Not-so-advanced Math and Relationships

I remember learning about summation in junior high math … you know, how to find the sum of 1+2+3+4+5 … There are several formulas:

  • Find the middle number and then multiply by the number of numbers; e.g., 7+8+9+10+11 Middle = 9 * 5 = 45 (the sum)
  • (F+L)*N/2 where F is the first term, L is the last term and N is the number of numbers in the sequence; e.g., (7+9)*5/2=45
  • (N2+N)/2. This gave me a sum of numbers starting with 1, which is what I wanted; e.g., 1+2+3+4+5 = (52+5)/2 = 30/2 = 15

Here’s the reason I was playing with this at all …

As a former coach and personal counselor, I used this summation formula to show the exponential growth of relationships when more people were added to a group. In counseling, I worked with families and couples to see the impact of going from just the two of them to 1, 2, 3, or more children. In coaching, this approach helped me understand the dynamics of managing a group of 10-15 athletes.

Now with some changes in the leadership in my department, I wanted to look at this again to get an idea of the number of relationships a department chair must attend to. So I did the simple math and saw that none of these formulas worked for this idea. For instance, if there are 2 people, there is 1 relationship, but if you plug the numbers into the formula, you get 3. If there are 10 people, the formula says there are 55; 20 people = 210 relationships.

The problem with all of these formulas is that they include the number itself – in this case each person in the group. And no matter who I am, I am not responsible for others’ relationships with themselves. So I took out the number of people in the group and this is the formula I came up with:

So let’s look at what happens when groups begin to grow. You can try it out by putting any number into the formula. Let’s pick 5 and then 25.

  • For 5 people: [(5*5 + 5)/2] – 5 = [(25 + 5)/2] – 5 = (30/2) – 5 = 15 – 5 = 10 relationships
  • For 25 people: [(25*25 + 25)/2] – 25 = [(625 + 25)/2] – 25 = (650/2) – 25 = 325 – 25 = 300 relationships

That’s right, by adding 20 people to a group, there is an increase of 290 relationships. Whoa!

To make it easy to see these exponential increases at a glance, I created a spreadsheet. Here it is: Relationships.

So what’s the point?

We have to first realize that groups are much more difficult to navigate the larger they get … and … when you add other factors, such as a new topic, a new skill, or a different setting, the importance of good leadership is amplified. We know many things about good leaders (and I’m including teachers in the mix). In no particular order:

Good leaders are organized. Not necessarily in a neurotic way, but they provide some type of structure that enables those they are responsible to and for to function at their best. If organization is not one of our skills, then we need to surround ourselves with people who have that skill.

Good leaders delegate. By choosing competent people as part of their teams, leaders are able to let go of some of the tasks of the school/department and focus on the priorities of their responsibilities. Utilize the skills and talents of those around us – whether those are students or teachers/administrators. No one can do it all, so let go and let them take care of what they’re good at.

Good leaders build an atmosphere of trust … I trust you … you trust me … and this is all about relationships. The easiest way to build trust … is to trust. To give people responsibility, provide them with what they need to be successful, and trust that they will do what needs to be done. They take every opportunity to build up, not tear down, their teachers/staff. Trust also occurs when there is an essence of predictability in the leader’s actions – not rigidity, but a range of habits and behaviors that are logical and trustworthy.

These simple principles have led me to design my classes, as many of you have, with small groups and multiple connections. I started doing this with my online courses and have found it to help me manage the relationships online. For instance, this semester I have 36 online students; 20 in one class and 16 in the other. Looking at my chart,  that’s 190 and 120 relationships, respectively. But it’s 36 relationships for just me. That’s a lot to follow and take care of while helping some students navigate a new environment and most students learning new information and skills. So, by putting my students in groups and giving them some place to post their questions I am able to focus on the less customary questions, issues, and problems. They help each other out with the garden-variety questions and issues.

So, the next time you walk into your classroom or you’re put in charge of a group, take a quick look at how many relationships there are, figure out who you can delegate to, and start building trust by trusting.

2 thoughts on “Not-so-advanced Math and Relationships

  1. As I read your post, my many fun days in statistics class and teaching these topics came roaring back.

    The part of your blog that stood out the most, for me, was the comment about good leaders being organized. The comment about “if it is not one of our skills, then surround yourself with those that are organized”. I think this should be taken further in leadership. A good leader will analyze themselves, find their weaknesses in all areas, then find a counterpart to fill that gap.

    I, as well, have and continue to coach. It never ceases to amaze me that a coach and assistant coach will work together, only because they work well together. They have the same beliefs and coach the same way. Well … their program is always the same, never improving. Their is no counterpart to say, “What you’re doing is wrong.” I think many times this is the same way in many departments in our school systems. At our school, in the past, we have hired many teachers whom teach the same way as the rest of the faculty. Therefore, not improving because we don’t see a different way to do things.

    Our challenge as educators … observe many educators and just because they are doing things different from the way we do, doesn’t mean it is wrong. Maybe we have a weakness that they can help us improve on.

  2. Tim,

    Thank you for your comments. I agree, we need to be looking for ways to better ourselves … and that is not always going to be comfortable.

    So, as we continue to lead – for we are all leaders – we have to remember that we must set the example and learn to look forward to the times of discomfort … for they probably mean we are getting ready to learn something and make a change… hopefully a change that will make us better people, educators, and leaders.

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