An Interesting Take on “Average”

Screen Shot 2013-07-01 at 10.13.11 PMWhen I’ve taught “measures of central tendency” to students in the past, I always asked them a simple question.  If given the choice, would they choose for a teacher to calculate their grade by using the mean, median, or mode?  I’d also ask them to justify their choice.

Students have always come up with interesting and primarily personal stories to justify their measure of central tendency choices.  I often wonder if this silly question bears more merit than I initially meant it to.  The concept of “average” ties deeply into assessment practices.  I’m not saying this is necessarily bad… I just wonder… is “average” good?  Best?

I have been wrestling with some very fundamental assessment philosophies in light of the tools we’ve been equipped with this past year, namely, iPads.  I hope to resolve some of my thoughts before fall, so I can implement new ideas this upcoming school year.  I struggle with how to “grade” homework, the idea of when something should even “count” for a “grade” and finally, once I have all of these “grades” what do they really mean?  (No pun intended on the use of “mean” there…)

I don’t have all the answers.  I’m not sure I have any answers – just a lot of questions.  In the midst of my thoughts about assessment and the idea of “average,” the following video was shared with me.  I like the message a lot.  In the end, I’m feeling the desperate longing for some concrete classroom examples.  (I’m also feeling a deep yearning for all of my “average” classroom desks to grow legs and walk away this summer, and instead, magically, classroom furniture that facilitates flexible grouping shows up instead… but I digress…)

Check out the video – how does this message impact teaching and learning in our classrooms?  Assessment?  Even furniture?  For mathematics specifically, doesn’t it ring true that we’re often assessing reading comprehension well before we’re assessing mathematics?  What do we do with this message?  How do we move forward?  (Well gee, aren’t my comments a big old spoiler alert!  Trust me – it is still worth the 18-minute investment to watch this video.)

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The questions begs to be asked… “Is it time to stop the average…?

 

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iPadpalooza ’13 Run-Down

photo - Version 2As tech-enthusiasts have moved on to #ISTE13 in San Antonio, I’m taking a moment to reflect on #iplza13… that’s right, iPadpalooza 2013!  I can’t describe the pride I felt being a small part of this big “festival of learning” in Eanes ISD.  The event takes place annually in our high school, Westlake High School.  A flood of Eanes educators and ed techies from all over Texas, the nation, and even from Canada this year, join in to share, celebrate, and move forward in this revolution in education.  I can’t think of a more exciting time to be an educator!

Some iPadpalooza highlights for me included:

Screen Shot 2013-06-22 at 4.20.39 PM* Seeing Sir Ken Robinson speak eloquently with quick-Brit-witt about creativity, and how we can encourage creativity with tools like the iPad.  Hearing such a well-respected educator speak common-sense ideas (that counter the direction education has been heading in recent years) was both refreshing and inspiring.  If you’ve never had the pleasure of listening to Sir Ken, check out these TED talks.

Ken Robinson says schools kill creativity

Ken Robinson: Bring on the learning revolution!

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* Meeting Rafranz Davis in person!  This kindred-spirit has a passion for math education and technology integration… my kind of gal!  She is just so darn positive and encouraging too!  Check out her blog here, her winning video for the iPadpalooza contest here,  and her fun Haiku Deck summary of iPadpalooza here.

 

* I also got to meet these great and dedicated “Tweeps”:

@mathtrain – Eric Marcos, whose students have created their own videos on mathtrain.tv  – what he’s facilitated with his students shows he was before his time.  With iPads, we can all strive to do more screen-casting, and allowing students to explain their thinking.

@bigpurplehat – Kristy Vincent, ed tech extraordinaire

@tracyclark08 – Tracy Clark, whose session on Formative Assessment rocked!  Her energy is absolutely contagious!  Here’s a link to her blog too.

@akbusybee – Andrea Keller, another great Twitter ed-tech presence with lots to share!

@4TeachProj – The Four Teachers Project is worth a look!  These guys are the real deal with lots of heart for education.  Check them out here.

Screen Shot 2013-06-22 at 4.56.51 PM* Seeing my husband @mryenca present on the big stage 

This may sound cheesy, but you have to understand… both my husband and I are passionate about education and technology integration… which means, we work the same hours for a good majority of our lives and rarely see each other “in action” as a result.  I swell with pride when I see my husband presenting.  It helps so much that we “speak the same language” in all of our conversations about education and the direction we’re headed as tools like iPads are infused into everyday teaching and learning.

If you’d like to see an archived Live Stream of iPadpalooza main stage events, check out this link.

* Presenting my “iYear in Review” and meeting folks who have followed my blog this year.  There aren’t too many things more rewarding than being told that I’m making an impact by sharing what I do and what my students are doing.  So humbling and energizing, all at the same time!

