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Classroom Dialogue - T-14: Establishing Relationships PDF
This knowledge construction function (KCF) or brain tool enables us to search for and establish relationships between experiences or sources of information. Without this KCF, students are passive recipients rather than active generators of information: Objects, events and experiences are treated as episodic and isolated from one another. This function energizes all of the KCF and especially those that are needed to generate information to solve tasks that go beyond imitation and reproduction. These are tasks that require the learner to transform an input to generate a desired output. To be solved, such tasks may require that the given sources of information are connected with one another, with information stored in memory, and with knowledge gained from hypothetical thinking and logical inference. All of these processes are energized by a need to search for and establish relationships.
Learners who have not received adequate mediation of this KCF orient to disconnected fragments of academic tasks, exhibiting shallow, low levels of performance. Such learners may excel on imitative and reproductive tasks since these tasks bypass the need to search for and establish relationships. However, from this it is a mistake to conclude that these students are unable to function successfully on tasks requiring higher levels of cognitive functioning. Instead, teachers need to mediate the development of the requisite KCF and central among these is the development of the need to search for and establish relationships.
Below are some examples of situations where this knowledge construction function is used. This is followed by a teacher-student dialogue that provides ideas you can use and adapt to introduce this KCF to the students in your classroom.
This knowledge construction function (KCF) or brain tool enables us to search for and establish relationships between experiences or sources of information. Without this KCF, students are passive recipients rather than active generators of information: Objects, events and experiences are treated as episodic and isolated from one another. This function energizes all of the KCF and especially those that are needed to generate information to solve tasks that go beyond imitation and reproduction. These are tasks that require the learner to transform an input to generate a desired output. To be solved, such tasks may require that the given sources of information are connected with one another, with information stored in memory, and with knowledge gained from hypothetical thinking and logical inference. All of these processes are energized by a need to search for and establish relationships.
Learners who have not received adequate mediation of this KCF orient to disconnected fragments of academic tasks, exhibiting shallow, low levels of performance. Such learners may excel on imitative and reproductive tasks since these tasks bypass the need to search for and establish relationships. However, from this it is a mistake to conclude that these students are unable to function successfully on tasks requiring higher levels of cognitive functioning. Instead, teachers need to mediate the development of the requisite KCF and central among these is the development of the need to search for and establish relationships.
Below are some examples of situations where this knowledge construction function is used. This is followed by a teacher-student dialogue that provides ideas you can use and adapt to introduce this KCF to the students in your classroom.
- Explaining even common observations involves the search for and establishment of relationships: What causes shadows to lengthen? What causes ice cubes to melt? What causes cookies to crumble? What causes the mercury to rise in a thermometer?
- When we try to solve a jigsaw puzzle we need to search for and establish relationships among the pieces that form the solution. We may try to establish relationships using spatial cues, color cues, and figure/ground cues.
- Doctors working to discover what causes a disease try to find the relationships that bring about the disease.
- Historians examine source materials to determine the relationships that brought about important changes within and between countries (e.g. the Second World II, the fall of Communism, the rise of the information society).
- Investigators study accidents to identify the relationships that brought about a disaster such as an airline crash or the destruction of a spacecraft (e.g. the Challenger and Columbia disasters in the U.S. space program).
- Families wanting to learn about their origins rely on this KCF to search for and establish relationships between them and their ancestors.
- When we try to use our knowledge in one area to solve a problem in another we need to search for and establish the relationships that identify both the similarities and the differences between the two areas. We generalize our knowledge by doing so. For example, knowing how to read and use a bus schedule makes it easier to learn to read and use a train schedule - provided we search for and establish the relationship between the two types of schedules.
Below is an example of an introductory teacher-student dialogue that reflects the intentionality of the teacher to mediate the development of the KCF of establishing relationships. The setting is a middle school classroom. Use this example to give you ideas about how you can introduce this function in your classroom. Do not hesitate either to lower or raise the abstractness of the examples in this dialogue, or come up with different examples, to suit the need of the students in your classroom.
