Weird Stuff Kids Think

My Algebra students completed a cooperative quadratic QR-code walk-about type task the other day.  They could work with a partner, use a graphing calculator, Desmos, the HMH Fuse app, their homework, notes… everything.  They scanned various QR-codes, which revealed practice problems for them to each complete on a paper work template.  The idea was to facilitate an environment where conversation was rich and necessary.  I find that my face hurts at the end of classes like this because I’m just so darn tickled to hear my students talking, justifying, and using academic vocabulary appropriately.  It’s fun to literally watch them learning… and even MORE fun to watch them TEACHING.

Amidst all this bliss, something quite bizarre happened that caught me completely off guard.  Problem A Part 2 seemed direct and unassuming to me… yet every. single. solitary. student. got. it. wrong.

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Students shared with me that they “didn’t know” they could rearrange the ordered pairs… or that I “never told them” they could do that.

I’m like… WHAT?

This misconception was common between all three of my algebra classes.  They looked at the x-values, and decided this couldn’t possibly be quadratic… if the x-values appeared to have no consistent differences, why even bother looking at the y-values…?!?

Needless to say, I did a little reteaching and represented the ordered pairs in tables like these, but this was not a misconception I had anticipated.

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How do you handle it when students think weird, unanticipated stuff?  When they create rules that aren’t there, and abide by them… en masse?

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

ThingLink as Collaborative Work Space

Screen Shot 2014-02-08 at 8.44.59 AMI saw this ThingLink and was immediately inspired to give the strategy a try.  Why not create a ThingLink to serve as a “collaborative plane” for my students?  I jazzed up a “Unit Organizer” from the “Strategic Instruction Model” with some color-coding by concept, and uploaded the PDF to ThingLink.  I made the link private within my ThingLink channel, then “shared” it by embedding it on my teacher website for students to access.  I wanted students to review for a unit test by working problems together in a provided paper study guide, while having this ThingLink in the “background” so big ideas, definitions, etc. could be added on a whim on their iPads.  A basic geometry unit seemed like a good first ThingLink attempt, especially since it was so vocab-rich.

In groups, students practiced review problems on paper and added key ideas they encountered as “nubbins” to the ThingLink.  As each “nubbin” was updated, all students could see it.  I liked this twist versus simply using paper graphic organizers alone.  All students could access a class-created organizer instantly.

Well, sort of.  In a perfect world that’s what might happen.  Still worth trying again, but here are a few lessons learned.

 Things I learned:

* I don’t think more than one person can edit a ThingLink simultaneously.

* When the wireless network goes down during a task like this, it’s not pretty.

* Students did not continue to add to the ThingLink outside of class time as I’d hoped.

What I will change/do next time:

* Say a prayer for our wireless network beforehand.

Screen Shot 2014-02-08 at 12.39.21 PM* Use an object (a hall pass, hand-on-a-stick, anything easily visible) to pass from group to group which gives only that group permission to have ONE member editing the ThingLink.  The whole class needs to know which group is editing the ThingLink, and take turns.  As far as experience tells me, a ThingLink can’t be simultaneously edited.

* Be more specific with directions.  Maybe assign one concept per group rather than free-for-all editing… or not…?  Maybe an organic free-for-all is better because it will reveal which concepts everyone wants to talk about, and which are being avoided like the plague.

* This could be a nice little extension as a homework assignment too.  Ask each student to make one contribution to the ThingLink, and include his/her name in the nubbin.

Here’s our first, very sparse, attempt!  Hoping to try this again soon.

UPDATE:  Literally, an update that makes ThingLink so much more exciting for classroom use!  Read this —> “Build Your ThingLink Classroom” 

Posted in Algebra 1, Pre-Algebra | Tagged , , , , | 3 Comments

Teaser…

I may or may not know the math teacher in this video, featured by Querium in their first-ever Tweet…

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ThatQuiz.org: Pre-testing and Post-testing

Screen Shot 2014-01-24 at 8.01.18 AMIf you teach mathematics, your students have devices with internet access, and you’re NOT using ThatQuiz.org… both you and your students are seriously missing out.  My love for this web-app continues to grow as I see its impact on my students, time and again.  My most recent use of ThatQuiz is to take full advantage of the “duplicate” feature built in to the site, allowing pre-and-post-testing with ease.

My algebra students, for example, were learning the basics about integer exponents.  We discovered patterns to justify mathematical truths about zero as an exponent and negative integer exponents, and students had traditional homework from the textbook’s practice workbook.  The next day, I started class by asking students to login to ThatQuiz and take a brief quiz assessing their ability to simplify expressions containing such exponents as I took a lap around the classroom to check homework.

