to handle abstract concepts and formal operations, and the like. One thought is that it may well be worth exploring the power of visualisations that help students to see what they are dealing with, and of course, experience with concrete and realistic cases will also help.

(My dad, in chatting with me about the upcoming storm, reminded me of a young man -- now a Math teacher -- who hated co-ordinates until he visited our home when there was a leak in the roof. By counting numbers of tiles out from the walls to give the location of the leak, we could tell the workman just where to patch. The light bulb went off as the young man realised this was a co-ordinate reference. He went on to major in Mathematics and to minor in education, and is now a Math teacher.)

So, let us see what is possible to begin a better approach to math education, first time through and remedial. More next time. God bless. END

Matt 24 watch, 167: Media discussions on a possible Middle East war with Iran and its proxies

The tensions are again ratcheting up in the Middle East, with talk of a month-long conflict involving an Israeli strike against Iran and conflict with several Iranian proxies neighbouring Israel.

According to the video below, this could involve hundreds of missiles striking Israel per day, and perhaps five hundred or more Israeli dead. And, with the 1973 war as a picture, oil could spike with its price maybe doubling or quadrupling, which we in the Caribbean need to think about very carefully indeed:

Grim news, and let us pray that good sense will prevail so we will see a stepping back from the brink. 

In particular, surely the Iranian leadership must know that a credible threat or actual use of nukes -- however disguised -- would obviously leave Iran as a smoking, glowing pile of slag within hours. And, once Iran nears such a capacity, Israel -- on the track record of 1967 and in light of the repeated genocidal threats made by Iranian leaders -- will definitely strike, strike as hard as it deems necessary and willingly accepting even appalling losses in return as the alternative they see is genocide. And, they will be grimly determined that a bad press or even global pariah state status is better than a good eulogy.

(We should all remember that Israel's credible capacity includes sea-launchable cruise missiles, with 1,500 km range. With all that that implies. Where also, Iran's leaders have shown a bellicosity that takes the sort of mutual deterrence that stabilised the Cold War situation for decades off the table. Israel obviously cannot afford to allow Iran to deploy nukes, and -- just using basic common sense -- it plainly will not.)

The path to nukes Iran has pursued since the 1980's cannot possibly come to a good end. 

It is therefore high time that Iran's leaders re-thought their policy, and turned away from patent folly. 

Let us pray to that end. END
______

U/D: Read Here.

Capacity focus, 55d: A specific application -- could a multimedia seminar room serving as language lab help with English Language remedial studies? What about multimedia-ready Tablet and Notebook or Netbook PCs?

(Two Sigma/Digital learning transformation series 
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 )

All across the nominally Anglophone Caribbean, English Language competence is a bugbear. 

Sometimes, even, among those who have passed their CXC's or the equivalent. 

So much so, that a key institution-based reader of this series has raised the question of using the ideas we have been discussing to address English Language remediation.

I think the key to this will be our confidence that with high interactivity, good feedback and a structured individualised mastery learning approach, we can see dramatically superior outcomes approaching that of the ideal 1:1 interaction Bloom raised in pointing to the two-sigma problem, as we have been discussing since the beginning of this series. 

Let us remind ourselves again, as the point Bloom brought to our attention is so revolutionary, so counter to our pre-existing notion that we have the "bright," the "average" and the "dunce" that we are prone to let it slip or to dismiss it:

In short, twenty-five years ago, Bloom -- you do not get more eminent than that in education -- and his colleagues showed that by shifting to the highly interactive, individualised, responsive approach that occurs naturally in a 1:1 tutorial setting, learning outcomes are so improved that a C student moves up two-sigma to being an A student and 98% are now passing. So the real challenge is to cost effectively capture the learning effectiveness gains in an affordable way. 

For that, I argue that modern multimedia computer technologies offer us a major opportunity. 

And, that is how I propose to tackle the specific challenge: mastering the artificial but important Standard English dialect, for "typical" reading, writing, listening and speaking tasks.

The main root of this challenge, of course, is that our street and home-level language experience is dominated by local, predominantly oral dialects that emerged over the course of our history. Nor should we neglect the slang and other informal varieties of English that come to us in ever so many ways on the street, including through popular music.

So, we need to start where we are, and find an individualised path to adequacy based on mastery of step by step tasks, each of which must be within reach. Where, obvious key themes include:

a: Understanding how our region's history has led to the various dialects of English that we experience, and how that can interfere with mastery of the Standard one. (And, I insist, Standard English is just another dialect.)

b: Appreciating why Standard English emerged as a reference variety and why it is so important in commerce, media, education, work, service and life. Namely, that standards are in-common.

c: The use of standard English in speaking and listening situations.

d: The use of standard English in text-oriented situations for reading, writing and spelling acceptably.

e: The use of standard English in public speaking, presentations, multimedia and traditional media.

f: Vocabulary, word power, problem-solving effectiveness and intelligence: words are major tools of thought and communication, so if we do not master them we can neither think nor communicate effectively.

g: Life-long learning of English: learning to be our own personal English tutors.

h: Etc.