* Meeting up with the folks on tour with the iSchool Initiative.  I had a brief interview with these visionaries, which can be seen by clicking the picture below:

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* After the conference was over, having the opportunity to follow-up and start talking about next year’s conference, and what we might do between now and then, with several of the infamous Eanes iVengers, including Carl Hooker, Lisa Johnson, Greg Garner, and Tanna Fiske. This wasn’t just a little chit chat – this follow-up was more of a think tank!  Again, humbled and blessed to be a part of the revolution!

 

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , | 1 Comment

iPadpalooza iYear in Review “Nuggets”

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Thanks for stopping by!  On Tuesday, June 18, I presented my iYear in Review at iPadpalooza and included links and other “nuggets” throughout my talk.  Here is your one-stop-shop to access these resources.  Enjoy!

Resources:

Dr. Puentedura’s SAMR Model:  http://www.hippasus.com/rrpweblog/archives/2011/10/28/SAMR_TPCK_In_Action.pdf

QR Codes! Set Up and Solve 1-Step Equations:  http://tinyurl.com/QRequations

QR Codes!  Factoring Polynomials:  http://tinyurl.com/QRpolynomial

My favorite QR code generator:  http://www.unitaglive.com/qrcode

Blog Post: Using Nearpod and Socrative “On The Fly”:  http://tinyurl.com/appsonthefly

Thatquiz web-app: thatquiz.org

My ThingLink channel:  http://tinyurl.com/thinglinkmathycathy

Animoto for educators FREE Animoto Plus Account: http://animoto.com/education/classroom

 

 

Posted in Algebra 1, Pre-Algebra | Tagged , | 2 Comments

Animoto Photo Celebration of Year 1 with 1:1 iPads

I made this Animoto movie for my students to showcase the new things we tried this year.  Many of the blurbs that fly by at lightning speed are featured in more detail on this blog.  Feel free to explore the tag cloud to the right of the screen for any key words that interest you, and enjoy!

P.S. If you’ve never used Animoto, you should!  You can apply for a FREE educator access account here.  Then, upload images and videos, choose some music, and let Animoto do the tough stuff!

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Teacher “Report Card” Using Google Forms

gradesThanks to @MrVaudrey and his blog post here, I was able to execute a Google Form today with my students, presenting the opportunity to “grade” me using a “teacher report card”.  My students’ eyes grew wide at the notion that they were being asked to give feedback about me and my teaching this year.  Some couldn’t hold back saying “YES!” at the thought of the little role-reversal.   Though I was nervous, I’m glad I did it.

Some observations and direct student quotes:

Students liked the classroom environment.

You are very happy and you lighten up the environment.

I like how energetic it is, because since it is pretty early we need things to perk us up.

It isn’t very boring like most math classes.

She tries to have fun in the class.

The size and comfortability.

It has a stable learning environment.

How we have the freedom to share our opinions about topics as a group.

How we all get along really well.  We work well together. Popularity doesn’t exist in the class.

I love how she comes up with her own easier methods on how to solve problems.  She “yencafies” them.

How much fun it is to come to class and know that I’m going to have fun today and looking forward to it.

This class was AWSOME! I loved how exciting it was and I even came out of my shell!

The material was easy to learn with an enthusiastic teacher that loves math!

 

Students appreciated using iPads.

How much technology is a part of our lessons. It’s almost like we are taking two classes in one. None of my other teachers do a lot with technology but mrs Yenca does and we enjoy it.

How much we use the iPad.

I like the people that are in my class and I really like everything we do on our iPads.

we use our ipads almost everyday

I love your way of teaching! I also love using the iPad for instant feedback on different things! I enjoyed using the fuse app and the socrative app as well.

We use the iPads for math.

We do a lot of activities on iPads.

We can use iPads.

I like the fact that Mrs. Yenca is always willing to try out new things, especially since we have the iPads. It’s such a refresher to not have a boring math teacher.

 

Students enjoyed working together on tasks,                                                              and many students wanted to do so even more… 

That we got to check over our HW with a group.

I like best that we can work together sometimes to see if we got the same answer

Group projects

The group work.

More group working time.

By letting us do more partner work

…yet others expressed concerns about the inevitable                                          noisy environment during group tasks.

 I think there was way to much talking and I got out of hand some times.

Have the class be less loud

Less distractions

More control over students volume during collaborative activities.

 

You can’t please everybody.

Have more free time. We have never had a day off I’m pretty sure.

It went at a too slow pace for me, spent too much time reviewing.

Maybe go a little faster on some topics. I found myself listening to the same ideas over and over at times

Do work slower.

Go a little slower.

more decorations and stuff on the walls so we can feel a little more excited in this room

I don’t think that my class period has anything wrong with it, but I do like the interior decorating and encourage to keep it up.

 

What can my students next year expect?

