Improving Student Learning Through Continuous Formative Assessment Stamatis Vokos Hunter Close Lane Seeley Physics Department Seattle Pacific University Eleanor Close Lezlie DeWater Jim Minstrell Pam Kraus Physics Department & School of Education Seattle Pacific University FACET Innovations, LLC

Supported in part by NSF grants ESI-0455796, the PhysTEC project, and the SPU Science Initiative Proportional reasoning A 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. B. C. D. The density of X is greater than the density of Y. The density of X is less than the density of Y. The density of X is equal to the density of Y. 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. A. B. C. D. (N ~ 1300 students grades 6-12) (36%) The density of X is greater than the density of Y (4%) The density of X is less than the density of Y (36%) The density of X is equal to the density of Y (23%) Not possible to compare without additional information Explain your answer. Performance on Density Question by Grade Level N ~1300 (Spring 2006) 100% 90% 80%

70% 60% 51% 50% 43% 40% 37% 30% 30% 28% 25% 20% 10% 6% 0% 6 7

8 9 10 11 12 170 209 46 Grade N= 131 18 400

710 How about college students? Data from Steve Kanim, New Mexico State U., and Gary White, SPS and AIP. The question that keeps on giving O rig in a l 80% 60% A B 40% 20% NWLSU Conceptual

NMSU Algebra NMSU Calculus UW Calculus The variation in student success rates on this question across populations is dramatic. 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 IDs, with assignment flipped on alternate class periods.

N=5 88 N=5 52 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? How does the density of 1 compare to the density of 2? 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. 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. 1 2 100% % o f S tud e nts % o f S tu d e n ts 100% A block of aluminum has been cut into two different size pieces, labeled 1 and 2.

62% 50% 50% 42% 30% 21% 6% 11% b 14% b c 0% 0% a

14% c d a d 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 Preinstruction Clay Postinstruction Aluminu m 56% X>Y 4% X2 53% 1=2 5% 1<2 possible 19% Not to compare Using Characteristic Properties

Select all measurements that would be the same if the two unknown liquids (1 and 2) are the same. PrePostinstruction instruction 14% 45% 12% 42% 53% 48% 14% Mass Density Volume Max mass of salt that can be dissolved in 1 mL of liquid Temperature each liquid boils Temperature each liquid freezes None of the above 12% All correct choices selected

52% 80% 44% 60% 74% 71% 2% Mass of 1 mL of liquid Density Time to heat each liquid to boil Max mass of salt that can be dissolved in 1mL of liquid Temperature each liquid boils Temperature each liquid freezes None of the above 11% All correct choices selected 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. B. C. D. E. F. Volume Mass Surface area

Density Temperature 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? Cognitive Dissonanc e? Select all that apply. (N ~ 1000) A.(19%) Volume (42% Mass only) B.(68%) Mass C.(7%) Surface area D.(26%) Density E.(13%) Temperature

F.(12%) Number of atoms Test Taking Sophistication Fall 2005 - The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal. 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 two objects? Based on this observation alone which of quantities are the same for the block and the cylinder? (N = 611)

Select all that apply. (N ~ 1000) A.(19%) Volume Mass only) B.(68%) (42% Mass C.(7%) Surface area D.(26%) Density E.(13%) Temperature F.(12%) Number of atoms (28%) A. Volume & Mass B. (21%)Mass & Density C. Volume, Mass and Density (16%) D. (5%) Volume only E. (27%)Mass only F. (3%) Density only

Fall 2005 - The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal. 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 two objects? Based on this observation alone which of quantities are the same for the block and the cylinder? (N = 611) Select all that apply. (N ~ 1000) A.(19%) Volume Mass only) B.(68%) (42%

Mass C.(7%) Surface area D.(26%) Density E.(13%) Temperature F.(12%) Number of atoms (28%) A. Volume & Mass B. (21%)Mass & Density C. Volume, Mass and Density (16%) D. (5%) Volume only E. (27%)Mass only F. (3%) Density only Fall 2006 The two objects shown below are put on either side of an equal-arm balance. The balance remains horizontal.

92% selected mass Based on this observation alone which of quantities are the same for the block and the cylinder? (N = 611) (28%) A. Volume & Mass B. (21%) Mass & Density C. (16%) Volume, Mass and Density (5%) D. (27%) Volume only E. (3%) Mass only F. Density only 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. 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 is larger for the block? (N = 560) Based on this observation alone, which of quantities are the same for the block and the cylinder? (N = 611) A.(21%) Volume & Mass B.(24%) Mass & Density C.(15%) Volume, Mass and Density D.(4%) Volume only E.(29%) Mass only F.(6%)

Density only 90% selected mass A.(28%) Volume & Mass B.(21%) Mass & Density C.(16%) Volume, Mass and Density D.(5%) Volume only E.(27%) Mass only F.(3%) Density only 92% 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 Density Nature of Matter

Data from the past 3 years comparing pre to post in 7th and 8th grades. On all comparable questions, this past years 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 Grade 06_07 07_08 8th Grade 05_06 06_07 07_08 POM was the curriculum this year 80% 60% Percent Corre 40% 20% 0%

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 years 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 Example 03_04 7th Grade 04_05

05_06 8th Grade 07_08 Pos vs. time Speed vs. time Pos vs. time Speed vs. time Pos vs. time Speed vs. time Pos vs. time Speed vs. time Percent Corr 80% No District Curriculum this Year 60% 40% 20% 0% Motion Example Average Speed from a position vs. time graph

03_04 Percent Corr 80% 60% 40% 20% 0% 7th Grade 04_05 05_06 8th Grade 07_08 10th Grade 05_06 Motion Example Instantaneous Speed from a speed vs. time graph 7th Grade 03_04 04_05 Percent Corre

80% 60% 40% 20% 0% 05_06 8th 07_08 10th 05_06