Week 3 - 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:  Educators are to become proficient in the use of the TI Nspire calculator in delivering Algebra and Geometry instruction to high school students.

Need:  The ISD has purchased the new technology for all Algebra and Geometry teachers to use with a newly developed curriculum.

Audience:  Mathematics teachers who have varying levels of experience teaching and use of the calculators.  Most are proficient in the use of the TI 83 and 84 graphing calculators.

The two learning theories I would use to achieve this goal are the Schema Theory and Cognative Load Theory pared with the Situated Learning Theory.

The components of the Schema Theory and Cognitive Load Theory which would benefit the learners are the connections to prior knowledge which most teachers already possess.  The schema is in place.  The integration of the new technology would include showing worked examples and partially completed problems would be the logical first step leading to more independent practice using the Situated Learning Theory.  The teachers would then select applications in context of what they currently need in the classrooms and continue to develop their knowledge of the calculator functions in what can be considered the learners practices of the community – the community of math teachers and problems in the context of their required curriculum.

Find a reference (other than the book) 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 in chapter 7 and describe how you would apply each of the first principles to the goal you've developed from the first activity in this reflection.

Find a reference (other than the book) 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 in chapter 7 and describe how you would apply each of the first principles to the goal you've developed from the first activity in this reflection.

First Principles of Instruction	Gagne’s Nine Events of Instruction
Problem Centered • Authentic real world problem • Whole problem of task • Instructional focus • Not too specific
Activation Does the instruction have students recall, relate, describe, or apply prior knowledge?	(1) gaining attention (reception) (2) informing learners of the objective (expectancy) (3) stimulating recall of prior learning (retrieval)
Demonstration Does the instruction show examples consistent with the content being taught?	(4) presenting the stimulus (selective perception) (5) providing learning guidance (semantic encoding)
Application Do learners have an opportunity to practice and apply their newly acquired knowledge or skill?	(6) eliciting performance (responding) (7) providing feedback (reinforcement)
Integration Does the instruction provide techniques that encourage learners to integrate (transfer) the new knowledge or skill into their everyday life?	(8) assessing performance (retrieval) (9) enhancing retention and transfer (generalization).

Gagne’s Nine Events of Instruction parallel to the First Principles of Instruction.   The  chart above illustrates how the Nine Events relate to the First Principles.

First Principles of Instruction	Introduction of TI Nspire Calculator
Problem Centered • Authentic real world problem • Whole problem of task • Instructional focus • Not too specific
Activation Does the instruction have students recall, relate, describe, or apply prior knowledge?	Ø  Recall uses of previous versions of graphing calculator products. Ø  Discussion of use in the classroom and features that need to be added. Ø  Introduce new calculator with a packet of the calculator features side by side.
Demonstration Does the instruction show examples consistent with the content being taught?	Ø  Demonstrate common graphing calculator activities such as math operations, graphing and creating tables. Ø  Demonstrate new format features of the calculator and where commonly used features can be found.
Application Do learners have an opportunity to practice and apply their newly acquired knowledge or skill?	Ø  Provide math problems for the learners to practice the newly learned skill.  Ø  Provide an opportunity for learners to share successes and questions.
Integration Does the instruction provide techniques that encourage learners to integrate (transfer) the new knowledge or skill into their everyday life?	Ø  Ask learners to demonstrate a newly acquired skill Ø  Have learners create a plan to integrate the technology into their learning plan or classroom. Ø  Provide learners the phone number of TI Cares.

Reference: http://tip.psychology.org/gagne.html Conditions of Learning  (R. Gagne)

Whole Task Approach

Calculator Training

For this topic I will continue with the example of calculator training.

Ø  Procedural, and conditional knowledge that is related to a specific task domain. 

o   The procedural and conditional knowledge needed for this task will be first, prior experience using calculators to teach mathematics.  Instruction will then move from a review of previous experiences to acquiring new knowledge related to the new technology.  This would consist of computation, tables, graphing and the use of the calculator indexing system.

Ø  Use of automated routines that allow an expert to solve familiar aspects of problems fast and with few errors.

o   Learners would complete problems related to computation, graphing, creating tables and use of the calculator indexing system.  The problems would increase in complexity.

