Fluency, Concepts, and the Order of Things

Posted on September 9, 2018 by Cathy Yenca

I’m back in the groove with a fantastic new-to-me crew of learners, spending short snippets of time on Twitter… and neglecting to blog!  It’s time to hammer down several threads that resonated with me and recent experiences with my own students in this mash-up post.

 

Knowing Order of Operations would be part of my own review with students, and likely a topic in many mathy classrooms, I shared “Twin Puzzles”.

 

I also shared another strategy to address Order of Operations – combining the famous Four Fours with Nearpod to capture and share students’ favorite equations that they believed no other student had come up with in our class.

 

Then, I caught this problem (both the math problem and the problem with the way a teacher seemingly used this math problem as a gotcha, causing students to second-guess their own math ability, making for a rocky start…)

 

And… this plea that there is no excuse to mention Aunt Sally… please!

 

Additionally, Dan Meyer’s recent blog post and thread on Twitter seems to speak to all of our Order of Operations discussions.

 

Whether you call it PEMDAS, GEMS, Order of Operations, or something else, the Order-of-Things procedure becomes extremely mushy to students… even though the “rules” don’t change, the problems do.

What have students looked like in my class who possess procedural fluency but lack conceptual understanding?

Students perceive these problems as being “wrong” because “multiplication comes before division” and “addition comes before subtraction”.

 

Students stop dead in their tracks at this problem, wrestling with their knowledge of number properties, and whether to distribute the 4, or subtract 5 – 7 first.

 

Students ask, “How do I know whether I should distribute first or follow the correct order of operations?” for a numerical expression like this, without realizing that BOTH methods lead to the same, correct answer, OR, that distributing first might lighten the load.

(Note: I created this activity with this premise in mind – that students don’t generally realize the result will be the same either way, or how to decide when distributing might be more efficient, and when Order of Operations might be more efficient.)

 

Students insist on doing the “grouping symbols” first in a problem like this, even though the parentheses only contain a single value.

Is it our use of mnemonics like PEMDAS or GEMS that have contributed to students’ confusion?  Is the solution to add context to these “naked problems”?  Do MORE problems, so that more exposure to lots of problems helps bring clarity?  I appreciated these questions on Twitter as well… as teachers sometimes we know what we SHOULDN’T do, but we’re not sure what TO do, especially when students have similar misunderstandings year… after year… after year.

And a final thought: Every misconception and question students ask that reveals some level of procedural understanding without conceptual understanding is a learning opportunity. What THEY do next and what WE do next matters too!  There’s no formula for how to handle these “teachable moments” with our own students.  However, fostering a classroom culture that values questioning, mistakes, and exploring multiple methods flexibly and respectfully is a great start.

Speaking of great starts, I hope your year is off to one!

And, if you want to explore many, many, many perspectives on fluency versus conceptual understanding, you’re in for a ton of food-for-thought here.

UPDATE:  And… folks are still discussing…!


 

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

Too Mathy, Too Techy.

Posted on August 8, 2018 by Cathy Yenca

Every time I attend a conference, I have a mini identity crisis.

When I attend math conferences, I thrive on the content and pedagogy shared.  It’s amazing.  My brain is filled with strategies and tasks that inspire and equip me to be better.  However, sometimes I feel “too techy” because I can’t help but run low-or-no-tech strategies presented through my own experiential tech filter to think of ways I might implement the tasks/strategies differently in a 1:1 iPad environment.

When I attend ed-tech conferences, I’m inspired by the capabilities of new tools, or ways to use familiar tools more effectively.  While we all can agree that there are ed-tech tools out there that are complete junk, many also have huge potential.  However, some tools with amazing potential leave me scratching my head… how could I use this in a math classroom?  Or even… I wouldn’t use this in a math classroom… too contrived… doesn’t apply to *my* content area.  I feel “too mathy“.

True Confessions:  Probably over a year ago, maybe more, pals on Twitter requested that I share about how I use Apple’s powerful tool, Keynote (cue the angelic voices from on high) to create math visuals.  Folks wanted to know, how do you make this stuff, Yenca?  I was invited to share on Global Math about Keynote creations for math… and I ducked out!  I felt like my sharing would disappoint people… that Global Math wasn’t the right place to share about this… that my sharing would be “too techy” for an environment that was “too mathy” to value what I’d planned to showcase.

Given that I’m still perseverating about this (ha) I’ve wanted to find a platform to share what I didn’t share on Global Math that day.  And… here it is!

I’ve just published a brief, FREE-for-the-taking eBook entitled, Using Keynote To Explore Math Relationships Visually.  It’s designed to be a quick, practical read for teachers, with the hope of extending math-visual-creating to our students too.  I address *WHY* math visuals are important, and *HOW* to use some nifty features in Apple’s Keynote to create and even animate math visuals.  I include examples for inspiration, and shout-outs to those who have created and/or implemented the use of math visuals, including Jo Boaler, Annie Fetter, Kyle Pearce, and Sara Vanderwerf.  Finally, I challenge you, yes you, to CREATE and SHARE math visuals that promote student discourse and conceptual understanding.  I suggest using the hashtags #KeynoteForMath and #EveryoneCanCreate to tag your goodies on Twitter so others can find and use them too.

