Student Thinking

1
Student Thinking

• By Daniel Lowell
• Chapple Newell
• Brandy Chambliss

2
Subitizing (Clements)

• Measurement focused on the whole.
• Counting focused on the unit
• Subitizing focused on the whole and the unit
• Perceptual Subitizing
• - Recognition (thats a three)
• - Conceptual (advanced organizer)
• eight can be organized into two
  groups of four.
  

3
Partitioning and Grouping

• Partitioning Ability to separate a whole into
  smaller parts.
  
• Grouping Ability to combine smaller parts into
  a whole.
  
• - Students Break down smaller units of five.
• Advanced organization of larger
  units.
  
• Examples from the videos are.

4
Examples of Partitioning and Grouping

• Video- Monkeys in Two Trees
• Teacher draws a line and separates a whole, 5,
  into several ways of making 5.
  
• The children thought of many ways to divide the 5
  monkeys into two trees.
  
• One child said that to check to see if you had
  all the possible answers, just cross out the 4 1
  and 14, and then you would know there were no
  more.
• Some students decided if there were fewer
  monkeys, there would be fewer possibilities.

5
More Examples of Partitioning and Grouping

• Video- Single Ten Frame
• Teacher had an arrangement of 10 boxes, some
  filled with pumpkins, some empty.
  
• Some students saw the boxes in groups of twos,
  others in groups of threes.
  
• One child said she knew what 4 looked like, so
  then there were only two more.
  
• One child saw a group of 3 on the top and a group
  of three on the bottom.

6
Conceptual Subitizing

• All of these thoughts the students were thinking
  reinforced the concept of
  
• Conceptual Subitzing- The learned ability to
  recognize a set of objects without have to count
  them by ones.

7
Patterns

• Patterns are the ability of students to think and
  organize whole into parts that they are
  comfortable with.
  
• Types Organized and Random, students able to
  recognize efficient pattern.
  
• Action Students able to transfer the organizing
  of patterns.
  
• Manipulatives tiles, fingers, dots, etc

8
Examples of Patterning

• Video- Dot Flash
• 5 dots flashed in an organized pattern for the
  students to see.
  
• One child said she saw 2 on top, 1 in the middle,
  and 2 on bottom.
  
• One child said he saw 4 and then 1 in the
  middle.
  
• The students came up with a variety of ways to
  group the dots that made the pattern easier to
  recognize.

9
More Examples of Patterning

• Cont. from Dot Flash
• The teacher then flashed a random pattern of
  dots.
  
• The students agreed it was harder to recognize a
  scattered or random pattern than an organized or
  easy pattern.

10
Examples of Patterning

• Video- Finger Patterns
• Teacher played a game with fingers and holding up
  numbers on their fingers.
  
• Some of the ideas were focused to have students
  learn doubles. 2 fingers on one hand, 2 fingers
  on another, how many all together?
  
• Video- Tiles (making patterns)
• Students used manipulatives to create a pattern.
  Most of the students made their patterns easy,
  such as grouping 3 on the top and 3 on the
  bottom, or side by side.
• Some students realized that if they scattered
  their pattern it would be harder for their peers
  to recognize.

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Conclusion

• Subitizing is naturally present in everyone and
  is a strategy that can be built upon.
  
• Partitioning and grouping strategies are used to
  organize numbers into larger than one
  thinking.
  
• Patterns are the ability of students to think and
  organize whole into parts that they are
  comfortable with.