There are two obvious technological interventions. 

First, the tablet and the netbook or notebook PCs are now routinely multimedia-capable and are capable of wireless web and local network connectivity, so they can serve as miniature language labs.

That potential is important, especially if we have headphones with boom-arm microphones [as we may use for a voice Skype chat session], keyboards and track-pads or mice etc. If the computing device has an SD card slot or the like, that allows for plugging in a module that can host software, creating a miniature "web" right there on the PC, maybe in a game-like environment or with slide show style lessons. (Smart phones will have a somewhat similar capability but will be much less standardised.)

The second possibility is to develop and use a web-connected, multimedia seminar room as a language lab. (I think as well, such a facility can serve as a lab for Mathematics, Technical Drawing and Design, basic Electronics and interfacing-control, basic Multimedia production, etc.)

A suggested layout is:

This suggestion is based on a facility I designed some years ago, and is meant to balance individual work with working together in small groups or as a whole group. Notice, it naturally allows oversight and supervision of work at a glance from the open end of the U. Some consideration should be given to using fairly thin clients for the student work stations on the U (but these should have SD slots that allow personalisation and boost capability). And of course, wireless capacity should be built in.

 The Cambridge GCE 1123 2014 English Language Syllabus -- the CXC syllabi are not accessible online -- gives us some idea of typical objectives for modern High School English courses:

A qualification in this syllabus demonstrates to universities and employers that candidates can communicate effectively in Standard English through:

•   communicative competence: the ability to communicate with clarity, relevance, accuracy and variety
•   creativity: the ability to use language, experience and imagination to respond to new situations, create original ideas and make a positive impact
•   critical skills: the ability to scan, filter and analyse different forms of information
•   cross-cultural awareness: the ability to engage with issues inside and outside own community, dealing with the familiar as well as the unfamiliar.  (This is not an assessment objective but forms the context of writing tasks and reading passages.)

 This is turned into assessment objectives:

Reading 

R1   Understand explicit meanings, through literal and vocabulary questions.
R2   Understand implicit meanings and nuances of language, through inferential questions and questions on writer’s craft.
R3   Scan and analyse text, by identifying and summarising required information, such as similarities and differences, or advantages and disadvantages, or problems and solutions, or causes and effects, or
actions and consequences.
R4   Identify and respond to main ideas of a text, such as follow a sequence or argument, identify conclusion, distinguish fact from opinion, and give a personal response to a theme in a text. 

Writing

W1  Communicate appropriately, with a clear awareness of purpose, audience and register.
W2  Communicate clearly and develop ideas coherently, at word level, at sentence level and at whole text level.
W3  Use accurate spelling, punctuation and grammar.
W4  Communicate creatively, using a varied range of vocabulary, sentence structures and linguistic devices.

It is immediately obvious that listening and speaking (including e.g. on the telephone!), presenting and the like are not being assessed. I understand as well that, say, the CXC syllabus does include an emphasis on typical writing/reading situations such as personal or business letters, a job application, a magazine article, a semi-popular technical article, etc. CXC also includes a basic critical thinking unit. Given the institution in view, I think Bible reading, research and study skills would also be relevant as a build-on extension to critical thinking skills.

Grammar, spelling and the like are not emphasised, but may be important for those struggling with the difference between our regional dialects and the standard one. I am partial to the Reed-Kellogg diagramming approach (cf. also here and software here; [NB here on the subtle complexities in so "simple" a sentence as "See Spot run"] )to learning the structure of sentences and to understanding the various ways words communicate.

For the sheer joy of it, let me bring you (HT: Cecil Adams) a sentence diagram for See Spot Run:

 
In balance to this, Kitty Burns Florey has a few choice comments in a NYT article:

What does diagramming sentences teach us besides how to diagram sentences? I would answer: It teaches us a lot. First of all, it illuminates points of grammar. When constructing a diagram, we focus on the structures and patterns of language, and this can help us appreciate it as more than just a vehicle for expressing minimal ideas . . . When we unscrew a sentence, figure out what makes it tick and reassemble it, we interact with our old familiar language differently, more deeply, responding to the way its individual components fit together. Once we understand how sentences work (what’s going on? what action is taking place? who is doing it and to whom is it being done?), it’s harder to write an incorrect one. Diagramming is basically a puzzle, and — as we all know in this age of Alzheimer’s awareness — puzzles keep our brains working. An attempt to tame a really complex sentence can oil your brain, twist it into a pretzel and make it do back flips.

(A truly spectacular case in point is given, so do click on the link!)


For key specific instance: in the Caribbean, we often have major problems with subject-verb agreement and with tenses.

Vocabulary building and spelling challenges are important, also. 

