Ratio
Description:
The term ratio refers to the amount of thinking students do compared to the teacher. The goal is to get the highest ratio possible for any given assignment. It is important, however, that it is deep thinking the students are partaking in; the ratio cannot be based on mere participation. Teachers should gage student progress and only give them more responsibility of thinking when they are ready for it. There are ten methods that increase the ratio of thought onto students:
1. Unbundle: Break an idea that is to be discussed into smaller questions that can be dished out to multiple students.
2. Half-statement: Make half of a statement, and ask a student to complete it.
3. What’s next: When discussing a question, ask questions about the steps involved to solve as much or more than asking for the answer.
4. Feign ignorance: Act like you don’t know the material, and ask students questions so they have to explain or correct you.
5. Repeated examples: When asking for an example of a concept, don’t settle for just one example. Keep on asking for more. To develop even deeper thinking, ask for more examples to be under various conditions.
6. Rephrase or add on: When a student makes a statement or answers a question, if possible, ask the student to revise his or her answer. You can also ask another student to explain what was said. This aids in student thought, because they have to do the thinking to improve their answers rather than the teacher jumping in and giving the best answer.
7. Whys and hows: Most statements can be followed by asking why or how, which automatically makes students go into deeper thought on possible reasons they would not have thought of otherwise.
8. Supporting evidence: Ask students to back up opinions they have, or give them opinions that they must find evidence for.
9. Batch process: Only once students are mature enough to handle this, allow your class to discuss a concept on their own. It’s important to note that students should be limited on the number of comments they make back and forth before you are in control once again. This is necessary so that they can stay on the right track while thinking for themselves. It is helpful to teach strategies of discussion so that they can learn how to improve their discussions.
10. Discussion objectives: When conducting class discussions, they need to be focused on attaining certain goals, or they’ll end up being a waste of time. Teachers can provide hints during discussions to guide students toward the goals.
Why does it work?
The ratio method works, because it involves several cognitive theories and research. On cognitive learning, it is supported by the idea of meaningful learning. Meaningful learning is the idea that information is best stored when it can be connected to something a student already knows. By requiring students to think deeply into material and have discussions that require them to make connections, they are more likely to remember the information presented to them. One of the strategies to push students towards meaningful learning is to elaborate on material, which is done through several of the methods listed above. Examples of the methods are unbundle, repeated examples, rephrase/add on, whys and hows, and supporting evidence.
Another concept from cognitive learning that supports this method is the idea of observational learning, which says that by watching someone else, we can learn a new behavior. This will occur more frequently in classrooms as the ratio of student thought is increased. As more students must participate in class and be reinforced or punished, more students witnessing will learn from their mistakes and praises. This will increase both their knowledge of how to discuss material and on the material itself.
From cognitive development theory, Vygotsky’s idea of the zone of proximal development supports the ratio method. This is the zone where students are handling concepts they can only figure out with guidance. By pushing more of the brainwork onto students through ratio, teachers will easily be able to identify the class’ zone of proximal development. And, by working in the zone of proximal development, students are more likely to learn and be challenged by the material.
Example:
Many of these strategies would be perfect to increase the problem solving efforts on my students rather than solving the problems mainly myself. For this example, I am focusing on the “unbundle” strategy. Say that I am teaching my class how to find the surface area of a rectangular prism. To have the class help figure out how to do this, I can ask them a series of questions, such as the following:
What are we finding by measuring the surface area?
What are the shapes of the faces of the rectangular prism?
How do we find the area of the rectangles?
Which faces have the same area?
How many faces are there? So how many areas are we adding together?
Take note that these would change according to class discussion.
The term ratio refers to the amount of thinking students do compared to the teacher. The goal is to get the highest ratio possible for any given assignment. It is important, however, that it is deep thinking the students are partaking in; the ratio cannot be based on mere participation. Teachers should gage student progress and only give them more responsibility of thinking when they are ready for it. There are ten methods that increase the ratio of thought onto students:
1. Unbundle: Break an idea that is to be discussed into smaller questions that can be dished out to multiple students.
2. Half-statement: Make half of a statement, and ask a student to complete it.
3. What’s next: When discussing a question, ask questions about the steps involved to solve as much or more than asking for the answer.
4. Feign ignorance: Act like you don’t know the material, and ask students questions so they have to explain or correct you.
5. Repeated examples: When asking for an example of a concept, don’t settle for just one example. Keep on asking for more. To develop even deeper thinking, ask for more examples to be under various conditions.
6. Rephrase or add on: When a student makes a statement or answers a question, if possible, ask the student to revise his or her answer. You can also ask another student to explain what was said. This aids in student thought, because they have to do the thinking to improve their answers rather than the teacher jumping in and giving the best answer.
7. Whys and hows: Most statements can be followed by asking why or how, which automatically makes students go into deeper thought on possible reasons they would not have thought of otherwise.
8. Supporting evidence: Ask students to back up opinions they have, or give them opinions that they must find evidence for.
9. Batch process: Only once students are mature enough to handle this, allow your class to discuss a concept on their own. It’s important to note that students should be limited on the number of comments they make back and forth before you are in control once again. This is necessary so that they can stay on the right track while thinking for themselves. It is helpful to teach strategies of discussion so that they can learn how to improve their discussions.
10. Discussion objectives: When conducting class discussions, they need to be focused on attaining certain goals, or they’ll end up being a waste of time. Teachers can provide hints during discussions to guide students toward the goals.
Why does it work?
The ratio method works, because it involves several cognitive theories and research. On cognitive learning, it is supported by the idea of meaningful learning. Meaningful learning is the idea that information is best stored when it can be connected to something a student already knows. By requiring students to think deeply into material and have discussions that require them to make connections, they are more likely to remember the information presented to them. One of the strategies to push students towards meaningful learning is to elaborate on material, which is done through several of the methods listed above. Examples of the methods are unbundle, repeated examples, rephrase/add on, whys and hows, and supporting evidence.
Another concept from cognitive learning that supports this method is the idea of observational learning, which says that by watching someone else, we can learn a new behavior. This will occur more frequently in classrooms as the ratio of student thought is increased. As more students must participate in class and be reinforced or punished, more students witnessing will learn from their mistakes and praises. This will increase both their knowledge of how to discuss material and on the material itself.
From cognitive development theory, Vygotsky’s idea of the zone of proximal development supports the ratio method. This is the zone where students are handling concepts they can only figure out with guidance. By pushing more of the brainwork onto students through ratio, teachers will easily be able to identify the class’ zone of proximal development. And, by working in the zone of proximal development, students are more likely to learn and be challenged by the material.
Example:
Many of these strategies would be perfect to increase the problem solving efforts on my students rather than solving the problems mainly myself. For this example, I am focusing on the “unbundle” strategy. Say that I am teaching my class how to find the surface area of a rectangular prism. To have the class help figure out how to do this, I can ask them a series of questions, such as the following:
What are we finding by measuring the surface area?
What are the shapes of the faces of the rectangular prism?
How do we find the area of the rectangles?
Which faces have the same area?
How many faces are there? So how many areas are we adding together?
Take note that these would change according to class discussion.