Blog Reflection 2

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

A specific learning goal that I would like to consider in this blog reflection is: The student will be able to multiply 2 digit by 2 digit numbers. I chose this because it is a learning goal that is part of my 4^th grade classroom and often a difficult new task for students to master. Due to this consistent difficulty, the topic is worthy of a deeper look at the process used for teaching the task to students.

I believe that two learning theories that could be incorporated into achieving this this learning goal would be Cognitive Information Processing Theory and Schema Theory/Cognitive Load Theory. 

Cognitive Information Processing Theory discusses three memory systems in the learner as sensory, short term and long term memory. Using this theory, 2 digit multiplication would begin in the sensory memory by looking at the patterns of the multiplication problem. This would allow the student to begin to perceive and organize the patterns in order to make sense of it and connect it to other information stored in their memory such as multiplication facts and multiplication using 2 digit by 1 digit. Through additional practice and immediate feedback students could perfect the multiplication process and transfer it to long term memory. This theory also discusses important strategies such as graphical diagrams to connect learning. I often begin two digit multiplication instruction by illustrating it visually before moving to the abstract methods. This seems to help students learn and retain the process.

Schema Theory/Cognitive Load Theory could also be incorporated into the design of teaching this learning goal because 2 digit multiplication relies heavily on previous learning of multiplication facts and 2 digit by 1 digit multiplication problems. The Schema theory would say that students already have a “multiplication file” created in their brains that they could access and build upon to acquire the new learning. The previous learning of multiplication facts would allow for the necessary automation in order to free processing capacity which would  make learning something more complex possible. Using this theory it would be critical for a teacher to ensure that students had the prior knowledge and experience with simpler multiplication before attempting to instruct students in the more complicated task of 2 digit by 2 digit multiplication.

·        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.

This YouTube video takes Gagne’s Nine Events and breaks them down into easy to understand concepts using a mnemonic device.

http://www.youtube.com/watch?v=i_8MB9F2cts

        Gagne’s Nine Events                                                      First Principles                           

Gain Attention	State the Problem
Inform learner of objective	Activation
Stimulate recall of prior learning
Present information or activity	Demonstration
Give guidance
Performance	Application
Feedback
Assess
Transfer and go beyond	Integration

Continuing on with my lesson on 2 digit by 2 digit multiplication I would begin by applying the ideas outlined in our text from chapter 7. I would start by stating the problem that our instruction will focus on for that lesson. By stating the problem I would attempt to make the objective relevant to the students. I would use items that they are familiar worth to give them a 2 digit word problem that we will be able to solve by the end of the lesson.

State the Problem:

Tomorrow because you are all wonderful students, you will each (23students)  receive 32 reward tokens. (That will catch their attention.) How many tokens will I need to have by tomorrow to hand out?

Activation:

We would draw pictures to help up figure out that this is a multiplication problem. We will recall our prior learning experiences of repeated addition patterns and the method of 2 digit by 1 digit multiplication.

Demonstration:

During the demonstration phase I will model several examples of the process for 2 digit by 2 digit multiplication. We will then create a group poster outlining the procedures. I will have models already worked out for them to see and take note of in their math journal.(I have included a poster from my classroom that we created.) At this point all I want them to do is watch what I am doing to solve the math problem.

Application:

After much modeling, I would ask student to begin attempting practice problems. The students usually practice on white boards. This allows me to quickly assess where a breakdown in the process occurs and students can easily erase and correct. I allow them to work a problem and I simultaneously work the same problem on the board so they can glance up when they feel stuck in the process.

Integration:

Students then move to working problems on their own with less guidance. Assessment and feedback is given. Students are asked to solve the original problem from the beginning of the lesson and turn in for teacher to formally evaluate.

·         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.

Continuing on with my 2 digit by 2 digit lesson I use the whole task approach by asking students to think about the word problem they are trying to solve and break it down into picture form first. I want them to have an overall conceptual understanding of when and why we multiply. I believe this is using their analytical abilities. I don’t want them to two see 2 numbers and just start multiplying.  Once they determine a problem is multiplication we rely on their procedural abilities to follow the steps of the 2 digit by digit problem. I often use hand motions or signals in my teaching to help students recall information. This allows them to use their motor skills along with their analytical skills.

In considering the scaffolding approach for 2 digit by 2 digit multiplication it would be important to show the students the process of multiplying in a part task model, but keeping the overall idea in mind. I do break down the idea of multiplying 2 digit multiplication by looking at how we multiply the ones place and then how we multiply the tens place. This scaffolding allows the students to see the parts of the process (partial products) in relation to finding the final product.

The mathmagenic approach would require the teacher to consider questioning that move students past the procedural understanding of 2 digit by 2 digit multiplication to gain a more abstract understanding. I attempt to show students both multiplication and division word problems to help them solidify their thinking about why a word problem is either multiplication or division.  My ultimate goal with the objective is for students to be able to solve word problems, I must teach them the procedure and the abstract reasoning skills. By giving both types of word problems I am hoping that students will develop a general abstract knowledge that will allow them to solve new word problems in the future.

·         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?

For this question I will approach it from the idea of introducing a group of students to the different genres available in the library.

ATTENTION:
Perceptual Arousal Inquiry Arousal Variability	I would have a variety of books laid out on each table for groups to explore. I would ask students to try to group their books using any method they agree upon. I would allow students to move to other tables to discuss ways they grouped their books with other students. I would then allow students to move about the library and find other books that would fit into the groups they have created at their tables.
RELEVANCE:
Goal Orientation Motive Matching Familiarity	I would attempt to meet the students’ needs of understanding the different types of genres. Students would have choices at the beginning about how they group their books, they would also have the responsibility to participate and locate other books. I would discuss with the class the types of books they enjoy reading or checking out when they come to the library. We would begin to create categories together.
CONFIDENCE:
Learning Requirements Success Opportunities Personal Control	Allow students to participate, have some choices and validating their ideas will lead to positive expectations. Once students feel that they can recognize different types of books they will have the confidence that they can understand the different types of genres, that genre’s are much like the categories they created earlier. Students will be given direct instruction and examples for different genres. They will then be asked to identify the genres for the same set of books they started with.
SATISFACTION:
Intrinsic Reinforcement Extrinsic Rewards Equity	Students should feel rewarded and a intrinsic sense of accomplishment as they are able to identify the types of genres that they check out from the library. Extrinsically the librarian can offer a small reward, token or even a verbal praise when students identify genres. Students will continue to visit the library and be asked to identify genres of books they check out. The positive feedback from the librarian will allow students to continue to work to understand genres.

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

One of the benefits of design research is that it causes the designer to think more deeply about what they are asking the learner to do. It brings into focus the why behind our instruction as well as the how. Understanding many of the underlying theories, processes and practices of design help us to achieve the goal of learning for our students, that is hopefully more engaging, more relevant and with a higher ability of transfer to future concepts and skills.