AP Stats at the STEM Expo

I moved up the timing of my statistical inference/experiment design test this spring (usually its the "capstone" project kids do as their final) so that we could participate in our district's STEM Expo tonight. (I think its really just the traditional science fair repackaged, but I'll go with it. LOL)

As I wrote a couple weeks ago, I enlisted the help of a doctoral student from Washington University to give some tips/insight on making and presenting their posters, and we spent the last 5 days of class working on our survey instruments, analyzing the results, and presenting them on a poster.

This is the first time these projects/experiments have ever had an audience beyond myself, so I'm really excited to see my students out in the "real world" talking about statistical inference. I literally had a student email me over the weekend and tell me she would change whatever I asked and do whatever I demanded so her poster could be perfect. You've gotta love that.

The NYU research poster guide and continued support from +Ryan Watkins ended up being a huge help, and after an assist from the CAD teacher downstairs, I'm real excited with how these posters turned out.

I had one student who could not make the Expo, so I had him present last week to our friends at another high school in our district in AP Chem.

There's always something special about seeing kids describe and defend their work that is better than most of the feedback that a teacher could ever give traditionally. They often find errors in their writing, their process, and bits that are confusing or could be more clearly explained as they try to sort out what their work SAYS with what it is actually supposed to be communicating.

We found a few errors in the graphical representations or calculations as we were sharing with parents at the Expo, but I was so thrilled that they found them and corrected the mistakes that I couldn't be anything but proud of them. If you'll notice the poster in the video, he has a lot less going on... he actually only did about half of the work, and I don't know if he noticed it until he got to the end of describing his methods after a couple minutes and didn't really have much to SAY about it - nothing to interpret. There's a verbal pause where (I hope) he realizes he's done, but shouldn't be.

Median - The Resistant Little Bugger

One of my most favorite things to discuss in a stats lesson about measures of central tendency is the value or situational advantages of uses mean or median to tell the story YOU want to tell when analyzing data.

While preparing a different post about Google Classroom and Edmodo, I dredged up this old assignment from my Edmodo archives and was smitten by my own work. LOL

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Median was described in class as being resistant to change from outliers.  Find a news or blog article online discussing "average" (mean or median) and

1.  Give the url of your article.
2.  Summarize the article - include the variables being discussed
3.  Determine if the article is using median or mean for "average".
4.  Was the article's use of median or mean correct?  Why or why not?

Places to find links with statistics in them:
http://www.freakonomics.com
http://www.census.gov
http://www.espn.com
http://fedstats.sites.usa.gov/
http://www.baseball-reference.com
http://fivethirtyeight.com/

OR - you could Google "average _______", anything really, and get a news article about it.  "Average salary" gave a lot of hits.

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To give you more info on the way I graded this assignment, I was looking for some understanding of how students might pick out the difference in use between the two. (Whether or not the article actually said average or middle, using an actual data set to pick that out, searching for clues in the context, i.e. an article discussing how athletes are overpaid would probably use a mean.)

I used this assignment more to generate discussion and thought than as an assessment, but I suppose if you were confident that your students would be successful at this, I don't know why it couldn't be the basis of a performance event or graded writing prompt.

Do you think there are any consistent sources of "stats" articles that I've left off?

Because Weighted Averages - Fighting Back the Points Hounds

Although we're continuing the conversation and including more teachers in standards-based grading training in my district, most all of the classes remain traditionally graded with categories for homework, formative assessments, summative assessments, and finals that were agreed upon by each high school.

It seems like most every class I grade on our traditional grading scale, I'll have kids who start to get homework bugs by November. "I'm doing all of my homework - how come I'm still failing?" is what they'll ask me. No matter the number of times I tell them that those 2 missing homework assignments are not the reason they don't have the grade they want, they insist that "every little bit will still help." While that is technically a true statement, it misses the point. Although we've devalued homework to 10% of our averages to stress assessments and projects in grade calculation (to stress evidence of learning), as long as we have a category that includes homework, the point hounds will be scrounging at the table for their point scraps.

Here's what I conclude:
As long as I include homework in the calculation of grades, I will always fight the students and parents that want to squeak out every homework point "just in case."

It takes persistence and perseverance through the first several weeks as students adjust, but I always feel most successful evaluating my students' learning the more I stress mastery, and I devalue points through standards-based grading.

In the meantime, I created this video to as a resource to my students who want to set goals and track their weighted averages.

Doing Statistics on Scientific Calculators, Grades 6-12

I'd be willing to bet that every approved syllabus on the College Board website for AP Statistics says that a graphing calculator (probably a TI, to be more specific) is required for success in the course. And while that probably IS true for AP Stats, that doesn't mean that all of the other kids doing statistics in your building need one!

Arguments Against Performing Statistical Calculations on Scientific Calculators
Whether you've said these things or know someone who has, I think its a prevalent attitude in schools because I've seen enough math teachers who cringe at the experience they had in college with statistics.