That the class is really fun and you will learn a lot. It will definitely help you prepare for high school.

You will almost never get bored. She makes sure you understand the lesson before moving forward.

If you ever need help you can always go to her.

She never stops smiling

She teaches really well and explains e.v.e.r.y.t.h.i.n.g.

She’s silly and she works us hard, but it pays off.

try your best and you will enjoy it. but if you dont try dont expect her to do the work for you

I would tell them that they will have to do their homework and study in order to get a good grade in the class.

She is a great teacher and really wants to teach you the material

People says shes cool but gives a lot of homework

She is an amazing teacher and she takes grades very seriously.

Awesome! She is great, make sure you do all of your homework and turn it in on time.

That even though you could write random numbers on the homework s that you can get a hundred for “completing” the assignment, I still encourage you to ACTUALLY do it, because the tests are a lot harder if you don’t pay attention and learn from your mistakes.

She is a great teacher so just try to have fun. You should pay attention in class because if she thinks your not paying attention she will call on you.

Be ready for no break and a teacher who talks in a perky mood

 

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Icing on the Cake:

Thank you for an amazing year and thank you for really caring about me towards the end I couldn’t ask for better. I really hope I have another math teacher that is so great at their job and cares as much as you do next year.

 

thank you soo much for everything you have taught us and by that I don’t only mean math!!!!

In the last years I have HATED math. And I mean hated it. I thought I was stupid and I would come home crying because I didn’t know how to do the work. My teachers could never teach me the right way and I would be so confused. Getting high C’s and low B’s on tests, which was not okay for me because I sorta kinda, okay I have major OCD. And perfection issues. So anyways, I have never been used to getting some of the highest grades in the class on tests and excelling in math, until this year. I think I just understood things more than my classmates. It’s been such a life changing experience having you as a teacher because I’m not afraid of math anymore. And I know I’m not bad at it, I’m actually pretty good! Thank you so much.

Here is the spreadsheet in all of its unedited glory if you’d like to check out my report card in its entirety – I only omitted student login information to protect student identities.  Also, I wasn’t able to complete this task with every class, but I got most students today.  I encourage you to give the “teacher report card” a whirl – some comments will hit you where it hurts, but others will refresh and inspire you! (See Mr. Vaudrey’s blog for a sample form to save on Google Drive to edit for yourself here.)

Teacher Report Card Anonymous 2012-2013

 

 

 

Posted in Algebra 1, Pre-Algebra | Tagged , , | 4 Comments

ThingLink Mobile – New Ways to Explain Student Work!

Screen Shot 2013-05-24 at 8.19.15 PMI read on Twitter that ThingLink had released a mobile app, so I wanted to give it a try.  If you know me, you know ThingLink has become my very favorite “pre-teaching” tool this year.

Once I downloaded the app on my iPad, I searched through my camera roll for an image to link some things to.  I stumbled upon some digital samples of student work from the “scratchpad” feature built in to the HMH Fuse App we used as a textbook this year in my Algebra classes.  To test ThingLink Mobile, I chose a sample showing student work for solving and graphing a 1-step inequality.

As I strategically placed my first nubbin 😉 I thought, why not have students create work using a drawing app, then use these “work images” in ThingLink Mobile to explain their thinking?  I have to admit… I did not plan this strategy at all… it just kind of happened!  I’m excited to give it a try, and I think it has great classroom potential!

Since students will generate their own mathematical work on a specific topic by “drawing” it, the math symbol issue that rears its ugly head so often when integrating technology and mathematics becomes a non-issue.  Kids can explain anything they can draw themselves!  On the flip side, with students using text in ThingLink to explain their mathematical steps, they’re forced to use language to describe their work succinctly.  Again, math syntax is a non-issue because we’d want kids to explain their thinking in sentences.  And how cool is it that a “nubbin” can be strategically placed within work without covering it up?  Imagine having many of these student-generated-and-annotated work samples for students to reference – what a cool way to study and review!

Filing this strategy away for the fall!  What do you think?

Curious about other strategies for using ThingLink in the classroom?  Check out this ThingLink Doc.

Posted in Algebra 1, Pre-Algebra | Tagged , , , | 6 Comments

Don’t Wait For PD – Join Twitter

imagesI initially signed up for Twitter several years ago.

Upon joining, I sent my first Tweet along the lines of:

“I signed up for Twitter… now what do I do?”

And there my account sat, untouched, for several years.

Fast-forward to July 2012…  (I downloaded my Twitter archives to see when I actually started using Twitter to connect with other educators.)    It is sincerely hard to believe I’ve had Twitter in my professional life for less than a year!

Why?

