My workflow for studying and learning in Mathematics and Computer Science, revised

Introduction

A couple of years ago I wrote a post detailing my whole studying process. A lot has changed since then, both in my workflow and in how I understand the process of learning. This post is a complete overhaul of the previous one.

Before diving into it, I should make clear that I am in no way an expert on the topic. Whenever possible I will cite references, although research in this field is lacking, and I will be drawing from my own experience as well.

The main inspiration for the change in my workflow is Justin Sung, whose YouTube channel I highly recommend. Many of the concepts I explore in this post are covered more thoroughly in his Report on Learning .

Preliminary concepts

I will begin this post by introducing several concepts. I do this in order to establish a convenient terminology.

Bloom’s revised taxonomy

The first concept is a taxonomy of cognitive skills. Bloom’s revised taxonomy of cognitive skills goes as follows :

  1. Remember. Retrieving information from long-term memory. This includes both recalling and recognising.
  2. Understand. Interpreting, exemplifying, classifying, summarising, inferring, comparing and explaining are all skills that fall in this category.
  3. Apply. Using the information to perform certain procedure. This includes execution and implementation.
  4. Analyse. Dividing the information into constituent parts and identifying the relationships between them. This includes, for example, differentiating, organising and attributing.
  5. Evaluate. Being able to judge the information. Critiquing and checking are examples of this.
  6. Create. Grouping elements together to form a novel and coherent whole.

The first three cognitive skills are typically summarised as Lower Order Cognitive Skills (LOCS), whereas the last three as Higher Order Cognitive Skills (HOCS). It is my understanding that applying information does not include the process of knowledge transfer, that is, linking the information to a novel seemingly unrelated problem. This skill would probably fall under the Create category.

As a general rule, LOCS tend to see information in isolation, while HOCS require to take into account the context and relationships.

As we go up in the education system, acquiring Higher Order Cognitive Skill is more and more necessary. Evaluation methods such us essays, difficult problems or short questions are more common. It is natural to think that when learning new material, one should begin with this taxonomy from top to bottom. Justin’s approach does the complete opposite.

Cognitive Load Theory

Cognitive Load Theory (CLT) is based on the premise that human information processing and memory operate through the mobilisation of fixed cognitive resources . The invested cognitive resources are called Cognitive Load (CL). One of these resources is working memory, which is known to be very limited. The natural question that arises is how can we overcome this limitation on Cognitive Load.

Cognitive Loads are generally divided into three categories :

Bannert describes three ways of managing cognitive load . The first one and most obvious is reducing ECL. The other two are based on the premise that there is no practical limit on the ability of humans to recall information from long-term memory, and that proper schemata seem to reduce the cognitive load generated by the information. These ideas are:

Nothing has been said thus far about the amount of (intrinsic or germane) cognitive load that a learning activity should generate to optimise learning. While I did not find a definitive answer in the literature, it seems that higher cognitive loads, if they do not overload our capacity, are better. For example, practicing recalling information without looking at the material (active recall) is far superior in terms of retention than other more passive techniques like re-reading or highlighting.

Relating back to Bloom’s taxonomy, practicing HOCS generally produces a higher cognitive load. Although a technique that focuses on HOCS does not necessarily train recalling information explicitly, in my own experience my retention is fantastic after using such techniques, much better than if I were to invest the same time in retention alone. It intuitively makes sense, it is easier to remember connected information than just memorising random facts. We start with building schemata to free up more cognitive load capacity

Constructivism and inquiry-based learning

Spacing

This refers to spacing out the learning activities in time. With the same amount of total studying time, spacing has been shown to improve both knowledge retention and knowledge transfer . The optimal amount of spacing is not clear, but one nigh of sleep should serve as minimum. I do not actively apply this concepts, it follows naturally from trying to stay up to date with the material.

My process

Conclusions