Skitch 1What’s fascinating is the real-time in-your-face (yet non-threatening) feedback ThatQuiz provides students AND me.  A quick glance at a homework “worksheet” completed by who-knows-who (Mom?  Dad?  Sibling?  Tutor?) fades to the background as real-time data truly shows what each student knows.  Right now.  As every student is faced with the summary screen of their own performance on the “quiz”, assumptions about each student’s present level of understanding are confirmed… or possibly interrupted.  Welcome to reality!

 

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I don’t “grade” this experience, but I’d venture to say students find it valuable, and many are thankful that it’s “not for a grade”.  After all, we’re new at this.  We’re practicing. We’re still learning.  And this is the first round of feedback each student has received since flying solo with these exponents.  It would be a shame to discourage students by putting a 50% in the grade book at this point, but seeing that 50% fuels students to seek help and ask questions that otherwise may have gone unexplored.

Skitch 3Fast-forward to later in the week.  Though we’ve begun to discover and generalize other properties of exponents, students are still practicing and applying ways to handle zero as an exponent and negative integer exponents too.  That’s when I login to ThatQuiz.org and use the “duplicate” feature to give students the same quiz from earlier this week, and call it version #2.  Yes, students have already taken this very quiz, but the content isn’t something that can be easily memorized… and with mean scores in the 60% range the first time around, there’s only one direction to go…!

Students welcome the chance to try the “quiz” again, and when met with the summary screen, feel accomplished at the improvement they see.  Does every student do significantly better the second time?  Not necessarily, but the feedback helps students see if they’ve grown.  If they haven’t, they know it, and so do I.  A little-one-on-one tutorial time is due, and perhaps erasing that score and letting the student try again would pack a confidence boost, even without the “grade”.  This experience provides a “safety net” before a “quiz” or “test” that *will* be graded.

Skitch 4Not every topic is conducive to this type of assessment, but fundamentals are great for this routine.  ThatQuiz generates quizzes on lots of topics, and if the one you’re hoping to assess isn’t generated by ThatQuiz, click on the “Browse” option to see if a kindred spirit out there has already created just the quiz you need.

I’d love to hear how you’re using ThatQuiz with your students!  Feel free to comment. 🙂

This post assumes you’ve already signed up for a free ThatQuiz.org teacher account, you’ve created classes, you’ve entered your students’ names and passwords, and you’ve found a creative way to share and maintain each unique class URL.  Doing this initial work is WELL WORTH IT, even if you start tomorrow.  Just sayin’. 😉

 

 

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , | 8 Comments

Exponents & Error Analysis

Screen Shot 2014-01-13 at 7.50.49 PMThere aren’t many strategies that tell me more about student thinking than “error analysis” opportunities.  When students “grade” another hypothetical student’s work, there’s something special about the experience – students’ senses are heightened.  They’re on a quest for truth.  They feel exceptionally “safe” speaking about the mathematics because the work belongs to “somebody else”.

Many textbooks do a nice job of incorporating the occasional error-analysis opportunity somewhere toward the end of a problem set.  I find error-analysis becomes a more engaging experience if you “set the stage” so-to-speak.  For instance, as my algebra students entered class, I handed each of them this sheet —> QRCodeFindNFixErrorAnalysis before they crossed the classroom threshold.   Then I said, nonchalantly, “Will you go ahead and grade this for me?”  Some students were eager to please me, smiled, sat down, and got to work.  Others looked at me as though I’d said something very strange!  One girl giggled and said, “Mrs. Yenca, I actually thought you just said you wanted me to grade this!”  My response?  “Yep!  That’s exactly what I just said!  Thanks in advance!”

They were on to my gimmick 😉 but that’s okay – each student “graded” the paper silently and individually first, red pen in hand, then paired up after a few minutes to compare with a peer.  Finally, students scanned the QR-codes to see if the revealed text message confirmed or denied their work.

But I never stop there – asking random students to take their work to the document camera to present to the class is where the true meat-and-potatoes of this experience happens.  As students explain the way they “graded” the paper, they reveal the darndest things about their *own* thinking.  MANY students confirm correct work, but for the *wrong* reasons.  MANY students struggle with using appropriate academic vocabulary, and need a little encouragement to “talk the talk”.  It’s enlightening to have students with different opinions present their work and allow discussion and debate to ensue.  Letting them talk is the best part.

