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)

Data Doesn't Have to Be Scary - How You Get it Matters

Do you ever feel like you're left with a pile like this after you've collected data for a survey or given a common assessment that needs to be graded and entered into a spreadsheet?

Yeah, I Know Someone Like That...
Gathering data to use for your building goals, data teams, or class statistics projects doesn't have to end with you and/or your colleagues spending hours in front of a spreadsheet entering values (and inevitably making errors). This TED Talk from global health consultant and pediatrician Joel Selanikio (@jselanikio) chronicles his experience with paper surveys in the developing world. What Dr. Selanikio realized from his field observations was that no matter how many nurses tramped through jungles door-to-door surveying families on child births, immunizations, deaths, and the like, dealing with the data was a cumbersome, daunting task that usually was abandoned. The result was "data-driven" decision making on vaccine supply that was formed from very small, very incomplete datasets.




What's This Mean for Me as a Teacher?
Dr. Selanikio's story is about the success of cloud-based, user-friendly, digital data collection methods, and I think we can experience the same in our schools. Beyond the results your state sends weeks (months?) after your spring standardized testing, how much of the data you gather about the student learning at your school is ever compiled electronically?

I think a lot of the one-more-thing mentally that many teachers associate with data teams in their schools is the result of their experiences grading everything by hand, tallying the scores on paper or in their grading software, and THEN taking the scores and (hopefully) copying and pasting them into some common spreadsheet. So how can you experience a similar explosion of efficiency like observed in the TED Talk?

If it cannot be gathered electronically, don't collect the data.

The Shift

Only collecting data electronically MAY mean that you and your team have to rewrite some assessments, but that might be for the best, anyway. Which is more valuable, asking a student to graph the equation of a line in slope-intercept form, (which would be hard to enter on a spreadsheet) or having the student graph the equation of a line and then tell something about its slope, intercept, or coordinates? Once students are taking what they do graphically and making textual conclusions or inferences, those responses can easily be matched and manipulated in Excel.

What Ways Can I Gather Data Electronically in My Classroom?

The secret is in taking advantage of mobile devices that you and your students already have.

Try an of these on for size:

• Google Forms (Here's how I did it)
• Socrative (Here's how I did it)
• MagPi

Never Smile Until 2nd Quarter (and Other First Day Myths)

I think the "never smile" rule was one of the first things my cooperating teacher told me before our first day before student teaching. That and wearing ties. But who made that up? Why is it still perpetrated? Here's a list of reasons I think to save our smiling for the 2nd Qtr.

1ST DAY CHECKLIST
Alienate students.

Inspire dread at the thought of coming to my class.
Ensure students don't think I care.
Build a connection between cold personal interactions and negative atmosphere toward learning my content.
Quench any fun.

I don't know about you, but I have a better time teaching the more I smile through the day. I cannot imagine getting through weeks of school forcing myself to keep a straight face in the midst of the silly things kids do and say. For another perspective on "never smile," here's a post middle school principal +Shawn Blankenship wrote a couple years ago. "Never Smile Until Christmas"

What about some others?

1. KIDS DON'T WANT TO DO ANYTHING THE FIRST DAY

Correction. They don't want to hear a lecture and produce a worksheet the first day. Of any days, the first day should perhaps be the MOST engaging. The first day of school is a time for first impressions for you just as much as for the students. Most of us would go out of our way to seem extraordinarily amazing and interesting on a first date or job interview - why don't we pull out the stops for that first experience for our students? There'll be other days for book cards.

Today in AP Stats, I'll be taking advantage of the massive crowds of schedule-changers and ID photo takers to provide a captive audience for my students' first attempts at data collection, and Algebra 1 will be developing linear expressions for modeling toothpick figures (although they won't know that until day 2)

The best example I've seen that wasn't content related is my friend Beth. She brings a whole duffel bag of stuff in and shares the experience of each trinket with her students. It really sets the stage for establishing a safe environment for sharing in her classroom.

2. I'LL NEVER LEARN ALL MY STUDENTS NAMES

Are you a "hit the ground running" teacher? I'm sure you probably cover more content than me, but at what expense relationally? Spend time in activities the first day that get you and your students talking to each other and saying each other's name. Keep up the deliberate name-learning activities for several days.

3. NEVER GIVE HOMEWORK/ ALWAYS GIVE HOMEWORK THE FIRST DAY

I think this one is hyper-contextually subjective. If you're teaching an honors, AP, or upper-level course, or intend to be super-dedicated and habitually with when students can expect homework, I think it sold be completely appropriate. If you're doing it to seem tough and shock some kids into changing their schedule, my opinion is that kids usually see through the ruse.

4. YOU MUST DISCUSS EXPECTATIONS AND PROCEDURES AS A CLASS

Definitely. Early and often. But going back to #1, find a way to make a game of it; get kids moving around.

Are there any others you've heard? Any you disagree with?

Teaching Argument Writing...for Preschoolers! (and Anyone Else)

I had the pleasure of attending a two day training over the summer with the Gateway Writing Project about teaching argument writing and how we can use it to support the need for evidence-based writing in the Common Core ELA and math standards. 

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• CCSS.ELA-Literacy.W.9-10.1 Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.
• CCSS.ELA-Literacy.W.6.1 Write arguments to support claims with clear reasons and relevant evidence.
• CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.