Grab the book here!  I’ve also added it to the sidebar here on my blog (scroll down to see it) –> so it’s easy for folks to find.  Because, you see, it’s okay to be purposefully mathy and techy. 🙂  Thanks for letting me share about something I’m passionate about, AND I enjoy creating, and stay tuned for more by checking out the aforementioned hashtags.

Posted in Algebra 1, Pre-Algebra | 2 Comments

The Mind-Blowing Power of a Global Community of Educators: #ADE2018

Posted on July 25, 2018 by Cathy Yenca

Fun Fact: That’s the Capital of Texas Highway, which takes you right to my house!

Every time I try to sit down and compose a blog post about last week’s Apple Distinguished Educator Global Institute… I can’t.

It’s not that I don’t want to!  I *literally* can’t type the words.  Even with every letter in the alphabet and every word in the dictionary, anything I attempt to share here will fall short.

How can I convey here the feeling I had when I walked into the first general session, realizing that nearly 400 educators with hearts like mine from nearly 40 countries were gathered there?  When I saw the back of the ballroom, and all of the telephone-booth-like contraptions all lined up, filled with global translators so that *every* educator could be a part of the conversations happening in that room, I was literally overcome with a wave of emotions.  Humility.  Anticipation.  Excitement.  Pride to be a part of such a unique community.

Through workshops facilitated by ADEs and Apple staff, we learned so much from the best of the best at Apple.  So many powerful feature updates with huge potential for creativity!

We collaborated in teams, brainstorming and offering feedback on our passion projects.  Familiar faces reunited, and new friends made in an instant that, without this opportunity, may never have crossed paths.  The focus – creativity.  A search on Twitter using the #EveryoneCanCreate hashtag won’t leave you disappointed.

A few of many, many highlights for me include:

Stephanie Thompson’s 3-Minute Showcase: Using ‘Equity Maps’ to empower students with relevant, accessible, and meaningful data.  You don’t want to miss this one – talk about “seeking students who hide” taken to a new level!  INSPIRING!

Working with “Homeroom 56” to brainstorm, share ideas, and begin working on our creativity projects. What a fantastic bunch – instant friends!  Here’s our ice-breaker video, exploring creativity in light of having access to so many tools and features.  Rather than get overwhelmed, we decided, to get started, it’s important sometimes to simply #ChooseOne.  The advice to “simplify, simplify, simplify” liberated us this week.

Activities in ADE Central, including “Expert Labs” where we could learn and receive feedback in a smaller-group setting about all sorts of Apple tools.  Light-hearted competitions like “Battle Mania” where folks dueled on the stage to share the most interesting tips and tricks brought many a-ha’s and a lot of laughs!

Rooming with my colleague and pal, Lisa Johnson!  Though we work in the same district right here in Austin, we’re at different campuses serving different roles, so having the chance to chat and debrief was a great opportunity.  She also compiled an amazing blog post of resources and ADE events that you should check out!

The Lobby Piano Concert Crew.  With a focus on creativity, and a piano in a cozy corner of one lobby area, singers and musicians alike couldn’t resist a good sing-a-long.  You’re looking at a group of us that stayed up singing 3- and 4-part harmonies until 3:00AM… for perhaps 5 consecutive hours?!?!  I think it’s safe to say that none of us teaches music as our profession, yet a common interest had us all sacrificing sleep for the opportunity to share our creativity through music – real piano, real voices, but technology close by to provide lyrics and chords.  What a blast!  I’ve added a few songs I forgot that I love to my HomePod favorites playlist, thanks to this bunch… and so many others who aren’t pictured here, who opted to sing for a time… and ALSO get some sleep! 😉

My favorite part of all?  The continued conversations and collaborations that keep happening even though our time together in Austin is over.  Brainstorming on Twitter, sharing ideas, taking action on things we said we’d do, offering and receiving feedback, and continuing to build professional friendships is what makes this a community, versus several days of excitement.  The Institute is AMAZING… but the global after-party is what really keeps us all moving and shaking.

Thank you for allowing me to be me.  A tweet by Jennifer Gonzalez was so timely this week.  She shared a post from several years back with an epic title:


I can completely relate to that blog post!  It’s powerful to be in a place personally and professionally that I take pride and joy in embracing the title of ‘dork’.  When my pal Michael Mills shared this photo he’d taken of me, rather than want to hide under a rock, I celebrated my positively dorky self, and all of those whom I’ve befriended who would also wear the dork title as a badge of honor.  Be joyful.  Have passion.  Trying too hard to be cool is just plain boring.

