Network Graph of Skills Learned in Algebra 2

Similar to this post from a couple years ago, recently I used Gephi to create a network diagram of all the skills that an Algebra 2 student would gain over the course of the year. It didn't turn out as good as I hoped, but I still think it's cool to look at and digest.

  • The size of the nodes (the skills, ex. Order of Operations) is based on the concept of betweenness centrality, a concept that Google's Generative Search summarizes as "Betweenness centrality quantifies how many times a particular node comes in the shortest chosen path between two other nodes" which to me means how vital or important it is. 
  • The position or centrality (how central it is) of the node is also a measure of importance, based on Gephi's Force Atlas 2 algorithim, which Generative Search summarizes as, "Force Atlas 2 is a force-directed layout that simulates a physical system to spatialize a network. Nodes repulse each other like charged particles, while edges attract their nodes, like springs. These forces create a movement that converges to a balanced state", which again to me means that it algo-balances it and finds the best shape somehow.
  • I honestly don't remember what the size of the edges (the connection between skills, that are in the same month) means.


The process I used was:

  1. Asked GPT-4 what topics it thought were most important that a student would learn in Algebra 2
  2. Asked it to break that list of topics into 8 different months worth of curriculum
  3. Asked it for 10 problems per month that an exemplar student would be able to solve
  4. Then asked it to list the skills needed to solve all of those problems, in order of how you'd learn them (earliest skill first, most recent last)
  5. Within each month, I created an edge for each skill paired with each other skill in that month. This created 525 edges (or connections, or times both skills needed to be known to learn that month's content) between the 50 nodes (skills)
  6. Used this tutorial again because I forgot what to do next


Here's the table of nodes (skills) a student should know by the end of Algebra 2:

Id Label
1 Basic Arithmetic Skills
2 Factoring Algebraic Expressions
3 Factoring Polynomials
4 Finding the Domain of a Rational Function
5 Graphing Exponential and Logarithmic Functions
6 Graphing Exponential Functions
7 Graphing Linear Equations
8 Graphing Polynomial Functions
9 Graphing Quadratic Functions
10 Graphing Radical Functions
11 Graphing Rational Functions
12 Order of Operations (PEMDAS/BODMAS)
13 Simplifying Algebraic Expressions
14 Solving Exponential Equations
15 Solving Logarithmic Equations
16 Solving Quadratic Equations
17 Solving Quadratic Equations by Completing the Square
18 Solving Quadratic Equations by Factoring
19 Solving Quadratic Equations using the Quadratic Formula
20 Solving Radical Equations
21 Solving Simple Linear Equations
22 Solving Systems of Linear Equations
23 Understanding of Asymptotes
24 Understanding of Coordinate Geometry
25 Understanding of Data Representation
26 Understanding of Exponents
27 Understanding of Exponents and Roots
28 Understanding of Fractions and Decimals
29 Understanding of Function Transformations
30 Understanding of Inequalities
31 Understanding of Logarithms
32
Understanding of Maximum and Minimum Values of a Quadratic Function
33 Understanding of Measures of Central Tendency
34 Understanding of Measures of Dispersion
35 Understanding of Polynomial Division
36 Understanding of Polynomial Roots and Zeros
37 Understanding of Polynomials
38 Understanding of Probability
39 Understanding of Probability Distributions
40 Understanding of Quadratic Functions
41 Understanding of Radicals
42 Understanding of Rational Expressions and Equations
43 Understanding of Roots of a Quadratic Function
44 Understanding of Sets and Counting Principles
45 Understanding of Statistical Inference
46 Understanding of Variables
47 Understanding of Vertex Form of a Quadratic Function
48 Understanding the Change of Base Formula
49
Understanding the Relationship between Exponential and Logarithmic Functions
50 Writing Polynomial Functions