Our Approach Explained

We started Math For The Masses because we feel there must be a different approach to math education other than the ones currently pursued in America. We feel the curriculums most common today either place too much emphasis on theory and abstract concepts or too much emphasis on formulas and rules rather than math's connection to real life.

The problem is that nobody thinks there can be a different approach.

We are here to prove that there is an alternative. Our idea is not revolutionary but rather just the result of listening to what math students have been saying all along. We are building lessons and a curriculum that constantly connect students' mathematics learning to their knowledge and experience of the world without dumbing anything down.

A Tale of Two Classrooms

Are you skeptical this can be done? Here's your opportunity to experience it firsthand. Please sit in on each of the two classrooms described below. Both classes are learning a lesson about "slope", a fundamental topic in algebra. Classroom A follows the current approaches in mathematics education and Classroom B follows our approach.

Classroom A

The teacher says, "Okay class. I am very pleased looking at your work that you did right now at the beginning of class. I saw how you discovered how a change in vertical distance can be compared to a change in horizontal distance. Also, you understood that you could look at a chart of numbers with two columns and see how the numbers in the right column increase by same value each time the numbers in the left column increase by one unit. Great job! Are there any questions yet?"

The class is silent.

The teacher continues, "What you discovered in the activity is called 'slope'. I'm now going to show you the slope formula which is the general form of what you just discovered on your own. The slope formula is extremely important because it helps us compare different lines and solve equations. It is the only way we can think critically and rigorously about how things change according to a constant rate."

The teacher walks to the whiteboard and says the following, "Let (x1,y1) and (x2,y2) be the coordinates of two points in the rectangular coordinate plane. Then the slope formula between the two points graphed here is defined as:

Immediately, students speak up, one by one.

"What is the letter m doing there?"

"What are those little triangles supposed to mean? I thought this was algebra class not geometry."

"Why are the y's on top and the x's on bottom? Shouldn't things be in alphabetical order?"

"Why are the little 1's and 2's a the bottom-right of the x's and y's rather than to the top-right like we are used to seeing?"

"Why are the 2's before the 1's?"

"Why is it subtraction and not addition?"

"What are the words 'rise' and 'run' supposed to mean? What's running? Couldn't something fall also?"

The teacher responds, "Yes, I understand that the slope formula is difficult at first. However, you did so well in the activity at the beginning of class so I know you can understand it. I'll explain each part of the formula now... "

The entire class zones out...

Classroom B

The teacher says, "Ok class. I hope you got something out of the short activity you just did. Just to recap - you saw that we can get an average rate of speed (like miles per hour) by dividing the total distance by the total time. So 120 miles in 2 hours means an average speed of 60 mph".

Now we're going to build on this lesson just a little more with a concept mathematicians call 'slope'. Slope is just another math vocabulary word that refers to a broad topic. It’s connected to things you normally associate with the English word 'slope'- like the slant of a ski slope or hill. But it actually means a lot more than that. We usually use slope to keep track of different rates, just like you did right now with distance and time. On a graph, we do this by making time a horizontal movement and distance a vertical movement. Here is an example:”

“Mathematicians have come up with a formula which applies to the numbers and not just the graph. Unfortunately it is incredibly confusing to most students. However, it is used in all textbooks these days so we will need to use it eventually. Therefore, I'll go slowly to ease the way into it so you are not thrown off by it. "

A student speaks up. "But I don’t get it. You said we understood things in the beginning activity so why do we even need another formula? Why do you need to make things harder than they already are?"

The teacher responds, "Great question. In the activity, I gave you the total distance and the total time. All you had to do was to divide the two numbers. The problem is that we don't always have all the information that we want. Sometimes a driver needs to calculate how far he has driven and the amount of time as well. For example, say a driver gets onto a highway at mile marker 50 and exits at mile marker 170. How far did he drive?"

The student replies, "Well that’s just 120 miles."

“Wonderful. The total distance is 120 miles because if we take where the driver ended and subtract where he started then that is the subtraction problem 170 - 50 = 120."

"Now let's talk about the time he traveled", the teacher says. "Suppose the driver started at 3pm and ended the ride at 5pm. How much time did he take driving?"

Another student answers, "Two hours."

"Great. If we take the end time or 5pm and subtract the start time of 3pm then we get the subtraction problem 5-3=2. Now I’ll show you the slope formula and how it connects the example from the beginning of class."

Slope Formula (Distance -Time Version)

"Are there any questions?", the teacher asks.

A student speaks up, "No. This makes sense. But, why do textbooks make it so much more difficult?"

"I wish I knew the answer to that one, but I'll just continue to teach you like this since it's working and their approach isn't- at least not for most students."

* * *

Which classroom do you prefer? Well, if it's Classroom B then we hope you will explore our website. Please be in touch because this is the way we envision math education should be.