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Exploring activity modification with a Cartesian Diver

Examples to modify explorations, analysis of expected understandings, planning, & questioning strategies

Questioning is the basis of all learning.

Overview

Introduction

This article introduces a Cartesian diver and uses it as a concrete example to show how activities can be modified to meet different needs for a range of learners from young to old or from novice to expert. Most who experience a Cartesian diver enjoy the experience. Therefore, it provides an interesting and motivational activity to do in a reasonably short period of time to explore pedagogical ideas.

We begin with a general discussion on how to modify activities, a video demonstration of a Cartesian Diver, longitudinal examples of learner's explanations of how Cartesian divers work, operational definitions for several levels, explanations of understanding from nivice to expert, a sample challenge for learners, a fourth/third grade instructional plan, a fifth grade plus plan, and an activity to practice questioning strategies and wait time while learners explore a Cartesian diver.

Here's hoping you enjoy this depth exploration!

Activities for what age or for a novice or expert?

Teachers, and others who seek activities to share with learners, continually reflect on the question:

Is an activity appropriate for my child or my students?

While most activities can be done at any age or grade level. The critical question is:

What outcomes are possible for my learners?

This is dependent on: the learning expectations or outcomes for learners at different ages or levels and their ability to achieve them to make decisions on how to approach or modify an activity to meet the needs of the learner.

This is achieved by asking:

The answers to these questions are dependent on: the learner's prior experiences, their levels of understandings, and their motivation to achieve different levels of understanding.

Based on this, we consider possible expectations, outcomes, or goals for our particular learners and modify an activity to personalize their experience.

To do this, our general knowledge of learning and development is used to guide our decisions as we consider what a learner or learners presently know and what possible information they might need to learn from a particular activity. We combine this information to decide appropriate concepts and outcomes along with other information (as in a planning framework) to plan experiences for them to explore and achieve the level of understanding appropriate for them.

To illustrate this, I've selected an activity with a Cartesian Diver.

A simple home made Cartesian Diver and its operation is demonstrated in this video.

Cartesian diver demonstration ...

 

Anyone who isn't familiar with it, usually enjoys experiencing it and puzzling over how it operates. For younger learners it is often a discrepant event and can be very motivational for them to discover how it works.

Whatever, the experience of the learner. A teacher or demonstrator needs to consider what they might expect learners to gain from their experience with a Cartesian diver. These different expectations are expressed in educational jargon as: goals, objectives, concepts, outcomes, and skills. More information for these terms may be found in the glossary of educational terms.

Additionally, when considering what they might learn, we should consider what they know and what they might be capable of learning. To do this we can use developmental ideas related to Piaget's constructivist learning theory to think about how the learner's current understanding might be processed and decide what questions to ask, what answers to expect, how to proceed, and when to conclude they have achieved peak learning goals or outcomes for their individual ability.

Characteristics of development can be reviewed at these links:

The following summarizes the explorations of different groups of learners from young to old.

Examples of learners & their explorations of a Cartesian diver system

Procedure

Groups of different ages investigated a Cartesian diver and were asked focus questions, answered them, and were pushed toward better understanding by presenting observational evidence (concrete operational) as suggestions for them to explain what was happening.

Preparation

A Cartesian Diver was created by filling a two-liter pop bottle with water, inserting a glass eyedropper, and capping it. The water in the eyedropper was adjusted so when the bottle was squeezed the eyedropper moved to the bottom; and when the pressure was released, the eyedropper moved to the top, as demonstrated in the video.

Focus Questions

  • Ask - How did the stopper go up and down?
  • Ask - What caused the stopper to go up and down?

