Today we begin confidence interval for means in earnest in AP statistics. Yesterday after the activity, the students explored what a t-distribution was via this Geogebra document and looked at how to determine a critical t* value from a table as well as from the Nspire. (sidenote: although we do find values using tables occasionally, I emphasize using their calculator to find these values as well as the area probabilities…its all about saving time on the AP exam, so training them now will help them to be comfortable using their calculator later during all of the inference procedures).
Today, we did our first write-up of a t-interval for means, emphasizing the conditions that need to be met. I am so glad that I “over-emphasize” these when they are learning about sampling distributions. Of course, we write one up together so they understand what needs to be shown and stated in the inference procedure.
As I’m writing this post, an idea popped into my head: a procedure wall! Just like the word walls used in algebra and geometry classes but with the proper name of the procedure. I’ll have a way to cover when they are taking an assessment. I can use sentence strips, and maybe color-code for proportions vs. means vs. others. Will have to ruminate on this a little more to flesh out the details…look for a future post on this!
So, yesterday, most of the groups got the statements sorted. Today they will create a poster of the incorrect statements and write underneath each one what the error is. I found a great explanation by Bock about the types of interpretation errors with examples and explanations. My students used this document to help guide them. And they eventually were able to identify correct and incorrect statments, but also were able to articulate what made interpretations incorrect. YAY!
I’m sure you’ve never experienced this: things seemed to be going well until you assess, and then you find out you were in dream land! That happened to me after the last mini-quiz I gave my AP statistics students on confidence intervals. Although I gave them the sentence stems in their notes followed by whole class writing practice as well as individual practice, the assessment showed that they really didn’t know what they were talking about…no real surprise!
So I spent last night putting together a card sort on confidence interval statements around the Pink Sweetheart conversation heart activity. I created 16 statements, some written correctly but using different wording, some incorrect, some based on the statements the kids wrote on their assessments. They first had to read through the statements as a group. Then they sorted into correct and incorrect statments. Thats as far as we got today. More tomorrow…..
I’m a sucker for all things Valentine and hearts. So why wouldn’t I have an AP Stats activity using Sweetheart conversation hearts? This year, my students endulge me better than most, at least feinting enthusiasm for these corny activities.
This activity was all about the proportion of pink hearts. The big question was, “What is the true proportion of pink Sweetheart conversation hearts?” They had to count the number of pink hearts and then determine a sample proportion for their box…we had to discuss our willingness to accept each box as a random sample from the population of all Sweetheart conversation hearts.
From there, they began their introduction to inference methods via the confidence interval. Using their sample value, they explored the possible shape of the sampling distribution, how it related to their previous understanding of sampling distributions, what conditions might need to be in place, etc.
The next step is to work on interpreting the confidence interval as well as the confidence level…their first foray into technical writing!
We had lots of Hershey Kisses left over from Tolo, so I decided to re-write the intro activity to confidence intervals to revolve around tossing Hershey Kisses. It is based on an activity I found on the internet by Lisa Brock and Carol Sikes, who found the activity on the website for Aaron Rendahl’s STAT 4102 activities at University of Minnesota. I revised it some more…don’t we all tweak things to make it our own?
My AP Stats students were feeling a little rushed and uncomfortable with the whole process of writing up a two-sample hypothesis test for proportions vs. confidence intervals. I completely understand! There are so many nuances and details to keep track of, so much to write and they just needed a confidence booster.
I thought I’d try something a little different. I copied lots of prompts from various textbooks, but without the question. Then I gave these directions:
Your and your partner will practice writing up a two-proportion inference procedure for both an inference test and confidence interval. You have 45 minutes to complete the poster (20 minutes for each question and 5 minutes for organization). Each of you is to write in a different color and sign your name in that color. Read the situation carefully. Glue the situation to the top of your poster paper; the poster is to be letter (not landscape) orientation. Write the title of the problem at the top of your poster paper.
- Write and answer an inference test question (Is there significant evidence that…) about this information. Select and state the a-level chosen. Describe the error you might be making with your decision.
- Write and answer a confidence interval question (Estimate the true difference…) about this information. Select and state the confidence level. Interpret the confidence level. Describe the additional information you gain from the confidence interval.
At the end of the time, we will do a gallery walk. You will be assessing two write-ups using the inference rubric. You will have 7 minutes to complete each assessment.
