Improving Student Learning Through

Continuous Formative Assessment

Stamatis Vokos Hunter Close Lane SeeleyPhysics DepartmentSeattle Pacific University

Supported in part by NSF grants ESI-0455796, the PhysTEC project, and the SPU Science Initiative

Jim MinstrellPam Kraus

FACET Innovations, LLC

Eleanor CloseLezlie DeWaterPhysics Department

& School of Education

Seattle Pacific University

Proportional reasoningA crucial skill Numerous examples

Density, concentration, solubility, heat capacity, specific heat, uniform velocity, uniform acceleration, pressure, intensity, electric field, electric potential difference, capacitance, inductance, etc.

In addition, certain properties are characteristic. Density, solubility, boiling point, specific

heat, etc.To what extent do students recognize certain properties as characteristic?

Density as a Characteristic Property

A block of clay is cut into two different sized pieces, labeled X and Y.

How does the density of X compare to the density of Y?

Select all that apply.

A. The density of X is greater than the density of Y.B. The density of X is less than the density of Y.C. The density of X is equal to the density of Y.D. Not possible to compare without additional

information.

Explain your answer.

Density as a Characteristic Property

A block of clay is cut into two different sized pieces, labeled X and Y.

How does the density of X compare to the density of Y?

Select all that apply. (N ~ 1300 students grades 6-12)

A. (36%) The density of X is greater than the density of YB. (4%) The density of X is less than the density of YC. (36%) The density of X is equal to the density of YD. (23%) Not possible to compare without additional

information

Explain your answer.

Performance on Density Question by Grade Level

131 18 400 710 170 209 46N =

How about college students? Data from Steve Kanim, New

Mexico State U., and Gary White, SPS and AIP.

7

The variation in student success rates on this question across populations is dramatic.

The question that keeps on givingThe question that keeps on giving

How about a narrower grade band? Data from a set of questions

administered before instruction to all 7th graders in a partner district. One of two versions of the density

question assigned randomly to students with even or odd ID’s, with assignment flipped on alternate class periods.

N=588

N=552

The teacher cuts a large block of clay into two different size pieces, labeled X and Y.

How does the density of X compare to the density of Y?

a. The density of X is greater than the density of Y.

b. The density of X is less than the density of Y.

c. The density of X is equal to the density of Y.

d. Not possible to compare without additional information.

A block of aluminum has been cut into two different size pieces, labeled 1 and 2.

1 2

How does the density of 1 compare to the density of 2?

a. The density of 1 is greater than the density of 2.

b. The density of 1 is equal to the density of 2.

c. The density of 1 is less than the density of 2.

d. Not possible to compare without additional information.

How about the effect of instruction? Data from all 8th graders in a

partner school district. Administered before and after

instruction using Properties of Matter (STC).

Npre = 956.

Npost = 935.

Density as a Characteristic Property

X>YX<YX=YNot possible to compare

Pre-instruction

Post-instruction

1>21=21<2Not possible to compare

Clay Aluminum

56%4%23%17%

23%53%5%19%

Using Characteristic Properties

14% Mass45% Density12% Volume42% Max mass of salt that can be

dissolved in 1 mL of liquid 53% Temperature each liquid boils48% Temperature each liquid

freezes14% None of the above

12% All correct choices selected

Pre-instruction

Post-instruction52% Mass of 1 mL of liquid80% Density44% Time to heat each liquid to boil60% Max mass of salt that can be

dissolved in 1mL of liquid 74% Temperature each liquid boils71% Temperature each liquid

freezes2% None of the above

11% All correct choices selected

Select all measurements that would be the same if the two unknown liquids (1 and 2) are the same.

Density is a difficult concept, which is not easily mastered.

To what extent have students mastered

the underlying concepts of mass and volume?

Fall 2005 - The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone which of quantities are the same for the two objects?

Select all that apply. (N ~ 1000)

A. VolumeB. MassC. Surface areaD. DensityE. TemperatureF. Number of atoms

Fall 2005 - The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone which of quantities are the same for the two objects?

Select all that apply. (N ~ 1000)

A.(19%) VolumeB.(68%) MassC.(7%) Surface areaD.(26%) DensityE.(13%) TemperatureF.(12%) Number of atoms

(42% Mass only)

CognitiveDissonance?

