Sort-of-Real-World Math

Dan Meyer’s latest post got me thinking about what seems to motivate students as far as “real-world-ness” goes.  What’s timely about this post is, I think some things my students did in class today go along well with reflecting upon, as Dan puts it, “theories of engagement”.  How “real-world” does the math have to be to be worthwhile to kids?

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Take my algebra students, for example.  Today’s objective was to “Solve Linear Systems Using Substitution.”  I started class with a little novelty and my students ate it for lunch.  In small groups and before any attempt at instruction on my part, students solved “The Leg Problem” by guessing-and-checking, drawing all sorts of interesting pictures, or by writing an equation that would later end up being half of our system – namely, something like 2x + 4y = 74 where x represents the number of chickens and y represents the number of cows.  What’s fun for me is showing them the problem statement, which is novel but certainly not a “real-world scenario”, yet no student has EVER complained.  They’re motivated enough to want to see this thing through to a solution.  They rise to the challenge, start talking mathematics, and can’t wait to share and present their methods to their peers.  Check out two work samples below.

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My pre-algebra students started today’s lesson with a graphic I found on Facebook.  It made an immediate impression.  Our objective – “Finding the Percent of Change”.

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Before talking about how to calculate a percent of change, I asked students to guess what they thought the percent increase was in the scenario.  Their guesses are shown below.

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We veered from the scenario and did some typical textbook examples… and once they got the hang of it, they were all trying to sneak back and solve the t-shirt problem.  One by one, they couldn’t contain their reactions as they realized we were talking about around a 900% increase.  By the time *I* was “ready to return to the t-shirt problem”, they were busting at the seams.  I love acting like I didn’t know what they had been doing… I love that they couldn’t resist returning to the t-shirt problem to test their guesses.  Why was it so irresistible?  Maybe because it truly was “real-world” to them.  Maybe it was the urge to find out just how great or how horrible their individual estimates were at the start.

All I know is, when it comes to “theories of engagement” it’s not an exact science… but when you reach that point in a lesson where the mathematics becomes irresistible, you’re in a good place.  🙂

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

Sunshine Award

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I’m honored to have been nominated for a Sunshine Award by Drew Frank – it’s great to connect with Drew via Twitter, and you’ll see from his blog that getting connected and using social media for learning are themes.  Check out Drew’s blog here.

The Sunshine award is an opportunity to learn more about me as well as 11 other bloggers, recommended by yours truly.  Here are the rules from Drew’s latest post:

  1. Acknowledge the nominating blogger. (That’s Drew!)
  2. Share 11 random facts about yourself.
  3. Answer the 11 questions the nominating blogger has created for you.
  4. List 11 bloggers. They should be bloggers you believe deserve some recognition and a little blogging love!
  5. Post 11 questions for the bloggers you nominate to answer and let all the bloggers know they have been nominated. (You cannot nominate the blogger who nominated you.)

 

11 Random Facts About Me

1.  I won the third grade spelling bee.  The winning word was “ankle”.

2.  I play piano by ear, but I can barely read music.

3.  I will sing in front of anyone, anywhere.  Ask anyone who knows me.

4.  I have a Vera Bradley… habit…

5.  I am a Barry Manilow fan.

6.  I find brain research fascinating and am a huge fan of Judy Willis.

7.  I grew up north of Pittsburgh, Pennsylvania.

8.  I married my college sweetheart, who was also a math major.

9.  Royito’s Hot Sauce is my weakness.

10.  My favorite pizza on the planet is the “bianca” at Backspace.

11.  My son has severe food allergies, and I wish the general public understood more about this topic.

 

Answer the 11 questions the nominating blogger has created for you.

  1. What is your favorite movie of all time?  Airplane!
  2. If you could have attended any concert anytime in history, what would it have been?  Not sure – not a big concert-goer typically
  3. What do you do for fun?  Hobby?  Walks and bike rides in Austin’s many amazing parks
  4. What two guests would make the best comedic pair as co-hosts for the Oscars?  Will Ferrell and Steve Carell
  5. Cat, Dog or Goldfish? Why?  Goldfish – my son is allergic to the other two
  6. How do you caffeinate?  Lipton black tea with a splash of milk
  7. Favorite twitter chat? #msmathchat
  8. Best place you ever vacationed? Disney World junkie
  9. Best book you’ve read in 2013? Brain Rules by John Medina
  10. Favorite television shows?  Parenthood and Grey’s Anatomy
  11. What is one thing you never/rarely share that you are exceptionally proud of?  Being chosen as an Apple Distinguished Educator

