### Post by rualani on Oct 7, 2016 13:20:03 GMT -5

Hello,

I've been math tutoring for, almost, half a semester and I've had some insights on what exactly is going wrong with peoples thought processes as they solve problem.

1) START/FINISH - Many times students will try to dive straight into the math of the problem without even conceptualizing what they are trying to accomplish. For example, I have one student trying to learn conversions for the first time and she was constantly getting lost while trying to solve the problem. She would try to fish for relationships to mix together stuff from the conversion sheet without any knowledge of why she was doing it. I first had to teach her to understand the beginning of her conversion chain and the end. She's getting better at conversions now but I have to constantly readjust her thinking so that she is keeping in mind the goals or objectives of the question.

2) ORGANIZATION AND HIERARCHY - Learning to go down a conceptual level or up for the tasks seems to be key to problem-solving. If I want to convert miles per gallons to the amount of CO^2 emitted by the vehicle it's important to I need to be able to figure out what each step is to the problem. Figuring out which units to convert from and to requires a higher view of the problem to understand what units one is dealing with. However, once you have an idea of the unit conversions required one has to zoom in to the problem to ensure proper placement of conversion fractions. The, one has to cancel out the units and muliply the fractions properly. Finally, the student has to zoom out again to understand if the primary goal of finding Carbon Dioxide emitted is true.

This requires multiple layers of organization from top to bottom with the top being an overall view of the problem and the bottom being the details required to solve it. Constantly, one has to toggle between the upper/lower views in order to fully solve a problem. I find that the people I am tutoring don't really have a feel for when to consider the entire problem and when to use that knowledge to set up the problem. Most of the time they try to jump right into the math without any conceptualization of what the problem is even asking for!

3) INTERPRETING THE DATA - This is one that even I have difficulty with and that's figuring out which information is pertinent to the problem. This is the highest layer of abstraction and it involves figuring out which pieces of data can be used to solve the problem. The student must have a general understand of how the problems are going to be solved so he/she can figure out which pieces of data can be USED for the problem.

Most of the problems in the assignment I've been seeing involve a few wordy problems that challenge the students on this. Problem is student needs to show great familiarity with START/FINISH and ORGANIZATION/HIERARCHY before going through this. Personally, I don't think 1) and 2) are being ironed out enough before they through out word problems from hell.

There you go, That's the secret to MATH.

You may have noticed that there wasn't any math involved in the problem-solving process, and that is the point. Makes me wonder if there is any way to teach proper solving without student learning it as NEEDED to solve problems.

I've been math tutoring for, almost, half a semester and I've had some insights on what exactly is going wrong with peoples thought processes as they solve problem.

1) START/FINISH - Many times students will try to dive straight into the math of the problem without even conceptualizing what they are trying to accomplish. For example, I have one student trying to learn conversions for the first time and she was constantly getting lost while trying to solve the problem. She would try to fish for relationships to mix together stuff from the conversion sheet without any knowledge of why she was doing it. I first had to teach her to understand the beginning of her conversion chain and the end. She's getting better at conversions now but I have to constantly readjust her thinking so that she is keeping in mind the goals or objectives of the question.

2) ORGANIZATION AND HIERARCHY - Learning to go down a conceptual level or up for the tasks seems to be key to problem-solving. If I want to convert miles per gallons to the amount of CO^2 emitted by the vehicle it's important to I need to be able to figure out what each step is to the problem. Figuring out which units to convert from and to requires a higher view of the problem to understand what units one is dealing with. However, once you have an idea of the unit conversions required one has to zoom in to the problem to ensure proper placement of conversion fractions. The, one has to cancel out the units and muliply the fractions properly. Finally, the student has to zoom out again to understand if the primary goal of finding Carbon Dioxide emitted is true.

This requires multiple layers of organization from top to bottom with the top being an overall view of the problem and the bottom being the details required to solve it. Constantly, one has to toggle between the upper/lower views in order to fully solve a problem. I find that the people I am tutoring don't really have a feel for when to consider the entire problem and when to use that knowledge to set up the problem. Most of the time they try to jump right into the math without any conceptualization of what the problem is even asking for!

3) INTERPRETING THE DATA - This is one that even I have difficulty with and that's figuring out which information is pertinent to the problem. This is the highest layer of abstraction and it involves figuring out which pieces of data can be used to solve the problem. The student must have a general understand of how the problems are going to be solved so he/she can figure out which pieces of data can be USED for the problem.

Most of the problems in the assignment I've been seeing involve a few wordy problems that challenge the students on this. Problem is student needs to show great familiarity with START/FINISH and ORGANIZATION/HIERARCHY before going through this. Personally, I don't think 1) and 2) are being ironed out enough before they through out word problems from hell.

There you go, That's the secret to MATH.

You may have noticed that there wasn't any math involved in the problem-solving process, and that is the point. Makes me wonder if there is any way to teach proper solving without student learning it as NEEDED to solve problems.