Level: 7th-8th
teacher: Today we will be talking about relationships. What comes to your mind when you hear the word 'relationship'?
student: Someone you know. Like a relationship with someone you know. Like a friend or something.
teacher: Yes, we often think about people when we think about the word relationship. What is the relationship between each of us and our parents?
student: I am the child of my parents. People are the children of their parents.
teacher: Yes, we are the children of our parents. There is a parent-child relationship between our parents and us. What is the relationship called between you and any brothers or sisters you may have?
student: A sibling relationship.
teacher: Yes, when you have a brother or sister you have a sibling.
teacher: Write the word on the board.
teacher: The two of you are siblings to one another. There is a sibling relationship between you. So, if someone asks you how many sibling relationships you have, what would you answer?
student: Two
student: One
teacher: Great. - Can we talk about relationships in situations other than those that involve people? Can we talk about relationships between objects? Is there a relationship between the two cups on my table?
teacher: Select two easily movable objects in the classroom.
student: It is like, there is and there isn't. There is if we want to make a relationship between them. Otherwise, there isn't.
teacher: Yes, that is well said. Relationships often depend upon the people who make them. We can use the relationships we are aware about. What kind of relationship could we say exists between the cups?
student: They are about a foot apart.
teacher: Yes, we could say that the distance between them is about a foot. There is a spatial relationship between them of about a foot. Is it possible for us to change this relationship?
students: Yes.
teacher: How could we change the relationship?
student: We could move one of the cups closer to the other - or move it farther away.
student: Or we could move the other cup. - Or we could move both!
student: We don't even have to move them away from where they are. We could just turn them so that the handles, let's say, either face one another or face away from one another, like pointing in opposite directions.
student: Or we could leave them just the way they are and put something in between them, like they were in separate spaces.
teacher: Yes, that could change the way we describe the relationship between them. If we put a pencil between them, we might say the two cups are a foot apart, just like we did before. But now we might also say that one cup is to the left of the pencil and the other to the right.
student: There sure are a lot of possible relationships. Can you imagine what would happen if we thought about the relationships between all the people and all the things in this room?
teacher: You are absolutely right. It could go on forever. There is really no end to the number of relationships that people can establish. It is infinite. That is why it is important to think carefully about the relationships we do establish to make sure they serve a purpose; that they enable us to solve a problem or better understand something. Let's think about some examples where it is useful to search for and establish relationships between things.
student: How about weather patterns and how they affect agriculture.
teacher: Yes, good. It is useful to discover which crops do best in different types of weather patterns. In this case we would be searching for and establishing relationships between climate and agriculture. What would happen if people didn't search for and find those patterns?
students: Farmers might plant the wrong kinds of crops. The crops might not grow and there might not be enough food.
teacher: Yes, so this brain tool is very important. Let's think of another situation where it is important to use this brain tool to establish relationships.
student: I know. I just built a model airplane. I had to make sure I put all the pieces in the right places. They all had to fit together.
teacher: Yes. And what might have happened if you had not searched for and established the right relationships?
student: I might have turned the wings upside down - I almost did!
teacher: Yes, good. And why is it important you didn't do that?
students: Airplanes with wings turned upside-down cannot fly. The aerodynamics to keep them aloft just don't work.
teacher: Ok. So you see that establishing relationships is a useful brain tool that assists us in our thinking. Can you think of another example where we need to establish relationships?
student: How about relationships between people? Like, in the world?
teacher: Sure. That is good. What do we do in our society, in our community, to establish relationships between people?
student: We have laws.
teacher: Yes, we create laws, rules and regulations. We use rules and regulations to establish relationships. Give me an example of such rules and regulations?
student: You have to drive on the correct side of the road. You can't just drive anywhere you want. If we did, people might run into each other all the time.
teacher: Good. Setting up a rule about the side of the road people need to drive on creates relationships between people that help prevent accidents on the road. Let's think of some examples that involve the creation of relationships between countries?
student: Countries agree to recognize one another and exchange ambassadors.
student: Countries establish relationships to promote trade between them.
student: The United Nations establishes relationships between all nations.
