My target audience is middle school students because entering into middle school is where students take “the test” and are assigned into the remedial, average, or accelerated math. After this assignment, it is possible for students to be downgraded, but virtually impossible for them to be promoted. I find that with just a few sessions it is possible for a student performing below grade level to progress and perform at grade level or above.
INTRODUCTION
I am an electrical engineer by training and I love math. I have two grown daughters and was puzzled when neither of them pursued a mathematics-intensive career. After they graduated college I started to investigate when, in the educational process, children started falling behind in math. What I discovered is what I call a “break point.” It occurs when children enter middle school. Upon entering middle school, most schools stop teaching what I call arithmetic and start teaching mathematics. That is also when they take “the test” which places them into one of the following math tracks. They are placed into the advanced, average or remedial math. From this time forward it is very difficult for students to move into a more advanced track, but relatively easy for them to slide back.
It was at that point that I decided to tutor math at my local middle school. In doing so I was surprised as it seemed that most students had the cognitive ability to understand grade level math. However, they struggled to get correct answers on their class work. In looking at a variety of students, it became obvious that most students struggled with at least on an aspect of basic mathematics. Looking further I saw that most students struggled with one of three basic skills. These skills were, multiplying one digit numbers without a calculator, working with negative numbers, and fractions.
I started to examine remedial math textbooks and found something that I didn’t expect. Most made gross assumptions about what the student already knew. Some started out explaining fractions without covering any of the knowledge that is required to grasp this complex math concept. I came to the conclusion that math teaching materials are written by those for whom math comes easily. I believe that is why it is difficult for some teachers to believe that a student does not understand a concept which the teacher thinks everyone understands. I have had students tell me that teachers have said they don’t believe a student doesn’t understand a concept.
This is why I decided to write my own workbook that covers from the most basic concept describing what a number is and includes all the material you need in order to understand basic algebra. The workbook includes exercises and chapter tests so students can know when they have mastered a concept and are ready to move forward.
The workbook has been used successfully for two years with middle school students and the concept behind the workbook with a variety of students including those who are preparing to take the GED as well as those who are taking remedial math in college. I find that students who follow the process can move from being math phobic to proficient within weeks.
Many students that I encounter have experienced repeated failure in math. Students may have deep seeded beliefs that math is all about memorization, or that they need a calculator, or that it is extremely complicated. None of these beliefs are true. However, in order to break through these beliefs, I find it extremely helpful to get a quick win with students.
When I learned my multiplication tables it was through memorization. It took flash cards and time to learn how to multiply. I have learned a way that doesn’t rely on memorization. It is simple and easy to understand. Often times when I explain it to adults who are proficient in math they will say to me, “how come no one ever taught me this?”
I have seen many students expressions go from blank stares to smiling when they “get it” as I watch their math phobia melt away and their willingness to embark on the work of understanding arithmetic sparked. This program is designed to be delivered to a student by a tutor. I recommend that tutors undergo training prior to working with students. However, an intense knowledge of math is not required as the workbook provides only a foundation of math understanding upon which students can progress on to the more advanced concepts of algebra.
To use a sports analogy, you wouldn’t wake up and decide to run a race without training. If you did you would likely feel bad physically and not very pleased with your performance. In order to succeed in sports, you need to train the muscles used in that activity. I feel strongly that math is a muscle. Expecting to do well with math requires that you train that muscle. The workbook facilitates a student’s training of their math muscle so that it is prepared for the adventure of math learning.
As in sports, not everyone has the same innate ability. However, in the same way, that, with proper training, you can finish a race and feel good about your performance, the same is true with math. You may never take advanced math. Upon completion of the math workbook, you will be able to use math effectively in your life and be prepared for more advanced coursework if you desire.
I also need to say that math is a contact sport. In order to use math effectively, the student must work through problems and progress their learning through the three levels of understanding. First, a student will be able to get the right answer for a problem. However, they will not be able to generalize the knowledge to solve similar problems. The second level is the student will know how to get the right answer. At this point, they can apply their knowledge and be able to solve similar problems. The third and deepest level are where the student can explain how to solve the problem. It is at this point that a student has internalized the knowledge and can move effectively to other concepts.
The essence of math is problem-solving. Math requires you apply what you know to a problem you have not yet encountered. This is one reason why I see math as a life skill. We are constantly faced with problems which require solving and your math knowledge will help you make the best decisions possible. It is important when approaching any problem to “not make stuff up” and to follow the process. If you work with what you know, success is your reward.