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.

SaveSave

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“.)

Screen Shot 2013-11-05 at 9.09.46 AM

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!

Posted in Algebra 1, Pre-Algebra | Tagged , , | Leave a comment

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.

Unknown

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).

unitag_qrcode_1382398182345

 

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.

Screen Shot 2013-10-21 at 6.53.04 PM

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.

Screen Shot 2013-10-21 at 6.59.14 PM

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.

Screen Shot 2013-10-21 at 7.10.28 PM

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

Posted in Algebra 1, Pre-Algebra | Tagged , , , , | Leave a comment

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.

Posted in Algebra 1, Pre-Algebra | Tagged , , , | Leave a comment

Pre-Assessing, Reviewing AND Teaching Using Socrative

My mission is to get my Pre-Algebra 8th graders ready for Algebra 1 next year.  I know that number theory concepts and vocabulary *need* to be mastered before things get too abstract.  I also know that some topics (which have been taught over and over again since upper elementary school) still escape these promising 8th graders I have the pleasure to teach.

How do I teach a unit on basic number theory when they SHOULD already know all that stuff… but DON’T?  I truly don’t have the time to spare, but how do I move forward?

Enter Socrative!

I created this Socrative (iPad student clicker) quiz as a means to activate prior knowledge, pre-assess, and get a rise out of my students today.

Screen Shot 2013-09-17 at 6.42.07 PM

Using the “Teacher-Paced” quiz option, only one question at a time was sent to students.  I logged in as the “teacher” (of course) and displayed my view on the big screen at the front of the class.  Initially, I hid the “Live Results” for each question, and when all students weighed in, I revealed the class bar graph to see how they did.  As they fell for my true-or-false tricks, they threw their hands in the air with joy as well as “I-should-have-known-that” reactions.  Make no mistake, it was an emotional experience!

Screen Shot 2013-09-17 at 6.42.44 PM

Screen Shot 2013-09-17 at 6.42.31 PM

As each question engaged students, my written comments after each question within the quiz itself served as a review lesson.  However, using iPads and Socrative to deliver the content, the desire to succeed and get an attractive class bar graph made the experience more like a game than a lecture.

Judging from our color-coded data reports, we didn’t have it all together the first time through.  It’s interesting to stack both data reports and note the similarly pink (A.K.A wrong) questions.  At a glance, I’d say we have quite similar results from both classes!  I do think we’ve cleared up some misconceptions.  Students didn’t realize that the quiz also served as a math lesson today.  The dialogue that happened between questions made for a custom lesson for each class, based on their needs in real-time.  LOTS of A-HAs!

Screen Shot 2013-09-17 at 6.36.34 PM

Screen Shot 2013-09-17 at 6.36.03 PM

Using this quiz was worth the 15-minute investment at the start of class FOR SURE.  How are you using Socrative?

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

Using ThatQuiz Before “THE Quiz”

My 8th graders are reviewing the basics… which happen to serve as a very important foundation for the rest of the year.  I sense some of them think they’ve got it all together.  Operations with integers?  Been there, done that.  I warn students that many common mistakes throughout the year date back to simple sign mistakes, so we want to get this thing right and save the bravado for another time.

Today, I whipped up a quiz using ThatQuiz.org and used it as a warm-up right before administering a “graded quiz” on adding integers.  Upon entering class, students zapped a QR-code which took them to our class ThatQuiz URL.  (Note – ThatQuiz is FREE, awesome, and allows teachers to easily set up password-protected classes, generates quick quizzes on all sorts of skills and concepts, AND allows teachers to design their own assessments.  Much love to ThatQuiz here.)  Students were prompted to log in to their individual accounts and take the (formative) quiz on their iPads while I spied on their real-time results on my own iPad.

Screen Shot 2013-09-06 at 5.43.12 PMI was able to intercept misconceptions before giving “THE Quiz” today – the “graded” one.  Without singling anyone out, I viewed incorrect responses, and addressed issues.  Several students were doing the negative-plus-negative-equals-positive gig, and doing a brief re-teach referencing yellow and red integer chips had several wide-eyed students going, “OH!”  Those same students aced “THE Quiz” today – the graded one.