teacher: OK, good. Let's see if we can come up with some examples of people who search for relationships as part of their work. Think about what you learned in science or social studies.
student: Scientists try to discover relationships between what we eat and how healthy we are.
student: Yes, like between calories and weight or between exercise and fitness.
student: Scientists use the ebb and tide of the oceans to discover relationships between the Earth and the Moon.
student: Courts try to determine what really happened when someone is accused of committing a crime.
teacher: Yes, these are all examples of the need to search for and establish relationships. Doing so is not always easy, and we often have to make an effort to be careful to avoid making mistakes. Courts try to avoid mistakes by having two sides, prosecution and defense, illuminate the case from opposite points of view. Each may bring in expert witnesses to provide information about critical relationships, and each side may question the evidence presented by the other. In the end, a jury may sort through all the evidence to decide about guilt or innocence. Scientists, too, must be careful to collect precise information about the relationships they study. For example, scientists who develop new drugs must carefully study the relationship between the medicine and the condition it is designed to treat. If the scientists are not careful, people may end up buying medicine that doesn't help and could even hurt them. - OK, let's see if we can come up with some examples of how we can use this brain tool in our schoolwork.
student: In math we have to find the relationship between the perimeter and the area of rectangles or between the radius and area of circles.
student: In social studies we make presentations where we connect ideas to answer questions about cause and effect. Like, what caused people to rush to California around 1850? Or what caused the near extermination of the buffalo?
student: To answer questions about why or how things happen, you really must search for and establish relationships. I can use this KCF in a lot of places!
teacher: Yes, that is very true. What are some situations where you can use this KCF at home?
student: Maybe I could use it to see why I sometimes end up late for school?
teacher: OK, what might be a relevant relationship?
student: Maybe the amount of sleep. If I get to bed early, I wake up rested with plenty of time to get ready. If I get to bed late, I wake up groggy and waste time to get prepared.
teacher: That is a clear relationship. You can test it. Think about how you can collect information to see if this relationship is correct.
teacher: OK, everybody, you have a good sense of this KCF and its importance. Keep it in mind and use it both in your school work and outside of school.
Note: Encourage your students to discover where this function is used within your academic curriculum. Recognize, model and reinforce its use. You can also create learning events that connect the function to your curriculum. The example below emphasizes the math curriculum but others, like science and social studies, could easily be the ones emphasized.
teacher: We are going to do an activity where you have to use the KCF of establishing relationships. You will be working in groups. Each group will identify a relationship it wants to explore. The only requirement is that you must use mathematical measurement to investigate the relationship. So, first discuss different relationship you may want to investigate. Pick the one you want to investigate as a group, come up with a plan to investigate it and carry out the plan. At the end of your investigation, discuss what you have learned from using this knowledge construction function. Following that, we will get back as a whole class to discuss what each group has learner.
Here are examples from two groups.
Group 1: Decides to investigate the relationship between distance and the sense of sound. To investigate the relationship they decide that a cheap toy clicker is best because it reliably produces the same clicking sound when pressed. The students decide to investigate the relationship using a quiet playground, fix the position of the listener and use mathematical measurement to identify five click positions 15 meters apart going in a straight line away from the position of the listener. Facing away from the click points, students each take a turn as the listener raising their arm to report hearing a click. Students verify each click at each distance and record (yes/no) whether the listener reported hearing it. They use the results to demonstrate that hearing accuracy decreases with increases in distance, but focus most of their interest on ways to explain the observed variation between listeners.
Group 2: Decides to investigate how mathematical measurement can be used to prove optical illusions. In the drawings that follow the length of the two horizontal lines is equal (Mueller-Lyer Illusion). The group uses mathematical measurement to verify this illusion, then identifies and examines additional optical illusions described in resource materials in the school library. The group discusses the impact that illusory impressions can have on judgment and decision making. The discussion shifts to include the efforts of media, advertisers and other groups in society to create impressions that may appear to be true without in fact being so.
The teacher brings everybody together to share what they learned from the small group activities and discuss what these insights mean for the development of the KCF to search for and establish relationships.
