Student Engagement and Learning

Last year, after having my formal observation by one of the assistant principals at my high school, we sat down for my post-observation debriefing. I try to maintain interactive and engaging classrooms, which was affirmed during the observation. The question that was posed was how do I know how much each individual has learned, other than during assessments? My assistant principal was asking me to push further, to make direct linkages to the learning objectives I set and verification that those objectives were met. She wanted me to push students to be more personally accountable for their learning.

I thought about this conversation over the summer and while I was teaching the introductory statistics class at MSU Denver. Due to the compressed time-frame of the class, I elected to give weekly quizzes that covered material from the previous week. Toward the end of each lesson, I tried to provide a problem that reflected what I would be quizzing on the following week.

I decided to implement a similar program in my Inferential Probability and Statistics course. I am giving a weekly quiz that focuses on last week's materials. The questions cover foundational knowledge that students need to be successful. During the week, I provide problems and ask students to write their responses in their notebooks.

In the past, I had asked students to answer the questions but did not require them to write down their responses. Of course, there would be some students who would appear to be thinking about the problem but were more likely thinking about where they were going to eat lunch that day and with whom.

After we discuss responses, I tell students my expectations toward their understanding. For example, in working through various sampling strategies, I provided scenarios and students needed to identify the sampling technique being described. I told my classes that the expectation is that they should be able to read a scenario and determine the sampling technique.

I realize this is the first two weeks and we're still in the "honeymoon" phase of the semester, but students seem much more engaged and attentive. The scores on the first quiz were quite good, approximately 85% of the students received an A or B grade.

I still need to make more explicit connections to the lesson's learning objective and what students are doing. I will continue to require students to write answers down when working through example problems. I will see if the level of engagement and learning continues to hold over the next few weeks and throughout the semester.

Statistical Graphs and Thinking About Data

This semester I have made a more direct message about why we graph data distributions. I think in the past my students viewed graphing as part of the response requirement but weren't really considering the ramifications of the data distribution. So I have decided to hammer this point home.

We generated some data and looked at graphs that displayed the data distributions. In looking at shape, I emphasized the aspect of symmetry tells us which summary statistics we can employ to describe the data. Moderately to extremely skewed data indicates that the mean and standard deviation are not appropriate to use; in this situation we should use the median and inter-quartile range (IQR).

The same goes for gaps and outliers. The presence of these adversely affects the mean and standard deviation. As I told my class, an outlier may be screwing up your analysis but you can't simply drop the outlier due to annoyance. We worked with how many movies each student watched in a movie theater this summer. The data contained an outlier. I said that unless we knew something about this data point, such as the individual was a movie critic, that we were stuck working with the outlier included. In fact, our work just increased because we need to understand what if any impact the outlier is having on the overall distribution. This means we calculate summary statistics with and without the outlier included.

Modes produces a different issue. Multiple modes typically indicates that distinct sub-groups are present in the data. This means we'll need to determine if the sub-groups exist and then analyze each identified sub-group separately--more work again!

It is important to realize that graphing is a key step in understanding what you can and cannot do with your data. I am hopefully that students will gain a better appreciation of this fact and become better at determining appropriate statistical measures that can be applied to the data.

Starting Statistics with Generating Data

This year, I have reverted back to beginning my Inferential Probability and Statistics (a one-semester, non-AP statistics class) with data collection. After teaching an introductory college statistics course this summer, I liked how starting with experiments gets students engaged quickly.

I began this semester's course with the penny stacking experiment, as I described over the summer. It was engaging and enabled me to cover many topics of experimental design and to build understanding of vocabulary.

I will be spending time on observational studies next and then move into sample surveys. Along the way we will collect data that we can analyze. I'll use these data to work through analysis techniques and graphs.

The first week is off to a good start.

AP Statistics Report Writing Self-evaluation

Last post I described using mentor texts to help students become better statistical report writers. The second step in the process is to have students become more reflective about their writing. To do this, I share the scoring rubric that is for their first writing assignment. I have students go through the rubric and ask any clarifying questions they may have. I want to be sure they have a good grasp of the assignment's expectations.

Students swap papers and then use the scoring rubric to assess the paper they are handed. The scoring and paper are then discussed. Reading another student's paper give additional exposure on ways to communicate statistical thinking. Each student now must use the feedback and learning from this scoring exercise to revise and improve their report.

I will score each final draft and provide written feedback. Students will then have one last opportunity to revise their work and make a final submission. I have found that this process builds important meta-cognitive supports to their learning.

AP Statistics Report Writing and the Use of Mentor Texts

My school has been participating in a district-wide program on literacy. This has been going on for a number of years now. One tool which we were shown a few years ago was mentor texts. These are texts that are models of what good writing should look like. Students are able to read through and analyze these text for elements that they should be striving to achieve in their own writing.

In statistics, there are any number of studies available to use for mentor texts. Unfortunately, most of these statistical reports are multiple pages (sometimes 20 or more pages) and are written for graduate and post-graduate-level readers. Definitely not appropriate for high school students.

