College Students’ College Students’ Conception of VolumeConception of Volume

College Students’ College Students’ Conception of VolumeConception of Volume

Do-Yong Park Do-Yong Park Tiffany LawlerTiffany Lawler

PurposePurpose

College students’ common pattern College students’ common pattern of conceptions about volume in of conceptions about volume in different task? different task?

Identifiable patterns of their Identifiable patterns of their reasoning in their answers?reasoning in their answers?

Scope of Understanding?Scope of Understanding?

Implications for teaching the Implications for teaching the concept of VOLUME? concept of VOLUME?

MethodologyMethodology

Sample: Sample: Group 1-Group 1- 4 Preservice Elem. Teachers 4 Preservice Elem. Teachers Group 2-Group 2- 3 College Students (1 Elem. 3 College Students (1 Elem.

Ed., 1English and Spanish, 1 Ed., 1English and Spanish, 1 Special Ed.)Special Ed.)Data Collection – Individual Interview in Data Collection – Individual Interview in the last Fall 2005the last Fall 2005Instrument: Four Different Tasks about Instrument: Four Different Tasks about VolumeVolume

Task 1Task 1

Both cups are the same size but different Both cups are the same size but different thickness.thickness.

Compare volume of cups A and B. Which cup has more volume between A and B and why?

3 mm 15 mm

A B

Task 2Task 2

Both clay balls below are the same Both clay balls below are the same size. size.

Compare volume of balls A and B. Which ball has more volume between A and B and why?

A B

Air No Air

Task 3Task 3

Compare the volume of two bowls. Compare the volume of two bowls.

Compare volume of bowls A and B. Which bowl has more volume between A and B and why?

A B

Empty Filled with Water

Task 4Task 4

Compare the volume of two balloons Compare the volume of two balloons

Compare volume of balloons A and B. Which has more volume between balloons A and B and why?

A B

Empty Filled with Water

ResultsResults

QQ College (P) N=4College (P) N=4 College (O) N=3College (O) N=3

Q1-BQ1-B

Q2-BQ2-B 2 1

Q3-BQ3-B 2 2

Q4-BQ4-B 2 1 & 1 (Same)

QQ College (P) N=4College (P) N=4 College (O) N=3College (O) N=3

Q1-AQ1-A 44 33

Q2-AQ2-A 22 22

Q3-AQ3-A 22 1-Not Sure 1-Not Sure 　　Q4-AQ4-A 22 1-Not Sure1-Not Sure

Students’ Conceptions of Students’ Conceptions of VolumeVolume

CategoriesCategories College (P) N=4College (P) N=4 College (O) N=3College (O) N=3

Space OccupiedSpace Occupied 2 11

CapacityCapacity 2 2

Students Conceptions of Students Conceptions of volumevolume

- Definition- Definition

Reasoning in Students’ Reasoning in Students’ ExplanationExplanation

CategoriesCategories College (P) N=4College (P) N=4(16 responses)(16 responses)

College (O) N=3College (O) N=3(12 responses)(12 responses)

Space OccupiedSpace Occupied Filled space -3*Empty space -3

Filled space-3Empty space-1

CapacityCapacity 9 3

Others (not sure, Others (not sure, same)same)

1 5 (Same-2 not sure-3)5 (Same-2 not sure-3)

* The number means number of individual * The number means number of individual responsesresponses

