Week 3

~Section 2:  Theories and Models of Learning and Instruction~

Identify a specific learning goal and how you would incorporate two learning theories highlighted in Chapter 4 to achieve this goal.

Learning Goal:  Third grade students are expected to engage in problem solving, communication, reasoning, connecting and representing as they recognize, describe or extend a variety of patterns.

Cognitive Information Processing Theory

The cognitive information processing theory focuses on the relation of memory’s (sensory, short-term, and long-term) ability to retrieve information, transfer information, and finally recall information.  When utilizing this theory effectively to develop and increase knowledge of patterns within a third grade classroom, the teacher must employ strategies that maintain the learner’s attention, encourage retrieval, and illicit effective repetition across learning situations and curriculum. 

To do this, the teacher would utilize a thinking map, and specifically a flow map to emphasize the relationship within sequencing and ordering numbers.  Thinking maps (graphic organizers) such as this help the student connect new information with prior knowledge.

Situated Learning Theory

The Situated Learning Theory focuses on knowledge acquisition through the development of problem-solving skills within a community.  Learning is much more “accidental” than intention-driven.  There are two basic principles that align with the situated learning theory.  These include an understanding that knowledge necessitates being presented in an authentic context and that learning requires social interaction and collaboration. 
Within the context of our learning goal to provide students with opportunities to develop a keen knowledge of patterns, the teacher would place students in groups of four or five.  Students would be given a paper with a pattern on it.  Initially, skip counting by 2’s, 5’s, 10’s, etc. should be utilized to again build on prior knowledge.  Groups are expected to discuss the numbers and their sequence while relaying any notable features regarding the number’s order to each other (within the group).  The teacher is the facilitator at this point.  His or her primary responsibilities include monitoring to ensure successful group discussion while providing guidance when necessary.  Next, the teacher would provide number patterns to groups that are more complex and do not follow as easy a pattern as the previous skip-counting numbers. 
This theory allows learners to be responsible for their own learning and application of knowledge within the small group setting.  Students working together and experiencing skills through meaningful encounters gain insight.  “Specifically, knowledge is presumed to accrue in meaningful actions, actions that have relations of meaning to one another in terms of some cultural system “ (40).

Find a reference that describes Gagne’s Nine Events of Instruction.  Then create a table or chart that compares and contrasts those events with the first principles described Chapter 7 and describe how you would apply each of the first principles to the goal you’ve developed from the first activity in the reflection.

The following link provides a presentation on Gagne’s Nine Events of Instruction:  C:\Documents and Settings\Administrator\My Documents\Library Fall 2009\ETEC 561 Wickersham\dickcarey.jpg

Gagne's Nine Events of Instruction	First Principles of Instruction
Gain Attention	Activation
Inform Learner of Objectives
Stimulate recall of prior learning
Present stimulus material	Demonstration
Provide learner guidance
Elicit performance	Application
Provide feedback
Assess performance	Integration
Enhance retention transfer

Activation:  Learners are directed to recall, relate, describe, or apply knowledge from relevant past experiences that can be used as a foundation for new knowledge (63). Recall and prior knowledge are activated by counting by 2’s, 5’s, 10’s, etc. 

Demonstration:  The next activity should address and demonstrate the learning goal.  This is done by taking the skip-counting numbers and applying them in such a way that the learner can recognize a pattern.

Application:  Next, learning is continued to be attained by allowing learners to experience the learning goal individually or within a group.  At this point, students in a group would be given sets of numbers to identify patterns in.

Integration:  Lastly, integration occurs when learners experience activities that allow individual ownership of the goal.  Learners  are expected to create their own patterns to exchange with a neighbor to synthesize actual comprehension.

Develop a new goal or using the one you’ve already developed, briefly describe how you might use the whole-task approach, scaffolding, and mathemagenic methods to help students learn to perform a task.

Whole-task approach- The whole-task approach is a holistic method to finding success within the instructional learning goal.  This is established through real-life activities to therefore realize the connections without losing sight of the relationships among the elements.  Within the setting of the 3^rd graders learning about patterns, this can be done by allowing students to experience and perfect their knowledge of patterns.  The extension is part of this in that students would be expected to recognize patterns, develop patterns, find the number in a pattern that doesn’t belong, and also relate patterns to their everyday life.

