Section 2: Theories and Models of Learning and Instruction

Specific Learning Goal
The learning goals I have for my students this year is for them to improve their Algebra skills.  Many of my high schools students come to high school with low mathematics skills.  Students do not understand the concept of variables and it is a difficult to teach this particular concept. I have used the five E model that is in the C-Scope curriculum and if you have taught at all one has used the Behavioral Learning Theory.   Cognitive Information Processing Theory is one I would use for improving skills by using graphical and imagery strategies to help students make connections between their prior knowledge and the new information.  Feedback is the key for this theory, students need constant feedback both positive and corrective.  Letting students make mistakes and having constructive feedback to correct mistakes is a great teaching strategy.  Another theory that I would use is Gagne's Theory of Instruction.  This theory is one that is so easy to adapt in all subjects and as educators we do so much of this but it is nice to have it written in a way that is easily followed.  Gaining student attention or I call it the gotcha moment is essential when teaching mathematics.  

2.  Gagne's Nine Events of Instruction/First Principles


                         Gagne's Theory of Instruction

Gagne	First Principles	Application
Gaining Attention	Activation	Look here…..
Informing the learner of the objectives	Activation	You will learn to…
Simulating recall of prior knowledge	Activation	What you already know….
Presenting the stimulus	Demonstration	Here is what we are going to learn……..
Providing learner guidance	Demonstration	Examples of this…..
Eliciting performance	Application	You will try……
Providing feedback	Application	This is how you did…..
Assessing performance	Application	Show what you know….
Enhancing Retention and transfer	Integration	How can you use this in the real world…..

                                Merrell's First Principles

References:

http://edutechwiki.unige.ch/en/Nine_events_of_instruction

http://my-ecoach.com/project.php?id=12152&project_step=28465

http://cito.byuh.edu/merrill/text/papers/ReigeluthCarrFirstPrinciples.pdf
http://www.e-learningguru.com/articles/art3_3.htm

http://www.my-ecoach.com/idtimeline/theory/gagne.html

http://www.ibstpi.org/Products/pdf/appendix_A-C.pdf

Whole-Task, Scaffolding, and Mathemagenic Methods
I will stay with my original goal of graphing linear equations.  I will first utilize whole task methods by teaching linear equations as one task instead of isolating each step.  To begin the scaffolding process the students will start with demonstrating pieces of the lesson by graphing only before solving the linear equations.  Students will then begin to add pieces of solving linear equations by plotting points.  All through the process students will be given teacher feedback and peer tutoring.  Once all skills are developed we will begin mathemagenic methods to solidify learning.  Students will be asked to relate linear equations to real life situations and solve the problems.  Students will also have the opportunity to practice problems individually and in a peer groups.

Table 9.2

Attention

Perceptual Arousal:  Shows an example of graphing using TI graphing calculator on the Smartboard. 

Inquiry Arousal:  Teacher ask learners to show how to graph linear equations. Asks learners questions about graphing.

Variability:  Have students come to the smartboard to demonstrate.

Relevance

Goal Orientation:  Know the data on each student so you may use some students as peer tutors.

Motive Matching:  Constant assessment of students will be ongoing and when appropriate students can demonstrate learning.

Familiarity:  Teacher will show examples of maybe cell phone plans or ski rentals for students to understand relevance.

Confidence

Learning Requirements:  Requiring the learner to produce a graph based on what has been taught enables the learner to confirm their learning.

Success Opportunities:  Assign a practice activity  by creating a graph on the calculator that focuses one of the problems assigned.

Personal Control:  Teacher gives immediate feedback to learners after activity so students will know their efforts is are successful.

Satisfaction

Intrinsic Reinforcement:  Independent practice forces students to use what they learned and apply it. Assessing such gives instructors a means of testing student learning outcomes.

Extrinsic Rewards:  Teacher asks learners to create activities using the graphing calculator to graph linear equations.
Equity:  Teacher also charges learner with teaching another learner how to use the graphing calculator to produce a linear graph.


Benefits of Design Research
Design research allows educators to look at various angles of students learning objectives and which way might best serve students.  Engaging in design research allows educators the options to choose which practices and theories they believe would be beneficial to their students.  It also allows one to keep informed of the latest trends in instruction.
Can we say what the ultimate goal of instruction?  Probably not however by studying recent instructional design theories we can lood at trends and what the professionals are saying.  Much of the recent theories have stressed the importance of making commections and relating it to real-world.  Technology is ever changing and has an effect on the way students learn and interact.