Our Approach

We believe students deserve a math education which is useful and speaks to their everyday experiences. So many students get turned off by the current curriculum. They feel it is boring and pointless. We totally agree. However, we know that math can be taught and tutored differently.

Do you have any doubts? Please sit in on the following two math classes. Both teachers are giving a lesson on "slope", a fundamental concept in algebra. The teacher in Classroom A uses current approaches. The teacher in Classroom B follows our approach.

Classroom A

The teacher says, "Okay class. I am very pleased looking at your work just now. You discovered how a change in vertical distance can be compared to a change in horizontal distance. Also, you understood that you can look at a chart of numbers with two columns and see how the numbers in the right column increase by same value each time as 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 this activity is called 'slope'. I am now going to show you the slope formula. The slope formula 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. Slope is the only way we can think critically, rigorously, and foster a deep conceptual understanding about how quantities 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 calculate 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. Today's lesson is about a topic 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."

"However, slope in mathematics 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 included in all textbooks so you need to know it. Therefore, I'll go slowly to ease the way for you. By then you will already have a clear understanding of the concepts. That way, the whole mess of symbols in the general formula won't throw you off."

A student speaks up. "But I don’t get it. You said we understood things in the activity we just did. 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 in real life we are usually missing key information. For example, sometimes a driver needs to calculate his travel distance and his travel time as well. Suppose 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 was he driving for?"

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 connect it to 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, That question is too hard for me..."

* * *

Which classroom do you prefer? We hope it is Classroom B. Please sign up for Tutoring to experience math the way that fits you.