# Student Bite Size vs Curriculum Portion Size

*Students eat meals of information at similar bite rates when each spoonful fed to them is sized appropriately relative to the size of their mouth. (Note that equal bite rates does not imply equal rates of food volume intake.)*

I previously wrote a critique of a paper’s conclusion that in a favorable learning environment, students learn at roughly the same rate per learning opportunity (i.e., per worked example or practice problem).

Thre is one setting in which the conclusions of the paper might make sense to me. It involves tightening the definition of “favorable learning conditions” to the point that it becomes more theoretical than practical, and it doesn’t imply that students actually learn at similar absolute rates, but here it is.

The paper limits its conclusions to the context of “favorable learning conditions,” which it described as follows:

*"a) provide immediate feedback on errors in problem solving or performance contexts (21, 22),**b) provide explanatory context-specific instruction on demand (e.g., ref. 23), including an example correct response if needed (24–26),**c) highly encourage or enforce students to enter or observe a correct response before moving on,**d) provide tailored tasks designed through data-based cognitive task analysis to practice specific cognitive competences aligned with course goals for improving student thinking (e.g., refs. 27 and 28), and**e) give repeated opportunities to ensure student mastery of these cognitive competences (e.g., ref. 29) in varied tasks that require appropriate generalized, but not overgeneralized, knowledge and skill acquisition (e.g., ref. 30)."*

I wonder if the definition of “favorable learning conditions” also needs to specify (in some more precise way) that the curriculum is sufficiently granular relative to most students’ comfortable “bite sizes” for learning new information, and includes sufficient review relative to their forgetting rates.

Under that definition, it would make more intuitive sense to me that (barring hard cognitive limits) such favorable learning conditions could to some extent factor out cognitive differences, causing learning rates to appear surprisingly regular. A metaphor: “students eat meals of information at similar bite rates when each spoonful fed to them is sufficiently small.”

Though, ceiling effects may confound when the curriculum is too granular or provides too much review relative to the learner’s needs – so perhaps the definition would need to be amended once more to specify that the curriculum’s granularity is equal to the student’s bite size and rate of review is equal to the student’s rate of forgetting. The amended metaphor: “students eat meals of information at similar bite rates when each spoonful fed to them is sized appropriately relative to the size of their mouth.” (Note that equal bite rates does not imply equal rates of food volume intake.)

This definition of “favorable learning conditions” would also allow for anecdotes / case studies of math becoming hard for different students at different levels, because the following factors affect students differentially as they move up the levels of math:

*Combinatorial explosion in the problem space*-- lowers the "bite size" more for students with lower generalization ability, or, equivalently, reduces the perceived granularity of the curriculum. (Side note: I've always suspected combinatorial explosion was the reason why I encountered so many high schoolers who did well in math but struggled in physics.)*Large body of knowledge to maintain*-- increases the amount of review more for students with higher forgetting rates. Also reduces effective "bite size" since an increasing portion of each bite will consist of reviewing fuzzy prerequisite material.

It would even allow for the concept of soft and hard ceilings on the highest level of math that one can reach:

- Say we have a student with low generalization ability and high forgetting rate. Then a favorable curriculum takes more time to work through (as compared to a favorable curriculum for an average student) due to increased granularity and review, and that multiplier increases as they go up the levels of math.
- At some point "it requires lots of practice to learn" becomes synonymous with "can't learn" -- first in a soft sense of "the benefits of engaging in this much practice do not outweigh the opportunity costs of neglecting to develop my skills in other domains that I find easier," and then in a hard sense of "the amount of practice required exceeds the sum of waking hours over the remainder of my life."