LaTex and the basis of mathematical communication
As it would be utopian to learn a language without knowing its alphabet and grammar, it seems equally utopian to attempt to understand math without mastering its symbols, syntax, and terminology.
Publish at November 06 2017 Updated October 12 2022
How to build an educational progression or sequence around a general objective ? How to organize activities so that they allow mastery of knowledge associated with a skill ?
Here are some tools to get started, accompanied by the pedagogical assumptions on which they are based.
In order to help teachers in vocational training, the Organisation Internationale de la Francophonie (OIF) has developed a series of guides for implementing a competency-based approach. There is little theory or nuance in the definitions, but pragmatic and immediately usable advice.
The guide also emphasizes consideration of the educational project of the institution or team. It gives some examples of axes among which we can mention the development of autonomy, the sense of finishing, respect for others and the environment, etc.
The authors of the guide take a competency-based approach. To this end, they use the 2005 definition of the Quebec Ministry of Education, Recreation and Sport:
"the power to act, succeed and progress that allows one to adequately carry out tasks, professional or personal life activities, and that is based on an organized set of knowledge: knowledge and skills from various fields, strategies, perceptions, attitudes,etc."
This is a definition in a few words that might not satisfy pedagogy specialists, but it can be useful for a trainer concerned with organizing and planning the learning phases of his groups.
The CPA begins with an analysis of the craft in context. The diagram below captures the main features of this analysis.

The guide is based on the assumptions of the socioconstructivist approach:

The guide finally gives us a generic method to support skill building.

The guide then suggests listing the skills, and breaking them down into a timeline based on the week they will be specifically worked on. The tool is presented as a large chart.
For each skill, the guide suggests creating worksheets. These cards are very structured, and we invite you to discover the examples presented.
The associated knowledge is accompanied by "tags," which clarify the expected level of achievement.

The Mooc from the University of Montreal, "Tools to help script an activity" extends this work. It proposes to help script an educational activity. The pedagogical model chosen by the Mooc team, and in particular Bruno Poellhuber, is learning through active and "sociocentric" methods.
The Mooc is a tool for the development of a pedagogical activity.
In simple and operational terms, the teacher develops an approach in which learners are most often active and in small groups. Before defining the activity, he invites us to specify the objectives using the method of Krathwohl, Bloom, and Anderson and to answer some questions. Bruno Poellhuber emphasizes dissemination.

Bruno Poellhuber's work has resulted in the creation of a scripting tool. For a general purpose, it has several phases:
The approaches presented above aim to give a structure to build training they are based on pedagogical assumptions that have demonstrated their interest, whether it is learning by doing or sociocentric. Starting from hypotheses from other pedagogical currents, such as neuroscience or connectionism, we would obtain other grids, also very relevant!
Illustrations: Frédéric Duriez
Resources
Organisation internationale de la francophonie - Design and production of an educational guide accessed on November 4, 2017
https://www.umc.edu.dz/images/guide-approche-par-comptence.pdf
Bruno Poellhuber: Scripting Tool accessed November 4, 2017
http://oas.ccdmd.qc.ca/app/scenario.php?demande=accueil