Let's review different ways to consider learners answers:

  1. The least scientific to the most scientific.
  2. Three different levels of development as operational definitions.

Cartesian Diver Explanations by levels of understanding / development

Or from the least scientific to the most scientific

Least

  • Described the cause as intentions of an object. It wanted to sink. The water wanted it to float. The water made it happen. The water pushed the air out so it would sink. (preoperational characteristics)
  • Described the cause from an observation of what they observed the entire system do or its subsystems.
    • Observation of the diver. It sunk or it floated. (System)
    • Observation of the bottle or hands. It was squeezed. (System)
    • Observation of the water or the air inside the diver. (Subsystem)
      • The water went in and out of the diver.
      • The air went in and out of the diver. (concrete operational characteristic) A misconception after observing the volume of water decrease and increase and referencing the idea that the air went somewhere else. Probably they have not experienced the compression of air.
  • Described the cause of the event as a result of an interaction with one variable. The diver sunk because the water made it heavier. The diver floated because the air went back in and made the diver lighter. When the bottle was squeezed the water and air went in and out to make the diver sink and float. (concrete operational characteristics) increase and referencing the idea that the air went somewhere else. Probably they have not experienced the compression of air.
  • Described the cause of the event as a result of two variables. The diver sinks or floats because of how the size and weight change. The amount of water in the diver changes to make it heavier and lighter. But the size of the diver doesn't change much (The pressure on the rubber stopper should be the same on the inside and outside). (concrete and formal operational with systematic use of variables as characteristics)
  • Described the cause of the event as a change of relationship between two variables. The volume of the diver stays pretty much the same when the bottle is squeezed. However, the air is compressed which allows more water to go into the diver and makes it heavier. It doesn't float or sink just because it is heavier. It is because it is heavier for its size (volume). I think the density is changing. (concrete and formal operational with systematic use of variables and proportional reasoning as characteristics)
  • See also operational definitions - third level
  • See also invention planning information for grade 5+

Most

 

Operational definitions for three different levels of development

Level one

Pre Kindergarten - grade three,

Learners' explanations will use observable properties to link cause to effect as the why.

Why did the Cartesian diver sink?

Because I squeezed it, or it was squeezed and it sunk. They can also chain events together in one to one to one... relationships. (preoperational, one-to-one, ego-centric,... not touching... floating, squeeze... goes down, let go... go up. ...)

Level two

Around third grade children’s experiences with the physical world and their intellectual development enables them to begin to recognize variables can be acting simultaneously to cause a specific effect.

They are able to select one cause at a time and use concrete operations and manipulations to associate additional variables acting together for a reasonable explanation as a report of conditions before an event, during an event, and what happened presumably as a result of the causal event of observed result.

For example - I squeezed the top of the bottle, which caused pressure to push the eyedropper to the bottom. When there was not pressure pushing it down it rose to the top.

If questioned further - By asking what will happen if they squeeze the bottom of the bottle?

For example, will it stay floating or will it sink? They might say it doesn't matter or they may say it won't work as they need to push it down.

In this case, they do not believe the pressure on the eyedropper is a simultaneous event so that when squeezed pressure will push on the eyedropper from all directions. (Concrete operational)

Level three

As they develop conservation abilities they begin to understand similar events create similar results in the world.

Coupled with this, is a better understanding of the physical world and the kinds of physical interactions that create change. And with a desire to make better predictions and inferences to explain their world, the embryo of rational explanations is created. Understanding that a squeeze of the bottle transfers to the water and the squeezed water will transfer to more water and be equalized across all the water so the pressure on the eyedropper is a simultaneous event that when squeezed the pressure will push the water which will push on the eyedropper equally from all directions. (Formal operational thinking)

Summary

Rational explanations are first explored with early physical inquiry skills developed through play and can be very generous with analogies tied to the concrete world (pressure is like what pushes water out of a hose or faucet).

As their experiences grow and their imaginative abilities increase, they will recognize cause and effect explanations that are not observable, but can be inferred as possibilities from observations. They also realize the possibility of simultaneous conditions as necessary for causal explanations that can be inferred from similar observations and used to make predictions.

However, they are troubled with complexity as they are not good at systematic and combinatorial thinking, which often creates uncertainty and they long for and ask - what is the right answer? (concrete operational)

Another jewel comes to light when learners create their own operational definitions, which are their explanations of what they learned. If we listen to enough of these explanations we can not only discover how understanding develops as they mature, but can organize the information into developmental levels.

