But as the scientists confirmed their numerical results across 27 datasets, they began to understand that we commonly misinterpret prior knowledge for learning. Some kids already know a lot about a subject before a teacher begins a lesson. They may have already had exposure to fractions by making pancakes at home using measuring cups. The fact that they mastered a fractions unit faster than their peers doesn’t mean they learned faster; they had a head start.
Like watching a marathon
Koedinger likens watching children learn to watching a marathon from the finish line. The first people to cross the finish line aren’t necessarily the fastest when there are staggered starts. A runner who finished sooner might have taken five hours, while another runner who finished later might have taken only four hours. You need to know each runner’s start time to measure the pace.
Koedinger and his colleagues measured each student’s baseline achievement and their incremental gains from that initial mark. This would be very difficult to measure in ordinary classrooms, but with educational software, researchers can sort practice exercises by the knowledge components required to do them, see how many problems students get right initially and track how their accuracy improves over time.
In the LearnLab datasets, students typically used software after some initial instruction in their classrooms, such as a lesson by a teacher or a college reading assignment. The software guided students through practice problems and exercises. Initially, students in the same classrooms had wildly different accuracy rates on the same concepts. The top quarter of students were getting 75% of the questions correct, while the bottom quarter of students were getting only 55% correct. It’s a gigantic 20 percentage point difference in the starting lines.
However, as students progressed through the computerized practice work, there was barely even one percentage point difference in learning rates. The fastest quarter of students improved their accuracy on each concept (or knowledge component) by about 2.6 percentage points after each practice attempt, while the slowest quarter of students improved by about 1.7 percentage points. It took seven to eight attempts for nearly all students to go from 65% accuracy, the average starting place, to 80% accuracy, which is what the researchers defined as mastery.
The advantage of a head start
The head start for the high achievers matters. Above average students, who begin above 65% accuracy take fewer than four practice attempts to hit the 80% threshold. Below average students tend to require more than 13 attempts to hit the same 80% threshold. That difference – four versus 13 – can make it seem like students are learning at different paces. But they’re not. Each student, whether high or low, is learning about the same amount from each practice attempt. (The researchers didn’t study children with disabilities, and it’s unknown if their learning rates are different.)
The student data that Koedinger studied comes from educational software that is designed to be interactive and gives students multiple attempts to try things, make mistakes, get feedback and try again. Students learn by doing. Some of the feedback was very basic, like an answer key, alerting students if they got the problem right or wrong. But some of the feedback was sophisticated. Intelligent tutoring systems in math provided hints when students got stuck, offered complete explanations and displayed step-by-step examples.
The conclusion that everyone’s learning rate is similar might apply only to well-designed versions of computerized learning. Koedinger thinks students probably learn at different paces in the analog world of paper and pencil, without the same guided practice and feedback. When students are learning more independently, he says, some might be better at checking their own work and seeking guidance.
Struggling students might be getting fewer “opportunities” to learn in the analog world, Koedinger speculated. That doesn’t necessarily mean that schools and parents should be putting low-achieving students on computers more often. Many students quickly lose motivation to learn on screens and need more human interaction.
Memory ability varies
Learning rates were especially steady in math and science – the subjects that most of the educational software in this study focused on. But researchers noticed more divergence in learning rates in the six datasets that involved the teaching of English and other languages. One was a program that taught the use of the article “the,” which can be arbitrary. (Here’s an example: I’m swimming in the Atlantic Ocean today but in Lake Ontario tomorrow. There’s no “the” before lakes.) Another program taught Chinese vocabulary. Both relied on students’ memory and individual memory processing speeds differ. Memory is important in learning math and science too, but Koedinger said students might be able to compensate with other learning strategies, such as pattern recognition, deduction and induction.
To understand that we all learn at a similar rate is one of the best arguments I’ve seen not to give up on ourselves when we’re failing and falling behind our peers. Koedinger hopes it will inspire teachers to change their attitudes about low achievers in their classrooms, and instead think of them as students who haven’t had the same number of practice opportunities and exposure to ideas that other kids have had. With the right exercises and feedback, and a bit of effort, they can learn too. Perhaps it’s time to revise the old saw about how to get to Carnegie Hall. Instead of practice, practice, practice, I’m going to start saying practice, listen to feedback and practice again (repeat seven times).