It felt good to use data to intervene today.  Not every math concept is so cut-and-dry, but I hope to use ThatQuiz when I can, simply to throw one final safety-net to my students before an assessment that “counts”.

Here’s a ThingLink that organizes my class logins this year – a simple one-stop shop for students to access ThatQuiz by class period as I add more quizzes throughout the year.  How do you use ThatQuiz.org?

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , | 9 Comments

Simplest Inquiry Strategy Ever (Discovered Completely by Accident)

I presented the Distributive Property today in my usual fashion (pun intended).

First, I tell students that they already know today’s lesson, and that they’re going to prove to me that they already know how it works.

Then I present this image (I tell them it’s from my wardrobe):

Screen Shot 2013-08-29 at 6.12.42 PM

I love how this scenario never fails me – inevitably when I ask – not for the final answer, but the process and thinking that students used to find the answer, someone shares that they thought of “outfits”:

3(20 + 25)

…and someone else shares that they thought of shirts and jeans separately:

3 • 20 + 3 • 25

 

Lesson taught?  Not quite – but it’s a great little scenario to reference as the lesson unfolds.  We define the property formally and generalize using the typical a’s, b’s and c’s, and then we try an example or two.  Mind you, I’m sticking with numerical expressions today – we’ll revisit this property again later once we’ve worked with like terms.

Next, I present a typical numerical example:

Screen Shot 2013-08-29 at 6.39.13 PM

 

After we simplify the expression, I say,

“And right about now is when a student always asks me a question.  Who’s got it?”

Something quite unexpected and almost magical happened next.  Students had a sparkle in their eyes, almost a mischievous curiosity.  This statement challenged them.  And then, one by one, students started asking questions.  Lots of them.  It took awhile to get to the question I expected, which was, “Wait a minute – why all the arrows?  Didn’t we just do “order of operations” and the whole “grouping symbols first” thing?  Why this?”  Instead, I was inundated with a variety of questions that told me a LOT about student thinking.  I wish I would have recorded them all – I was so excited about what was happening that I can barely remember all the points they brought up.  And after every question, they asked me, “Was that it?  Was that THE question?”  It was fun to say, “That was a GREAT question, but nope, that wasn’t it.”  They ate. it. up.

When we finally got to the one question I was anticipating, students were already in a questioning frame of mind, asking,

“Wait – if we just follow “order of operations” will we still get the same answer?”

“Will we?” I put on my poker face (so hard for me!)

Everyone’s scribbling furiously, and students realize, one by one, that by Job, we DO get the same answer either way.  Discussions ensued about which method students preferred, which was the perfect segue to the homework – a parallel comparison which guides students to do each problem twice – once following “order of operations” and once using the Distributive Property – then prompts students to write about which method they preferred, and why they preferred that method.

This lesson was about more than the Distributive Property…

I discovered a strategy that I’ll keep in my back pocket forever.

At any point in any lesson, couldn’t we just tell a little white lie and say, “… and right about now is when a student always asks a question… who’s got it?”  

This prompt provides a safe place to question mathematics – after all, it’s about asking the question that some “other” student asked at another time in history 🙂  Somehow it made it very safe, challenging, and dare I say FUN to question mathematics today!

“Was that THE question?” 🙂

 

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

Nearpod Author, Part Deux…!

IMG_0758Just a quick post to celebrate my new role in the Nearpod Store – Thanks to @GuidoNearpod for the amazing opportunity, I’ve had the pleasure of creating and sharing my own “folder” of NPPs (Nearpod Presentations) with the world!

If you haven’t noticed, I’ve shared here on my blog the many ways that Nearpod has changed the way I instruct and assess my students.  Its all-in-one seamless approach to content delivery and assessment in real-time has helped my students get to know their own thinking too.

Humbled and grateful.  Thank you Nearpod, and thank you Guido!

~Cathy

IMG_0759

 

Related Posts Plugin for WordPress, Blogger...
Posted in Algebra 1, Pre-Algebra | Tagged , , , , , | Leave a comment