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:
- Asked GPT-4 what topics it thought were most important that a student would learn in Algebra 2
- Asked it to break that list of topics into 8 different months worth of curriculum
- Asked it for 10 problems per month that an exemplar student would be able to solve
- 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)
- 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)
- 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 |