Level: 7th-8th
teacher: Today we will be talking about relationships. What comes to your mind when you hear the word 'relationship'?
student: Someone you know. Like a relationship with someone you know. Like a friend or something.
teacher: Yes, we often think about people when we think about the word relationship. What is the relationship between each of us and our parents?
student: I am the child of my parents. People are the children of their parents.
teacher: Yes, we are the children of our parents. There is a parent-child relationship between our parents and us. What is the relationship called between you and any brothers or sisters you may have?
student: A sibling relationship.
teacher: Yes, when you have a brother or sister you have a sibling.
teacher: Write the word on the board.
teacher: The two of you are siblings to one another. There is a sibling relationship between you. So, if someone asks you how many sibling relationships you have, what would you answer?
student: Two
student: One
teacher: Great. - Can we talk about relationships in situations other than those that involve people? Can we talk about relationships between objects? Is there a relationship between the two cups on my table?
teacher: Select two easily movable objects in the classroom.
student: It is like, there is and there isn't. There is if we want to make a relationship between them. Otherwise, there isn't.
teacher: Yes, that is well said. Relationships often depend upon the people who make them. We can use the relationships we are aware about. What kind of relationship could we say exists between the cups?
student: They are about a foot apart.
teacher: Yes, we could say that the distance between them is about a foot. There is a spatial relationship between them of about a foot. Is it possible for us to change this relationship?
students: Yes.
teacher: How could we change the relationship?
student: We could move one of the cups closer to the other - or move it farther away.
student: Or we could move the other cup. - Or we could move both!
student: We don't even have to move them away from where they are. We could just turn them so that the handles, let's say, either face one another or face away from one another, like pointing in opposite directions.
student: Or we could leave them just the way they are and put something in between them, like they were in separate spaces.
teacher: Yes, that could change the way we describe the relationship between them. If we put a pencil between them, we might say the two cups are a foot apart, just like we did before. But now we might also say that one cup is to the left of the pencil and the other to the right.
student: There sure are a lot of possible relationships. Can you imagine what would happen if we thought about the relationships between all the people and all the things in this room?
teacher: You are absolutely right. It could go on forever. There is really no end to the number of relationships that people can establish. It is infinite. That is why it is important to think carefully about the relationships we do establish to make sure they serve a purpose; that they enable us to solve a problem or better understand something. Let's think about some examples where it is useful to search for and establish relationships between things.
student: How about weather patterns and how they affect agriculture.
teacher: Yes, good. It is useful to discover which crops do best in different types of weather patterns. In this case we would be searching for and establishing relationships between climate and agriculture. What would happen if people didn't search for and find those patterns?
students: Farmers might plant the wrong kinds of crops. The crops might not grow and there might not be enough food.
teacher: Yes, so this brain tool is very important. Let's think of another situation where it is important to use this brain tool to establish relationships.
student: I know. I just built a model airplane. I had to make sure I put all the pieces in the right places. They all had to fit together.
teacher: Yes. And what might have happened if you had not searched for and established the right relationships?
student: I might have turned the wings upside down - I almost did!
teacher: Yes, good. And why is it important you didn't do that?
students: Airplanes with wings turned upside-down cannot fly. The aerodynamics to keep them aloft just don't work.
teacher: Ok. So you see that establishing relationships is a useful brain tool that assists us in our thinking. Can you think of another example where we need to establish relationships?
student: How about relationships between people? Like, in the world?
teacher: Sure. That is good. What do we do in our society, in our community, to establish relationships between people?
student: We have laws.
teacher: Yes, we create laws, rules and regulations. We use rules and regulations to establish relationships. Give me an example of such rules and regulations?
student: You have to drive on the correct side of the road. You can't just drive anywhere you want. If we did, people might run into each other all the time.
teacher: Good. Setting up a rule about the side of the road people need to drive on creates relationships between people that help prevent accidents on the road. Let's think of some examples that involve the creation of relationships between countries?
student: Countries agree to recognize one another and exchange ambassadors.
student: Countries establish relationships to promote trade between them.
student: The United Nations establishes relationships between all nations.