My Sunshine Award Blogger Nominees

1.  rndesigns.com

2.  mrvaudrey.com

3.  tapintoteenminds.com

4.  techchef4u.com

5.  hookedoninnovation.com

6.  Teaching Like It’s 2999

7.  hacktheclassroom.ca

8.  restructuringalgebra.blogspot.com

9.  mathequalslove.blogspot.com

10.  futura.edublogs.org

11.  fawnnguyen.com

Finally, according to the Sunshine Award rules, it’s my turn to ask 11 questions of my nominees:

1.  What’s your favorite thing about blogging?

2.  Favorite hobby?

3.  Favorite movie of all time?

4.  Favorite place to travel?

5.  Favorite Twitter chat?

6.  Favorite educational website?

7.  Least favorite food?

8.  Favorite book you’ve read in 2013?

9.  Your unique talent?

10.  Proudest moment?

11.  Funniest thing you ever said in front of a group of students/educators?

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Seriously? A Storify

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Happy ThingLinksGiving

If you haven’t heard, ThingLink is offering FREE premium access to teachers who sign up through the end of December 2013!

Here is a link to join!

I haven’t begun to take advantage of the “premium” features yet, but I aspire to.  Creating custom icons, image analytics, and the ability to create class “groups” all look promising.

I’ve used ThingLink to create content for my students, but would LOVE to shift more in the direction of STUDENTS creating content.  Using ThingLink as a student space for creating collaborative, interactive study guides, or for students to “annotate” images of their mathematical work would absolutely rock.

Here’s my latest!  Thanks also to Desmos.com for being awesome.

Posted in Algebra 1 | Tagged , , | 1 Comment

A Message to 21st-Century Pre-Service Middle School Math Teachers

Screen Shot 2013-11-16 at 7.13.03 PMThis is an amazing time to be an educator.  If you’re truly of the “lifelong-learning” philosophy, you know that access to resources, professional development, and information in general has made a huge shift.  Technology is a key player in this shift.  If you missed the memo, the teacher is no longer the sole bearer of information, and the student is no longer the sole receiver. Learning is a multi-faceted experience, and in this era, we’re all learners.

Reflecting on several months of collaborating with my student teacher, Lauren, as well as examining how my own practice has changed and grown within the past year, this blog post has been churning in my brain for a while.  Here’s my attempt to brain-dump concisely.  While my target audience is implicit in the title, feel free to glean tidbits that are relevant to you regardless of your experience.

A Message to 21st-Century Pre-Service Middle School Math Teachers

1)   Know Your Content – Know Your Audience

You may have all the flashy technology in the world, but if your content is not rock solid, none of the bells or whistles matter at all.  Has it been a few years since you learned this stuff?  Study up – use books, websites, tutorial videos, blogs, and mentors.  Information is available at your fingertips literally anytime – tap into that reality intentionally.  At the risk of stating the obvious, teaching a concept can be a completely different ball of wax than initially learning it.  As you plan, seek the perspective of the students – what do you want them to know and be able to do?  What should the student be doing during each minute of your lesson?  How will you determine whether they have learned the content you intended to teach?  This lesson thing… it’s really not about you, is it?

2)   Curate Purposefully

The availability of resources online is endless.  This is a blessing and a curse.  Let me say that again – this is a blessing and a curse.  “Don’t believe everything you read on the Internet.”  We expect our students to understand this premise, but this is true for educators too.  Best-intentioned teachers go online to find useful resources to supplement lessons, and many teachers are successful in finding just the right resource at just the right time.  I’m truly thankful for teachers who share via blogs, Twitter, and Teachers Pay Teachers.  There is SO MUCH great stuff out there that has influenced my practice, and grown my students.

There is just as much crap out there.  There, I said it.

As the teacher, you are responsible for your students’ learning.  You have to know the “standards” and “learning targets” for each lesson.  Just because something you found online is visually appealing, or looks fine at first glance, fine-tooth-comb that thing with your learning targets and be sure it meets them and is worthwhile for your students.  Work the problems yourself ahead of time – EVERY time.  Don’t get caught in front of a class of students with a resource that doesn’t fit, or is riddled with mistakes.  Spare your students of crap – quantity does not guarantee quality.

3)   Know Yourself – Own Yourself

I hear the voice of my former principal Jackie Santanasto saying something like, the single most influential factor in student learning is the classroom teacher.  This general idea was her mantra when I worked with her at Nitschmann Middle School.  Think deeply about this statement and the responsibility it entails.

You are a key part of each student’s day.  You may be a stable presence in the life of a student whose experiences beyond the school day lack stability.  Students look to you as a teacher, but also as a fallible human being.  They appreciate authenticity – a “real” person to guide their learning. Decide who you are as a teacher, and own it.  Sell it.  Be your best you.  Have passion and emotion.  If you show that you love what you do, that energy is contagious.  For the record, negative energy is contagious too.  To quote the late Rita Pierson, “Kids don’t learn from people they don’t like.”

