## Day 91: Mathematical Mindsets

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.

## Day 90: Gimme A Kiss

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?

## Day 89: The Never-ending Journey

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!!

## Day 88: Grading, Grading, Grading

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 🙂

## Day 86: Presenting Technology to Our PTSA

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.

## Day 85: Polar Equations Finished!

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.

## Day 84: Hands on Polar Equations

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

## Day 83: Assessment using Google Forms

As I mentioned yesterday, I am becoming a big fan of Google Forms for an easy and flexible medium for assessing student work. Needless to say, the possibilities for building in student voice in the classroom are so broad.

Today, I began to read through and grade my AP Statistics students’ Bias Projects. The posters were hung in the classroom, as you saw yesterday. I took my high stool and my iPad and worked my way around the room. The Google Form I set up made it easy to assess and record. I used the “4” or top rating descriptors under each category to help me focus on the key aspects of the category. For instance, one category is Data Collection. The descriptor included

- Method of data collection is clearly described,
- Includes appropriate randomization,
- Describes efforts to reduce bias, variability, confounding,
- Quantity of data collected is appropriate.

The descriptors helped me gauge the quality of my students’ product and the Google Form drop-down made it a breeze to quickly grade.

I spent about 7 minutes per poster reading and evaluating the quality of the work.

Once I finished assessing the final products, I posted them outside my room to share with the school. As students and teachers walk by, I hear lots of interesting comments…I sure hope it translates into increased enrollment next year.

## Day 82: Response Bias Project

I just want to thank Josh Wilkerson once again for helping me create meaningful experiences for my AP Statistics students. As I mentioned earlier this year, I am hoping to replicate his Community Service Learning Project as the end of year experience for my students.

One suggestion Josh gave was to give two smaller projects during first semester to see how students work together. I have found that they also give opportunities for the students to revisit previous concepts in a real world setting. In first quarter, my students completed an Infographics Project. In second quarter, I had them complete the Response Bias Project he suggested. And I love the results!!

The projects were due today. As part of the evaluation process, students needed to complete a peer review of 4 other projects. I used GoogleForms for students to enter their evaluations as well as include comments. They had about 8 minutes to read through the poster and evaluate it. I thought they’d need 10 minutes, but they didn’t

What I like about the Google Form is it is easy to make accessible to my students, by using our school login I get an automatic signature and the students can keep resubmitting the form. In addition, the results end up in an Excel spreadsheet so I can then add up the totals, sort by student being evaluated as well as those who did the evaluating.

Student earned points from the average of their peers’ evaluations as well as points for thoughtful and meaningful evaluations of their peers. I now hope to merge the comments into a personalized Word document so each student can get their peers’ feedback anonymously. Here are a few of the peer comments:

- Originally I liked the idea of flaps but as soon as I had to reach on my tippy toes to hold the flap up I grew tired of it. Then I took the poster down from the wall and I liked the design again.

The plentiful analysis in the conclusions is good and clear. I’m surprised 20 males said they didn’t support feminism, especially since we’re talking about XXHS students! - I like how you chose a topic extremely relevant to all of us. You did a good job explaining the difference in the questions and why that would elicit different responses. Don’t forget your table! Do you think underclassmen would give different results? I might interview them too in order to remove bias.
- I thought the experiment was very well thought out and thorough. You lovely duo did a great job articulating your points. Maybe in the future you should experiment with whether putting one of the names first affects the results? I might also put less text and more visual stuff on the poster. Great job though
- I feel like the questions are a little vague, as they could present a large amount of bias. Some students might not like the teachers, even though they are learning a lot and they are satisfied with the learning, prompting more “no” answers than should be present. However, I love the organization of this poster, it is very neat.
- I like how you captured an interesting concept (extra information bias) very simply. But, given that your population is American Women, I think it is statistically incorrect that you only found samples from XXXXX’s Facebook contacts who do not represent all American women. A better population would have been Teenage girls in XXXXXXXXX.

I love how my students used the statistical vocabulary with ease and relatively correctly! This project is definitely a keeper.