Ø  Metacognitive knowledge necessary to monitor and regulate task-related activities in the domain

o   The final learning activity would include an integrated problem solving scenario which require the use of all of the applications learned in the previous learning situations.  For example, the activity might be to prepare an algebra lesson to integrate word problems, tables, equations and computation.  The learners would prepare a lesson integrating the technology and its application.

Scaffolding

Ø  Scaffolding referenced the use of Bloom’s and Gagne’s taxonomy.  For this learning scenario I will use Bloom’s.

Scaffolding using Bloom’s Taxonomy
Project:  Data collection and analysis
Knowledge, Comprehension, Application	The project would continue the lessons in the Whole Task Approach Model.  This lesson stopped at the application level. ·        Procedural, and conditional knowledge that is related to a specific task domain.  ·        The procedural and conditional knowledge needed for this task will be first, prior experience using calculators to teach mathematics.  Instruction will then move from a review of previous experiences to acquiring new knowledge related to the new technology.  This would consist of computation, tables, graphing and the use of the calculator indexing system. ·        Use of automated routines that allow an expert to solve familiar aspects of problems fast and with few errors. ·        Learners would complete problems related to computation, graphing, creating tables and use of the calculator indexing system.  The problems would increase in complexity. ·        Metacognitive knowledge necessary to monitor and regulate task-related activities in the domain ·        The final learning activity would include an integrated problem solving scenario which require the use of all of the applications learned in the previous learning situations.  For example, the activity might be to prepare an algebra lesson to integrate word problems, tables, equations and computation.  The learners would prepare a lesson integrating the technology and its application.
Analysis, Synthesis	This step would include analyzing and synthesizing the work product and the assessments of the students who participated in the teacher created integrated lesson.
Evaluation	The learners would evaluate the effectiveness of the lesson and technology from the analysis.  The leaners would make judgments and modify the lesson

Mathemagenic

The statement  in Chapter 8 of our text, “methods that give birth to learning as opposed to reaching specific objectives” correctly identifies what education should be.  This approach is a holistic design which focuses on the transfer of information rather than covering objectives and identifies tasks that are common to learning and transfer.   What learning do we want transferred?

In learning any new technology, software, calculator, we do not want to learn steps which will not transfer, but the overall picture, structure, makeup of the hardware of software.  With the calculator scenario I would use the approach of the learners discovering the format and indexing system of the calculators.  From that they can apply prior knowledge to solve problems.

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

Attention
Perceptual Arousal: Inquiry Arousal: Variability:	Have an abacus for display Ask how this was used to compute Have groups solve a problem with paper and pencil, the abacus and with a calculator
Relevance
Goal Orientation: Motive Matching: Familiarity:	Learners will understand the need to adapt to new trends in technology and to integrate new technology into their teaching Group discussions on the changes in technology throughout careers and how they have enhanced instruction Have leaners report out experiences.
Confidence
Learning Requirements: Success Opportunities: Personal Control:	Provide students with a learning goal – what they will be able to do and what they will create by the time the course is over The course artifact will serve as an example of what they can use in their classroom. The student success will be determined by individual and group participation and the final product.  They will know in advance what they will produce.
Satisfaction
Intrinsic Reinforcement: Extrinsic Rewards: Equity:	The skill acquired will be evidenced in the artifact.   The participants will give feedback regarding the artifact. Learners will create a journal entry regarding their new learning and the quality of their artifact.

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

The organized, purposeful instructional design is goal oriented, well planned and provides learners with a hierarchy of activities that meet their goals and needs.  The research is particularly necessary with the new learner and the dependence on technology.  The most effective delivery design must be researched in order to insure the transfer of the new learning into the classroom or workplace.  I see this is one of the major issues.  Many participants do not touch the technology or utilize the newly acquired skills once they leave the sessions.

Another area of design research is the connection with increased student performance and improvement in institutional performance goals evidenced by data.  There must be a connection between the professional development provided and an increase in productivity or test scores in order for similar projects to be budgeted or funded.