How do you use error analysis to enrich classroom discussion?  Confirm mathematical understanding? Reinforce vocabulary?  Reveal misconceptions?

Andrew Stadel has some rocking resources for error analysis too – check them out here.

Here are a few more I’ve used as well.

 

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Nearpod “Best Practices” For Math Class

Screen Shot 2013-12-28 at 7.30.08 PMI kid you not – when I say, “Get out your iPads and go to Nearpod” my 8th graders literally say, “YESSSSS!” and give a little fist-pump… every time.  It’s not necessarily Nearpod that they love, but the peer interactions and instant feedback it facilitates.  In a nutshell, making your Nearpods about “them” and not about “you” is the way to go.  Think about what the students will be doing versus what you, as the teacher, will be doing.  Students should be engaged and have ample opportunity to show what they know during any NPP (Nearpod presentation).

Perhaps having a few days away from the classroom is getting those creative juices going in the minds of math teachers.  This week I’ve been contacted several times by different math folks all aspiring to use Nearpod in their mathematics classrooms.  Even more specifically, mathy people are wanting to use Nearpod more effectively, and have asked me for ideas regarding “Nearpod Best Practices” in the mathematics classroom.

Here are some excerpts from e-mails I’ve been sending to individuals – I hope these first-hand experiences and tips will help as you Nearpod in the New Year!

Yes, I just used Nearpod as a verb.

 

Nearpod ≠ PowerPoint

It’s tempting to just refresh those digital presentations you might already have by dumping them into Nearpod.  This idea in and of itself isn’t a bad one, but if there are more static slides than opportunities for student input, your Nearpod may fall flat.  I’ve had success in limiting the number of “static” slides in a NPP and adding lots of assessment tools that constantly gauge student thinking.

In my humble opinion, Nearpod is best used as a segment of a lesson, not the ENTIRE lesson.  Consider a Nearpod at the start of class to pre-assess or review homework.  Consider a Nearpod to introduce a topic.  Or, use Nearpod to review and assess after a lesson has taken place.  Just as a PowerPoint or Keynote shouldn’t last 50 minutes, a NPP shouldn’t either.

 

Nearpod “Draw” = Instant Error Analysis

Work SamplesIt’s really not about the NPP – it’s about the peer relations Nearpod facilitates with ease.  “Draw” doesn’t have to mean “draw a picture” – mathematical work can be “drawn” too!  Present some content, then ask the students to solve a problem and “draw” what they know.  (AKA “show your work!”)  This allows you to virtually send every student to the board!  Think of the paper “exit ticket” of the past, but administered when needed during a lesson (rather than only at the end) with instant digital work samples from every student (rather than annoying little piles of paper to sort in hopes of helping your students tomorrow.)  Nearpod redefines the “exit ticket” concept completely.

Don’t be selfish and keep all of those awesome work samples to yourself.  Launch correct and incorrect work to ALL students’ screens, or at the front of the class, so discussion can immediately ensue.  Consider framing each anonymous, launched work sample by saying, “Tell me something you like about this student’s work, and then tell me something you don’t like about it.”  Or, “Tell me something you notice about this problem, and then tell me something you’re still wondering about.”  Students are happy to comment on their peers’ work, especially in an error-analysis mode.  Being able to scan instant student work samples is powerful data for the teacher, but gains the MOST power when shared with students to encourage rich mathematical discussions.  Trust me, they are very happy to comment on their peers’ work.

 

Nearpod “Polls” and “Quizzes” = Positive Peer Pressure

QuizStudents also love polls and quizzes, but please don’t keep that pretty pie chart to yourself!  When launching a poll or quiz, I put my iPad under the document camera and zoom in so only the moving pie chart is visible on the screen at the front of the class.  They LOVE this – we even have weird sayings about these graphs during “quizzes”.  Since green sectors indicate correct submissions, and red sectors show incorrect submissions, my students yell for “key lime pie” (green) and get all worked up when a graph starts turning red (“No!  No more cherry pie!  C’mon guys!!!”)  This is a silly thing that has developed in my own classroom, and they really do like it… and own it.  Peer pressure plays a positive role in Nearpod “quizzes” and “polls”.

 

Do you feel like your Nearpods are boring?  Here are some questions to consider:

  • Do you have enough interactive features in your NPPs versus static slides of information?
  • Do you try using Nearpod for shorter spurts of the lesson rather than for an entire class period?
  • Do you encourage student dialogue as a key part of Nearpod experiences?
  • Do you display class data for everyone to see, versus keeping it only on your own screen?

