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Managing learner diversity

The challenge that a diverse learner group creates, and what trainers can do about it.

A diverse group of learners is a challenge for any training activity. It raises questions like how much content is just enough and what pace of instruction is just right. To complicate things, as a training program progresses, the diversity may even increase. That’s because learners may take different trajectories: fast or slow on the uptake, engaged or turned off, confident about implementing learning or not, and so on.

In the middle of all this, sometimes, trainers will scramble and stretch to meet disparate individual needs, revisiting content or answering more questions; and that carries the risk of disengaging a few learners who wait impatiently for more advanced stuff to begin. At other times, trainers will take the easier route of sticking to the original “one-size-fits-all” teaching plan, leaving struggling learners to fend for themselves.

But is there a middle path? Or a completely alternative way to handle this? I want to answer this question in two steps. First, I will investigate learner diversity in some detail. Next, I present a practical way out of having to choose between extremes.

Skill-Will matrix

The familiar Skill-Will matrix is a useful tool to understand learner diversity. To cover a broad range of possibilities, we define the two terms as:

A learner with high WILL: is eager to learn, to stretch, has bought-in to the usefulness of the training program, wants to use new learning to her own situation.

A learner with high SKILL: understands concepts, is able to replicate whatever is covered in the workshop

In the skill-will construct, these two dimensions are considered independent of each other… a learner may score high on one and low on another.

With those definitions, we can plot the mental state of learners (blue dots) on a skill-will diagram. You could imagine that these learners are in the middle of a typical training program, and the words in red reveal what they’re thinking.

Of course, the 4 neat quadrants are arbitrarily chosen. Learners can be found anywhere on the diagram. The quadrants, which represent extreme states, give us some terminology(Q1,Q2,Q3,Q4) and help us understand and articulate the learner’s mental landscape.

Note that people in Quadrants 1,2 and 3 are struggling with either will or skill issues or both. Quadrant 4 is the ideal situation, where we want everybody to be.

Handling diversity in an intervention

What can we do about such diversity? I thought of a way, based on 4 principles:

1. Design the intervention as two halves, separated by gap of a few days

This allows us to take corrective action midway through the intervention. We can plan this corrective action in advance, rather than rush about and improvise in the midst of an in-progress training workshop.

2. Test for will/skill after the first half

The ‘will’ element can be assessed by asking about the learners beliefs about the usefulness of the training program and intention to put effort and implement learning. The ‘skill’ element may be assessed in the traditional way: a written quiz for knowledge; a demonstration for abilities. The results of the assessment will help us identify where learners are on the skill-will diagram. In a largish group, it is usual to find at least some learners in every quadrant.

3. Engage Q1/Q2/Q3 learners as per need

This step tries to narrow the skill/will gap within the group (bring the blue dots together, nearer Q4).

The closing of the will-gap (for Q1/Q3) is about addressing doubts about the usefulness of the training provided. This is more like an exploratory conversation for both trainer and learners. Practical possibilities for usage, barriers to implementation, relevance of training content are the issues that could be discussed. Its entirely possible for the trainer to discover that it is the training content which needs tweaking; that the learner are justifiably morose!

The closing of the skill-gap (for Q1/Q2) is about revisiting concepts, answering questions or providing more practice.

These extra engagements need to be scheduled and announced in advance, the assumption being that at least a few learners will gain from them.

4. Continue the rest of the intervention (again with the entire group)

Hopefully, the previous step would have helped learners be more in sync with each other. Those who had lagged behind in skill would have caught up. Those who were skeptical would have newfound interest in the programme. With this more homogeneous group, the second half of the intervention may proceed.

The diagram below shows the learning journey of the 4 types of learners.



The usual way of handling learner diversity is to cater to the ‘average’ learner. The hope is that the “far from average” learners will adjust somehow. This enables a logistically simple (less expensive too) intervention, at the cost of learner engagement.