For example: preoperational learners have no problem with push or pull as an explanation as to why something moved. Both of which are included among the early physical inquiry skills. So if the science curriculum includes force in second grade, then a developmentally appropriate concept for a second grader would be - A force is a push or pull. Oh, what a jewel! - Something that pushes or pulls on another object is a force. WOW! Which is written as an Operational definition. Another jewel! And it can be the outcome of the first level of a scoring guide or rubric in a curriculum document. See information in the science glossary about operational definitions and their use for scoring guides or rubrics.

 

How to use the information to create Learning Plans (lesson plans)

To further explore how different preparation might be let's create two different lesson plans: One for grades 3&4 and another for grades 5 and above.

First, a Planning framework for a Cartesian diver challenge can be created. Then, a more detailed plan can be created, like ...

 

Challenge: Make a Cartesian diver

Create a Cartesian Diver with a capped two-liter pop bottle, water, and a glass eyedropper.

So that when the bottle is squeezed the eyedropper moves to the bottom and when released the eyedropper moves to the top.

 

 

Why does the eyedropper go up and down?

Hint: Draw a before squeeze, during squeeze, & after squeeze diagram. Make careful observations!

 

 

 

 

 

 

Investigating a Cartesian Diver (Grades 3-4)

Overview

  • Introduction
  • Science content
  • Science inquiry and process
  • Resources and materials
  • Pedagogical ideas
    • focus questions
    • exploration
    • invention
    • bridge
    • value claim
    • discovery
  • Definitions
  • Lessons and activities detail

Introduction

Learners observe a Cartesian Diver system and use their observations and understandings of sink, float, matter takes up space and can't occupy the same space as other matter at the same time, and mass as weight to reason explanations for what happens.

See video.

Science content - what science says

Enduring understanding, big ideas, generalizations

Properties of matter - takes up space (volume), two objects can't occupy the same space, matter has weight or heavy, every object is made of matter.

When two object exert a force on each other the object with the greater force moves the object with the smaller force.

Supporting ideas from unpacking the big idea (facts, concepts, generalizations)

  • Objects heavier than water float.
  • Objects lighter than water sink.
  • Water takes up space.
  • Air takes up space.
  • Water has volume.
  • Air has volume.
  • Water is matter.
  • Air is matter.
  • Objects can exert a force on each other.
  • Water flows.
  • Air flows.

Outcomes

Properties of matter - When the bottle is squeezed, the air is pushes more water into the eyedropper, making it heavier and causing it to sink.

(It is okay at this level for them to disagree whether the rubber stopper expands to hold the air and make more room for water to be pushed into the eyedropper. Additionally they may claim the air leaves the stopper when the bottle is squeezed and when it is unsqueezed it enters the eyedropper. You can challenge them by asking to find proof of air leaving [bubbles ... ], but if they are not disequilibrated and search for another explanation, then it is okay to let it go. They have years of education to construct the idea of pressure, compression ... )

Science inquiry and processes - how science knows

Enduring understanding, big ideas, generalizations

Science uses observations of objects, systems and subsystems, to gather evidence to reason and understand cause and effect interactions in our world.

Supporting ideas from unpacking the big idea

  • observations of eyedropper and the amount of water and air;
  • isolate observations to the eyedropper subsystem
  • Connection of observations to properties of matter - matter takes up space and can't occupy the same space as other matter at the same time, and matter has weight - mass.

Outcomes

Learners observe a Cartesian Diver system and use their observations and understandings of weight (developmentally appropriate understanding of mass) and volume to reason and explain what happens. Example: more water in the eyedropper makes it heavier and it sinks.

Resources and materials

Two liter plastic pop bottle, glass eyedropper (obtain from your local pharmacy, if you're a teacher and mention it, they will often provide them free) , water.

