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!!
Yup, I’m a grading machine! Lots of finals to assess, lots of lives to change. Well, not really, but I think my students sometimes think that’s the case. As I grade, I try to keep in mind final “growth” in understanding for each student. Isn’t it tough to pick questions that give a good snapshot (and that is all the questions are, just a snapshot) of a student’s understanding at that moment. So much pressure to make a final assessment that truly reflects each student’s knowledge and understanding at the end of the semester.
I’m also a “muncher” as I grade, so I tried to be more healthy…see the grapes 🙂
Awe, shucks! I didn’t think I was doing all that much more integrating technology into my classroom than anyone else, especially the young teachers. But I must be. Last week, I was part of a panel of 4 teachers which presented to our PTSA; they continue to be interested in how iPads are being used since the technology levy passed that enabled the high school to be a one-to-one iPad school. We all had very different ways we used the iPad and technology in our classrooms. It was so exciting to see what others are doing!
I think I have always been an education tech junkie from my earliest days…having a Commador Pet computer in my first classroom and using the overhead projector (yes, that was high tech back in the Stone Ages) in innovative ways. For my first geometry classes, I used the school computer lab with Geometer Sketchpad to do explorations and develop conjecturing. Over the years, I’ve incorporated various mathematical software such as Fathom, TI-Interactive and TI Student Software to enhance student learning and projects. I was one of the first teachers at the time to have a website that was a go-to resource for my students. I clamored to be on any tech committees in the building I’ve taught.
As the years went by, I began using the TI-81 graphing calculator and have used all of its variations since (except for the TI-91). When I could get a grant written and approved, I purchased and use the TI-Navigator as my first student response systems. I also advocated for a SmartBoard (actually an ActivBoard by Promethean) when they were first available. And used the Promethean Clicker System as well.
Once the internet became readily available in schools and students had access, I began to explore how to use online resources to enhance conceptual learning. Geogebra, Desmos, Quizlet and various applets have made their way into my classroom over the years. In addition, once we became a one-to-one iPad school, I looked for ways to actively engage students through online student response systems such as Socrative, Kahoot!, NearPod, etc.
But I must say that a few years ago, I felt overwhelmed with all of the new possibilities and felt I wasn’t keeping up. I don’t have an educational technology degree so I sought out those that did to help me keep up. As I puruse various blogs and Twitter, I am in awe of what some teachers out there are doing.
Although I have tried many things, I find that there are still a few tried and true technologies that are consistently used in my classroom: TI-Nspire and Navigator, iPad apps that include Notability, Geogebra, Khan Academy, Quizlet and Desmos, internet sites including MathXLforSchools, GradeCam, our online textbooks, Rice University stat simulations, RossmanChance simulations and our current learning management system, Schoology. These are the things I shared in my presentation.
I hope to keep things fresh and alive for my students and technology seems to be the way to support them in an engaging and meaningful way.
They are done! The polar equation graphs my precalc students started on Friday are finished…in fact they came into class asking if they could have time to finish ‘cuz they really wanted to see the final results. I like the component of finding the name of their equation type as well as researching then sharing least 2-3 interesting facts about their polar equation.
Many years ago (I don’t want to say how many but it was before we had access to graphing calculators), I had my students hand draw various polar equations. Having technology so readily available now, this project had been shelved and collecting dust. I decided today that I wanted my precalculus students do experience a tactile activity today. Although I love polar equations, it just didn’t fit the timeline this semester (maybe we’ll revisit next semester). But why not give them an initial exposure to Polar Equations and their graphs as a way to review polar coordinates just before finals…and besides, the graphs are fun and unexpected.
I wrote up the activity and made some decisions about how to have students make posters. A few years ago our department invested in large boxes of poster paper (you can see the poster paper in many of my posts) which was a pretty cheap investment for the amount of paper…and the box seems to last for a couple of years at least. I wanted the paper to be a square in order to find the center and create the polar graph paper. Once I folded to create the square, I thought, why not use the flap for added info. Here is my prototype that I had posted on the front white board.
I then wrote up the directions, including a chart for my students to record the r-values for their equation. I did not tell them the names of the graphs, just handed out various equations; each student got a unique one. I was ambitious with what I wanted them to do afterwards (and we didn’t get that far), but I would keep the “interesting facts” part of the activity.
Then I handed out the directions and away they went. I had hoped they would finish in the class period, but some of my students are very meticulous so it took a while for them to create the polar graph paper on the poster. I am still pondering how to improve that aspect of the activity. Anyway, here are some photos of the activity in progress:
Hopefully they will finish on Monday. Happy Week-end