In contrast, the multiple paths different learners take in the skill-will based approach needs some extra logistics effort. But it allows us to re-engage those participants who would otherwise be ‘lost’, had we continued unmindful of their different learning needs. It makes sense to do it this way if learner engagement, and ultimately, training effectiveness is the No. 1 goal.


Photo credit: Nathan Dumlao via Unsplash

The Dread of Mea Culpa

How many well-intentioned training interventions are inadequate, because they ignore the elephant in the room!

A manager’s confession

“I head a business unit. And I run it ruthlessly… without compassion or mercy. I consider the wages paid to my people as fair exchange for the tough grind I subject them to. What more do they want, anyway?

So, I have built a reputation for extracting the last drop of effort from my team by force of authority and threat of retribution. It gets me results, because I always find some people in my BU who need to be driven hard, some doormats who will do my bidding. Or to put a positive spin on it: some people who will “rise to the occasion” whenever I demand the moon.

Meanwhile, there is collateral damage. My juniors copy me and transmit the pressure and insensitivity down the line. The result is burnout, resentment, stress and high attrition throughout my BU. But I keep such disturbing news at the periphery of my attention, preferring to take pride in this ‘survival of the fittest’ culture that I’ve created. I think it is a small price to pay for the big gains that come my way.

My manager is alarmed by the downsides of my methods. She values the results I get, but fears the downsides. She wants me to face the truth and “see the light”, so she nominates me to a developmental intervention. It is innocuously called “New Leadership Paradigm” or something similar, so that I’m not offended.

The intervention is a shocker. It lays bare the ill effects of my deeds. Through feedback I receive, I discover that I’m not popular. Could it be that my team isn’t enjoying the challenge but barely hanging in there, hating me all the while, till they find a better job outside? I also learn alternate ways of dealing with people… compassion and respect, valuing the good in them, giving them autonomy, viewing mistakes as learning opportunities, taking a genuine interest in their lives and needs etc.

Faced with all this evidence, I am now a changed man. I truly start believing in the new gospel. I see the faces of people in my team, whom I have wronged, and I want to make things okay again. I want to treat them well, as individuals with hopes and feelings and preferences. I want to earn their respect from scratch.

But there’s a problem: behaving differently would mean admitting that I was wrong all along, a mea culpa! The tough-guy image I had cultivated so carefully will crumble. What a loss of face it will be. I can see the dirty looks my people will give me … some will smirk knowingly (He’s come to his senses finally!), others will radiate hate or even pity (Poor sod, look at you now!). Should I subject myself to this? Am I not better off with the status-quo? So I shrink back into the shadows. I decide to sleep over it. Maybe I’ll unveil my new ‘compassionate avataar’ some other time.

A week or two later, I don’t feel so terrible. I’m back to my usual old ways. This is so much more comfortable. That leadership course was such a nightmare. Crisis averted!”

  • — A senior manager

What gives?

Here’s the sad reality: Very often, shame trumps good intentions. The threat of our old identity shattering, and the fear of embarrassment stops us from taking any real actions which are in consonance with our newfound beliefs.

In organisations, it is common for change interventions to lose steam like this. No doubt, they start promisingly, as evidenced by ‘Today, I am born-again’ comments on end-of-workshop feedback forms. But when we look for the change some months down the line, its business as usual. The story above typical, but here are some other change contexts:
– From a parochial mindset (blind hate based on region, religion, gender) to a more inclusive one
– From “Our product is great & whoever doesn’t buy is an idiot” to a more customer-centric philosophy
– From “I must win every negotiation” to a more nuanced long-term view

In each, we face the ominous prospect that the public reputation we have built (strong views, confident, hard bargainer) will crumble, if we change visibly.

Inadequate Interventions

If the change intervention stops at creating the desire for change, then it is inadequate, even irresponsible. It is akin to opening a wound and failing to stitch it up. In the ongoing example, I will end up in greater torment because I will know that my behavior is wrong; I have lost the luxury of not-knowing. I might even resort to extremes of ruthless behaviour, to mask the guilt and shame I feel (like the school-yard bully who thinks “Yeah, so I’m a bully. That’s what I will do, and do very well”). It’s probably better to not have such half-baked interventions at all.

