mathcoachblog

Getting close to the end of the semester here, with just a few days remaining before final exams. In Algebra 2, one of the last units of the course is on parametric equations. With changes to our HS courses, and having not taught Algebra 2 for many years, I have never taught parametrics before. But a new unit to me became fun and hopefully relevant to my students through technology and some great class discussions.

HOW JERRY JONES’ OBNOXIOUS FOOTBALL STADIUM PROVIDED A FUN ACTIVITY….FROM AN EAGLES’ FAN

In this short unit, my ultimate goal was to expose students to projectile motion expressed parametrically.  This was a contrast to material learned earlier in the semester, where quadratics are often used to model motion and explore max/min of projectiles.  Now we had the ability to think about how the horizontal and vertical position of an object were both dependent on the time.  After a quick trig review, we used these equations for our projectile problems.

I wanted a culmuniating assignment for this unit which would allow students to work collaboratively, and demonstrate their comfort with utilizing the parametric equations.  To start the day, teams had netbook computers to use, and I showed the following video to start discussion:

After a brief discussion about football and the uniqueness of the Cowboys Stadium scoreboard, I told they class they had two questions to answer:

• Is the Cowboys Stadium scoreboard too low?
• How far could a punter kick a football?

Groups were allowed to use the internet to research any information they needed, as well as the Desmos calculator to help model their ideas.  Most teams found information they needed:

• What angles are ideal for punting a football?
• What are plausible initial velocities?

I did have to stop class at one point to explain that a good angle for hitting the scoreboard may NOT be ideal for hitting a punt as long as possible; the two questions I am asking are separate from each other.  I was happy with my students’ arguments and hope to do this activity again.  Below, one group turned in most of their work in a Desmos file, which shows an “average” punt, a punt which would hit the scoreboard, and an “ideal” punt for distance.  Click below to open the graph.

HOW THE UNIT STARTED

Desmos was also used to start the unit, and allow students to see how parametrics behave.  With netbooks, partners opened the Desmos file below, and were given the instructions:

Thanks to the Desmos folks for adding the path trails to the file.  Cool addition.  Many students were able to desribe the paths they observed, often writing a rectangular equation to describe, but could not quite explain the motion.  Some student paraphrasing:

I think it is an equation, and the slider somehow controls the domain.

Note, this falls apart some when we get to example 4, the circle.

I think the slider controls the value of x, and this controls y.

Getting closer

I think the slider somehow controls x and y.

Now we are there.  A parameter, here “a”, controls the values of both x and y.  After discussion, students opened the folders and observed the structure and behavior of the equations.  This opener made the “buy-in” for the need for parametrics so much stronger, and I hope to use this again!

You can find more Desmos class files in my Desmos Virtual Filing Cabinet!

The most interesting classroom-related Twitter conversation of 2013 took place within the last week of the year, and has carried over to the early days of 2014.  An intense debate between a twitter “member” named @StopSBG, committed to “Stop Standards-Based Grading (SBG) in Ankeny Schools”, and a number of education professionals has produced spirited back-and-forth on the nature of grading, standards, test retakes, and what we value in our communities.

I can’t fairly summarize the many webs woven and arguments made over the past week, and encourage you to look up Frank Noschese, Ken O’Connor, and Rick Wormeli, and the many others who have joined the conversation.

https://twitter.com/StopSBG/status/418636802807697408

Kudos to Frank, and his many, MANY tweets over the last few days in trying to defend best practices in grading.  In my own building, I have moved towards retakes in my classes, which I have blogged about here, and have worked to defend my ideas and practices with colleagues.  I have had some success in convincing colleagues to join me in making retakes part of their classroom culture.  But change of long-held practices takes time, reflection and discussion.  For me, my classroom guidelines on retakes are based on 3 conclusions:

1. It’s best for student learning.
2. It’s best for student reflection.
3. It’s best for student feedback.

And aren’t those the most important things?  My opinions on retakes certainly didn’t develop overnight; I read literature, sought out research, shared ideas with colleagues, and found opportunities to hear experts share their ideas (which is much easier with things like YouTube and Twitter around to facilitate self-directed PD).