Since one of my first writing assignments in AP Statistics requires the writing of a newspaper article, I decided to make use of data-driven newspaper articles for mentor texts. I make use of six articles that are brief, contain specific data references and graphs, and provide a decent introduction and conclusion regarding the topic.

I have used mentor texts for the past three years and have found that it helps get students more focused on staying to the facts and referencing explicit statistics. To remind students of what they found in the mentor texts, I post a list or a wordle of their findings.

Below is this year's wordle. As you can see, words such as percentage, data, examples, and charts all are prominent in the display. This puts students on a fast-track to writing better statistical reports.

Document Cameras and Tablet PCs

This year I have one AP Statistics class in my normal classroom and one in my computer lab. I am used to traveling back and forth between classroom and lab, so that is not much of a big deal. The computer lab isn't ideal in terms of configuration to have students work collaboratively, but we'll work around it.

I do use a document camera on a regular basis, so I took an extra one that was in our math office and set it up in the computer lab. I tested it out and everything was working beautifully on Monday.

Today in class we were going over exploratory data analysis for categorical data. One question asked students to create a segmented bar graph. In past years, students have struggled with creating a good graph and I use the document camera to display both well and poorly drawn graphs. So, as the discussion progressed, we reached the segmented bar graph piece and I asked students to share their graphs. I picked the first graph turned toward the desk that held the document camera and NOTHING!!! Someone in my department had decided that the document camera was not be used enough across all of the periods and removed it without letting me know.

So there I sat, paper in hand with no document camera. I was not happy and I told my class, this is my not happy face (which they will see on occasion throughout the year). I had no choice but to move on.

During lunch I found out it was my good friend who made the decision. The only thing is he failed to tell me and made no plans to accommodate my need for a document camera during my AP Statistics class. Great.

We talked over the situation and as we talked, the idea bubbled up (I honestly don't recall who first mentioned it but I'll take credit since it's my blog) to take a picture of the document using a tablet PC. I then thought about simply connecting the tablet via USB and opening up the picture folder on the tablet and opening the picture in preview mode. Our school computers have Smart Notebook software and Smart Ink installed on them, so I can write comments and annotate the picture on the Smartboard and then capture it to a Smart Notebook file. My friend said it might be even better if the image could be displayed on individual computer screens. We actually have software installed in our computer lab that allows me to do this.

I tested the basic functionality out during my planning period and everything seems to work as envisioned. I'll have my next AP Statistics class in the lab on Friday. I'll try it out then to see how things go. If this works, it means we could buy tablet PCs for people in the department for roughly $200 versus spending $600 for a document camera. Plus, a tablet has so much more functionality!

So even though I was very annoyed today, it turns out that it could be a big blessing in disguise.

Thoughts on the First Day of Class

Classes started and I'm off and running on another school year. I spent time reviewing grading so students understand what is expected of them.

Establishing Group Norms I also spent time on formally establishing group norms since I have students sitting in groups of three or four. I didn't go through this process last year and had issues with student behavior. By letting students set the norms and expectations of working in groups I hope to eliminate many of the poor behaviors I saw last year. My first step was to have each student write down three norms or expectations they had for working in groups. I then asked the students in their groups to come to a consensus on three norms. I then had groups share out their list and added items as we moved through the room. Once the entire list was up I asked students if there were any questions or concerns about any of the items. Finally I asked students to show their agreement by raising a thumb straight up; if there were any concerns or questions they should hold their thumb out to the side. Each class gave a thumbs up to their norms and they are now posted in the classroom.

A Safe Classroom Environment? In one class, we were discussing ideas concerning why a survey was administered. We knew the facts as to who was asked questions, the types of questions asked, but were not told why the survey was given. As the discussion was wrapping up I asked if any other students had ideas. Two students who I have had for the past two years were sitting next to each other. One student indicated that the other had an idea. I encourage this second student to share his thoughts. He said several times that he really didn't. I then told the class "There are no incorrect responses and you all should feel safe sharing your thoughts, unless you say something stupid." This elicited many laughs from the class. Nothing like getting the class off to a good start.

Getting Ready for the 2013-2014 School Year

After teaching an introductory statistics course as MSU Denver this summer, I have been tweaking my Inferential Probability and Statistics course content. I am also planning on introducing some new investigations and tasks to my AP Statistics course this year.

For the Inferential Probability and Statistics course, I have gone back to starting with a unit on generating data. The sequence will be experimental design, observation studies, and then survey sampling. From there, we'll move into a unit on organizing data and describing data distributions using summary statistics. The third unit will cover probability with an emphasis on simulations. The fourth unit will then transition to using probabilities and simulations to make inferences.

I will not provide a day-to-day recap of each lesson, as much of the material was documented last school year. I will spend time covering new activities and I will comment on how the sequencing is either helping or hindering students' understanding of statistical analysis.

I wish everyone a successful school-year. Please feel free to post comments and questions regarding what you are doing in your classes.