Take the 2 liter plastic pop bottle, fill it with water, drop in an eyedropper with some water in it, but not enough to make it sink, put the lid on tight, squeeze the bottle to make the eyedropper sink, and release the bottle to make it float.

To reduce the hassle of getting the eyedropper out of a bottle when it doesn't float, get a balance of water in the eyedropper so that it barely floats in a glass of water, then try it in the bottle.

Pedagogical ideas

Focus questions - What causes a Cartesian diver (eyedropper) to sink and float?

Misconception - Air goes out of the eyedropper. Pressure inside the eyedropper is different than the pressure outside the eyedropper.

Exploration - Results The water went up into the eyedropper the more the bottle was squeezed. It appeared the air left and returned but there were no bubbles observed leaving the eyedropper. The more water in the eyedropper the lower it floated or sunk. The more air in the eyedropper the higher it floated. The more air in the bottle the harder you had to squeeze to get the eyedropper to sink.

Invention -

Bridges - Drawing of before and after pictures that include enough information to create an operational definition. - Observational evidence included on the diagrams - the eyedropper floated, the eyedropper sunk when the bottle was squeezed, the air remained inside the eyedropper since no bubbles were observed leaving the eyedropper, the air must, and the amount of water in the eyedropper increased when the bottle was squeezed.

Operational definition - When the bottle is squeezed the water pushes the air into the eyedropper so it is squeezed into a smaller space/volume. Making more room for more water to flow into the eyedropper. With more water in the eyedropper system it was heavier so it sunk. When the pressure was released the ....

Discovery, application, extension -

Value Claims - It's amazing how when you really observe something you can figure out what is happening.

Definitions

  • properties of matter as takes up space (volume), two objects can't occupy the same space, matter has weight or heavy, every object is made of matter.
  • push is a force on an object that can result in a motion away from the pusher. As opposed to pull being toward.
  • mass is the amount of matter in an object or system.
  • volume is the amount of space an object takes up.
  • pressure is a continuous force an object exerts on another with physical contact.
  • compress is to squeeze with pressure.

 

 

Investigating a Cartesian Diver (Grades 5+)

Overview

  1. Introduction
  2. Science content
  3. Science inquiry and process
  4. Resources and materials
  5. Pedagogical ideas
    • focus questions,
    • exploration,
    • invention, bridge, value claim,
    • discovery
    • Definitions

Introduction

Learners observe a Cartesian Diver system and use their observations and understandings of mass and volume to reason and explain what happens.

See video.

Science content - what science says

Enduring understanding, big ideas, generalizations

  • Two objects can't occupy the same space at the same time.
  • When two object exert a force on each other the object with the greater force moves the object with the smaller force.
  • Pressure is a force over a particular area.
  • Objects float if they are less dense than the substance they are in.
  • Objects sink if they are denser than the substance they are in.
  • When forces are equal, then there is equilibrium.

Supporting ideas from unpacking the big idea (facts, concepts, generalizations)

  • Water takes up space.
  • Air takes up space.
  • Water has volume.
  • Air has volume.
  • Water is matter.
  • Air is matter.
  • Objects can exert a force on each other.
  • A greater force moves an object with less force.
  • Water flows.
  • Air flows.

Outcomes

Understand the properties of matter to explain that when the bottle is squeezed, the air is compressed and pushed into the rubber on the eyedropper, which expands and makes more room for water to be pushed into the eyedropper making it heavier and causing it to sink.

Science inquiry and processes - how science knows

Enduring understanding, big ideas, generalizations

Use of observations, systems and subsystems, evidence and reasoning to understand interactions in our world. Create an operational definition.

Supporting ideas from unpacking the big idea

  • Observations of eyedropper and the amount of water and air;
  • Isolate observations to the eyedropper subsystem. Amount of air and water in the eyedropper.
  • Connection of observations to properties of matter, volume, and air condensing for a cause and effect sequence or operational definition.

Outcomes

Use observations, systems and subsystems, evidence and reasoning to explain interactions and create an operational definition for a Cartesian diver.

