Renee Tysinger, 6/27/2016, Blog Entry #1

As I read through the introduction I found myself agreeing with the authors on a few different occasions. The first is that problem posing enables a deeper understanding (Brown and Walter, 2005). I constantly encourage my students to ask questions after reading through a problem, while solving a problem, and after  solving a problem. I feel that it is important for them to understand how a procedure works and  whether or not their solution makes sense. I also feel that it is important for them to self monitor their progress. All of these things are done through problem posing. I have a list in my classroom of possible questions to ask that we add to throughout the year as a class. I remind the students that this list is only to be used as a reference for there is no such thing as only one right question. Which leads me to the next point that I align with, that students fear they will not be able to come up with the right  answer (Brown and Walter, 2005). I think this is especially true in math. Unfortunately there is not enough time to teach all of the different approaches to solving a particular math problem. I teach my students a method or two but I also allow them to share their own methods. If their method is consistent and brings them to the correct solution then I will give them full credit. I believe this helps to discourage the "right way" syndrome that the authors mention in the introduction.

Reference:
Brown, S. & Walter, M. (2005). The art of problem posing (3rd ed). New Jersey: Lawrence Erlbaum Associates, Inc.

Renee Tysinger, 6/27/2016, Weekly Problem #1

Proportions are a large part of the 7th grade Math curriculum and thus why it was my first strategy to solve the above problem. The size of the car does not change throughout the problem which allows the use of equivalent ratios to find the missing quantity. This is of course not the only way to solve this problem. I have listed 3 other strategies that are common among my students. The second strategy also uses equivalent ratios by multiplying the denominator and numerator by the same number. Since 16 must be multiplied by 4 to get 64 then we must multiply 6 by 4 as well. This strategy results in the same solution as my first strategy.

The third and fourth strategies use unit rates to find the missing quantity. The third strategy determines that .375 of the toy car takes up 1 inch of the row. We can determine how many cars take up 64 inches of a row using multiplication. The fourth strategy determines that 1 car takes up 2 and 2/3 inches. We can find how many times 2 and 2/3 fits into 64 using division. Just like the previous 2 strategies, the solution is 24 cars in a row that is 64 inches long.