“Lantern glass” interventions

Interventions aiming to create awareness and more responsible actions must be like lantern glasses. They must protect the tender flame of good intentions from being snuffed out. Two characteristics of such interventions are:

1. Turn shame into acceptance
A good intervention will help me view “my past bad behavior” as something to be looked at in the eye, accepted and then transcended. I must be made to see that “my past behaviour was the best I could manage at that time, with whatever awareness and capability I had. My newfound awareness is a resource, and with that, I can do better. My behaviour is fluid, responsive to new learning, and unchanging perfection is a myth”.
A skilled facilitator can do this in a variety of ways. He can spur self reflection, and I may realise that my journey has always been one of constant learning and change and growing upwards; that my recent behaviour was but a rung of this ladder, a temporary resting point; I may then be more willing to move on. He can use the learning groups’ shared stories to help the realisation that I’m not alone; that my challenge of changing my ways has been surmounted by others before me.

This shift towards self-acceptance and humility may look subtle, but it has far reaching effects. The impetus for change then comes not from guilt, shame or need for atonement, but from a space of positivity and ease. I will be more resilient when I face the ‘What will people say?’ question, more willing to persist with my change efforts.

2. Handhold people as they take baby-steps of change
And later, when I attempt to put my good intentions into practice, which is always tough, I could use a helping hand. With support, I could convert this daunting task into relatively small actionables which slowly but surely, take me in the direction of change. As I assimilate my changed beliefs into my everyday interactions, it will be useful to share updates of little successes and setbacks with a listening buddy. During moments of indecision, I could borrow courage and seek advice. This timely support may make the difference between giving up and continuing the journey to the end.

The elephant in the room

The shame about accepting a mistake is the elephant in the room that few acknowledge. Ignoring it doesn’t help because it continues to impede progress in people’s change efforts. When a change intervention fails, we often continue to deny the elephant’s existence, preferring to find safer scapegoats: “hard to break habits” or “too busy to implement change” or “something more important came up”. But for any “change of belief” intervention to run its course, the existence of shame & fear and their effects must be acknowledged and addressed.

To converse better, do this!

Self-help books that teach better conversations tell you that it’s very difficult to master. Really?

Say the word communication and a plethora of related words come rushing in … listening, articulation, tone, pace, clarity, confidence, conciseness. And then some more: body language, sensitivity, biases, vulnerability and relevance. If we’re talking about developing the skill of communication, it seems like a tall order, having to cover so much ground.

Last week, I asked myself the question: must we learn to communicate better the hard way, working our way through each of these dozen attributes? Or is there a more manageable (fewer) number of more basic things that one can work on? Truth be told, I was not very optimistic, but I seem to have arrived at one such set.

My list of 3 core things to get right is:
1. Clarity of purpose
2. Present-moment awareness
3. Honesty

Metaphorically speaking, the first is about the destination, the second about the journey and third is about the attitude one carries during that journey. Let’s see if our dozen abilities can be tackled if I purposefully practice the shorter list above.

Clarity of purpose / Knowing the destination

I’m thinking back about conversations where I rambled on, missed the point of the discussion or ended up burying the important stuff in verbosity. In these conversations, my audience’s eyes glazed over, they fidgeted or interrupted me with questions. Often, something they said took the conversation elsewhere. All this happened whenever I hadn’t thought of a purpose before the conversation (“I’ll just wing it”) or where I lost sight of it midway.
So being clear about the purpose of a conversation can keep my communication relevant and clear.
I like to think of the purpose as a bright star on the horizon. During a longish journey over uncertain territory, if I keep the star in view or glance at it once in a while, I can stay the course, find a straight path and not go around in circles.