Resources and materials

Two liter plastic pop bottle, glass eyedropper (obtain from your local pharmacy, if you're a teacher and mention it, they will often provide them free) , water.

Take the 2 liter plastic pop bottle, fill it with water, drop in an eyedropper with some water in it, but not enough to make it sink, put the lid on tight, squeeze the bottle to make the eyedropper sink, and release the bottle to make it float.

To reduce the hassle of getting the eyedropper out of a bottle when it doesn't float, get a balance of water in the eyedropper so that it barely floats in a glass of water, then try it in the bottle.

Pedagogical ideas

Focus questions - What causes a Cartesian diver (eyedropper) to sink and float?

Misconception - Air goes out of the eyedropper. Pressure inside the eyedropper is different than the pressure outside the eyedropper.

Exploration

Explore the Cartesian diver system and record the results and explanations.

Draw before, during, and after diagrams and share them.

  • The water went up into the eyedropper the more the bottle was squeezed.
  • It appeared the air left and returned but there were no bubbles observed leaving the eyedropper.
  • The more water in the eyedropper the lower it floated or sunk.
  • The more air in the eyedropper the higher it floated.
  • The more air in the bottle the harder you had to squeeze to get the eyedropper to sink.
  • I couldn't see the rubber on the eyedropper move - expand or contract.
  • The more air in the bottle (less water) the more we had to squeeze the bottle to get the eyedropper to sink, if it did.

Invention

Use the information below to help move the discussion along by asking probing questions and maybe a few suggestion such as ... I have heard others claim ...

Bridges - Drawing of before, during, and after pictures that include enough observational information to create an operational definition. - Observational evidence included on the diagrams - the eyedropper floated, the eyedropper sunk when the bottle was squeezed, the air remained inside the eyedropper since no bubbles were observed leaving the eyedropper, the air must, and the amount of water in the eyedropper increased when the bottle was squeezed.

Operational definition - When the bottle is squeezed the water pushes the air into the eyedropper so it is squeezed into a smaller space/volume. Making more room for more water to flow into the eyedropper increasing the mass. This changed the proportion of mass and volume, which means as the mass increases and the volume is the same, the density will increase.

Supporting information - Since the air was not observed leaving the eyedropper it must remain inside (air mass). It might be possible that when the bottle is squeezed the air in the eyedropper is condensed (squeezed into a smaller space/volume) making more room for more water to flow into the eyedropper (water mass + squeezed in water mass). With more water in the eyedropper system the mass was increased but the volume was the same eyedropper volume). This caused the density to increase and the eyedropper system (eyedropper, air and water in it) to sink. If the air wasn't compressed and caused the rubber to expand, then the density of the eyedropper would not change (if the mass and volume would increase proportionally). Therefore, I think the air had to be compressed.

BEFORE Density = (AIRmass) + (WATERmass) / (DROPPERvolume)

After Density = (AIRmass) + (WATERmass + SQUEEZEDINWATERmass) / (DROPPERvolume)

Another reason I don't think that the rubber on the eyedropper expanded was because the force of squeezing the bottle was transferred to the eyedropper. I mean that the hand squeezed the bottle which squeezed the water, which squeezed the air from all directions. At the bottom through the small opening and at the top by squeezing on the rubber. When this happened the same amount of pressure would be put on all sides of the rubber and it couldn't expand or blow up like a balloon with the air being pushed into it.

Another reason I think the air was compressed is that when we had more air in the pop bottle it was harder to make the eyedropper sink. When we squeezed the bottle the bottle would really bend in much more before the eyedropper would sink and when we filled it only half full we couldn't push on it enough to make it sink.

Value Claims - You really need to observe every variable before you can figure out what happens and even then it takes some creative thinking to be able to put the pieces together and you can't be real sure your right even then.

Discovery, application, extensions

Use a glass bottle and make a Cartesian diver. This will work best with a glass bottle that has a convex side.

