I think that there should be two main components to math instruction. First, an exploration of each topic that promotes true understanding. We like to use manipulatives whenever possible. There’s something about being able to touch math that makes it real for kids. Base 10 Blocks, chips, fraction circles and towers (or fraction Hershey bars – yum) and other manipulatives help students to see what they are doing and why they are doing it. We also use toy cars, blocks, and other household items as manipulatives in an attempt to make math more real. I think that the other dimension of math instruction, whether it is at home or in the classroom, needs to be a self paced and individualized program. I have a serious problem with math workbooks and math homework. I just don’t think they are logical – when a student does not understand a concept, workbooks can be frustrating and even worse, they can reinforce an incorrect answer.

An example: a student is sure that 5×6=35 and that student practices this fact several times in her take home workbook. Because there are 25 students in that math class, the teacher corrects and returns the workbooks several days later. The group has already moved on to a different multiplication fact when the student discovers that she has learned the incorrect information. Because she practiced it several times, it is now more difficult to correct the mistake and it becomes an issue for her as she progresses through school.

Now, if that same student had worked on this problem with an online, self paced program, she would have had a different experience. After her first attempt, the program would have shown her the error and the way to fix the error. She would not be able to move on until she practiced a similar problem and completed it correctly. This method also allows an entire classroom of students to move at their own pace, so there is a better chance that the student actually absorbs the material instead of getting lost in the crowd. Self paced instruction is an efficient way to meet educational standards, and a way to make math less stressful for students who are struggling. Many of us have math anxiety that stems from being in the lowest math group or from being called on in rapid succession to call out the answer to a problem. Computer aided math instruction eliminates this issue and could help students to have a better view of math as they move through the grades. It is also a great solution for home school, where you might have a second grader, fourth grader and fifth grader (that’s what I have) who are all at different levels and respond to different types of instruction.

There are many online math programs. Please comment on this post if there is one that has worked for you. Here are the ones that we use at our house:

Stanford EPGY Math: This is a program for gifted learners. It really appeals to students who are driven and can understand abstract concepts. It is definitely not for everyone. The student who does well in a lecture based academic environment will thrive in this program. The student who needs constant incentives and bells and whistles will not enjoy EPGY math. The program challenges students who might otherwise become bored in a traditional classroom, moving at a traditional pace.

Reasoning Mind: Reasoning Mind is a great combination of math instruction, animation and incentive programs. It presents information in a variety of ways and tries to appeal to a very broad student base. The problems are differentiated in three levels – the concept is explained with the basic and easy to solve questions, then the students are challenged with two more levels of difficulty. If a student is not ready for a particular level, the program skips through it and allows the student to return later. When the student answers incorrectly, the program reinforces the steps to determine the correct answer. I would recommend this program for any student (2^{nd} grade and up), whether they are struggling, average performers, or ahead of the game.