Tech Minds - Individual Discussions

1.  Identify all the changes involved in the principle, and write a generality that includes the changes and the relationship among the changes. References are needed.

2.  Share the proposed media selection for modifying the instruction as appropriate to each change for your Case Study. Clearly define the forms of behaviors applied to the changes.
For example, a video game is proposed to replace the PowerPoint presentation to let the students practice on Math multiplication. State the forms of behaviors applied to this change.

After a long discussion via Skype, we collaboratively found some additions and modifications to the borrowing lesson we used for Module 4 and worked together to find the references and proposed media selection for the changes in our case study.

First, we would like to add in the definitions of the parts of a subtraction problem.
       Minuend  -  Subtrahend  =  Difference
This will help students to understand the terms for the subtraction problems they are coming into contact with and will make it easier to describe which number the teacher is referring when teaching borrowing. For example, instead of saying is the bottom number smaller than the top number, the teacher can say is the number in the one's column of the subtrahend smaller than the number in the one's column of the minuend. If not, you will need to borrow...
Reference:  http://mathworld.wolfram.com/Subtraction.html, http://mathworld.wolfram.com/Minuend.html, http://mathworld.wolfram.com/Subtrahend.html
Proposed Media Selection:  http://www.mathsisfun.com/numbers/subtraction.html
This website gives students the ability to see the numbers (arranged as they would be in a subtraction problem), clearly labeled with the terms listed above. It is also done in vibrant colors giving clear definitions of each of the labels listed for the subtraction problem.

Second, we thought the process of regrouping should be broken down into simpler, easier-to-follow steps for the students. This could first be done by breaking down subtraction, in general, and giving students a refresher course in subtraction. Oftentimes students were unable to grasp the concept entirely the first time it was taught, and by refreshing their memories on subtraction before implementing borrowing, this would help to do so.
Reference & Proposed Media Selection:  http://www.mathsisfun.com/numbers/subtraction-regrouping.html
This website gives students step-by-step examples of subtraction problems, beginning with a problem that does not need regrouping and developing into a problem that does. There are videos that show the students this, as well as printable worksheets and sample problems to try after watching the videos.
Other Proposed Media Selection:  http://www.khanacademy.org/math/arithmetic/addition-subtraction/v/basic-subtraction
For those students needing even more basic explanations of subtraction, this is a great video. This video begins by showing an addition problem and then, using the same numbers, shows a subtraction problem to "introduce subtraction" and eventually explains the concept of fact families. The video shows someone demonstrating a drawing, as well as a number line to visually show addition and subtraction (use of manipulatives).

Third, we found that the use of manipulatives and showing students how to use manipulatives to better understand the process of subtraction and borrowing would be a great addition to the lesson. "The use of manipulatives enables students to explore concepts at the first, or concrete, level of understanding. When students manipulate objects, they are taking the necessary first steps toward building understanding and internalizing math processes and procedures."
Reference:  http://www.teachervision.fen.com/pro-dev/teaching-methods/48934.html
Proposed Media Selection:  http://www.brainpopjr.com/math/additionandsubtraction/basicsubtraction/
This BrainPOP video allowed students to see the use of different manipulatives to use in subtraction problems. Annie and Moby began with a scenario of birds flying away and trying to figure out how many are left. In this problem, they used many different methods to help them subtract: drawing a picture, using counters (manipulative), and writing a number sentence. Later in the video, they used a number line to do a subtraction problem (something very efficient that students can do on a corner of their page to help with subtraction problems).
Another Proposed Media Selection:  http://www.mathplayground.com/howto_regroupI.html
This video shows students how to use base 10 blocks to better understand regrouping and why, when taking from the column in the ten's place, they have to add a "1" in front of the number in the one's place. This method and video explain this thoroughly and show yet another manipulative that can be used to help with subtraction problems.

RESEARCH TO FOLLOW