This points to a place for vocabulary building reading and writing exercises and the provision of a spelling skills/dictionary access feature. (The utility of the dictionary is an excellent way to teach the value of correct spelling. And, yes, there may be an attitude challenge here. [That brings in the Bloom et al Affective Domain.)

Similarly, there is a major challenge with constructing written compositions and speeches, including the mystery of creating successive paragraphs.

As an aid, I suggest an extension of the classic introduction- body- conclusion format, one informed by the canons and principles of persuasion used in Rhetoric. Here, I of course emphasise Quintillian's ideal for persuasive communication: the good man, speaking well.

Or, writing -- or, presenting - well. (And, it is not just men . . . )

I suggest an extension to the classic 123-IBC approach (more details here):

1 --> INTRODUCTION:

Lead: The first thing you want to bring to the attention of the audience, to draw and hold attention, winning favourable or at least respectful attention.

Focal point: The main point you want to make or issue you want to address

Bridge to body: moving into how you are going to give supporting details, facts and reasoned argument. This may include an outline of what is to follow.

2 --> BODY:

In the body, the case in the main should be laid out, and anticipated objections countered. The main detailed points, are laid out in paragraphs with connectives that bridge from one to the next forming a smoothly flowing chain. A paragraph, being a unit of thought that starts from the communication situation in view if it is the opening one, or follows on from what preceded in the course of the communication, makes one main point that adds to the communication, and bridges to the next, or else draws the conclusion. (Cf. suggestions for teaching paragraph-writing skills here on.)

3 --> CONCLUSION:

Summing up the case and again making the main point, inviting a response explicitly or implicitly.

(I think that Lincoln's Gettysburg Address is an excellent case study, from a speech that is also a short newspaper-type opinion piece and essay that is ranked with The Sermon on the Mount for sheer impact. Of course, case study no 2, for the more extensive discourse, would be the famous sermon. And, for the more academic level of writing, I would point to Luke's opening remarks in the first four or so verses of his Gospel (in the context of the first several chapters), as a classic on how to make a thesis in a delicate situation and then begin an argument.)

To develop the content, I strongly suggest a software package that has already been highlighted in the Capacity Focus series as very useful for laying out learning frames in a presentation-style format suitable for education, XERTE.

The Web Language Lab site has a useful illustration of what is possible, even with fairly simple slide type learning frame presentations:

An example of a web-resident, slide-based teaching frame used for teaching language based on integrating text and audio with hyperlinks. Note the navigation panels, the multimedia element and the frame for text. The use of a fill in the blanks exercise for language instruction is particularly interesting. Notice as well, how a screen capture package has been used to turn the original lesson into a second tier of learning.

We could go on and on.

For instance, I strongly believe in the development of electronic course manuals, readers and workbooks, and suggest that something like the Risograph machine allows us to produce effective print materials at relatively low cost for short production runs.

Similarly, I advocate the good old three-ring binder folder and paper based exercises. There is nothing so flexible as pen or pencil and paper.

Speaking of which, I think that learning calligraphy using one of the inexpensive fountain pen based kits, would be an excellent and highly enjoyable way to practice writing and getting spelling right. (How painful it is to have drawn up a wonderfully attractive piece, only to see -- horrors -- it is spoiled because a word has been mis-spelled.)

And so forth.

Obviously, to develop a remedial English unit based on the ideas above would require significant effort and investment, initially. Also, it should be obvious that we are not going to get it perfectly right on the first pass, and across time there will be a desire to adjust and improve it. That points to a spiral development path, where successive versions of the curriculum are to be developed, tested, debugged and put to use then improved.

However, it seems quite feasible to use digital, multimedia approaches to dramatically improve remedial -- or first time through! -- English instruction in our region.

So, can we try? How soon can we start? END
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F/N: Critical thinking skills (cf. online book and a discussion on teaching such skills) are a vital focus in an age of info-glut where ever so much rhetorical or outright propagandistic rubbish and misinformation or just plain sloppy thinking or ignorance on public display lie all around. Such materials, which can pose as education or corrections to imagined conspiracies, or exposes of targetted groups or institutions, are unfortunately persuasive- to- those- who- do- not- already- know- what- is- being- conveniently- left- out, but is not sound. We need to underscore that arguments persuade by appealing to our emotions, or to sources or presenters we think credible, or to facts and logic in light of "reasonable" assumptions and methods of inquiry. However, our emotions are no better than the quality of the underlying perceptions and judgements, no authority is better than his facts and reasoning in THIS case, and it is only when the true and decisive facts are in view, and are handled with good reason using reliable methods, that conclusions are trustworthy. And, often the most trustworthy conclusion is, we do not know for sure, though this seems likely. Students need to be given critical thinking primers (cf my example here) and need to be trained in Internet age research skills. They also need to know a bit about fallacies and sound and cogent reasoning in light of basic worldview issues.  For this last, I think a simplified version of the "turtles all the way down" discussion here on may be a point of departure.