Although the requirements for thinking abstractly and putting together objective, argument pieces are not introduced until grade 6, the foundation of vocabulary, thinking and process of gathering evidence, making claims, and evaluating warrants could ideally begin in earlier grades as students write explanatory pieces.

Before I get ahead of myself, let me quickly define for you a warrant and a claim as from this book by George Hillocks, Jr., Teaching Argument Writing, Grades 6-12.

"Warrants may be common sense rules that people generally accept as true, laws, scientific principles or studies, and thoughtfully argued definitions." (Hillocks, pg xxiii)

Claims are the statement or value you are trying to prove the evidence supports. (Hillocks, pg xix)

But What Does That Have To Do With Teaching Preschoolers?

I had the pleasure of spending so much time watching my children, 3 years, 8 months, and 2 years learn and play this summer, so most of what I'm processing as a teacher right now is through my lens as their teacher this summer. Also, if you can communicate an idea to a 3 year old, you know you're set for the intended audience. :)

Of course, I wasn't sitting down with my daughter this evening and discussing vocabulary with her - we weren't even writing anything. Our exposure to argument and reasoning was during story time before bed.

Breaking It Down

We read Pinkalicious: The Princess of Pink Slumber Party, which recently came from the library.

The plot of this story doesn't really matter. You just need to know that Pinkalicious has a slumber party, and one of the friends ends up having a fear of falling asleep at another house.

Pinkalicious gets the girl to imagine various sounds and smells around the house are from a happy guardian dragon.

We met the dragon and I thought, "Interesting time to test some reasoning," so, very naturally, in my best inquisitive voice, I asked Lucy, 

"Do you think this is a mean dragon, or a nice dragon?"
"It's nice."
"How do you know?"
"Because its smiling!"  ::she points to the dragons mouth::
"Ah, and so usually when people are nice, they smile."

We continue on the story, and I'm happy to report, the little girl has no problem falling asleep.

Connecting to Terminology

Lucy did not produce an entire argument on her own, of course, but would you even expect that of all your middle schoolers or 9th graders? With some scaffolding questions, she was able to show the bones of some basic reasoning, however.

Claim: In response to my leading question, Lucy's claim is that This is a nice dragon.
Evidence: When I asked Lucy how she knew, she easily pointed out that the dragon was smiling.

In the experience of my own classroom with something like classifying functions, the process has been the same. I might ask, "Is this a quadratic function," to which a student at first may only respond, "Yes," but after I ask, "How do you know," she will often be able to point out a defining characteristic from a table, graph, or equation.

Warrant: As defined by Hillocks, a warrant is often something generally known. Kids learn quickly that they can usually trust adults or other kids that are smiling. Lucy left this off of her "argument," but warrants are the bones that support claims.

While warrants in an English or Social Studies class may be a little more subjective, I think STEM subjects generally have a stronger leg to stand on when picking out and using warrants. I explained warrants to a colleague today in the math office as being the properties and laws our students (often) write down and (rarely ever) use in their problem solving.

In the Classroom

The first several times you attempt argument writing with your students, I think it may end up looking and feeling a lot like my conversation with Lucy. I think that has to be okay.  Use guiding questions in pre-reading. Support them with definitions and clarify/refine their usage of warrant/ claim/ counterclaim. Restate their conclusion so they can have a chance to analyze if it "sounds" right once they've heard it outside of their own head or from their paper.

Tech Integration Tip: Try New Things With One Class At A Time

You've got a new piece of hardware, app, or website you want to try out in your classroom. You've thought through some of your students' potential difficulties, what could potentially go wrong, and what you can do to mitigate those problems, but there is still an element of the unknown until you or a colleague try it out in the context or your own district or school.

"Pilot!" you think, excited to see what may come of your idea. But who pilots for the the early adopters in your building? What about the late adopters who are slow to adopt a tool until they've seen it work in their classroom?

Where Do I Start?
Pilot for yourself! I got the idea of using my own classroom as both experimental and control group from a university study on clickers I found while working on an action research plan in graduate school. The professors wanted to incorporate and investigate the use of a student response system (clickers) for generating feedback for their students, but had trouble getting colleagues to participate in their study.

To get as large of a test/control group population as they could, the professors each had half of their students acting as control and half acting as experiment groups for a portion of the semester. Having students in the same section serve as both control and experimental groups in the course of the study mitigated variables of individual student achievement, hour of the day, day of the week, and individual teaching style. It boiled the clicker study down to this question:

Is there a significant different in these students learning using clickers to generate immediate feedback, or not?

What's that mean for my team and my classroom?
I'm sure my data team has not been alone in the past in wondering when we collect data on common assessments if the differences in student scores were the result of any of several factors, including but not limited to teaching style, hour of the day, and students in the class. These are all factors that in comparing two sections of the same course are important to consider.

Establishing (and rotating) experimental and control classes within your day eliminates all of the uncertainty of what those other factors may be contributing and narrows your focus to (as close as possible) ONE single variable.

Can it be replicated?
Once ONE of the teachers in your subject area or data team have had positive results using a new technology or strategy, others can have confidence in trying it out for themselves, in their own context.