Sample Group 1Sample Group 1

- 4 Elem. Ed. Majors - 4 Elem. Ed. Majors - Seniors, Seniors, - All females, All females, - 12 semester hours of 12 semester hours of

science,science,

Student #1“Volume is the amount of something in an object - capacity

Task 1-Task 1- “ “Cup ACup A is going to have a greater volume is going to have a greater volume because it can hold more space inside”because it can hold more space inside”Task 2-Task 2-““Ball BBall B will have a greater volume holding will have a greater volume holding capacity.capacity.Task 3-Task 3-““Bowl BBowl B has a greater volume because it’s has a greater volume because it’s holding water in it. Well, .. It has more optional holding water in it. Well, .. It has more optional volume space. It has more opportunity to fill up volume space. It has more opportunity to fill up because everything in it is the volume and right now because everything in it is the volume and right now there’s only air in it….. Both have the same volume there’s only air in it….. Both have the same volume only if they’re both filled up with the same thing.”only if they’re both filled up with the same thing.”Task 4-Task 4-““Baloon BBaloon B has a greater volume because of has a greater volume because of the water in it. The other one has the opportunity to the water in it. The other one has the opportunity to hold the volume and if it had to stay the exact same hold the volume and if it had to stay the exact same size, you could fill it up with the exact same size, you could fill it up with the exact same amount.”amount.”

Student #2“Volume is the space that is taken up inside of an object - space occupied

Task 1-Task 1- “ “Cup ACup A would be more space inside, would be more space inside, so there’s more volume.”so there’s more volume.”Task 2-Task 2-“I really don’t know which one has “I really don’t know which one has more volume. A has a higher volume. But more volume. A has a higher volume. But B B has a high volume because there’s only air in has a high volume because there’s only air in it so there’s more room.”it so there’s more room.”Task 3-Task 3-““Bowl BBowl B has more volume .. because has more volume .. because you can measure the volume that’s in there you can measure the volume that’s in there because there’s substance in there.“because there’s substance in there.“Task 4-Task 4-“I think I would say the same thing. I “I think I would say the same thing. I would say the water-filled would say the water-filled one (B)one (B) has more has more volume because you can measure the space volume because you can measure the space taken up”taken up”

Student #3“Volume is the space inside of an object that is occupied – space occupied

Task 1-Task 1- “ “Cup ACup A has more volume has more volume because it can hold more space inside”because it can hold more space inside”

Task 2-Task 2-““Ball ABall A is going to have more is going to have more volume because it has more space than volume because it has more space than Ball B that all the space is occupied.”Ball B that all the space is occupied.”

Task 3-Task 3-““Bowl ABowl A has more volume.” has more volume.”

Task 4-Task 4-““Ballon ABallon A has more volume.” has more volume.”

Student #4“Volume is how much space is inside of an object - capacity

Task 1-Task 1- “ “Cup ACup A has more volume because has more volume because there’s more space that can be taken up.”there’s more space that can be taken up.”Task 2-Task 2-“I think maybe “I think maybe Ball ABall A will have more will have more volume because there’s more room.”volume because there’s more room.”Task 3-Task 3-“I would say “I would say Bowl ABowl A has more has more volume because there’s a lot more space in volume because there’s a lot more space in it available.”it available.”Task 4-Task 4-““Baloon ABaloon A would have a bigger would have a bigger volume because the water takes up space volume because the water takes up space and nothing else would fit in there.”and nothing else would fit in there.”

Sample Group 2Sample Group 2Student A-Student A- – Gender: MaleGender: Male– Year in School: SeniorYear in School: Senior– Major: Elementary EducationMajor: Elementary Education– Science Background: Some high school and Science Background: Some high school and 12 hours12 hours of of

college courses in sciencecollege courses in science

Student B-Student B- – Gender: FemaleGender: Female– Year in School: SeniorYear in School: Senior– Major: English and Spanish Major: English and Spanish – Science Background: High school and Science Background: High school and 18 hours18 hours of college of college

courses in science (Physics, Biology, Chemistry)courses in science (Physics, Biology, Chemistry)

Student C-Student C- – Gender: FemaleGender: Female– Year in School: SeniorYear in School: Senior– Major: Special EducationMajor: Special Education– Science Background: Biology and Chemistry class in high school Science Background: Biology and Chemistry class in high school

and Chemistry class in collegeand Chemistry class in college

Student #1“Volume is how much mass something is, I guess. How much, like, let’s see, it is occupied by.” – Space occupied

