Paul K. Strode, Lori Cairns, Peter Szameitat Boulder Valley School District, Boulder, Colorado Statistics is simply the most important tool of the sciences. Framework for K-12 Science Education (2011) By grade 12, students should be able to: ●Analyze data systematically, either to look for salient patterns or to test whether the data are consistent with an initial hypothesis. ●Recognize when the data are in conflict with expectations and consider what revisions in the initial model are needed. ●Use spreadsheets, databases, tables, charts, graphs, statistics... Data and Error Analysis in the Science Classroom

Schlotter, N. E A statistics curriculum for the undergraduate chemistry major. Journal of Chemical Education 90: Data and Error Analysis in the Science Classroom

Schlotter, N. E A statistics curriculum for the undergraduate chemistry major. Journal of Chemical Education 90: Data and Error Analysis in the Science Classroom

Schlotter, N. E A statistics curriculum for the undergraduate chemistry major. Journal of Chemical Education 90: College instructors have semesters. We have 14 semesters in Grades Data and Error Analysis in the Science Classroom

Chapter 3: Dimension 1: Scientific and Engineering Practices; Practice 4: Analyzing and Interpreting Data The National Academies Press (2011), p Data and Error Analysis in the Science Classroom

2013 nextgenscience.org Data and Error Analysis in the Science Classroom

MS.ETS1 Engineering, Technology, and Applications of Science HS.ETS1 Engineering, Technology, and Applications of Science 2013 nextgenscience.org Data and Error Analysis in the Science Classroom

The College Board (2012), p. 98 The College Board gets a little more specific

The IBO does even better, but really? Error bars to indicate uncertainty Mean and Standard Deviation Student’s t-Test Correlation and Regression Impossible!

What can we do for our students in science by the end of 12th grade? ●Calculation of Variance, Standard Deviation, and using 95% Confidence Interval error bars to illustrate uncertainty in summarized data ●The Chi-square Test to compare observed with expected distributions ●The Student’s t-Test to compare two means ●One-Way Analysis of Variance (ANOVA) to compare more than two means ●The Pearson Product-moment Correlation Coefficient (r) and Linear Regression (r 2 ) to determine the strength of a relationship ●But we also must build a solid foundation: The meaning of the hypothesis/explanation in science. The difference between a hypothesis/explanation and a prediction. The null statistical hypothesis (H 0 ) p-values Degrees of freedom (df) We can do ALL of this for SOME of our students and we can do SOME of this for ALL of our students.

How does this look in middle school? ➢ A Pretest given at the beginning of the year--focusing on student understanding of the scientific process, but especially data analysis

Results of the Pretest Most students ➢ Found the difference in mass for each sample ➢ Created a bar graph showing the difference for each sample ➢ Used a key to show pH 4 and pH 7 samples A Few Students ➢ Found the total change in mass ➢ Left the question blank ➢ Created a line graph of pH 4 and pH 7 results Even Fewer Students ➢ Calculated an average change in mass for pH 4 and pH 7 ➢ Created a bar graph comparing the average difference

Density Lab ❏ Skill Practice ❏ Use of unit labels ❏ Analyze real world occurrences using density ❏ Same lab & purpose ❏ Changes: Remove one real world analysis question, replace with... ❏ Compiling a class set of data projected on the board ❏ Calculating the average for the class using excel ❏ A short discussion of our results not being the “as expected” How does this look in middle school? ➢ Activity One: Minor Tweak Last Year This Year

➢ Students showed interest in results of class data. ○Which class got closest? ○Why did our results not match the expected 1.0 g/mL? ➢ Students from early class periods were interested to see the results of the later class periods the next day. ➢ Activity allowed discussion of error vs. variation. ➢ Activity also showed the usefulness of calculating an average. ➢ No extra time was involved. Results of the Density Lab Tweak

Tinfoil Boats ❏ Use density as a comparison between two objects ❏ Understand how changing volume and/or mass change density ❏ Expanded lab & expanded purpose ❏ Changes: Add a second round of boat testing where everyone tests the “best”boat shape ❏ Compile a class set of data projected on the board ❏ Calculate the maximum expected capacity of boat based on volume ❏ Create a frequency graph of number of pennies to sink the boat ❏ Discuss distribution of data noting variation and unexpected result s How does this look in middle school? ➢ Activity Two: Major Tweak Last Year This Year

Results of Tinfoil Boat Tweak ➢ Students questioned data without being prompted, asking how one group’s boat held more than the calculated maximum. ➢ Activity became a richer learning experience. ➢ Activity required one extra class period. ➢ Students complained about the math.

➢ Activity Three: Minor Tweak Differential Heating of Soil and Water ❏ Compare the heating and cooling rates of water and soil ❏ Apply to specific heat capacity of water and effect on climate ❏ Same lab & purpose ❏ Changes: Work through data analysis as a class with a class set of data ❏ Compile a class set of data in excel ❏ Calculate average change in temperature ❏ Create a bar graph comparing average temp change for soil to that of water ❏ Place error bars on graph after teacher demonstrates calculations with the data How does this look in middle school? This Year Last Year

➢ Will take less time graphing, but more time with data analysis, but the same overall number of class periods. ➢ Instead of creating a heating and cooling graph for individual data for soil and water, students graphed the average amount of heating for soil and water. ➢ In addition, students calculated the variance and standard deviation for the data from their own class period. Results of the Differential Heating Lab Previous graph style New Graph Style

Results of the Differential Heating Lab ➢ Students were given chart to use as a template for calculating variance and standard deviation ➢ Calculations for soil were modelled on the projector

➢ Students calculated values for water on their own. ➢ Graphed Mean Temp. change with Standard Deviation error bars. ➢ They had very little difficulty completing the work. Results of the Differential Heating Lab

➢ The formula was shown after all work was completed. ➢ Students were AMAZED!!! ➢ Word traveled quickly back to math classes. ➢ Statistics are easy!

