# The DNA of Math

The DNA of Math is the master breakdown of the skills of mathematics, starting with learning about integers and basic equations in Pre-Alegbra, all the way through advanced topics in Calculus and Differential Equations. Breaking math into digestible pieces allows for all kinds of efficient analyses and makes all the content of Mr. Math's vast well of resources possible - from algorithms that can figure out what topic you're learning based on your homework, to effective recommendations of prerequisite topics to help you identify why a new subject might be difficult, to showcasing the most commonly taught subjects and skills in easy to search formats.

Every topic of discussion starting with what integers are and going up to and beyond integration by parts is its own lesson. To make naviagation manageable and organized for students, lessons are stratified by course, chapter, and section. This way, lessons not only fit in to a streamlined, premeditated math story, but are also easily idenitifiable. Each lesson ID is comprised of elements that dictate exactly where they lie in the DNA scheme. Here's an example:

The first two characters dictate the course (PA = Pre-Algebra, AT = Algebra Two, CA = Calculus, etc.). The third character is the chapter number (1, 2, 3, etc.). The fourth character is the section (A, B, C, etc.), and the remaining characters are lower case roman numerals that represent which lesson in the section it is. Chapters are a loose collection of related lessons in a common topic (e.g. Trigonometry), while sections zone in on a particular aspect (e.g. Right Triangle Trig) and lessons are specific to a set of intimately related skills (e.g. Solving Right Triangles with SOH-CAH-TOA).

Each lesson is earmarked with several important metrics.

### 1. Priority

Any given lesson is assigned one of four major levels of importance:

• VIP Knowledge (Very Important Piece of Knowledge): Incredibly essential for the future and widespread as a foundation for many, many future lessons. Mastering VIP lessons is of the utmost importance for success in math.
• High: Fairly commonly used skill that will either be used a lot permanently for the rest of your math career, or is very important for the upcoming lessons that follow. You will probably have a bad time without knowing these lessons well, at least at some point.
• Normal: This is the most common lesson type. Normal lessons will build upon your knowledge and are fairly localized to the part of the DNA to which they belong. Their knowledge and skills are going to pop up from time to time in future lessons, but not frequently enough to earn the High or VIP badges. That doesn't make them unimportant to learn, only that you may or may not be sorry in the future without the knowledge from these lessons, relative to VIP and High prioirty lessons.
• Optional: Believe it or not, there are actually topics that are not that important in math (yes, let me see your shocked face). They are important enough to include in our comprehensive journey, but they are very isolated from other topics. Optional lessons are not intricately woven into the fabric of math. When your class is working on a topic that Mr. Math calls optional, rest assured that, while you need to learn it for the quiz or test, you will probably never see it again after that.

Note that when you look at lesson directories on Mr. Math, you can see the priority. You can also filter at the top of the lesson list page to see only the priority lessons you are interested in.

### 2. Prerequisites

Each lesson has up to seven prerequisite topics listed with it. These prerequisites are visible when viewing the web based version of the lesson. Fueled by the organizational power of The DNA of Math, the prerequisites for each lesson refer to the handpicked few most important prior lessons that should be mastered before. This is a powerful way to diagnose the reason why you might be having trouble with a new topic your class is working on. For example, a student may figure out that he or she is getting half the questions wrong when calculating the slope between two points because they never mastered subtracting negative numbers, which is a necessary skill in that topic.

### 3. Objectives

Objectives can be viewed either by clicking on a topic in the lesson list, or at the top of a lesson page. Objectives make it really clear what each lesson covers, so that if you're studying a dense topic like Logarithms that spans several lessons, you can quickly see which lessons contain which skills.

### 4. Topic Tags

Tags on a lesson indicate what general theme the lesson belongs to (e.g. Variable Exponents or Solving Equations). This makes it easy to filter all lessons for exactly what you want, and is a great way to round up common topics across all courses.

View Lesson List by Course »

Explore the DNA of Math below! View Lesson List » to see it in text form!

Traditional math educations systems work great, but have a few shortcomings that often cause gaps in math learning. Missing math knowledge typically leads to students' occasional struggle at best, and a permanent lack of math confidence at worst. One cause of this is the necessary lack of consistency in teaching year-over-year. On one hand, having a new math teacher every year has its perks - after all, you don't want your Kindergarten teacher prepping you for the SAT. But while teacher-changeover each year is a necessary part of education, for the right student in the wrong situation, knowledge gaps are created when a student starts a school year with a new teacher who doesn't correctly know or assess what a student already knows - because the student sure as heck doesn't know what he or she doesn't know. Another common cause of math knowledge gap happens because skills from long-ago are lost, or because textbooks teach you new topics without systematically identifying the building block skills from your past that are prerequisite. Mister Math cannot change education holistically, but he can address these common problems.

The DNA of Math solves both the "instruction continuity" and the "prerequisite tracking" issues. Unlike a single text book, which necessarily has a scope of a single year's course, The DNA of Math seeks to interconnect every skill from Pre-Algebra through Advanced Calculus. You can think of it like one giant course, but digestible and appropriately organized. When you think about it, there really is a skill-by-skill way to start with your grade-school knowledge in the humble beginnings of Pre-Algebra (what integers are, what variables are, fraction skills, etc.) and end with Calculus knowledge, without "restarting" every September. That singular road is long and multifaceted, but there is a story to tell - a plot, so to speak. And just like any story, some parts are more important than others. Accordingly, each Mister Math lesson is earmarked for degree of importance. And also just like a story, some parts make more sense when you remember what happened earlier in the tale. Once again, each Mister Math lesson links to which other skills are prerequisite so that you can instantly assess whether or not you know the math you are already supposed to know, before wasting your time by ineffectively fumbling through material which you don't yet have the foundation for.

## What the DNA Allows

This streamlining of knowledge is only possible due to the organization and singular completeness of The DNA of Math. Additionally, such a thorough curriculum allows for things like:

• Efficient Learning - No more course-by-course "restarting". Every Algebra (and sometimes Calculus) book you pick up starts with Pre-Algebra topics. This is potentially wasteful, nearly always confusing, and leads to a lack of unity in math. Ten algebra teachers would write ten different year plans for the skills they plan to teach in an Algebra 2 course, none of which is necessarily aligned with a student's past and future experience. Mister Math's story is one whole. "Courses" are used to classify skills for organization and convenience, but because the picture is complete, there is no need to explicitly repeat material. Instead, prerequisites skills are always identified for students to assess their readiness for a lesson's material.

• Unified and Connected Curriculum - It doesn't matter that one school puts this topic in its "Algebra I" course, while the school in the next city over puts it in "Algebra II". Mister Math keeps each lesson in one place, and connects it to the right prior lessons to make sure the skill doesn't show up too early or too late in the "storyline" of math. It also helps students ensure no skill falls through the cracks that will be important in the future, just because their teacher that year happened to run out of time or elect to skip it.

• ID My Homework - for example, students can use this MM search tool inspired by the game "20 Questions" to figure out that what they're working on for tonight's homework is really called "solving radical equations", and jump to the lesson on it if they want, or find extra practice problems.

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