Task 1-Task 1- “Cup A has more volume. “Cup A has more volume. There is more space for liquid than B”There is more space for liquid than B”Task 2-Task 2-“Ball B, because it occupies “Ball B, because it occupies more space. There is no room for air more space. There is no room for air compared to A.”compared to A.”Task 3-Task 3-“B has more volume. Something “B has more volume. Something is occupying more space- other than is occupying more space- other than air inside of it.”air inside of it.”Task 4-Task 4-“B has more volume. That’s “B has more volume. That’s because water has more mass than because water has more mass than air.”air.”

Student #2“Volume is how much can fit in something; how much of something there is in something.” - capacity

Task 1-Task 1-“A has a greater volume because “A has a greater volume because it is bigger. There is a 12mm difference. it is bigger. There is a 12mm difference. 144 times height of difference of volume 144 times height of difference of volume times pi.”times pi.”Task 2-Task 2-“A has more volume of air and B “A has more volume of air and B has more volume of clay.”has more volume of clay.”Task 3-Task 3-“A has more volume of air and B “A has more volume of air and B has more volume of water.”has more volume of water.”Task 4-Task 4-“A has more volume of air and B “A has more volume of air and B has more volume of water. Actually, they has more volume of water. Actually, they are probably all equal. (Referring to are probably all equal. (Referring to volumes of all objects presented)”volumes of all objects presented)”

Student #3“How much something can hold.” - capacity

Task 1-Task 1-“I don’t remember! (Pauses “I don’t remember! (Pauses for about 62 seconds and thinks) for about 62 seconds and thinks) (Asks me) So A would be because it (Asks me) So A would be because it can hold more?” can hold more?”

Task 2-Task 2-“A, I don’t know why, maybe “A, I don’t know why, maybe more open areas.” more open areas.”

Task 3-Task 3-“I’m confused if it’s how much “I’m confused if it’s how much fits in or how much open space.”fits in or how much open space.”

Task 4-Task 4-“A and B are the same “A and B are the same because they hold the same amount.” because they hold the same amount.”

ConclusionConclusion

The students were not confident with The students were not confident with their answers and responses to the their answers and responses to the questions.questions. Many of their ideas were Many of their ideas were misconceptions or not fully misconceptions or not fully developed ideas about volume.developed ideas about volume. The student have multiple The student have multiple dimensions of understanding about dimensions of understanding about the concept of volume.the concept of volume.

Model of Understanding Model of Understanding StructureStructure

Nominal UnderstandingNominal Understanding – – Students Students often come to class with.often come to class with.

Functional UnderstandingFunctional Understanding – – Students Students can describe a concept but have a limited understanding of can describe a concept but have a limited understanding of it.it.

Structural UnderstandingStructural Understanding – Students – Students (a) develop personal relevance and are interested in the (a) develop personal relevance and are interested in the study of a concept, and (b) constructed appropriate study of a concept, and (b) constructed appropriate meaning of the concept from experiences. meaning of the concept from experiences.

Mature Understanding Mature Understanding – Students obtain – Students obtain additional knowledge or skills, and (c) apply knowledge of a additional knowledge or skills, and (c) apply knowledge of a concept to related subjects and to solve a problem or concept to related subjects and to solve a problem or answer a question. answer a question.

Modified from Developing Biological Literacy, BSCS, 1993.Modified from Developing Biological Literacy, BSCS, 1993.

Teaching Goal?Teaching Goal?

How far could/should/must we How far could/should/must we teach in terms of the teach in terms of the Understanding Model? Understanding Model?

How far are we able to achieve How far are we able to achieve the teaching goal in light of the the teaching goal in light of the Model? Model?

Strategy of Teaching for Strategy of Teaching for UnderstandingUnderstanding

KnowingKnowing

ExplainingExplaining

Applying Applying

TeachingTeaching

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