"continuity": a continuous function

dis·con·ti·nu·i·ty

   /ˌdɪskɒntnˈuɪti, -ˈyu-/ Show Spelled[dis-kon-tn-oo-i-tee, -yoo-] Show IPA

noun, plural dis·con·ti·nu·i·ties.

1. lack of continuity; irregularity: The plot of the book was marred by discontinuity.

2. a break or gap: The surface of the moon is characterized by major discontinuities.

3. Mathematics . a point at which a function is not continuous.

4. Geology . a zone deep within the earth where the velocity of earthquake waves changes radically.

 I wanted to include this definition of "discontinuity" from dictionary.com because I thought it was interesting that it relates to so many subjects.

Piaget's Theory is the most elaborate and encompassing of all developmental theories. I FINALLY had to just pick a few key concepts relative to my model and ideas about learning. Piaget's view gave new depth to my key points and also pushed me to rethink some of my original ideas. First, the concept of motivation; I said children are NOT naturally eager to learn. Piaget says they are and need little incentive from adults. But then he goes on to define the concept of disequilibrium.

 I was thinking about the comfort children get when they are in a state of equilibrium, as Piaget would say. They have no incentive at this point to develop a new understanding. Suppose the child would continue to idle in this point of view until something (an experience) persuades him into a state of disequilibrium. Discontinuity is a healthy thing, in this case, because it promotes a change in view point. Experience motivates learning! A teacher can be a resource of experience to the students in her classroom. She can both share knowledge from her own experiences and create knowledge building experiences for her pupils (usually it's a combination of both that I have observed to be effective in my field experience). I would now like to apply this and several other Piaget concepts such as: "nature and nurthur", "social relationships","the active child", and "the child as a scientist"  to my original model and example of a boy learning to fish. Pay attention to my added text in dark blue and terms directly pertaining to Piaget ideaology are in red.

Observation and Introduction:
 The boy watches and listens to his elder fish.
The student observes members of a community before becoming a member of the community. Social Relationships.

The boy wonders about fish. Develops Hypotheses
The student uses what he already knows to weed out what isn't known. It is the teacher's job to make subjects relative to students. Teacher must become familiar with the "Nature and Nurthur" of her students in order to engage them and best convey knowledge according to the uniqueness of the individual student/class.  
Example: Who here has ever been fishing? Caught a fish?
Creates questions for exploration. Creates disequilibrium.

Exploration and Practice: The boy fishes. Forming Experiments. Collecting data to support possible solutions/conclusions.  
The student takes his learning into his own hands.

Children are not always naturally active participants in their own learning. It is the teacher's job to inspire, tap their interests, get them involved and actively participating so they can get past any anxieties and enjoy learning. (tapping their interst means relating it to something they are already familar with)

Teacher should guide experience to the target concept without dictating or hindering possible perception differences. Every child has a uniqueness that is a resource to the classroom community. (Social relationships)

Reflection, Analysis, and Furthering learning. Drawing Conclusions
The student reflects on what he learned during exploration and practice; making connections and seeing the broader picture. The classroom is a community, a social group.The teacher should collaborate each unique experience to make the most out of the common experience. But learning shouldn't end here! Teacher uses a questioning method to both facilitate discussion and open up doors for future learning. This is a opportunity for discontinuity/ disequilbrium. In this way, the teacher puts things off balance and starts the whole learning process over again bring about broader and brighter view points thus educated individuals. Notice that some terms/concepts in this stage are also seen in the beginning stages of the learning process. It's a cycle!

Student should have something to show for his learning be a new skill, a poster, presentation, paper, project. This gives them something visual to sum up their specific learning experience and also something tangible to be proud of their achievement. Self pride is the best positive reinforcement and motivates them to learn more.

Piaget's Theory - Week 6

In Piaget's theory, the students are the active role in the learning process. They construct their own knowledge from personal experiences and also through trial and error. They can work with each other to create new ideas and to solve different problems. According the Piaget, "children learn through assimilation and accommodation." With assimilation, students work with each other to form new ideas and then with accommodation,  students work to resolve problems with their former ideas and to accommodate for them.  Hands on activities are crucial in Piaget's theory.

For my activity, the level is much lower so this activity would most likely be for younger students. The activity would include students being given multiple primary colors and then mixing them with other colors to form new ones. They would be given specific colors that they need to create and then work with each other to try to make those colors.  They'd learn through trial and error to find out which colors work with each other to form the colors they need to find. This activity will allow students to have hands on experience and to challenge different ideas.  Which color worked with another color? Which color didn't work and why do you think it didn't work? Students can create different hypothesis as to why one color worked and other one didn't.  

Week 6 - Olivia Shouse

My Theory is that students learn best when a teacher lectures them on a subject and then the students are able to work work with their peers doing an activity so they can experience an activity on multiple levels to reach different types of learning.

 I have changed my model slightly based on the Vygotsky reading. One of his ideas is that students like to be teachers, therefore by allowing them to work together on an activity the students can teach each other and hopefully learn and remember the material better.

My activity: The teacher would lecture the students over an introduction to fractions. She would give examples on the boards and the students would emulate him/her, either on paper or on white boards. By doing this the students would hopefully stay engaged in the lesson and have a good grasp of the concepts being taught. After the teacher has completed her lesson, they will divide the class into pairs and each pair will receive a bag full of m&ms. The students will then have to work in pairs to complete a worksheet that asks them to determine the fraction of a whole with each different color. Each student would have to fill out their own worksheet but they would be completing the activity as a pair, allowing them to learn and teach off of each other. This would also allow the teacher to walk around the classroom and observe how the students were doing and answer any questions if necessary. After everyone is finished, the class would go over the worksheet and each pair would have to talk about what they found, because all of the answers would be different.

Reflection: I based the changes to my model and activity design this week on the Vygotsky reading, because I really liked the idea of children wanting to be teachers. Just from babysitting I can see that children are always wanting to show you what they know, and that's no different in a classroom. By being in a classroom and through my own experiences, I have also seen that concepts can be easier to learn and remember if you are working with someone. By explaining what you know, it helps yourself remember it, and your partner may be able to answer something that you don't know. The students are remaining engaged in the lesson by responding to and following the teacher, and then are showing what they know by completing the following activity and working with their peers.

Piaget Model