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…..
Late last year, via Twitter, a discussion revolved around how to give AP Stats students more and regular experience with multiple choice questions. One idea put forth by @druink was to have an MC Monday experience. She shared a form she created and asked for input and collaboration around the viability of the form: number of questions, student reflection, etc.
I wanted to use the form but tweak it some more to allow me to track both general student progress as well as progress in the four strands of the AP Stats curriculum: Exploring data, Generating data, Probability and Inference methods. Part of this is to complete my teacher evaluation student growth component, but also to help me see if there are areas that need revisiting later in the course (of course, there always are, but in the past it was hit or miss rather than data driven).
One hindrance for tracking via components was how to identify each question easily so it didn’t become a time-suck. In addition, I needed a reasonably easy way to generate questions that were essentially at the AP level. So my department purchased a new ExamView test generator for our text which already had the questions identified by the AP standards. I also found that GradeCam can assign a learning target to questions. Unfortunately, the available targets were CCSS or state standards; luckily, in the CCSS there are “almost matching” statements around the 4 big strands, so I could label questions. Because I have been using GradeCam for unit tests as well as Midterms and Finals, students are very comfortable with the process of scanning their answers for me.
So today was the first day of trying out the process and I think it went great! Now I’ll be able to track long-term retention of the key ideas as well as monitor individual students’ growth (or lack there of).
One of the things I’d like to use more often in my Precalculus classes are multiple choice questions to promote class discussion. Today as part of the opener I gave my first MC question. Fairly straight forward question because I wanted to get the kiddos logged into the Nspire Navigator, which we haven’t done for a while. The students wrote down on their Opener-Exit slip the answer along with any calculations they needed to do to determine the best choice. Then the Navigator, through a Quick Poll, collects their answers. Once I stop the poll, I can project the responses in a bar chart.
As you can see, there were two popular answers. I asked my students in their groups to discuss their choices and try to determine which one was actually the correct answer along with supplying a reasoned argument for their group’s choice. Some great conversations! I then resent the Quick Poll to see if they could arrive at the correct answer without my confirming the answer.
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!
This is the first day for my students in Precalculus for looking at logistic functions. They completed an exploration from Foerster’s Precalculus book that had them look at a set of data points and then try to fit an exponential curve. They quickly realize that the exponential is only accurate at the beginning of the data set. They are then given the general equation and asked to determine the missing coefficients from specified points using a system of equations. Good discussions along with reviewing old concepts and processes used in new ways.
One thing I’d like to do is create a graphic organizer to help explain (or have the students determine) what the various coefficients control. Lately I have found more references online regarding this which didn’t seem available a few years ago. Will have to share the websites at a later date
As part of my instructional coaching duties, I offer various PLC’s throughout the year. I am really excited about this one: Mathematical Mindsets based on Jo Boaler’s new book. I read Carol Dweck’s Mindsets book this summer (and did a book study with a colleague) where I wanted to try to incorporate some of the principles in my classes. However, I found it challenging at times to find the right venue to share, re-enforce and deepen students understanding of their mindsets. Also, I was struggling with using the vocabulary and verbiage that supports a growth mindset.
Along came Jo Boaler’s book that specifically talks about the mindset aspects in mathematics. One idea I found particularily interesting is compression, which basically says that people can compress conceptual ideas after a bit of intellectual struggling with them, whereas procedural methods are simply not compressible. you can make room in your brain by connecting concepts but process and memorization doeesn’t necessarily link to compress. More about that idea later.
If you get a chance, I think this book is a must read for mathematics teachers (especially secondary teachers) because we often forget (or don’t recognize) how important it is to teach and value all of the ways a student can approach a problem.
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?
Getting ready to begin the journey into next semester starts Monday, so it’s time to organize the next chapter. I have a year plan (that is always in flux) to guide my timing so I don’t rush at the end of a semester. I always build in what I call “buffer” days so that if my kiddos need more time to wrestle with a new concept, I can build it in. Over the years, because of my year plan, I have a sense of the time needed to develop a concept…but its never set in stone because kids and classes are different. The year plan also helps me to think about what worked super well, what worked adequately and what didn’t. To keep things fresh for myself, I will change out some activities based on what I’ve seen on blogs, twitter, conferences, etc.
On a side note, one of my students dropped by after school today and brought me some gorgeous freesias and an even better note to thank me for the time I spent with him this past semester. The little joys of teaching!!