Make a Cartesian floater. Make it so the diver starts being sunk and when the bottle is squeezed it will float to the top. This will work best with a plastic bottle that is oval shaped so that when it is squeezed from the side the volume inside is increased.

Make a bottle system with two ... one diver and one floater depending on how the bottle is squeezed.

Definitions

  • properties of matter as takes up space (volume), two objects can't occupy the same space, matter has weight or heavy, every object is made of matter.
  • compress is to squeeze with pressure.
  • mass is the amount of matter in an object or system.
  • volume is the amount of space an object takes up.
  • density is the relationship between mass and volume. D = M / V.
  • pressure is a continuous force an object exerts on another with physical contact.

 

Cartesian Diver Activity for Questioning Strategies

Overview

An activity to practice questioning strategies to facilitate learner's construction of an explanation for what happens in this challenge.

Materials

  • Plastic pop bottle (1 or 2 liter), Glass eyedropper, Water, Recording device

Procedure

  • Read this entire activity and the information preceding this activity for any background information you desire.
  • Get a recorder, video or audio record the experiment and discussion.
  • Get a one person or a group of learners (age 10 and up).
  • Have an eyedropper system or Cartesian diver ready for them to explore.

Set up for the eyedropper - Cartesian diver or Pop Bottle System.

  1. Put enough water in the eyedropper so that it will just barely float. You may want to do this in a large container before placing the eye dropper into the plastic pop bottle.
  2. Fill the plastic pop bottle with water.
  3. Place the eyedropper into the pop bottle.
  4. If the eyedropper does not float you will need to remove it and reduce the water in the eyedropper until it floats.
  5. Put the lid on the pop bottle.
  6. When you squeeze the pop bottle the eyedropper may sink. If the eyedropper does not sink then you need to remove the eyedropper and increase the amount of water in the eyedropper.

Procedure for Interacting with learners

Let them explore the eyedropper system.

After 5-10 minutes ask questions about their observations.

The purpose of the questioning is to help them construct possible causes of the interactions.

YOU ARE ONLY TO ASK QUESTIONS.

Guide their observations with questions so they construct their own reasons for themselves.

Do not tell anything.

Have people distinguish between observation and inference. Quick review check out Snow White comic ...

Possible questions:

  • What happened?
  • What did you observe?
  • What observation gave you that inference (idea)?
  • Do you agree with ______ (person or idea)? Why?
  • Did you observe what ___ said?

Desperate questions:

  • What happens to the eyedropper on the bottom?
  • What happens to the eyedropper on the top?
  • What is the difference?

Have them summarize their explanations for what they believe happened.

  • Could have them draw before/after & during pictures or write a summary.

If they construct an explanation for the experiment fairly quickly and need some more questions, then use the following:

  • Ask, What is a variable?
  • What are the variables in the system?
  • What would happen if these variables were changed?
  • Ask questions to get them to use their observations to support their answers.
  • Help them to distinguish between observations and inferences if needed.
  • Ask. Do you think you could make a system where a sunk diver could be made to float?

Processing your Questioning Strategies

Listen to your recording and collect the data needed to complete the following.

1. Write two of the most open ended (divergent) questions you asked.

 

 

 

2. Time the total number of seconds for your number one wait-times (after you asked a question). Record the information below.

Number one wait times for each question

                   
                   
                   

Average number one wait-times

 

3. Time the total number of seconds for your number two wait-times (after a learner responded and before you responded or asked a question). Record the information below.

Number two wait times for each question

                   
                   
                   

Average number two wait-time.

 

4. If you slipped and told them some information what did you tell?

 

 

5. How many times did you repeat their answers?

 

 

6. If you used a learners idea, write it.

 

 

7. Summarize what you learned.

 

 

8. What goals do you have for your questioning strategies and why?

 

 

 

For more information on science discrepant events

 

Planning framework

Planning guide with explanation for categories

 

Planning Framework for a Cartesian Diver Challenge

Planning framework for Cartesian diver

 

Blank planning framework

Blank Planning framework

 

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