# Instructional Innovations

## A Case for Statistics in High School Math Curriculum

By Clay Kitchings, Ph.D.

What would you say is the "pinnacle" of the mathematics curriculum in K-14? You might be tempted to consider calculus as the answer. However, there seems to be a growing argument to suggest that statistics, not calculus, is a better choice for many citizens. Mathematician Arthur Benjamin made this point on a very popular TED talk roughly five years ago (https://goo.gl/KNJ6rj). I have come to agree with this notion that statistics, not calculus, should be the culminating experience of high school mathematics students.

Consider A Case for Statistics

I often hear weeping and wailing when I mention statistics courses to friends and colleagues. This is most unfortunate, and it typically indicates that these individuals did not have a great experience -- often because they experienced poor instruction (which is sad). Many of us in education who took "research" courses in statistics often experienced terribly boring statistics courses. Taking all of this in stride, I would argue, however, that statistics, the language of data and variability, is learning in the real-world.

Our world bleeds variability at every turn. We see it in our students, our weather, our bank accounts, our politicians, sports... you name it. Statistics concepts are applicable in nearly every industry: education, manufacturing, medical fields, forensics, and criminal justice (to name a few). Further, students are ripe and ready for discussions of variability. Many students already come with informal (correct) notions about variability, and we can leverage this to promote engagement. For example, we touched on some statistics in our AMDM course earlier this year. In order to promote a discussion about variability, I took a deck of cards that I'd "rigged" so that it only contained hearts and diamonds (red cards). I began asking students, one-by-one, to select one card from the deck, show it to the class, and replace it back into the deck. Typically, after 4 or 5 red cards, students begin to protest and tell me I did something to the deck. (They don't know it yet, but I've now highlighted their intuitions about variability.) The students always expect to obtain some spades or clubs in a few random draws from the deck of cards.

Statistics need not be all about formulas and definitions. Statistics can be modeled using simulations, and students can make powerful inferences by using simulations to model real-world phenomena. For example, one activity Adam Firebaugh and I used was a discrimination activity. The long and short of it is this: In the 1970s, male bank supervisors were provided with 48, essentially identical bank employees' personnel files. The only differing factors were that 24 were labeled "male" and 24 were labeled "female." In the study, 35 people were promoted. There were 21 males promoted and 14 females promoted. The question posed was this: "Is this a clear case of discrimination?" (I'll not give the answer here, but if you're still reading, you're probably slightly curious!) Students can informally create hypotheses and test them even without a formal knowledge of a z-test, t-test, or other statistical tool.

Statistics also provides numerous opportunities for students to pose their own problems. Einstein and Infeld (1938) suggested that the formulation of problems is much more interesting and important than the solving of problems. In fact, many statistics standards involve asking students to formulate hypotheses and test them. We do not do this nearly as often in calculus or other subjects. Do we not want our students to leave high school and be able to identify and pose problems in society? Our students so often experience problems in a passive manner -- we tell them, "this is a problem; please solve it." In statistics, students have more opportunities to make problems more personal and even formulate their own problems. Students tend to be more engaged when problems are personal to them.

Statistics teaches students how to analyze information. As Arthur Benjamin mentioned in the link above, a lack of wide-spread statistical literacy likely contributed to such a large downfall in our economy in the early 2000s. Statistics also affords many cross-curricular opportunities in the sciences and in the social sciences.

Don't get me wrong: I love calculus. It was calculus that taught me I really wanted to pursue mathematics and mathematics education. My calculus teacher inspired me to pursue mathematics as an occupation. Calculus opens the doors to engineering and other high-powered scientific fields. Calculus is an amazing subject, and anyone interested in the sciences should pursue calculus. However, I feel statistics deserves another look for the possible culminating mathematics course for seniors (whether Advanced Placement, or not). Students who regularly engage in statistical reasoning will learn to think more deeply and critically about their world. If we can graduate more seniors who think deeper and more critically, I submit that we will naturally develop more productive citizens in the long run.

## PBIS and Classroom Management

We know that PBIS (Positive Behavioral and Instructional Support) benefits our kids, but for many of us PBIS gets put on the back burner as we work to create our learning environments. In reviewing the PBIS website: www.pbis.org, I came across a great presentation created by George Sugai of UConn. I thought I'd share some of its basic tenets as a reminder of good classroom management strategies.

Sugai's List of Essential Behavior and Classroom Management Practices

1. Minimize crowding and distraction to elicit appropriate behavior.

Is your classroom arranged to allow easy traffic flow? Do you have or need a seating chart in place?

2. Maximize structure and predictability.

Do you have teacher routines and student routines?

3. State, teach, review, and reinforce positively stated expectations.

Have you established behavioral expectations? Have you taught rules in the context of routines? Do you prompt students of a rule prior to entering a specific situation, e.g. group work?

4. Provide more acknowledgments for appropriate than inappropriate behavior.

Maintain at least a 4 to 1 ratio of positive acknowledgments versus negative ones.

Interact positively once every five minutes. Follow correction for rule violation with positive reinforcer for rule following.

5. Maximize varied opportunities to respond.

Vary individual vs. group responding. Vary response type: oral, written, etc. Increase participatory instruction; get your kids actively involved in their learning.

6. Maximize active engagement.

7. Actively and continuously supervise.

Move, Scan, Interact, Remind, Positively acknowledge

8. Respond to inappropriate behavior quickly, positively, and directly.

Respond efficiently to students displaying inappropriate behavior and positively acknowledge those students displaying appropriate behavior.

9. Establish multiple strategies for acknowledging appropriate behavior.

10. Generally provide specific feedback for errors and corrections.

Always indicate correct behaviors and link those behaviors to context.

As you look through this list, evaluate yourself on each tenet. How are you doing? Do you need to reintroduce/reinforce one of the tenets? Getting control of your kids in January can be difficult if you haven't already established routines and expectations--but it can be done. Notice that Sugai and PBIS focus on rewarding good behavior. If you're struggling with managing your classroom, start there.

If you'd like me to walk through and rate how you are implementing any of these tenets in your classroom, let me know. Sometimes it helps to have another set of eyes watching the interaction between you and your students.

## Technology Tidbit: Giffy

by Kelly Cassidy

Gliffy.com

Gliffy.com is the best and most useful online graphic organizer and collaborative program. It integrates with google drive and each student can create diagrams by obtaining a free account. Each free account can save 5 diagrams at a time for continuous addition and editing. Once you have completed the diagram, just grab a screenshot to save it as an image for later viewing and that frees up a new spot for a new diagram. Many examples can be found at Gliffy.com for inspiration. This is a great online program for teachers and students who might not have access to Office or other paid programs at home.