Where we begin in High School ▪ Students tend to default to drawing conclusions from single- measurement comparisons. Example: Are a person’s height and arm span the same? ▪ These tend to be heavily influenced by preconceived (often anecdote-originating) misconceptions. Example: “I’ve heard that they’re the same. They look pretty close, so this confirms that they’re basically the same.” studentheight (cm)arm span (cm)conclusion Charity148152No, H < AS Clifton158159No, H < AS Edward172 Yes, H = AS Ashley155150No, H > AS

The natural next step would be to have them look at means of the data… ▪ Example: Does the mass change when two solutions mix and a precipitate forms. ▪ We can probably agree that using a larger body of evidence to support a conclusion is a move in the right direction. studentMass before rxn (g)Mass after rxn (g)conclusion Charity Yes, B < A Clifton Yes, B < A Edward1.72 No, B = A Ashley Yes, B > A Average1.58 No, B = A

Take it just a bit farther… ▪ I would argue that expanding on a data collection event can lead to more opportunities to change student conceptions about science. ▪ By introducing opportunities to analyze data using statistical analysis we’re delving into the very nature of what separates science as a knowledge- seeking endeavor.

It starts with More Data! ▪ Start by looking for opportunities for students to work with larger data sets from the same experiments you’ve always done. ▪ Have students enter their results on a shared spreadsheet. (one period or multiple periods)

This has several benefits ▪ Drawing conclusions from more observations can lead students to question their individual results and/or be more sure (confident) in their conclusions. ▪ It gives students that have made large errors the ability to still work with real data. ▪ It gives those students an opportunity to come to the conclusion on their own that they may have made some errors.

More benefits ▪ It provides some competitive peer pressure to provide quality results. ▪ It allows greater opportunity for cross- communication of methods and outcomes. ▪ It opens up lines of discussion about all those scientific skills that are so critical for kids to develop.

All data has variability ▪ By creating a simple histogram of the distribution of results, we lead them naturally to a discussion of how variability affects our confidence in the results.

Individual vs. Group vs. As Many As We Can Get

Large data sets beg to be simplified ▪ Statistics is the tool we need to use in order to convey the variability and relative size of a set of observations (data) in just a few numbers. ▪ Statistics summarize and provide the ability to easily compare data sets.

Build confidence ▪ Most calculated statistics are based on two underlying measurements: 1.) sample size (# of observations) 2.) variability (deviation) The more of the first, and less of the second you have, the more confidence your statistic will convey.

Patterns of Inquiry ▪ General patterns of analysis I seek to have students able to draw conclusions about in 9 th grade: ▫ 1.) Is Y different than X? (Does something change?) Statistical test- 95% confidence interval ▫ 2.) How does Y change as X changes? (relationship) Statistical test- Regression Analysis w/ coefficient of determination.

Looking at data statistically brings the nature of science to the forefront ▪ A large body of evidence is required to support conclusions. (Sample size matters) ▪ Scientific knowledge differs from the way most people gather “everyday“ knowledge (generally hearsay and anecdotes). ▪ Science has a very high threshold of certainty (often greater than 95%), but ▪ is always open to new data leading to new explanations. ▪ Quality of data matters. (consistency) ▪ Communication is required. ▪ Critical analysis helps us hold one another accountable.

What can we do for our students in science by the end of 12th grade? ●Calculation of Variance, Standard Deviation, and using 95% Confidence Interval error bars to illustrate uncertainty in summarized data ○Build data and error analysis foundation in 8th Grade Science ○Hone skills in Pre-IB Chem/Phys, Adv. Phys Sci, Regular (College Prep) Biology ●The Chi-square Test to compare observed with expected distributions ○Regular (College Prep) Biology ●The Student’s t-Test and ANOVA ○Pre-IB Biology, Adv. Biology, IB/AP Biology ●Correlation Coefficient, and Linear Regression ○Pre-IB Biology, Adv. Biology, IB/AP Biology, All Chem and Physics ●The Foundation: Emphasize Throughout ○hypothesis/explanation in science. ○H 0, p-values, df We can do ALL of this for SOME of our students and we can do SOME of this for ALL of our students.

Data and Error Analysis in the Science Classroom

Soyeun at Dartmouth: “Knowing statistics makes it easier to assess the credibility of research.” Evan at Wash U.: “It's quite easy now to dismiss studies and evidence because of a high margin of error or small sample size.” Lulu at American: “Simply put, learning statistics in high school really just helped overall in providing a sharper grasp of critical thinking and analysis that can be applied in myriad aspects.” Claire at U. of Colorado: “Learning statistics definitely gave me an advantage in my college biology classes. Understanding the applications and meanings of the different tests helped me a lot because we have to do a lot of higher level critical thinking, and it is considerably easier knowing the mechanics and implications of the tests.” Nate at Trinity: “I've found the knowledge of statistics I was given in HS Biology to be absolutely essential in the physics labs I have done thus far. While I also took a statistics class in high school, I don't think I really retained any of that.” Nina at U. of Miami: “I found that learning statistics and specifically how statistics apply to sciences in high school biology was essential to college understanding. Primarily, it helped me to better read and understand scientific papers. But it also put me ahead of the curve--many if my peers still do not understand how to properly use a t-test.” Ved at Harvard: “It's irresponsible to not teach statistics in biology. Many of the common misconceptions that are held by large numbers of people in the United States stem from not understanding how data are interpreted to draw conclusions that end up affecting our day-to-day lives. Teaching statistics is a good place to start fixing this widespread problem. What students are saying about learning statistics in high school science:

Addendum Based on Audience Feedback Data Resources: MathForum WorldBank Statsci