The best way we know of to accelerate growth is to slow down and teach in ways that foster deep understanding. It may be counterintuitive, but slow learning really does accelerate growth!

In the post entitled, If you want students to develop faster, stop trying to speed up learning, I presented evidence that schools with curricula that promote deep understanding accelerate growth relative to schools with more of a focus on covering required content. In this post, I'm going to explain what we've learned so far about the relation between deep understanding and the rate of development. (I recommend reading the earlier post before trying to make sense of this one.)

Lectica's learning model, VCoL+7, emphasizes the importance of giving students ample opportunity to build deep understanding through cycles of goal setting, information gathering, application, and reflection. We argue that evidence of deep understanding can be seen in the coherence of students' arguments—you can't explain or defend an idea coherently if you don't understand it. Furthermore, because poorly understood ideas provide a weak foundation for future learning, we would hypothesize that over time students who demonstrate lower levels of understanding—through the coherence of their arguments—will grow more slowly than students who demonstrate higher levels of understanding.*

We tested this hypothesis by examining data from a sample of 276 students attending low SES (socio-economic status) inner city schools. Each student had taken the LRJA (our reflective judgment assessment) 3 times over 3 1/2 years. Some of these students were in grade 4 at time 1, and some were in grade 6 at time 1. Each LRJA performance received 2 scores, 1 for its developmental level (shown on the vertical axis in the graphic below), and one for its logical coherence, rated on a 10 point scale.

We conducted a hierarchical regression analysis that examined the relation between time 1 argumentation score and developmental growth (after controlling for developmental level at time 1).

For the figure below, I've borrowed the third graph from the "stop trying to speed up learning" post, faded it into the background, then superimposed growth curves predicted by the hierarchical regression model for three hypothetical students receiving time 1 coherence scores of 5.5, 6.5, and 7.5.* These values were selected because they are close to the actual time 1 coherence scores for the three groups of students in the background graphic. (Actual average time 1 scores are shown on the right.)

As you can see, the distance between grade 8 scores predicted by the hierarchical regression is a bit less than half of the difference between the actual average scores in the background image. What this means is that in grade 8, a bit less than half of the difference between students in the three types of schools is explained by depth of understanding (as captured by our measure of coherence).

In my earlier post, "If you want students to develop faster, stop trying to speed up learning," I concluded that socioeconomic status could not be the main cause of the differences in growth curves for different kinds of schools, because two of the groups we compared were not socio-economically different. The results of the analysis shown in this post suggests that almost half of the difference is due to the different levels of understanding reflected in coherence scores. This result supports the hypothesis that it is possible to accelerate development by increasing the depth of students' understanding .

We cannot even attempt to explain the remaining differences between school groups without controlling for the effects of socio-economic status and English proficiency. We'll do that as soon as we've finished rating the logical coherence of performances from a larger sample of students representing all three types of schools featured in this analysis. Stay tuned!

Lectica's nonprofit mission is to help educators foster deep understanding and lifelong growth. We can do it with your help! Please donate now. Your donation will help us deliver our learning tools—free—to K-12 teachers everywhere.

*You can learn more about our developmental scale on lectica**live**'s skill levels page, and our argumentation scales are described in the video, New evidence that robust knowledge networks support development.