4)    Get Globally Connected to Other Educators

Getting connected has never been simpler than in our current era.  Choose your favorite flavor of connectedness – blogs, Twitter chats, Pinterest, Facebook, YouTube, Google+, webinars, and on and on and on.  You are not alone.  You have ideas worth sharing.  You have questions worth asking.  Ride the wave.

Learning.  Never.  Stops.

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

Intro to Intercepts

When planning lessons with my student teacher, Lauren, there has been a common theme lately.  Rather than bore students with too much direct instruction, aim to create the need for the mathematics we want them to learn.

Today, for instance, one topic on our list is using intercepts to graph a line.  Too many books and resources START the lesson by telling students to substitute a few zeros. Mathematical robbery.

I like to let the students struggle a bit with an equation given in standard form.  I simply ask them to graph it.  Ordered pairs don’t come as easily as they’d like.  The equation looks so easy – why is this “hard”? 😉  (Note: These algebra newbies haven’t learned slope-intercept form yet, so they tend to try to force x and y values into this function rather than rewrite the thing and “solve for y“.)

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Every year, someone realizes that substituting zero for and then zero for gives us two easy points to graph.  Ironically… those points park on the axes… now, the ideas of intercepts and using the “Cover-Up Method” to find them gain credibility and meaning. In my experience, simple, subtle twists like this should not be underestimated.  Student buy-in is a precious commodity.

How are you planning lessons to create the need for the mathematics you’re about to “teach”?  Please share – this is an aspect of my own practice where I hope to continue to grow!

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Giving graphingstories.com a Go!

Living vicariously through my student teacher, Lauren, we came upon the “Interpreting Graphs” lesson in Algebra, and I suggested that she give graphingstories.com a go.

Today, each class period had a brief discussion about the general usefulness of graphs, and how commonplace they are in the media.  Students shared some examples they’d seen recently.  We all agreed that this topic had value beyond the classroom walls.  Lauren presented some background and examples, as well as some graphing lingo that matched various parts of a sample graph.  This provided students with a “phrase bank” of descriptors like “increases rapidly” or “remains constant” as well as samples of both continuous and discrete graphs.

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Side Note:  I usually use this graph, but forgot to mention it to Lauren today.  This is the brain’s natural tendency.  This graph motivates me as a teacher BIG TIME.  When I do my lesson planning, I see this graph in my mind’s eye, and try to plan activities that keep students’ brains from the dreaded mid-lesson dip (not always successfully, I’m afraid).

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Next, students zapped this QR-code, which took them to this website Lauren found.  Surprisingly, it was iPad-friendly!  Sweet!

Using the tasks on the website, students had several opportunities to practice describing and sketching graphs for various scenarios.  Students presented their work to the class, and those who were extra proud of their graphs took screenshots and e-mailed them to me.

Enter graphingstories.com.  We saved the Graphing Stories PDF template in eBackPack for students to retrieve virtually and annotate using DocAS on their iPads.  Lauren displayed the graphingstories.com website on the big screen at the front of the class.

Which video do you think middle school students wanted to watch first, based only on a quick glance at the title screen?  You guessed it – Bum Height.

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Students found this task more challenging than both Lauren and I had anticipated.  Even though the seconds passing were noted on the screen, many students missed the idea that the graph started at time = 0, and that the little girl didn’t slide down right away.  Likewise, since the bum height was at its maximum height at time = 0, this threw students off; some expected to start their graphs at the origin rather than analyzing what each axis meant in this scenario.  Very interesting stuff.  Discussions ensued and we moved on to the next video.

The choice for video 2 was Distance From Camera.  While the general shape of students’ graphs was consistent, an interesting theme was that the “waves” touched down to the x-axis on the majority of students’ graphs.  We talked about how the video might look if it modeled a graph that touched the x-axis after every spin – not ideal for the cameraman.

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The last video we tried today was Ponies in Frame.  First of all, these 8th graders had to understand what the “frame” part meant – I’m not sure if they were looking for a literal picture frame or what… once we got that part straightened out, I heard the most awesome muttering as soon as the video began… “Oh!  I get it… this one’s discrete…”  We ran out of time and didn’t have the opportunity to follow-up on these videos in a manner we would have liked, but it was worth the visit to graphingstories.com today.

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Just keeping it real… it wasn’t all lollipops and rainbows… a comment laced with negativity that resonated with Lauren and me was an outburst that “graphing used to be so easy, and this just made it hard.”  How would YOU take a comment like that?  What does that comment say about the student’s true level of understanding?  Another piece of feedback was that the y-axis was shown in each video too quickly for students to label it on their own graphs prior to the video starting.  We simply pressed pause every time to take care of this.