Present moment awareness / Journeying mindfully

This involves paying attention to all that is happening during communication. When I speak, I’m sensitive to the effect I’m having on my audience – are they perturbed, excited, confused, relieved, bored? And that feedback, received in real-time, guides my pace, tone and conciseness. As I sense that the other wishes to say something, I stop speaking and listen with attention. As stray thoughts cross my mind, I inspect them for biases and filters; at times I decide that a certain thought is premature or reflects my prejudices.
So if clarity of purpose is about preparedness BEFORE the conversation, then present-moment awareness is about taking it as it comes DURING the conversation.

Honesty / Attitude during the journey

Reams have been written about the art of selling or “winning friends and influencing people”. In some of these texts, the premise seems akin to dishonesty. The authors would have us believe that one has to be crafty to get something: “Show genuine interest in others so they like you back”, exhorts one such popular tome.
I’d like to submit that plain and simple honesty is a better bet.
It allows me to be confident, because there’s nothing to hide, and no worry about being found out. It results in genuine and appropriate body language, rather than faked poise. Honesty automatically implies vulnerability… I’m transparent about how the conversation is going for me, and I have no desire to hide my delight or disappointment during the conversation. This vulnerability forges a deeper connect with the other, and indeed is a better way to befriend and influence.

Is that it?

So, are we saying, just master these 3, and you don’t have to bother about the 12 separate skills. Well, almost, but not quite.
One notable exception is the ability of articulation. It owes much to even more basic skills: grammar, vocabulary and diction. Being honest, mindful and goal-focussed won’t help if one doesn’t have a good command over language.
Also, in conversations where knowledge of the subject is important, there is no substitute for it. It directly affects confidence, clarity and ability to listen.

Not the only set of 3

Problems like these usually have multiple solutions. My list of 3 could be one such solution (and a debatable one at that!). Do you have a favourite set of 3-4 ‘meta-skills’ for communication?

Featured Image Credit: Pixpoetry via Unsplash

Can’t, Won’t, Don’t: Helping people change

Photo by Sarah Cervantes via Unsplash

This post explores different reasons why people resist change; and how one can them.

My kids CAN’T yet swim the backstroke. They sometimes WON’T share their toys. And they DON’T chew their food well enough.

What should my response be? A different approach in each case? Or an omnibus method that I can use, whatever the occasion?

In an earlier article on effectiveness of workplace training, I argued that after the customary workshop (where some knowledge is provided), follow-up support is crucial. It helps people as they struggle to implement learnings to their jobs. Now, I expand on that theme and describe the kind of follow-up support needed.

The skill constraint: when someone CAN’T

Consider the following situations:
– New guy cannot operate a machine
– Fresh face needs to learn how to use Pivot Tables in spreadsheet software
– Students needs to learn how to interpret financial statements
– A manager needs to learn how to perform a quality audit
– You’re good at something, but now you need to teach others how to do it

In these examples, there’s a clear skill gap. So we start by providing basic knowledge through a workshop. After that, the “long tail” of practice starts. Since opportunities to apply the new knowledge may be sporadic, the learner will use it, then lose it and then again regain it. The ‘regaining’ is where the learner needs our support.

Sometimes, timely information is the best support: instruction manuals and telephonic helpdesks do that. At other times, scheduled practice sessions and feedback do the job (fire drills in the office are an example).

This situation represents the simplest training task, where the constraint is only of skill.

The will constraint: when they WON’T

The second kind of constraint has to do with hesitation or opposition to something new. The learner may be capable of doing something, but doesn’t want to do it. Some examples:
– Praising a good deed (as opposed to pointing out only mistakes, and ignoring good work)
– Delegating authority (as opposed to closely controlling everything)
– Offering feedback (without ‘wronging’ the receiver)
– Consultative selling (as opposed to ‘pushing’ products)
– Saying ‘No’ assertively (as opposed to submitting meekly)

In the above examples, there is a pre-existing mindset or fear which prevents people from adopting new behaviors. So what kind of post-workshop support would be best?

Oodles of encouragement to adopt new behaviors is the need. Think role models. Think seeing someone else benefiting from use of new skills.