teacher: OK, good. Let's see if we can come up with some examples of people who search for relationships as part of their work. Think about what you learned in science or social studies.
student: Scientists try to discover relationships between what we eat and how healthy we are.
student: Yes, like between calories and weight or between exercise and fitness.
student: Scientists use the ebb and tide of the oceans to discover relationships between the Earth and the Moon.
student: Courts try to determine what really happened when someone is accused of committing a crime.
teacher: Yes, these are all examples of the need to search for and establish relationships. Doing so is not always easy, and we often have to make an effort to be careful to avoid making mistakes. Courts try to avoid mistakes by having two sides, prosecution and defense, illuminate the case from opposite points of view. Each may bring in expert witnesses to provide information about critical relationships, and each side may question the evidence presented by the other. In the end, a jury may sort through all the evidence to decide about guilt or innocence. Scientists, too, must be careful to collect precise information about the relationships they study. For example, scientists who develop new drugs must carefully study the relationship between the medicine and the condition it is designed to treat. If the scientists are not careful, people may end up buying medicine that doesn't help and could even hurt them. - OK, let's see if we can come up with some examples of how we can use this brain tool in our schoolwork.
student: In math we have to find the relationship between the perimeter and the area of rectangles or between the radius and area of circles.
student: In social studies we make presentations where we connect ideas to answer questions about cause and effect. Like, what caused people to rush to California around 1850? Or what caused the near extermination of the buffalo?
student: To answer questions about why or how things happen, you really must search for and establish relationships. I can use this KCF in a lot of places!
teacher: Yes, that is very true. What are some situations where you can use this KCF at home?
student: Maybe I could use it to see why I sometimes end up late for school?
teacher: OK, what might be a relevant relationship?
student: Maybe the amount of sleep. If I get to bed early, I wake up rested with plenty of time to get ready. If I get to bed late, I wake up groggy and waste time to get prepared.
teacher: That is a clear relationship. You can test it. Think about how you can collect information to see if this relationship is correct.
teacher: OK, everybody, you have a good sense of this KCF and its importance. Keep it in mind and use it both in your school work and outside of school.
Note: Encourage your students to discover where this function is used within your academic curriculum. Recognize, model and reinforce its use. You can also create learning events that connect the function to your curriculum. The example below emphasizes the math curriculum but others, like science and social studies, could easily be the ones emphasized.
teacher: We are going to do an activity where you have to use the KCF of establishing relationships. You will be working in groups. Each group will identify a relationship it wants to explore. The only requirement is that you must use mathematical measurement to investigate the relationship. So, first discuss different relationship you may want to investigate. Pick the one you want to investigate as a group, come up with a plan to investigate it and carry out the plan. At the end of your investigation, discuss what you have learned from using this knowledge construction function. Following that, we will get back as a whole class to discuss what each group has learner.
Here are examples from two groups.
Group 1: Decides to investigate the relationship between distance and the sense of sound. To investigate the relationship they decide that a cheap toy clicker is best because it reliably produces the same clicking sound when pressed. The students decide to investigate the relationship using a quiet playground, fix the position of the listener and use mathematical measurement to identify five click positions 15 meters apart going in a straight line away from the position of the listener. Facing away from the click points, students each take a turn as the listener raising their arm to report hearing a click. Students verify each click at each distance and record (yes/no) whether the listener reported hearing it. They use the results to demonstrate that hearing accuracy decreases with increases in distance, but focus most of their interest on ways to explain the observed variation between listeners.
Group 2: Decides to investigate how mathematical measurement can be used to prove optical illusions. In the drawings that follow the length of the two horizontal lines is equal (Mueller-Lyer Illusion). The group uses mathematical measurement to verify this illusion, then identifies and examines additional optical illusions described in resource materials in the school library. The group discusses the impact that illusory impressions can have on judgment and decision making. The discussion shifts to include the efforts of media, advertisers and other groups in society to create impressions that may appear to be true without in fact being so.
The teacher brings everybody together to share what they learned from the small group activities and discuss what these insights mean for the development of the KCF to search for and establish relationships.