# Monthly Archives: February 2014

## Nix the Tricks – AP Stats Edition

For AP Stats teachers, this is the time of year where we move from innocent ideas like scatterplots and experimental design, and into uncharted waters; those topics which require sharper focus, and more time and reflection to develop properly. Sampling distributions, the Central Limit Theorem, confidence intervals and hypothesis testing…new and scary ideas.  With the crush to cover content before May, it’s easy to fall into traps where we shortchange discovery and real meaning and replace them with quick tricks.  Here I present one of my least favorite Statistics “tricks”, and hope you “Nix this Trick”!

“Nix The Tricks” is a powerful, free document for math teachers of all grades; a crowdsourced collection of math shortcuts and well-intentioned devices teachers employ to assist students with math mechanics; devices which ultimately under-cut student understanding of mathematics.  Along with the tricks are suggestions for developing math concepts in your classroom without tricks; encouraging communication of ideas and language.  It’s a labor of love, compiled and edited by Tina Cardone, who I admire for her dedication to this project.  Some of my ideas from a blog post last year on phrases from math class which need to be expunged have been absorbed into Nix The Tricks, and I am thrilled to have had even a small part in building this document.  Share it with your math friends, and let the debates begin!

Back to Stats-world, and a phrase we need to Nix.  It’s time for hypothesis testing, a new world of strange symbols for the null and alternate hypothesis, lots of conditions and tests to think about, and making logical connections between computed values and real-life consequences.  Writing tight, meaningful conclusions takes practice, revision, and patience. But why struggle, when we have a cute shortcut?

When the P is low, reject the Ho!

This is the short version of the general argument that when we have a sufficiently low P-vale (below alpha), we have evidence against the null hypothesis, and in favor of the alternate. But why go through all of this meaning, when we can talk about Hos in math class!

So, what’s wrong with this catchy phrase?  Well, first, and probably most importantly, it’s damn offensive.  For teachers, talking about Hos in class, or even providing a “giggle” momnent about the idea, is out of bounds.  We all get that, right?  Good.

In stats-world, the problem with this phraise is that it provides students an excuse to not develop real understanding about the connection between P-Values, Alpha, and the null hypothesis.  As an AP Reader, I enjoy the opportunity to see how students craft their conclusions to a hypothesis test. In 2012, I read question 4, which was a full 2-proportion z-test.  It was fascinating to observe the clear differences between the written approaches to conclusions; which textbook they probably used, what mnemonic devices did their teacher push, how much attention was paid to written practice.  In addition, while many approaches relied upon a canned template, where students simply fill in blanks (with mixed success), I also enjoyed well-developed explanations which demonstrate clear evidence of understanding of the logic of hypothesis testing.

At last year’s AP Stats Reading “Best Practices Night” Luke Wilcox did a wonderful job explaining how he challenges his students to become clear communicators from day 1. You can download his presentation, and many other “best practices” resources, at the famous APStatsMonkey page.  Here’s a fantastic example from Luke’s class, which demonstrates clear understanding of the process:

In AP Stats, communication is essential.  Here are some thoughts and ideas to keep in mind:

• A strong conclusion has linkage between a computed P-value and a defined significance level (alpha).  This is the computation piece.  The art of statistical writing is taking this numerical result and using it to reach a conclusion about our population.
• My students write, write and write, and my boards are covered with samples, which we critique and revise.  I like to randomly assign students to work together (I often use playing cards for this), so that “group think” does not set in. I want students to debate language, and I can see from afar which groups are on-point by having them on boards around my room
• My document camera is also a valuable resource here. As an opener, I’ll have students examine a homework problem, and write their conclusion on an index card. Random cards are selected and critiqued.

As many Stats teachers head toward their hypothesis testing units, let work together to Nix this Trick, and improve student writing!

## Some of My Students Failed Today! Woo Hoo!

A new semester has just begin here at my high school, and one of my classes is a co-taught course we call Prob/Stat.  The Prob/Stat course is one we offer to our 9th graders, as a follow up for Algebra 1.  It includes concepts in probability and statistics, along with algebraic concepts like systems, polynomial operations, and matrices.  The students in this academic class will take the Pennsylvania Keystone Exam in May, a graduation requirement, so this course is quite important for them.

My math department colleague and I, along with both co-teachers, agreed that we did not want this to “feel” like math courses they had taken up until now.  We wanted our students to become more reflective in their approach, think about their strengths and weaknesses, and devlelop their own learning paths.  We have embraced Standards-Based Grading and a policy of re-dos and retakes to help meet our ideals for this course.

On the first day of the class, I wanted to set the tone that communication and discussion would be valued in my classroom.  I asked the students to arrange their desks in a circle, which brought many questioning looks and rolling eyes.  But once we established our circle (actually, it was more like an oblong), I passed around small slips to paper to every student.  I asked the group to list any factors which had caused them to not perform well in their past math classes.  Many students were willing to share their stories: “I don’t do homework”, “Teacher X didn’t like me.”, “I don’t like to ask for help.”…the list was rich.  Placing a trash can in the center of the floor, I instructed students to ball up their slips of paper, and toss them into the bucket…they are in the past! I stole this idea from my time at the Siemens STEM Academy, where we started the week by catapulting our educations hold-backs into the chum bucket (it was Shark Week at Discovery Ed).  You can read more about the chum bucket activity on the Siemens STEM Institute blog.

Next, I asked the students to write something they could do, moving forward, to improve their math outlook.  What an awesome conversation!  One student shared her fear of reading problems in math, but a desire to work through it and seek help.  Many students confessed their need to complete assignments.  Others communciated the need to start self-advocating, asking more questions.

For many students in my class, this is their first experience with Standards-Based Grading.  Before the course began, I took all course concepts and arranged them into 4 anchors, mimicking the anchor language of the PA Keystone Algebra 1 content.  Each anchor contains 5-7 standards, written as “I can” statements.  The document also contains room for multiple attempts on the same standard.  As students complete notes or assignments, I instruct them to write the standard we are working on clearly at the top of the page.

In this course, we start off with the probability sections, so we actually led off with 4.5 “I can find the probability of a simple event”.  Probability is a topic which haunts students of all ages, sizes, and ability levels.  And while many students did just fine on their first quiz, a number of students struggled.  Under normal circumstances, this would cause deep sighs from me, and steamrolling on. But, to be honest: I HAVE NEVER FELT MORE ENERGIZED ABOUT STUDENTS STRUGGLING IN MY CLASS!

All students in the class have their own binder, which houses the Standards Tracker, and all assessments. During the next few class meetings, my co-teacher and I will develop groups for small group instruction to discuss mis-conceptions, and work towards the re-do on their 4.5 quiz.  At the same time, we have moved forward into 4.6, multi-stage events.  We are striving to set-aside time each Friday to be reflection and redo time, in order to establish regularity with these new grading concepts.  I find myself looking forward to students dicussing their needs, and working with them to do better next time.  It’s early in the semester, but already things feel different.

Check out some of my earlier blog posts on Redos, Retakes, and Standards-Based Grading:

Rick Wormeli – Redos and Retakes