An appropriate forum for this is a practice-group. Such a group of 4 to 8 people meets regularly (say weekly) for an hour or two. Sessions may be moderated or not. The focus is on bringing forth stories of struggles and successes; on peer learning. The idea is that the reluctance gets whittled away bit by bit, if people see their peers struggling, then adopting and then benefiting from new behaviors.

The habit constraint: When they DON’T

This category of constraint has to do with pre-existing habits, ingrained through long use. A person may be able to act differently when consciously attempting it (say, within the confines of a training workshop), so there’s no skill constraint. He may even be eager to do this (no problem of lack of will). The problem is: he simply forgets to do it. That’s how habits work… we’re on auto-pilot, instinctively doing something before we even think of it consciously. And the fact that we have the knowhow and willingness to act differently doesn’t matter…. the deed is done before conscious thought intervenes.
The following examples fall in this category:
– Gathering data before arriving at conclusions
– Thinking of consequences before taking action
– Staying calm under duress or provocation
– Catching one’s own biases
–  Being mindful of others while speaking
–  Paying attention to details
– Paying attention to the big picture

Such situations can be helped to some extent through a ‘daily check-in’ system, which is just something to keep us mindful that we’re working on a particular ‘change project’. Think of a daily alarm on your mobile-phone. Or a 2-minute phone call to a supportive buddy or coach at a fixed time everyday.

A practice-group (which can be renamed the mindfulness group here) can also help people. The work in this group will be about setting up personal cues for action (“when I feel impatient next time, I’ll take a mental breather”). And about deciding alternative strategies to handle situations (“…and I will ask myself, do I have enough data to reach this conclusion?”)

Tougher cases

Of course, people and their situations don’t fit into neat buckets. A manager may believe people respond only to fear, habitually throw his weight around the office and not even know other ways of dealing with people… that’s will, skill and habit all rolled into one. Try having him change his beliefs and behavior, and its a lot of patient work. But then, there have been successes. I know of a senior (read: know-it-all) sales professional who fits the above description. I clearly recall his 3-month journey…
FROM wearing a permanent sneer during the workshop
… TO trying out more respectful methods at work tentatively
… TO finally becoming a poster-boy for “managing people through feedback and coaching” within 3 months.


In the world of training and development which I inhabit, people’s challenges look deceptively similar, but scratch the surface and they come in many flavours. Each of these flavours deserves a slightly different training response. This difference is at two levels:
– at the macro level, the structure of the training intervention changes, depending on whether knowledge or skill or belief is the crucial aspect. I’ve discussed this at length in this article
– at the micro level, the kind of post-workshop support needed differs, as the current article argues.

A one-size-fits-all approach to training is sub-optimal. It’s akin to me giving an earnest lecture to my kids everytime they struggled at swimming, refused to share toys or gobbled up their meal. I should know… I’ve tried that approach before I became wiser. Now, I know that the swimming problem needs more practice. The sharing problem needs me to share MY things more often, thus role modeling desired behavior. And the chewing problem… constant reminders.

Photo credit:  Sarah Cervantes via Unsplash

Rock-Star trainers: double-edged sword?

Everyone loves trainers who can captivate audiences. But there is a dark side to it.

Trainers often project a persuasive and energizing style, as a differentiating factor. Clients actively look for these attributes; and are happy when post-program feedback from learners confirms that the trainer had these attributes. But this power to hold audiences in thrall does have a dark side to it. Let us look at a few trainer-behaviors to illustrate this point.


Act 1: Three Trainers

A trainer wants her audience to believe that “When feedback isn’t a personal attack, it works”. To buttress the claim, she quotes 5 anecdotes from her personal experience, where inoffensive feedback produced results. She decides that counter-evidence (instances when the concept did NOT work) need not be presented at all. She skips talking about pre-requisites too: for instance, the concept works only when there is a significant relationship of interdependence between people giving and receiving feedback. Of course, her audience has no clue about what she chose not to speak. Suitably impressed by the coherent evidence lined up before them, learners will conclude that the concept is unassailable, all-weather, guaranteed to work. This was the persuasive trainer in action.