But my opinions aren’t sufficient if I can’t defend my policies.  And they need to be defensible, not only to colleagues (who I hope to get on-board as part of a department and building network), but also to:

• Students – who have mostly been exposed to “traditional” classroom practices.  How do I get them to become better learners by investing themselves and trusting in my classroom practices?
• Parents – who may have legitimate questions about their child’s education.  Can I defend how my practices are best for their learning?  Also, can I explain my practices without throwing other teachers “under the bus”?
• The community – who often only hear about schools through quick bites of often mis-leading information.  How can I be an effective communicator of how schools are adapting and evolving?

This is where the recent Twitter debate has been so fascinating.  A chorus line of edcucators, well-versed in best-practices in the classroom, have been debating the nuts and bolts of education policy with a non-education professional.  And while I trust some head-way has been made, it will take a lot more folks with the will and persistance of Frank Noschese to deliver clear, well-researched messages in order to forward the national education debate.  I find myself often sitting on the sidelines when debates intensify, and I feel the conversations of the last week have given me inspiration to become more involved in 2014….so there’s my New Year’s Resolution!

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At the end of January, we start a new semester at my school, and I will have a 9th grade Prob/Stat course.  This is a course I have taught many times before, but this time around will be after a 2-year absence in the classroom, and this will be an “academic” level class – for students who have traditionally required more intense instruction.  I am eager to implement a Standards-Based Grading system, and have been poring through blogs and readings on SBG to help craft an approach I think will be manageable for my classroom.  Despite my enthusiasm and planning, the success of my programming will only be as good as the communication I provide, and the clear goals I set.  The past week’s debate has provided an opportunity to clarify my goals, and think about their importance in the process:

• Create a culture where students routinely reflect upon their progress.
• Provide opportunity for students to communicate their strengths, weaknesses, and needs.
• Allow for multiple opportunities and avenues to demonstrate skill mastery.
• Help guide students “out of the pit” (a Rick Wormeli phrase!)

I appreciate the vast network of professionals I have connected with through Twitter, and their kind assistance in helping shape my goals.  It’s quite a time to be an educator…it’s also a better time to be an cheerleader of best practices!

April 2012 edit: interested in how I present this activity, and many others, to teachers?  Check out my talk at the AMTNJ Tech Conference: 2014 Desmos Talk

Here on the blog, the conic sections project we use at my HS in Algebra 2 is one of the most popular posts, generating lots of hits and e-mails to me asking for more information.  I am just now grading conic sections projects for this year, and want to share some new additions to the project, and a rubric you can use.  The projects are all over my living room now, just waiting to be graded.

For the newbies to this project – the concept is simple: use equations you have used, specifically conic sections, to draw something.  The Desmos calculator is perfect for this task, and students turn in their graph-based picture, then a completed, colored picture.

So, what’s new this year?

FOLDERS AND LINKS

In the past, students printed their equations and submitted them.  This year, students instead shared a link to their Desmos product using Edmodo.  Also, using folders has improved student organization, making it easier to locate and edit crucial equations.

VERIFYING SYSTEMS

In my conics unit, students learn to solve both linear-conic and conic-conic systems.  This year, I asked students to choose two systems from their drawing and verify the intersection points.  This served as a personal review of the chapter, and students had an investment in linking the algebra they had learned to their picture.

SCREENCASTS

Last year, I participated in a Desmos webinar where I explained the evolution of the conics project.  For the webinar, one of our sophomore students recorded a screencast where she explained an aspect of her picture.  Having a student comment and reflect on their work was so powerful that I made it a requirement for all students this year.  Many students chose ScreenCastOMatic to record, and the reflections were excellent.  Edmodo was used to share links, though some students had tech issues which I will work to head off earlier the next time I give this project. Below is a screencast from Nick, who was kind enough to allow me to share his work with you:

I have received many e-mails from folks asking for guidelines and a rubric for this project, and am happy to share with you a more detailed document.  Feel free to use any part of it, and let me know how it works in your classroom!

Download the project description and rubric

MORE RESOURCES:

My first blog post on the conics project

More conics news

The Desmos YouTube Channel – Classroom Conics Project: