- Identify a specific learning goal and how you would incorporate two learning theories highlighted in Chapter 4 to achieve this goal.
The two learning theory that I will discuss in relationship to teaching students how to generate equivalent fractions are Behavioral Learning Theory and Schema Theory. It is my opinion that these two theory will aid in achieving the desired result of students understanding the concept of equivalent fractions.
From a behavior learning theory learning is best understood, explained, and predicted if we look at events that can be observed. As educators we tend to judge if our students understand a particular concept based on what we observe our students doing and how we see them performing in our classrooms. This theory states that to see if we achieve the desired outcome that we should observe the behavior before and after a teaching strategies has been implemented. This is how I would incorporate this learning theory with teaching students to generate equivalent fractions. First, I would give the students fractions strips of various sizes. I would have the students generate halves first and see if the students could explain if and why they are equivalent. I would offer feedback each step of the process to reinforce desired behavior. I would then model and discus using concrete model what an equivalent fractions is and then have the students generate equivalent fractions using models only. I would offer feedback to reinforcement the students in their learning of the new concept. I would then go from concrete to pictorial to generate equivalent fractions along the way breaking the learning into small steps and offer consistent feedback. We would finally go from pictorial to concrete where they learn to generate multiples of the denominators to generate equivalent fractions.
SCHEMA THEORY
In a Schema Theory environment a learner can only process so much information at one time. Students need to have some working memory to draw upon to process new information. This particular theory is great for teaching the concept of equivalent fractions. Students must have a working knowledge of fractions. This is why it is important that they begin with manipulates and see that 1/2 and 2/4 or even 8/16 all represent the same amount. Once students have a working knowledge of this then you can then have them begin to create equivalent fractions such as 2/3 and 4/6. Students are not ready to generate equivalent fractions by multiplying by a fractions equivalent to 1 because they do not have the schemata in their long term memory to understanding fractions. Educators must build upon the information that students know and have stored in long-term memory in order to for the students to make connections in their learning.
- Find a reference(other than the book) that describes Gagne' 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 reflecion.
Gagne's Theory VS First Principles of Instruction
Gaining Attention | Problem |
Informing the Learner of the Objective | Activation |
Stimulating Recall of Prior Learning | |
Presenting the Stimulus | Demonstration |
Providing Learning Guidance | |
Eliciting Performance | Application |
Providing Feedback | |
Assessing Performance | |
Enhancing Retention and Transfer | Integration |
This is how I would apply the first principles to the goal of generating equivalent fractions.
First I would have the students seating in pairs. I would give each pair a small bag of skittles and have them divide it equally between themselves. I would then have them write what fractional part of the skittles that they have. I would have them put half of the skittles back in the bag. I would then have them once again have them divide the remaining skittles equally between each other and write the fractional part they each have once again. I would do this division of skittles one more time. I would then see if the students could tell me the how the fractions they have written are related.
Next, I will tell the students to get out fraction strips and we will generate equivalent fractions. We will begin with generating 1/2 and relate it to the previous activity with skittles. We will discuss why the fractions are equivalent and what makes a fractions equivalent. We would model several examples together.
Then, students would demonstrate an understanding of equivalent fractions by generating equivalent fractions using fractions strips and pictorial models in groups.
Finally, after I have modeled and students have worked through examples with me then I will let them demonstrate that they have an understanding of the concept by creating and drawing there own examples of equivalent fractions.
- 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
In this approach the educator must encourage the learner to develop an integrated knowledge base without separating skills, knowledge, and attitudes from each other. This is a more holistic instructional design. I would you a real life examples to relate equivalent fractions for students to understand. Students would learn the concept of fractions as part to whole and relate it to equivalent fractions in that the part to whole ratio has not change.
Scaffolding
This approach is more like Bloom's taxonomy. Where you begin a concept on the lower level and build up to higher order thinking skills. I believe that depending on the students knowledge level you may have to begin on the lower level but you goal is to more them to higher level of thinking.
Mathemagenic Methods
I like this method because if talks about variety in theway the concept is presented to the students. The concept should be taught using hands on activities. Students should be questions throughout to ensure they are learning the concept and are able to abstracting perform the task which will be the goal in learning equivalent fractions.
- 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?
ARCS Model Categories and Subcategories |
Attention |
Perceptual Arousal: I would utilized candy to capture their interest Inquiry Arousal: Create equal groups of candy to share with your partner Variability: I would use fraction pieces and crackers. |
Relevance |
Goal Orientation: I would tell my students the objective and would have completed student inventory to know how to best reach my students. Motive matching: Students will be given chose on how to show me they understand the goal. Familiarity: I would relate fractions to students in a variety of real world situations. |
Confidence |
Learning Requirements: I will monitor students each stage of the learning process and give feedback and encouragement. Success Opportunities: Students will be given examples and the teacher will model. Students will be step by step instructions and will be told the learning expectation. Personal Control: Teacher will meet with students individually and offer continuous encouragement. |
Satisfaction |
Intrinsic Reinforcement: Students will be given a variety of ways such as models, pictures, worksheets to model their learning. Extrinsic Rewards: Students will be provided with stickers and praises from teacher. Equity: Students will know the benefit of learning new knowledge and realize that they are only competing against themselves. |
- Finally, after completing these activities, discuss the benefits of engaging in design research.
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