September 15, 2010

Introduces different systems of counting including the Egyptian base ten, the Babylonian base sixty, the Hindu system using three symbols, and the abacus and computer systems.

How Does Explicit Instruction relate to Constructivist Teaching?

• A teacher should use both strategies.  It is good to let students explore in their learning, but sometimes students can explore forever, but never come to the correct conclusion.  It is good to let students explore, but the teacher should guide their exploration.  Students can explore and come to the wrong conclusions.  Some students can't come up with strategies on their own.

Addition

• Addition is combining two numbers.
• Kids start adding by counting.  For example, if a students has 8 unix cubes.  The students will count each cube individually until they count to 8.

When should students be able to do these addition strategies?

• Count all - students should know this by Kindergarten
• Count on - students should be able to do this by 1st grade
• Count on from larger number -  students should know something about addition, so students in 1st and 2nd grade should be able to do this.
• Make 10 model - 2nd graders
• Make 10 from larger - 2nds graders
• Double +1 - 2nd grades
• The first three years of teaching addition is crucial.  Students should master addition strategies by 2nd grade. 

Parker Book, pgs 14 - 23

• pg. 14 Addition in relationship to set and measurement.  An issue that can come up with using set, students learn to manipulate objects rather than manipulate numbers.  
• Properties of Addition:
• Identity - anything plus zero remains that same number.  Adding something to zero, gets the identical number.  Don't say, "Adding a number to zero doesn't do anything."
• Commutative - order doesn't matter.  4+5 = 5+4.  This can fuel fact families.  Stressing this property can help students see the relationship with numbers.  Build on this, build the foundation to help students get the automaticity.  
• Associative - grouping doesn't matter.  (4+5)+6 = 4+(5+6).  Students will use associative property so the numbers are "more friendly" to add together.  For example: 3+5+7.  Group the 3 and 7 to get 10, then add the 5 to get 15.
• Compensation: 6+9 = take one from the 6 and add it to the 9 to get 10 then add the remaining 5 to get 15. (bottom of pg 17)
• pg. 18 - shows student getting the right answer, but using the equal sign incorrectly. It is important to help students understand how to use the equal sign.  Math is a language. Students need to understand and learn to use this math language to communicate.   

Hundred Chart

• fractions
• adding
• rounding
• an easy way for students find the "nice" numbers
• prime number
• skip counting

Assignments for next week:

• Reflection
• no readings
• Share a difficulty.....