Look at the problem above. This is an example of a bar model.
Can you find the answers?
Yes, there is more than one answer to this problem, even though there is only one question mark.
Did you find it?
The answers are: The whole bar equals $50. Each square equals $10. The remaining squares equal $20.
Were you right?
This seems to be a simple problem. Simple addition and subtraction. However, expecting an eight-year old to complete this problem is a challenge. Many students struggle with math due to the abstract concepts which are posed. National testing is ever more pushing the abstract in order to "keep up" with other developing nations. Our testing does not account for the factors of home life, behavioral issues, learning abilities, or development.
As students enter Kindergarten most have already been taught the ABC's and 123's; and others can recount last night's events in detail but have no idea as to what is "the alphabet". By the time students reach the 3rd grade they are expected to have mastered number names, place value, addition, and subtraction. This poses to be a problem for some students. Some students entered the game of school behind due to the lack of educational stimulus, and the simple construction of an addition problem is mind boggling.
So, researchers have developed the idea that leveling students based upon needs in a subject will be the solution. Right idea in theory? Teach, re-mediate, teach, re-mediate, and so on? Reality is a different scenario. This tiered system with the combination of rigorous curriculum has created "learning holes" in many students.
The Learning Hole :)
The concept of how to revolutionize the education system is underway. The execution of the plan is where the downfall lies. My theory for changing the system is to integrate one new idea at a time. Incremental chunks would work better than a straight blow to a known and understood curriculum. At times, new curriculum will take assumed student knowledge and apply that to lessons. This assumed knowledge sets back the class due to the need to teach a new concept of how to tackle a problem.
Example:
Problem - Addition
Concept- Bar Model
Challenge- Workbook page asks students to answer the problem using a bar model. Students were to have learned bar modeling in prior grade. Prior grade level used a different curriculum. Workbook assumes students know how to use a bar model.
Using a bar model is a great way to solve an addition problem. Plus it will be useful as students move into higher mathematics. Right now, however, it is apparent where holes in student learning are formed. There is no room for learning the WHY of a problem, it is all about the HOW. We learn how to finish a problem but never understand why. We push forward but we are learning without understanding.