Eight to Late

Sensemaking and Analytics for Organizations

The calculus of project teams

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Calculus is an important part of the mathematical toolkit of scientists and engineers. I’m sure some of my readers have (perhaps, not so fond) memories of many (perhaps, not so entertaining) hours spent in learning calculus during their late high-school / early college years. Calculus has two main branches: differential calculus and integral calculus.  The first branch deals with a mathematical technique called differentiation,  which enables one to calculate the variation of a quantity with respect to another  – for example, change of distance with respect to time, aka speed.  The second branch deals with integration, a technique to compute the net (or summed) effect of small variations  – for example, speed*time, summed up over all time slices, yields the total distance travelled.  As the examples suggest, the two techniques are the inversely related. In this post I draw an analogy between these operations of calculus and two somewhat opposite, or inverse, things a project manager has to do in order to ensure the smooth and effective functioning of a team.

Project teams consist of individuals, each with different skills, aptitudes and personalities. Yet the team has to function as a unit, pulling together, ensuring that every individual’s effort contributes to achieving the team goal. In order to do this, the project manager has to employ the inverse techniques of team  differentiation and integration as I outline below.


It’s a given that no two people are the same. Yet many managers deal with all  their team members in exactly the same way. This is a mistake. One has to tailor one’s management approach to suit individual personalities and quirks. But even before this, one has to take the time to understand what makes each individual tick – knowledge, skills, professional interests, approach to work,  career aspirations etc. This isn’t always easy to elicit (no, a questionnaire won’t work!). One has to get to know people one-on-one, taking time to talk to them in different situations and contexts. Over time one builds up a picture of the things that make them different and unique from everyone else on the team.

Why is this important? Well, if you really understand the folks who make up your team, you’ll develop a feeling for what they will be able and willing to do on a project. You’ll get a sense for their strengths and weaknesses, both technical and otherwise. This is knowledge that is useful in all stages of a project, but particularly so in times of crisis.

Differentiation, in essence,  boils down to developing individualised work relationships with each team member.  All the outstanding project managers I have known have been able to do this effortlessly, and in a non-intrusive way. I reckon this (not so common) skill is one of the important factors that sets the brilliant apart from the run-of-the-mill project manager.

A few words of warning though: Although the best way to get to know people is through conversation, remember to be sensitive to differences in personality, and also to avoid topics that may be construed as personal. Further, be genuine – there’s nothing worse than false interest or bonhomie; and it shows a mile away!


Differentiation is one aspect of team management, the other is integration: i.e.  integrating diverse personalities and skills into a coherent team. Most mainstream theories of team development are built around Tuckman’s four-stage forming-storming-norming-performing model. In brief: the first stage corresponds to team formation; the second to debates / confrontations between individuals on the team; the third to settling down and development of trust; the fourth to working on the task that the team has been charged with. The project manager has a supervisory (I prefer the word, integrative) role in all four phases, but especially so in the first two.

In an ideal situation the project manager has had a chance to get to know team members prior to team formation. If so, through differentiation, he or she already knows the strengths and weaknesses of each individual. The project manager can thus match project requirements to individual skills and aptitudes to come up with an optimal team. Once the team is formed, the project manager can facilitate project discussions, armed with a good sense for who might be able to contribute in specific areas. Furthermore, he or she will also be able to defuse conflicts or mediate disagreements between team members more effectively than would have been the case without this knowledge.


In mathematics differentiation and integration are the basic operations of calculus. In this post, through analogy, I have discussed the importance of the two  techniques in the context of project teams. Much like the engineer who has to master differentiation and integration, the project manager has to be adept at both techniques of the calculus of project teams.

Written by K

September 15, 2008 at 8:35 pm

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