We had a block period (90 minutes) to work on the posters AND do the gallery walk. Time was a little tight, but the discussion was fabulous! I love getting to walk around and listen to peer discussions and I had a great opportunity to connect with my struggling students in order to clarify things based on their questions. I really liked how the activity made the students write the question – I hope this will help when they read unfamiliar questions as we prep for The Exam.
It’s hard to believe that I’ve stuck with this challenge for 100 days! Amazing and gratifying!
Today I had one of my formal observations today in AP Statistics. And it is FRAPPY day. The evaluating administrator is a former LA teacher and so the fact that a math class is actually doing technical writing (as per the Common Core English Standards) was well-met. Prior to today’s activity, I shared the Frappy process, the intent of each part and that my students were “well-trained” in the process.
And my students were exemplary! Everything I shared would happen did happen. The students were focused during the writing phase. They collaborated about their answers and adjusted with green pen ONLY after they discussed changes. They thoughtfully discussed the two student answers and wrote suggestions or questions along side the responses. They used the rubric to assess and score their own writing in red while asking clarifying questions about the rubric and the statistical processes and communication. They wrote thoughtful reflections about their level of understanding while also including suggestions to improve their understanding and communication. Here are some examples of their reflections:
While looking for a new, food-driven activity to introduce confidence intervals for proportions in AP Stats, I found this activity on Jason Molesky’s StatsMonkey AP Best Practices website, which was attributed to Aaron Rendahl (STAT 4102, University of Minnesota). You can get the Hersheys Kiss Activity handout and a Gimme a Kiss! power point created by Lisa Brock and Carol Sikes. I made some modifications including not having the students create a big chart of all of their confidence intervals since we had already done that with Jelly Blubbers. The materials needed are:
- Gimme a Kiss! Handout
- 5 Hershey’s Kisses per student…I used Valentine Kisses 🙂
My statisticians collected the data as asked and I decided that instead of repeating the entire class chart of confidence intervals, I’d have their group pair up with one other group to use the 8 proportions to draw confidence intervals on a chart like this:
Then on Monday, we’ll talk about why these CI are not the same length like they were in the Jelly Blubber activity. This was a fun way to end the week and have data ready to go for next week’s pursuits. Happy Friday!
Today we finished the Jelly Blubber activity and looked at our results…had 7 kids gone yesterday for an LA field trip to see a play, so the data is a slightly sparse. I revealed the true average length of the population of 100 Jelly Blubbers to be 19.4 mm and drew the red line down the chart to show its location.
We then counted the intervals that actually captured the true mean, filling in the dot. Any confidence intervals that missed the true mean, I redrew in red and also put an x in the dot.
Using the proportion of CI that captured the true mean, we developed the concept of the confidence level. We then talked about how to interpret an individual confidence interval and practice writing the interpretations. I like to use a lighthouse analogy: either the lighthouse sees or doesn’t see a ship that is within its range…and the range of the light is like the confidence interval. We followed up the conversation with a discussion about the mechanics of calculating a confidence interval. Tomorrow I’ll have an opener problem to see if they really did get it! How do you check to see if students “get it” and “retain it?”
Today we completed the Jelly Blubber Activity…wish I knew who originally put this activity together, but it is a “classic” among high school statistics classes. I first got the activity while attending an AP Summer Institute with Robin Rubinstein. Over the years I’ve seen variations on the basic idea. I adjust the content to fit the school and surrounding area. The kids measure the lengths and record on their worksheet via their iPads.
Once they had their data, I used the Navigator to collect all of their sample averages and then displayed them so we could look at the approximate sampling distribution….great time to review the important concepts of a sampling distribution that we’ll use in inference. Pretty nice displays, huh? Actually we had a couple of “outliers” and the kids suggested that perhaps some students had entered their data in centimeters instead of millimeters. Of course I praised them enthusiastically, pointing out how much they had grown in their ability to look at data critically. When asked, a couple of them fessed up and so I adjusted those values and got the display below. The predictability of the CLT never fails to amaze me! Such a stats geek!
My students answered some more questions and were led through the process of calculating confidence intervals with a known population standard deviation, since there are only 100 total Jelly Blubbers. I asked them to randomly select one of their five CI using randint(…I was worried that the time it’d take to have all of my students put up all 5 of their CI would take the whole period. Using sticky dots, big graph paper, and markers, they drew in their chosen CI. Didn’t finish so the rest is for tomorrow.