At Kairos Academy Pathfinders we are called to help people scale the mountains of educational effectiveness, leaving the foothills of efficiency behind. Our aim is always to help children to succeed: enabling each child to truly master each subject they study and to see how all that they learn fits into getting to know and learning to follow Jesus–the Way, the Truth, and the Life.
We understand that those who choose the path of effectiveness have chosen the way to success, whereas those who choose efficiency over effectiveness in teaching attain neither. Effective teaching is exponential. Each little thing you do multiplies the results of the previous steps. Efficient teaching is a linear function. Each little bit that you do adds a little bit to the results.
In the beginning, the efficient, linear approach seems better. Each step in the linear addition of efficient teaching is always roughly the same size. From the very start of a linear experience you can see the progress you are making. That small hill in front of you is soon conquered. Whereas, with exponential growth the first steps are so small they are not even noticeable and it seems like that first hill will take forever to climb. But, after exponential growth has gone on for a while, each new step becomes huge and before you realize it you are striding up mountains. Let's look at two illustrations of these principles to help us all orient ourselves as to what this might mean in an educational or discipleship context.
The (Rich) Wise Architect
The classic example of the value of exponential growth over linear growth is found in the following oft-changed illustration: A king hires an architect to transform his palace in 30 days. He puts before this miracle worker two options for his pay. If the architect takes option one, he will be paid $10,000 each day. If he takes option two he will only receive a penny on day one, but his total pay will double every day until the end of the project. Thus, his total pay after the second day will be two cents. After three days, he will have earned a total of four cents. And so forth, with his total pay doubled every day until the end of the 30 days. So, which one should the wise architect choose?
In the first scenario, he receives $300,000 by the end of the 30 days. That seems like an awful lot more than the penny he would get his first day in the other scenario. Surely that is the way to go. Right? Well, after 10 days, the first scenario sure still looks better. The pay for the exponential scenario has only reached $10.24, as compared to the $100,000 he would have received in scenario one at this point. At 20 days, the exponentially growing total just barely reaches $10,485.76–that total is just the daily pay for the linear scenario. That means he is behind what he would have gotten in the first scenario by a whopping $190,000. By day 24, the total for the first scenario is $240,000 and for the second scenario the total is $167,772.16. From here on out the pay from the second option zooms past that from the first. Indeed, by the end there is no doubt that the exponential choice is better than the linear – with a total of $10,737,418.24 (over 30 times as much as the $300,000 the architect would get from the first scenario). Such is the power of exponential growth, if you are patient enough to see it come to fruition.
That same principle can be seen at work when we compare efficient (linear) educational approaches and effective (exponential) ones.
Exponential Growth in Learning
My wife and I have a daughter who has Down Syndrome. When Hannah was approaching school age, we were encouraged to enroll her in a special full-day kindergarten. Through her IEP (Individualized Education Program) report, the teachers and administrators involved assured us that they could teach Hannah to read at a third grade level by the time she graduated from high school. They proudly reported having achieved that level of success with other children with Down Syndrome. Indeed, they expected us to agree with them that such a goal was a lofty one for us to set. In their system, as soon as Hannah mastered the alphabet, she would immediately start memorizing the appearance of a series of words.
With the efficient whole language learning process they planned to employ, her IEP writers aimed to get her started reading right away. That would allow her to maximize the number of words she would eventually memorize -- with an expected plateau of the reading vocabulary of an average third grader.
Having met people who followed a very similar path to the one the writers of her IEP planned for Hannah, I have no doubt that their estimates of her ceiling were about right…as long as she was stuck in a system that valued efficiency over effectiveness.
We chose to educate Hannah at home. As with her sisters, we used a tried-and-true phonics method to teach her to read. Her reading lessons were highly relational and time-consuming. To all appearances there was nothing efficient about the process. The one-on-one attention she received as she worked through each lesson certainly didn’t look efficient. Rather than steadily marching through a list of lessons once, she repeated each of her first 100 reading lessons at least three to five times. With each repetition she understood a bit more, but she didn’t seem to be moving forward very quickly all that time. It took at least six years for her to get to the point where she was confidently reading at a first grade level. At that point, she was far behind peers who were learning to read by memorizing whole words. However, we just kept plodding along with her and encouraging her.
After all that “inefficient” repetition, as she finally began to understand the code the lessons were imparting to her, her improvements picked up speed.The time she took to go from first grade level to second was shorter than it had been to get to first. Going from second to fourth, when we finally told her she was done with her learning-to-read book, took less than a year.
I don't know the exact timing of when we reached the crossover point. But Hannah has long ago passed by the peers who were taught using whole language learning. She kept mastering more and more of the code of phonics such that she zoomed past the third grade level that the IEP writers projected as her final ceiling some time in her late pre-teens to early teens. By now, she reads at a fairly advanced level.
Though she reads slowly, Hannah has read a number of classic books that are far beyond the ken of a typical third grader including A Christmas Carol by Charles Dickens and The Hobbit by J.R.R. Tolkien. For Hannah, as a reader, the sky's the limit.
Had we taught her to read through the linear method, she would have slowly but surely approached a firm cap for her abilities. One of the reasons that whole language learners generally don’t get beyond a third-grade reading level is that the human mind can only memorize so many words, whereas the phonics code gives a reader access to an unlimited number of words. But, her teachers would have been able to report regular progress all through her schooling. The process would certainly have seemed efficient along the way, with measurable incremental improvement from day one and for years afterward.
By teaching her the code, we taught her effectively. We set her up to learn to read as well as she wishes, improving her skills exponentially over time. She knows the code well enough she can go after learning more of it herself. And, each improvement in her understanding of that code adds a huge number of words and concepts to her repertoire. Such improvement just takes time and effort on her part.
Hannah has so enjoyed reading that she has taken up writing stories of her own. The vocabulary she uses in those stories is stunningly advanced for a young woman whose ceiling was once pronounced to be the equivalent of a typical third grader.
Life Application
Effective teaching tools don't always translate into quick results. However, with persistent loving application the rewards of using such tools are far greater than those tools that are deemed efficient by so-called experts. Students who are taught effectively may seem like they are behind for a long time but are ultimately enriched relative to their efficiently taught peers–in much the same way as the wise architect who chose to start with a penny and double his pay each day was enriched over the fool he would have been had he chosen to receive the initially attractive fixed daily allowance.
Genuinely effective teaching requires love, grace, and the willingness to take the time to allow each student to blossom. At Kairos Academy Pathfinders we understand that truth and seek to help every leader and parent live it out. Everything we are building aims to make such loving effectiveness the norm for every parent and leader in every Academy. Come join us in our choice to leave the foothills of educational efficiency behind, encouraging leaders and parents to teach effectively, and lead each child to the majestic peaks they were meant to conquer in life.