A learner makes a presentation during a Presentation Skills workshop. The trainer wishes to encourage the learner. So, while he comments on the presentation, he highlights the positives and downplays shortcomings. And he says “Wow! You beat my expectations”. And points out the improvement since the start of the workshop. The result: the learner gets a heightened sense of capability. All thanks to the encouraging trainer.

In another program, a trainer believes that batting practice at the nets is the first step to overcoming real life obstacles. So, he constructs a controlled, simulation in the classroom (a “sandbox”), within which learners practice their skills. Since such a sandbox is quite tame, and the trainer provides generous support and encouragement during practice, learners do well. Buoyed by this “success experience”, learners come to believe that they can replicate the same performance back at the workplace. The credit for this goes to the supportive trainer.

It is easy for trainers to leave learners 
happy and confident at the end of a workshop.
But is that always a good thing?


Act 2: Climax

Someone who has been fortunate to learn from persuasive, encouraging and supportive trainers will now believe that:

– he has an all-weather tool

– he is good at applying it

– he is battle-hardened and ready for action


Act 3: Aftermath and Crisis

Brimming with confidence, the learner dives headlong into fixing all that is wrong in his world. Of course, results don’t come easily. There are unexpected roadblocks which the sandbox-practice didn’t cover. Unlike the trainer, his peers and managers don’t seem to notice much change in him…the appreciative looks on their faces are missing. So, confidence takes a nosedive. Skepticism about training arises. Worse, the skepticism extends to concepts in general (“Theory never works in real life”), which reduce openness to all further learning. The only refuge: “good old” dysfunctional behaviors.

In our story, the trainer does a disservice to learners. He raises their expectations beyond what is feasible in their real-life contexts. This is the dark side of persuasion and energizing.

Confidence without proven skills is like a bubble.
The happiness will be short-lived.


Why do trainers do this?

The reasons for this are several. For one, it is the easy thing to do. Cherry picking examples in aid of a concept is easy. It is much harder to put forth balanced evidence, while arguing in favour of a concept. Picture this: the trainer says “In my experience, the concept works 70% of the time, but I still suggest you adopt it” and faces downcast expressions on learners’ faces!

There are some short-term gains from a pep-up kind of training. Customers say “We must end the program on a positive note”. So, the trainer makes sure that learners leave the training program on a high. Not necessarily more determined, serious or realistic; but simply happy and confident. Success is measured by the post-program “happy sheet” (so aptly named!). The happier this sheet looks, the higher the chance of repeat business.

Thirdly, buyers of training services unwittingly invite such behaviour from trainers. They would argue that program effectiveness is elusive anyway; dependent on so many factors beyond the intervention’s control. So, the best one can do is to ensure that the trainer keeps learners riveted during the workshop. And one way of ensuring this: seek out trainers high on persuasiveness and energy.

The pressure to show results within a short time also contributes to the problem. Intervention design is notoriously front-loaded. A typical intervention has a group workshop right at the start and has a rather sparse tail for implementation practise. The workshop is where all the action is supposed to be… eager learners, the top bosses making cameo appearances and expectations of transformed learners right after the workshop! It is tempting for a trainer to end the workshop with a bang, and that one way to do that is making sure that learners are happy by the last evening of the workshop.

A combination of convenience and 
pressure to show quick results 
causes trainers to take a short term view.


A way out

The most obvious way out of the problem is self-regulation by the trainer. She must ask herself, “What is a fair use of my training techniques”? Praise, anecdotes and sandboxes all are useful tools when used fairly. When a concept is abstract or complex, hence difficult to grasp, anecdotes provide a way to make it tangible, easy to understand. Some encouragement or praise prevents a learner from withering and dithering in early stages of learning. And sandboxes serve to focus a learner’s attention on the ONE skill she is trying out, rather like a first driving lesson on an empty road.


If you are a buyer of training, you can significantly impact the issue. Here are 4 concrete actions:

1. Insist on a program design which caters as much to post-training implementation, as to engagement during the training.

2. Ensure that the trainer is familiar with the real-world of learners; that will enable him to build more realistic training sandboxes.

