Preoperational Students (Preschool - First Grade)
Preoperational (Kindergarten - Second Grade) --->>> Concrete Operational Students(Third Grade - Fifth Grade) --->>> Formal Operational (Fifth grade - Adult)
Can use symbols or mental representations. Therefore, mentally being able to manipulate symbols and mental representations is the abstraction of thought.
Symbolic play is when an can be thought of as another during play. Blocks become cars and guns. Teddy bears my child or friend.
Creates mental Images
Think step by step one step at a time
Deferred imitation
Likes to Draw
Verbal likes to talk about everything and everyone nonstop.
Egocentric thinking - Everything is based on their senses. It is not a selfish point of view. They don't recognize that other people may have a different point of view or that another point of view could exist. Ask questions as to what do you think Chris saw? Why did you pick this one? Why did she pick that one? What did the character in the story think? What did another character in the story think?
Irreversibility is the inability to reverse a thought. Reversibility is the ability to work a problem in both directions. This is essential to understand the order of events in time. In mathematics that the position of an object doesn't change the object. In that the object can be reversed from one position to another and back again.
Being able to move four objects from one position to another doesn't change the cardinality (the number of objects) as they can be reversed to the original position.
Being able to imagine water being poured from a measuring cup into a tall narrow container and then from the tall narrow container to a short wide container will have the same amount, because pouring it back into the tall container would reverse the process and the amount would still be the same.
Being able to take two wires of equal length, bend one, set them side by side and mentally reverse the process of unbending the wire to its original length and declaring them to be equal in length.
Knowing that if 3 + 4 = 7 then 7 - 4 = 3 is the reverse process. If you add four and get seven, then if you have seven and remove four the process has been reversed.
If exercise causes you to breath faster, what could you do to breath slower?
If water makes ice how can it be reversed?
If salt is added to water can it be reversed? If it can, can the salt be reversed again with more water?
Water evaporation and condensation.
Balancing activities like those in FOSS for second grade as well as balancing on an equal arm balance.
Mixing paint and watching the color change. Can paint be made to go from light to dark to light again?
What about light from a flashlight? If we slowly add slips of waxed paper what happens? What if we remove them one at a time?
What about unrolling a ball of string? How long is it? If we roll it up and unroll it again how long will it be?If you are feeling pretty smug about your ability to use reversibility, then think about being in a market and looking at all the different shapes of containers and trying to identify which are equal or which has more or less. I bet the packaging companies know which containers look like they hold more than they actually do, because of our inability to use reversibility well.
Uses centering focuses on a characteristic as an explanation or cause, that may or may not be accurate, without consideration of other options. Decentering is the ability to change ones thinking from one characteristic to another when considering an explanation or cause.
Does not recognize transformations. Transformation is understanding that change can involve an infinite progression of steps, usually incrementally small. However, a progression that becomes infinitely large would be included as well.
Sequencing objects of different lengths (Piaget's famous dowel rod experiement)
Drawing pictures of the animation of a pencil or other object falling from a hand to the ground.
Animation by making flip books
Mixing paint and watching the color change. Add a little bit more darker at a time to lighter or lighter to darker.
Flying paper airplanes and see how slowly changing the weight (add one paper clip to the nose, fly it five times, measure the distance to the nearest yeard or meter, record it, and add another paperclip and repeat till five clips. or fold the ends of the wings a little more at a time and see how it changes the flight.Uses transductive reasoning
Lacks conservation of reasoning - Children in the primary grades need to taught as if they are lacking conservation skills. Anything that involves measurement needs to be experienced by the children actual size. If students are studying animals, then the animals need to be drawn or traced on sheets of paper to the exact size of the typical species outline. If the height lenght is being referred to them pieces of string, yarn, or adding machine tape can be used to mark the sizes.
Solar system models create similar complications. A bigger problem with a solar system model is scale. Students don't begin to develop the abilities for scale until about fourth grade. Then when a solar system model is made the scale for the size of the planets as well as the distance from the Sun need to be similar for an accurate representation.
Similarly for time. A time line can to be drawn with times in increments of the students' lives or generations for their parents and grandparents.