Because, Twitter has helped me connect with other educators who are just as passionate and crazy as I am about mathematics, education, technology, and most importantly, students!  I learn so much that I can hardly remember what I did without Twitter.  Connecting with people and content through Twitter is a regular, daily part of my practice.  Here are a few highlights of specific ways Twitter has impacted me, and can impact you too:

1) Twitter helps me reflect about teaching and learning.

 

2) Twitter helps facilitate ongoing, relevant professional development.

 

 

3) Twitter helps me connect with educators worldwide – check out the Global Math Department! #globalmath

 

4) Twitter allows me to connect with app developers and make an impact on new tools by providing classroom feedback.

 

5) Twitter allows me to compare teaching strategies with other teachers in no time at all!

Would you believe a teacher in Canada, a teacher in California and I have made videos of how we teach factoring polynomials just to share with one another to compare methods?

 

6) Ever wish another teacher was in your classroom so you could laugh with someone else who “gets it”?  Twitter makes that happen too.

 

7) Twitter helps educators unite and know we’re not alone in our thinking!

 

8) Twitter helps me find quality resources I can use in my classroom tomorrow… then provides a platform to discuss how the resources impacted instruction.

 

Follow me, I’ll follow you, and let’s get learning!  

Also check out #mathchat and #ipaded as a few hashtags to get you started on finding other kindred spirits to follow.

Posted in Algebra 1, Pre-Algebra | Tagged , , , | 2 Comments

Teachers Pay Teachers: Kids Benefit Most!

Screen Shot 2013-05-12 at 7.58.54 AMI was thrilled to see this news report out of Clearfield, Pennsylvania on wjactv.com.  The emphasis on quality materials and student engagement makes my heart sing.  I’ve been sharing resources on TpT since 2010, and it’s been an exciting experience to know that other teachers are using resources I designed.  Receiving feedback of teachers using my “stuff” in ways I never thought to use it helps me implement my own materials better!  Likewise, when I use a resource another teacher created and my students go bonkers, I can’t wait to provide feedback to let that teacher know how much my students enjoyed it.  Teachers Pay Teachers provides a great way for teachers to help one another grow our students… and grow ourselves as educators.

I love the support that administration very clearly articulates here as well.  There is immense value in gaining perspective about how other teachers are engaging students through high-quality resources.  When administration supports and understands that, it’s a good thing!

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http://tinyurl.com/encouragingTpT

Side Note: I always cringe, however, when the title of such reports calls TpT a site where teachers sell “lesson plans”.  I don’t think “lesson plans” are what TpT  is all about.  Teachers plan lessons based on learning targets/objectives for the “what” of lessons.  TpT helps with the “how” by providing teacher-created classroom-tested resources and activities.  The “what” and the “how” are quite different.

Final Thoughts:  There are certainly TpT critics out there… (I often wonder just how many products the critics have even closely examined… it is so easy to criticize something one knows nothing about…) so I wanted to share just one of many precious pieces of feedback I’ve received in my own TpT experiences.  Authentic feedback like this is quite rewarding!

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HCMS Shares iPad “In-Site”

This past week, Hill Country Middle School hosted its third and final iPad Site Visit of the 2012-2013 school year.  I couldn’t resist my title’s “punny” play-on-words… if you know me at all you know my sense of humor is quite dry!

With “TechChef4u” Lisa Johnson as our hostess and emcee, teachers and students welcomed colleagues from other districts to visit classrooms, take part in panel discussions, and present the realities of implementing iPads one-to-one this year.  I was honored to be asked to share about apps and tools that have enhanced my students’ mathematics experience this year!

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If you’d like a sneak peek into the activities of the day, check out the archived LiveStream videos here:

 

 

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Visualizing Domain & Range From a Graph

I learned a nifty domain and range trick from an online workshop about using stickie notes to help “frame” the graph of a function.  The idea is to use 4 notes so that all you see is the graph, which can make identifying the domain and range a little easier.

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Slide a stickie note from left to right until you “bump into” the function, and stick it on the paper.  Likewise, slide a stickie from right to left, top to bottom, and bottom to top, until the graph is framed, like so:

Now, students can see that the domain can be expressed as -5 ≤ x < 5 and the range can be expressed as 0 ≤ y < 6 (It’s easier to see on a graph whose axes are numbered a little better, but you get the idea if you peek at the original graph above).

I like the strategy a lot –  it’s tough for kids to visualize domain and range with the plethora of unusual and squiggly graphs out there.  Since I’m guessing most of my students won’t walk into the EOC with Post-Its in their pockets, I like using highlighters to color-code things a bit.  Here are several work samples from students today showing their different interpretations of the strategy.  I like how they took the stickie strategy and made it more practical based on the writing tools they *will* have when taking the Algebra 1 EOC next week.

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Update!

Check out this idea I found on Pinterest – another nifty way to help students visualize domain and range:

Posted in Algebra 1 | Tagged , , , , | 6 Comments