3. Relieve the pressure on the trainer to show quick results.

4. Postpone collection of learners’ feedback to a later time when learners can judge better if training really worked for them.

If trainers self-regulate,
and buyers of training temper expectations,
the learner will benefit 
from a long-term view of development.


End piece

It all comes down to a simple question: are we focussed on short or long-term impact?

Short term thinking encourages actions which inflate the learners’ perceived sense of capability to a peak, right at the end of the workshop. But this is like a bubble about to burst.

Long term thinking keeps learners’ post-workshop challenges squarely in view. The entire intervention arranges itself around this central challenge. And it takes the form of a measured, gradual approach to changing learners’ habits and capability. It doesn’t aim at “peaks”; rather it thinks of reaching a higher, stable level of performance.


Photo credit: Jesse Darland via Unsplash

A sense of numbers

If you’ve been saying to yourself, “I am no good at Maths”, here is hope!

Ramanujan and John Nash definitely had it. Your neighbourhood grocer has it. And some kids in my son’s elementary school have it. But I’m guessing a lot of us don’t.

I am talking about a “feel for numbers”.

And it’s more than just knowing our multiplication tables. Or the number of zeroes in a million or the number of bytes in a gigabyte.

I’m talking about feeling the passage of time. How many of us can estimate accurately the time needed to read out a 1500-word speech to our teams? 1 minute? 5 minutes? More?

I’m talking about doing the math in our heads quickly. During your company’s onboarding exercise, each of the 30 new employees needs to undergo an 8-minute medical test and we need to wrap up the whole exercise in an hour, how many doctors should we arrange? (Quickly now, please, before the elevator stops!)

I’m saying, it’s a rare person who can sense the extremities of data, if informed that the mean is 5 and standard deviation is 0.8.

I’m saying, not many of us can look at a largish crowd and estimate accurately how many people there are. Two thousand and ten thousand will look the same to us (both are “lots of people”). Ditto with terabytes and petabytes…both look like “more memory than I’ll ever need”, before we’re proved wrong!

This feel for numbers is about speed, acceptable accuracy and familiarity with numbers. It’s about the numbers talking as much to your gut as to your brain.

Why aren’t we all good at this?

It’s a gaggle of reasons.

Some things are intangible, hence tough to grasp. Time is one example. Another example is human-invented metrics like average, standard deviation or correlation coefficient, which can’t be “seen” in nature but are essentially computations.

Other things are tangible, but weren’t taught to us correctly during early years. Examples are distances, areas, weights, fractions, densities, volumes and counts. Instead of “feeling” or “seeing” them, we experienced them as numbers written on paper. That robbed them of the multi-sensory experiences they could have been.

Our understanding of large numbers suffers because we “see but don’t count” when we encounter them. We’ve all seen “hundreds” of people at a busy railway station or rock concert, “thousands” of stars in the night sky and “millions” of grains of sand on a beach. But this kind of “seeing” is fleeting and passive. We don’t spending time and effort in actually estimating how many we saw. As a result, we will be fairly accurate when estimating the number of biscuits in a small box, but our answers will be way off when counting larger numbers.

We aren’t quick at mental calculations (unlike the grocer) because we don’t do it often enough, waiting for the answer to come from the calculator or the other person we’re talking to. Practice matters here.

What can be done?

I read somewhere recently, “The best time to plant a tree was 10 years ago. The second best time is now”. It’s the same with developing an intuitive sense of numbers.

Early education does much to make or mar our understanding of all things quantitative.
If you have a small child, let them “sense” the numbers before you prod them to “read” numbers. At Swadhaa, the Waldorf Kindergarten my kids attend, primary schoolers learn about distance in a very “feeling-sensing” way. They first construct their own metre-scale out of a strip of wood, getting a sense of millimetres and centimetres. Then, they step out of school and walk a kilometer, measuring the road a thousand times with the metre scale.
More examples…
To learn about weights, they sit on one side of a huge beam balance while the teacher sits on the other.
To “feel” multiplication, they use a number wheel, (see picture, credit Jennifer Compton) doing as much work with their hands and eyes, as with their brains. And they play games, where they rhythmically clap or stomp their feet in sets of 3, then 6 and so on. It’s almost as if the “body” learns the math before the “mind” does it.