Test TakingSophistication

Fall 2005 - The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone which of quantities are the same for the two objects?

Select all that apply. (N ~ 1000)

A.(19%) VolumeB.(68%) Mass C.(7%) Surface areaD.(26%) DensityE.(13%) TemperatureF.(12%) Number of atoms

Fall 2006 – The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone which of quantities are the same for the block and the cylinder? (N = 611)

A. Volume & MassB. Mass & DensityC. Volume, Mass and DensityD. Volume onlyE. Mass only F. Density only

(28%) (21%) (16%) (5%) (27%) (3%)

(42% Mass only)

Fall 2005 - The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone which of quantities are the same for the two objects?

Select all that apply. (N ~ 1000)

A.(19%) VolumeB.(68%) Mass C.(7%) Surface areaD.(26%) DensityE.(13%) TemperatureF.(12%) Number of atoms

Fall 2006 – The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone which of quantities are the same for the block and the cylinder? (N = 611)

A. Volume & MassB. Mass & DensityC. Volume, Mass and DensityD. Volume onlyE. Mass only F. Density only

(28%) (21%) (16%) (5%) (27%) (3%)

(42% Mass only)

Fall 2006 – The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone which of quantities are the same for the block and the cylinder? (N = 611)

A. Volume & MassB. Mass & DensityC. Volume, Mass and DensityD. Volume onlyE. Mass only F. Density only

(28%) (21%) (16%) (5%) (27%) (3%)

92% selected mass

Are these results reliable?Fall 2006, Version A – The two objects shown below are put on either side of an equal-arm balance. The block goes down and the cylinder goes up.

Based on this observation alone, which of quantities is larger for the block?(N = 560)

A.(21%) Volume & MassB.(24%) Mass & DensityC.(15%) Volume, Mass and DensityD.(4%) Volume onlyE.(29%) Mass onlyF.(6%) Density only

Fall 2006, Version B – The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

Based on this observation alone, which of quantities are the same for the block and the cylinder? (N = 611)

A.(28%) Volume & MassB.(21%) Mass & DensityC.(16%) Volume, Mass and DensityD.(5%) Volume onlyE.(27%) Mass onlyF.(3%) Density only92% selected mass90% selected mass

It is this type of topic-by-topic analysis of student learning that promises to help teachers improve student achievement.

Student Question Set for Student Question Set for DensityDensity

Nature of Matter

Data from the past 3 years comparing pre to post in 7th and 8th grades.

On all comparable questions, this past year’s 8th grade student outperform all the previous years’ data.

These improvements were seen on identical questions as well as questions in which we changed the context so that it was novel to the students and teachers.

Density Example

7th Grade06_07 07_08

8th Grade05_06 06_07 07_08

PREPOSTPREPOSTPREPOSTPREPOSTPREPOST

0%

20%

40%

60%

80%Percent Correct

POM was the curriculum this year

Same as 07_08 8th graders

Motion, Force and Energy

Data from the past 4 of 5 years comparing pre to post in 7th and 8th grades.

On all comparable questions, this past year’s 8th grade student outperform all the previous years’ data.

These improvements were seen on identical questions as well as questions in which we changed the context so that it was novel to the students and teachers.

Motion Example7th Grade

03_04

Pos vs. time Speed vs. time

04_05

Pos vs. time Speed vs. time

05_06

Pos vs. time Speed vs. time

8th Grade07_08

Pos vs. time Speed vs. time

PREPOSTPREPOSTPREPOSTPREPOSTPREPOSTPREPOSTPREPOSTPREPOST

0%

20%

40%

60%

80%

Percent Correct

No District Curriculum this Year

Motion Example

7th Grade03_04 04_05 05_06

8th Grade07_08

10th Grade05_06

PREPOSTPREPOSTPREPOSTPREPOSTPREPOST

0%

20%

40%

60%

80%

Percent Correct

Average Speed from a position vs. time graph

Motion Example

7th Grade03_04 04_05 05_06

8th07_08

10th05_06

POSTPOSTPOSTPOSTPOST

0%

20%

40%

60%

80%

Percent Correct

Instantaneous Speed from a speed vs. time graph