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).
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.
Today we revisited the Rossman/Chance Reeses Pieces Simulation to look at once again the sampling distribution of proportions. Using this simulation, we reviewed notation, which is so challenging for students when they first see it.
We then used the Rice Virtual Labs to set the groundwork for the assumptions and conditions of a sampling distribution of means and the two situations for knowing it is approximately Normal: Normal population vs. unknown population.
My AP Stats students, using their iPads, explored what happens when the population is Normal, when it is not, and whether they could come up with a population that would not yield an approximately Normal sampling distribution. Once again, we reviewed the notation and also determined the formula for the standard deviation…they actually came up with the rule!!
Love having technology at my students’ finger tips! And thanks to Rossman/Chance for updating the applets to work with iPads…so much better when students do their own exploring rather than watching me do it at the front.
Today I wanted my precalculus students to recap the coffee filter activity. But how to do it in an interesting way?! I found a great website site that has some awesome .gif files of mathematical concepts in picture form. Check it out!! There are some pretty amazing visual depictions of important (or not so important) math ideas.
Here is the one I found for visually communicating the definition of a radian. Love it!!
So the Opener question I asked was this:
Explain how this .gif demonstrated the definition of a radian. What is the conversion relationship between radians and degrees?
Also, as an added a reminder of the mathematical practices, I asked my kiddos which math practices they used to complete their write-up. Lots of bang for the time allotted! I think I will continue to use this as a follow-up to the “What in the World is a Radian?” activity.
As I stated in an earlier post, I am having students help write the rubric for their “Infographic about Me” project. Using this GoogleForm:
I collected this information in spreadsheet form:
and compiled their responses into this rubric:
We will talk next week as a class to decide whether their rubric captures the components and descriptors they wanted. Using GoogleForms has proved to be easier to get student voice into making decisions about how they are evaluated!
I have mentioned before that I have tried to go paperless in my classroom using Schoology as a LMS (learning management system). Students submit their work electronically and I can then grade it using my iPad.
Schoology has made some improvements in this process, one of which allows me to write comments on the student’s work. We had hoped that after grading assignments in Schoology we would be able to upload the scored directly into our Grade management system called Skyward. Unfortunately, the two systems didn’t get talking so I need to grade, then transfer by hand, the students’ scores. I still like the fact that I don’t have to copy so much and I don’t have to cart around arm-loads of paper to grade.
What types of electronic aids help you reduce your paper load and how does it help?
I love multiple choice and true/false questions as vehicles for authentic student argumentation as per the 3rd CCSS Mathematical Practice (highlights are mine):
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
Good MC questions are hard to come by, but even some of the questions from our book create that focal point for students to build an argument, present it to their peers, and critique the reasoning of others. On today’s worksheet, I inserted 8 MC and TF questions along with a GradeCam blank form for students to record their final choices. This gives students a chance to listen to their peers arguments, but have the ultimate decision to accept the choice or go with their own argument.
Once students decide on their choices, they come up to my computer and have their iPad scanned in student mode to see how they did. GradeCam in student mode identifies the problem number of incorrect choices, but does not tell them the correct answer…also keeps it anonymous from other students so the “fear” of public mistakes is alleviated. Students know which questions to go back to and are eager to “fix” their thinking.
Well, not totally paperless. I started trying to evolve my classroom practice to include a digital classroom using Schoology (for course management), Notability (for organizing and taking notes) and MathXL for Schools (for online HW around skills practice). My students find the transition from paper to digit challenging and a little frustrating. Even more so this year since we’ve had lots technology issues with the start of school due to new rooms with new technology, getting Schoology to uploading grades directly to our online grading system and moving to a Google platform…and the students got updated iPads! It is stressful and frustrating at the beginning of the year, but I believe worth it in the long run.
There has been some talk on Twitter lately about whether a digital classroom is conducive for long-term learning. I think David Geurin makes a good point! The reason you are using the technology MUST be rooted in sound and purposeful instructional decisions.
Today, my precalculus students are working in groups on some problems using Notability to work out and record their results. I like my students to do this work on their iPads in Notability because they can organize by topic and then I can ask them to pull up old work for discussion in light of new learning. Students also have a portfolio of their work for the entire year.
One concept in AP Statistics that is not totally instinctual is the idea of what standard deviation really measures. A few years ago I attended a session on Statistics in the CCSS at the TI International Conference in Chicago.
I picked up this Mean and Standard Deviation game and have found it to be a quick way for students to develop their intuitive sense about standard deviation. And they like it, too!
One of the main staples of an AP Statistics class is prepping for the AP Exam, and one of the most challenging things for students is choosing the right inference procedure for a situation. So Larry Green’s Categorizing Stats Problems Applet has been used extensively. This link plays well with iPads, too!
Every year, my students comment very positively about their experiences with the applet.
Here is an example of the type of problem and the choices students can make. When they choose correctly, they get a smiley face. If they choose incorrectly, they get hints to help them narrow their next choice. I advise my kiddos that initially they will be humbled, but as they continue through the problems, they will get better. And the nice thing is, they do!