Such learning is deeper… haven’t we often noticed that we forget names and numbers and facts within a short time, but our body easily recalls how to swim or ride a bike after a gap of years.

But if you (just like me) missed the bus at that age, what are our choices now, as adults?

For one, immersion and effortful engagement. We live in a sea of numbers, and if you take the time, it’s possible to dance with these numbers. At the airport, guess how many people are there in the boarding queue, then actually count them and compare the results… you’ll find that you’re getting better with time. During the office commute, estimate time and distance, and then cross check using your watch and the car’s odometer. In the kitchen, when the cake recipe asks you to measure out “115 grams of butter”, take a moment to weigh it (feel it) in your palm.

Some other things aren’t amenable to such casual rumination. So, a more “classroom style” approach helps.

To develop an understanding of percentages (fractions), I sometimes try this exercise in a workshop. Take a sheet of paper, tear it into half. Tear one part into half again. Repeat. Just the act of handling and watching ever smaller pieces of paper helps get a feel of fractions. We can see “just how small is one sixteenth, or 6.25%”.

To develop a sense of data distributions, I have learners imagine birds sitting on a stick. Then, the “average” is the fulcrum, the point where the stick can be balanced on a finger. The “median” bird has an equal number of neighbours on its left and right. Given 2 such sticks with birds sitting on each, the stick with lesser “standard deviation” is the one where the birds crowd around the center. Later, learners double check what their intuition says, by doing the math with real numbers.

To help develop an ability of quick estimation, exercises like this help: 43 people per batch * 3.5 hours per person * 19 batches = How many hours in all? It sometimes devolves to a problem of which 2 numbers to multiply first, and where can a rounding-off be done. There are several ways… my mental chatter was “approximately 40*4*20, but a little less”. I arrived at 3000 hours, an acceptably accurate in some situations (The exact answer is 2859.5 hours)

The practical question

All this is fine, if being good with numbers is intrinsically valuable for you (Csikszentmihalyi’s concept of Flow comes to mind)

But, if it’s a means to an end, is the effort worth it? Could having a way with numbers confer an edge? Could it help you get ahead in life?

My assertion is this: an understanding of time, physical space, magnitudes and proportions underlies many areas of decision making. With an intuitive grasp of these, we’re faster and more likely to make the right decisions. Without it, we’ll still manage, but only after much delay and struggle with the minutiae of spreadsheet models.

If you’re an account manager / salesperson on the move, and good with numbers you’d spot opportunities faster, and act quickly without losing momentum. You could do the mental math quickly and make a decision, rather than say “Umm… Could you please email this to me. I’ll look at the numbers more closely, and I’ll get back to you”. In deal making, seizing the moment is key.

If your work involves planning and estimation, the quality of your decisions would go up, if you had a feel for “large” numbers. Example: How much circulation space should you plan for, if you’re expecting footfalls of 10,000 to 15,000 people during a 3-day symposium? If this boggles your mind, you’re losing time and you may make arrangements that are either inadequate or too extravagant.

If you’re a data scientist, you could take a look at what the computer spat out and say “Wait a minute, this doesn’t seem right. Let’s inspect the input parameters again”. It’s like being able to smell a rat before you see it.

My perspective and yours

My point of view is that of someone who likes numbers… I compulsively count, measure and estimate (which does get in the way of simply savouring the moment, I admit). So, for me, number crunching doesn’t have to be “profitable”. But I’m curious about what others think.

If you’re reading this article, I’d like to know your perspective. Is quickness with numbers all that useful in your work? Which kind of number-work do you find most challenging? Does any of you specialise in numbers which are either very large or very small?

I’m all ears.

Photo credit: Heather Zabriskie via Unsplash and Jennifer Compton via Etsy