• "I barely ever get to stats in my curriculum, and when I do, my students just do mean/median/mode. It's a lot easier to just have them calculate that by hand, than teaching them how to use their individual model of calculator."
• "There's more value in having students perform these by hand so they can practice perseverance and have an understanding where the numbers come from."
• "If kids want to study statistics, they can do it in high school. We just do means and averages in my class."

Once Again, Common Core Changes Everything
As soon as the 6th grade, students are to be able to use descriptive measures like mean, median, and standard deviation to make decisions. Trust me when I say I don't really rely on a middle school student's ability to consistently compute a variance or standard deviation for a data set using the formula.

You can make the process look simpler, but then you have a big chart on your paper, which also stresses kids out

Here are a few of the standards from 6th to high school: (from corestandards.org)

• CCSS.Math.Content.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by:
• CCSS.Math.Content.6.SP.B.5a Reporting the number of observations.
• CCSS.Math.Content.6.SP.B.5b Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
• CCSS.Math.Content.6.SP.B.5c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
• CCSS.Math.Content.6.SP.B.5d Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered

• CCSS.Math.Content.7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

• CCSS.Math.Content.HSS-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
• CCSS.Math.Content.HSS-IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
• CCSS.Math.Content.HSS-IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
• CCSS.Math.Content.HSS-IC.B.6 Evaluate reports based on data.
• CCSS.Math.Content.HSS-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

How Are My Kids Going To Do All of This??
The good news: A built-in function to most every scientific calculator is the ability to enter a simple list and run a 1-variable stats analysis to get (at the very least) the distribution's count, mean, variance, and standard deviation.
More good news: According to Smarter Balanced's testing manual, students taking the high school tests will have access to statistical calculators on the test.

• "Will Smarter Balanced allow the use of calculators on the summative assessments?"
• Smarter Balanced Test Administrator User Guide (calculator use begins on pg 68)

The bad news: The keystrokes are a bit different on every model, so teaching your students to use their scientific calculators to get measures of center or spread from a dataset will have to be more about principles of the process (entering the data into a list, finding the button/menu that has your mean/median/standard deviation in it), than it will be about walking through specific keystrokes with the whole class.

Tutorials To Share
You don't have to be an expert. Watch these yourself, share with your students on Edmodo or your class webpage and students can review the video relevant to their needs.

TI-30XS (Multiivew)

TI-30XA


TI-30X IIS

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Casio fx-991ES


Casio fx-85ES


Casio fx-83MS

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These are all the calculators I see MOST frequently in my lower level math classes. If you or your students have a different model, a simple Google or YouTube search with "statistics on [your model here] should at least get you started.

Emergency Lesson Plans: AP Statistics

Someone came to the blog via this search a few days ago and found this post about my son's hospitalization as catalyst for my decision to finally MAKE emergency sub plans, but I'm sure they left disappointed, because I didn't actually share my plans in that post. :)

Principles for Emergency Planning

In the previous post about emergency sub plans, I laid out these principles I was going to follow as I crafted my plans:

1. When choosing learning objectives, I'm going to focus on things we are currently addressing in our PLC Smart Goal, or critical skills that consistently need reinforcing. 
2. Have a back up to the emergency plans in case students finish quickly
3. Crowdsource your emergency plans with co-teachers.
4. To give yourself ultimate flexibility (particularly in your emergency back-up), keep a class set or at least enough for 2 kids to share of your course textbook in a closet or cabinet nearby.
5. Make it something you'll at least consider grading when you return.

Emergency Planning for AP Statistics
I have three thematic goals for my AP Stats students throughout the year: data gathering, data crunching, and technical writing, so all of the options listed here, so if I stick to those goals (principle #1), I'll have something that can be mostly applicable for students no matter where we are in the curriculum.

• AP Practice Exam: The College Board releases items from old exams on their website. Might as well take advantage.
• 1997 Released Practice Having students complete this all in one hour would be an impossibility, so you've got at LEAST two days of material here. I would have students work in pairs on either the multiple choice or free response and collaborate quietly.
• Free AP Stats Practice Exam This test is secured behind your College Board Course Audit login, so be sure to have that info handy.
• Data Collection/Experiments
• "How Long Is a Minute" Materials and resources are usually intentionally scarce on guest teacher days, so its impractical to have plans that require elaborate handouts or materials list. This experiment is my current emergency plan, and I love it because its easily approachable early in the year before we've done a TON of stats work, and only requires a clock in the classroom with seconds.
• Probability Simulator TI 83/84 app + this handout The handout is actually for a more extensive project, so you'd have your students BEGIN the project on this day (and work on it periodically over a matter of days), or just have students complete a portion of the work.
• Probability Based Gaming
• Ever heard of Perudo or "Pirate Dice"? I blogged here several years ago about using it in my freshman seminar class. (Handout Included)