Scaffolding- Scaffolding is the process of building knowledge through a series of levels which get progressively more difficult as the knowledge is established.  With 3^rd graders and number patterns, this would start with basic skip-counting and progress to a deep understanding.  This would also extend into the beginning of developing knowledge regarding the next skill, multiplication. 

Mathemagenic- This method is employed to

The basic elements of number patterns should be established as well as their relation to previous foundations and real-life.  The higher-level thinking skills can be addressed and provoked through the lesson by allowing students to see the relationships in simple ways (skip-counting) and acceptable ways (creating their own patterns) but let’s take this learning goal to a whole new level of understanding that working with number patterns leads directly to the concept of functions in mathematics: a formal description of the relationships among different quantities.  This would include taking pattern advances from sums to products.

You have been hired to design a course for a topic in your area specialization.  Using Table 9.2 as a template, what would you incorporate into each subcategory to motivate learners?

ARCS Model Catagories and Subcatagories
Attention
Perceptual Arousal	What can I do to Capture their interest?
Inquiry Arousal	How can I stimulate an attitude of inquiry?
Variability	How can I use a variety of tactics to maintain their attention?
Relevance
Goal Orientation	How can I best meet my learners needs? (Do I know their needs?)
Motive Matching	How and when can I provide my learners with appropriate
	choices, responsibilities, and influences?
Familiarity	How can I tie the instruciton to learners' experiences?
Confidence
Learning Requirements	How can I assist in building a positive expectation for success?
Succes opportunities	How will the learnin experience support or enhance the students'
	beliefs in their competence?
Personal Control	How will the learners clearly know their success is based upon
	their efforts and abilities?
Satisfaction
Intrinsic Reinforcement	How can I provide meaningful opportunities for learners to use
	their newly acquired knowledge/skill?
Extrinsic Rewards	What wil provide reinforcement to the learners' successes?
Equity	how can I assist the students in anchoring a positive feeling
	about their accomplishments?

Attention:

Before students arrive for school arrange their desks in a boy, girl, boy, girl fashion to stir their curiosity.  Once they arrive, tell the students that the there is a one-word explanation that will be given to them: pattern.  Students are to then write down why they believe their desks have been rearranged in such a way.  Upon completion of this, a discussion should ensue regarding their thoughts about patterns.  Have students come to the front of the room and put them in a specific order that relates to a pattern (ex. red shirt, red shirt, blue shirt, white shirt, red shirt, red shirt, etc).  Provide the students with different di-cut shapes in groups and ask that a pattern be made.  Compare patterns from each group.

Relevance- Learners will understand patterns in relation to established prior knowledge/skills.  This would include skip-counting, addition and subtraction with numbers.  Students should be asked to make statements based on their knowledge of  patterns in their everyday life in terms of not just numbers but seasons, word patterns, and world around them.  Students will be given dominos in groups.  Students study number patterns within the dominos. They observe dominoes to determine the next domino in the sequence. After studying the dominoes, they write an expression to represent the pattern.

Confidence- Students work in pairs to develop patterns for each other to solve.  This could be done with dominos, Skittles, Cuisenaire rods, blocks, or just with pencil and paper.  Students continue to receive positive feedback from the teacher.  Next students would work to create a pattern book focusing on their knowledge of how to create and design a pattern.  Students will have control as to what kind of pattern they would like to make, how the pattern is represented, and what elements of mathematics are utilized in the creation.

Satisfaction- Satisfaction will be self-evident by establishing pride in understanding the concept and also in the creation of their books.  Also sharing the books with the class will allow for positive recognition and feedback from peers.  Reinforcement will be carried over into the next skill of multiplication.  Positive feedback will also be given by the teacher.

Finally, after completing these activities, discuss the benefits of engaging in design research.

        We live in a data-driven society.  This is especially so in education.  Within the last ten years parent conferences alone have gone from the teacher “telling” the parents areas of weaknesses and strengths to today’s world where it has to be “backed-up” with distinct supportive research.  Administrators expect teachers to verify needs for students with data.  Engaging in design research might seem like “putting the cart before the horse” but in all actuality is the foundation of evolving into better educators.  Rather, think of it as being one step ahead of the game.  Having a foundation to build from warrants expectations of exemplary success!