Saturday, February 6, 2016

The Power of "C" for Correct.




I have my students do “Check for Understanding” worksheets at the beginning of my flipped class.  These worksheets are typically 3 to 5 questions covering the basics of the lesson they watched before class.  Having students complete these problems provides many interactions between the students and me to make sure they do understand the material.  If they do not understand then I can work with them and help them learn the material.   For students who are shy or quiet these worksheets provide opportunities to really know what they understand.  

Students are expected to complete these problems and have me check their work before starting their normal assignment.  I am surprised at the power of me putting a “C” for correct on their problems even for my juniors and seniors in high school.  Many students won’t start their daily assignments until they have a “C” on each problem of their “Check for Understanding” worksheet even if I tell them that their problems are all correct.  They want that “C” on every problem. (see image)








Last spring I had some students whose goal was to get the “Big C” which was one big “C” on the whole page indicating that all the problems were correct.  (see image)






 






 
I surprised one of my students who often get the “Big C”.  One day I did not give him his normal “Big C”, I supersized it by taping eight more pieces of paper around his page making it a 3 by 3 big page then I put one “Mega C” on it.  (see image)  He loved it and took it home.  The “Mega C” has been hanging on his parents refrigerator for months.










Some of my students from this last fall heard about that students “Mega C”.  They decided that they wanted to beat that students “Mega C”.  So everyday they would do their “Check for Understanding” worksheets and they wanted me to check their work and answers but they did not allow me to put any “C’s” on their pages.  They had a plan to make a supersized “Mega C”.  At the end of the semester they taped all their worksheets together into a 12 by 12 page and had me paint one huge “C” on it.
 

I am surprised that something as simple as putting a “C” for correct on a problem for a student will motivate them to work hard.  Even a this simple “C” motivates my juniors and seniors to go above and beyond what is expected.  Look for ways you can motivate your students to succeed as you check for understanding or learning of your content.



Monday, October 26, 2015

Arithmetic and Algebra, are They Different?



I have not had a lot of time to reflect this year since I have an overload (classes all day and no prep period).  But last Thursday I was at a meeting were they were discussing number/math talks (Making Number Talks Matter).  One of our tasks was to solve a problem then try to think about all the different ways a student might solve a problem, like 55 – 17 of which I thought of four ways to solve it however doing this problem with students the presenter stated that there are eight common ways to solve it.
All this got me thinking about arithmetic and algebra.  I know that algebra is very powerful and more powerful than arithmetic but are there some similarities.  Are arithmetic and algebra really that different?  Consider the following parallel.
Model
Arithmetic
Algebra
Algorithm
      12
 X  14
    4  8
1  2  0
1  6  8


Algorithm Expanded
         10  +  2
   X   10  +  4
         40     8
100  20         .
 100 + 60 + 8
      
            a + 4
      X  2a + 3
          3a + 12
2a2 +  8a         .
2a2 + 11a + 12
Expanded “foil”
  (10 + 2)(10 + 4)
100 + 40 + 20 + 8
    100 + 60 + 8
       
2a2 + 3a + 8a + 12
  2a2 + 11a + 12
Area


   100 + 40 + 20 + 8

     2a2 + 3a + 8a + 12
Summary
Pair each digit of one number with digit of the other number
Pair each term of one binomial with each term of the other binomial
Extending It
    123
X 456

    100 + 20 + 3
X 400 + 50 + 6

(100 + 20 + 3)(400 + 50 + 6)

Pair each digit of one number with digit of the other number



     a + 2c + 3
X 4a + 5c + 6

(a + 2c + 3)(4a + 2c + 6)

Pair each term of one trinomial with each term of the other trinomial

“Algebra” is really doing the exact same processes with numbers that we do with variables, which shouldn’t surprise you considering the variables are representing numbers.  Drawing connections between our algebraic concepts to numerical calculations is important to our students understanding of mathematics.  Many times we as educators will need to redraw these connections as students get farther and farther into the algebra courses.