 

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , | 10 Comments

Algebraic Proportions Relay Race (Thanks Fawn!)

Screen Shot 2013-10-13 at 3.48.18 PMI saw the “relay race” strategy idea from Fawn Nguyen  as she uses it to pre-assess students’ understanding of applying the correct Order of Operations.  I mentioned the strategy to my student-teacher, Lauren, and asked her if she thought it might work for an upcoming topic.

We decided to give it a whirl when solving algebraic proportions, and sneak a little rational operations review in the mix by asking students to do something extra to the solution at each phase.  This solution-plus-extra-operation we coined to be the “relay answer” for each problem.  Each row of 5 students had to find the total of all “relay answers” before submitting their row’s paper to Lauren or to me.

Watching the race itself was both entertaining and painful!  The pressure! 🙂  Students learned quickly that accuracy may be more valuable than speed, as first-finishers handed papers to Lauren and me for approval, only to be rejected.  If a row’s paper was given back, we encouraged the 5 students in the row to clump together and find the error(s) on their paper.  Rows were allowed to resubmit their papers.  The first row to submit a completely accurate paper earned bragging rights.

This was a worthwhile strategy to be sure!  At first, I worried that only 1 engaged student to 4 unengaged students might be an unpleasant ratio… but the anticipation and healthy dose of pressure due to the individual accountability this task ensured kept all students on their toes.

Here are two handouts Lauren designed.  They worked great!  For future tweaking, we thought about adding a column for students to write their names next to the problem they solve.  After class ended, we found several papers left behind on desks with telling errors as well as perfect work.  It would have been nice to know whose specific work we were looking at.  Though we hadn’t intended to collect the sheets after the race, having student names on there would have made this a better formative assessment worth collecting.  I think students needed more practice distributing negatives, so that may be an additional edit next time.

Proportions Relay Race!

Have you used a relay-race strategy?  What tweaks have you done to this strategy that made it more successful/informative?

 

 

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

QR-Codes and Classroom Prizes – Fun, Novel, and Free!

1QUIZptA wacky schedule is looming, and not every class will meet this Wednesday.  My clever student-teacher, Lauren, has decided to use the class periods we *will* meet with to design a little extra practice a-la Bingo games.

Today over lunch, we brainstormed about prize options, and decided to use QR-Codes as a novel way for students to select various prizes.  Here’s a sample we created, with directions to make your own custom “prizes” if ours don’t suit you.  Enjoy!

QR Code Prizes

My favorite QR-Code reader —–> QRafter

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Student <---> Teacher

Screen Shot 2013-10-05 at 8.41.41 AMI love hosting/mentoring a student-teacher.  This is the first time I’ve invited a student-teacher to my classroom at the start of a school year (versus having one in the spring semester) and I have to admit, I was unsure of how this might work.  I’m still getting to know these lovely 8th graders, build relationships with them, establish expectations, and set a firm foundation of mathematics for the rest of the year.  Would having a student-teacher this early in the school year cramp my style?

Au contraire.

Firstly, it has been priceless to have another set of eyes and hands early-on to monitor and discuss my students.  Getting to know these folks together and simultaneously has been nothing but a plus.  There are SO MANY TIMES while teaching that I’ve wished there was somebody else in the room to see/hear/experience what I’m seeing/hearing/experiencing.  Having two teacher-brains is better than one.

Secondly, detailed planning with someone else improves instruction.  I have tried certain resources and strategies in the past, and having another teacher take those ideas in different directions enriches me too.  It’s a joy to mentor and “coach” a fresh, willing learner, but all the while I’m refreshed too.  Together, we are making lessons better.

Thirdly, as I am taking a step back and handing my students carefully over to someone else, I am freed up to reflect and be more creative.  Thankfully, as I brainstorm ideas with my student-teacher, she’s willing to run with the ideas and make them happen.  I am making my own practice better by being her “coach”, and in essence, I am coaching myself to be better.  Sharing the teaching load with another person frees me to think more clearly, versus getting bogged down in ALL the grading, ALL the planning, ALL the e-mailing… those very necessary things that quickly fill our days also tend to zap reflection and creativity.  Well, I’m taking back reflection and creativity!

Selfishly, I get to have my cake and eat it too – I loved the role of full-time “math coach” in the past, but longed for my own classroom… MY students… when serving in that role.  Being a classroom teacher WITH a student-teacher allows me to keep one foot in the classroom and one foot as a “coach”.

As we move forward in the coming weeks, I look at the label “student-teacher” as one fitting for myself, and my students too.  We are all learners through this experience, and we’re all teaching one another too.  If you’ve never hosted a student-teacher… do it.  You’ll be better for it.

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