I’d love to hear how you’re using Nearpod with success in the mathematics classroom! Feel free to comment below.

To hear me share more “Nearpod love” check out this interview.

To see Nearpod content I designed, click here.

Thanks for the mention on the Nearpod blog!

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Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , , , | 22 Comments

“Pittsburgh Protractors”

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While visiting my home town, I couldn’t pass through without locating a few “Pittsburgh Protractors”.  For several years, painted protractors have been mysteriously appearing all over the city.  While no one seems to know why the protractors keep popping up, or who is the culprit, blogger Eric Lidji has made it a mission to number and track the protractors via a Google Map.

 

I tested the map today and easily located three protractors… several were lodged behind dumpsters, but I was able to get close enough to pose with Protractor #153 in the Strip District.  A quirky math mystery indeed!

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Defending “The Worksheet”

In this era, “the worksheet” has gotten a pretty bad rap.  The seemingly popular push to go “paperless” doesn’t help the cause.  Are worksheets and paper inherently evil in the 21st-century classroom?

In the ed-tech realm, I sense a little hypocrisy in worksheet trash-talk.  I liken it to the excuses folks make when they blame technology for “distracting students” (your students were already distracted before the iPad showed up… they’re kids… they just passed notes when you weren’t looking… or doodled in their notebooks… or ignored you… but I digress…).  Maybe you’ve heard that worksheets are boring… worksheets don’t engage students… they’re “busy work”… friends shouldn’t let friends hand out worksheets… I think over-generalizations can damage any cause, and that’s why I’m here to defend the worksheet.

To defend it, we have to define it… or perhaps redefine it.  I think this is key to understanding do’s and don’ts of worksheet use.  In the spirit of SAMR, here’s my very simple hierarchy of the worksheet, ThingLink-style.

“Practice” – I think this level of worksheet use is the one that potentially gives all worksheets a bad name.  The worksheet is not evil, but its misuse can be.  Giving repetitious problems in mass quantity is bogus.  This is where phrases like “skill… drill… kill…” originate.  Copy these as-is, assign every problem every day?  Yep, you’re the target of the trash-talk.

“Transformation” – Just because a worksheet begins its purpose as an 8.5″ by 11″ sheet of paper doesn’t mean it has to stay that way.  Start small – take a worksheet of the “Practice” nature, and cut the thing up.  Group students randomly, and give one problem to each group to solve and ultimately present to the class.  Encourage communication, provide a menu of presentation tools (the board, a document camera, a screencast using Explain Everything or Tellagami) and you’ve just transformed a worksheet.  That was easy!

Not only can paper be cut… but it can be folded too! 😉  Ever use “foldables” in your classroom?  Kids love them – they’re great for organized and interactive note-taking, and students take pride in them because they’re more like a product than yet another sheet of lined paper in a notebook.

I don’t think any teacher would poo-poo hands-on learning experiences.  Did you know paper can be cut, manipulated, and sorted?  Can encourage rich mathematical communication?  Can cause students to defend their mathematical point-of-view?

Okay, so I am getting very tongue-in-cheek here, but my point is this – mathematical communication, problem-solving and even hands-on learning can occur from paper worksheets if used correctly.  I like this action research review and the cited research on physical and virtual manipulatives – they both matter (and this teacher’s students seemed to prefer physical manipulatives to virtual ones – see pages 33-34).  Don’t throw the paper out  just yet.  Do your students a favor and transform a worksheet!

Need some ideas?  Explore the ThingLink to see what bloggers are up to in the “worksheet transformation” realm.

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

Texas-Sized Snowman

Perhaps it’s the knowledge that the probability of snow here in Austin, Texas is close to zilch that inspires my neighbors to buy such a massive inflatable yard snowman.  When I bike past this house, I giggle every time at the sheer silliness of this fellow.  I’m standing next to it to help you think of questions to ask and investigate.

In the spirit of www.101qs.com what’s the first question that comes to your mind?

How will you attempt to answer it?

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2013 Edublog Awards

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There are amazing folks sharing about the wonderful things they’re doing through reflections and resources on blogs.  Getting globally connected and inspired has never been simpler.  If you’re not blogging… you should be!  🙂

Please take a moment and scan all the names of folks whose blogs and tweets have enriched your practice and your life, and give them a vote!

Edublogs is using List.ly for voting this year.   Check out all the categories here:

Voting has officially begun!  Thanks so much for the nominations!

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