I mentioned that ADEs were charged with a project, so here’s a sneak peek at the work I’m doing. I’m working on an opportunity to share through an eBook about my love for math visuals, Apple’s powerful “presentation tool” Keynote, and combining the two as a creative outlet that’s supported by brain research… be on the lookout for the final draft!  Fun fact: I used the new Drawing feature in Keynote to trace over a video of my own eyes, creating an animation that’s truly personal!  Another note: I placed quotes around the words “presentation tool” when describing Keynote because I find that most other “Keynote Dorks” use Keynote for everything! Sometimes “presentation creation” is the last thing we do with this most versatile tool (though it’s GREAT for presentations… but it’s also GREAT for so many other things… visualizing math conceptually being one of those things!)

So, reading this back, it falls short of describing the whole experience, but I guess that’s how it’s supposed to be.  So many conversations, big and small.  So many ideas and friendships.  And thanks to all sorts of social media, our conversations never stop – we’re just getting started!  Maybe you’re curious about becoming an Apple Distinguished Educator and you’ll apply next year?  In the meantime, you and I can enjoy the continued sharing by searching through the hashtags below.

#AppleEDUchat, #ADE2018, #EveryoneCanCreate

Sincerest thanks to everyone who played a role in planning and executing this Institute!  Your hard work and intentional planning were apparent in every experience!

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

Summer 2018 Plans & Goals

Posted on June 21, 2018 by Cathy Yenca

Since today’s the Summer Solstice, I hope you’re officially enjoying your break.  I won’t rub it in that our students’ last day of school annually is prior to Memorial Day.  Whether you’re just getting used to that alarm clock NOT going off, and eating and peeing whenever you’d like, sans bells, or if you’re just learning how to NOT wake up at regular school time, surely you’re thinking about the 2018-19 school year.  What you want to do the same because it went AWESOMELY well in 17-18… and what you’d like to change… and professional conferences… books to read… and oh ya, VACATION.

Here’s my summer, in 7 chunks.

(1) Conferences

Yes, we dressed alike. On purpose.

Our school district hosted iPadpalooza for six years, and has re-framed it (in beta this year) as LearnFest ATX. Rather than our usual global crowd of 1000, we had a smaller, mostly local crew of 300 this year.  The name of the “Learning Festival” shows the shift away from a device toward a focus on learning.  I had the pleasure of presenting a session with our high school math department chair, Nadine Herbst, featuring Desmos Card Sorts as a way to promote collaboration and communication.  You can find our resources here, which were inspired and created by many of YOU! Thanks, as always, for sharing awesome activities!

I’m looking forward to the Apple Distinguished Educator Global Institute next month.  This year, rather than welcome a new class, alumni from (literally) all over the globe get together for a week of unmatched PD and collaboration.  Can’t beat the location this year… they could have chosen any city in the world… and they chose…. AUSTIN! 🙂

(2) What I’m Reading

I’ve had this Mathematical Argumentation book in shrink wrap for TOO long, so it’s on my list.  I read Denis Sheeran’s latest book, Hacking Mathematics, in two sittings.  It will be great to reference next year!  Our math departments at the middle school level are doing a summer book study on Taking Action, using Google Classroom to respond to questions and one another.  I’m loving it!  And, I’m reading Ready Player One with my sonny boy as our own little book study at home.  We each have our own bookmark, and debrief regularly.  Saw the movie first.  Kind of glad about that, as I don’t think book-first-movie-second is commutative in this case.

(3) What I’m Wrapping My Brain Around

Those who DON’T TEACH often seem to think that our so-called “summers off” are our greatest perk.  I disagree.  The fact that we have the chance to start NEW and FRESH every year is the BEST PART!  We can try new things, fail at new things, and succeed at new things.  We have a clean break right now to make any change or adjustment to our practice that we want to!

I was reminded about “lagging homework” in Hacking Mathematics and took to Twitter.  Conversations and ideas abound in this thread!  I’m trying to figure out a “transition plan” for myself and my students.  Not sure how this might look yet.

Desmos Computation Layer, you are amazing.  I had every intention of sitting down and learning you by brute force, but that’s not working out.  I think I will watch and re-watch these kind webinars by CL Guru Mr. Chow.  For me, the key is creating a need within an activity FOR the CL, and I need to understand more about the capabilities before I create something and give it a go.  BABY steps.

The amazing Sara Vanderwerf shared this blessing of a post, and I’m on a mission to more intentionally include Stand & Talks in my classroom in 2018-19.  Here’s how I’ve started planning!

 (4) Closing My Rings

You know, teaching is a physical sport!  In the summer, when that sport comes to an abrupt end, I have to be intentional about staying active and fit.  Last September 18, it clicked for me that I should be “closing my rings” on my Apple Watch every day.  So, that’s what I’ve done (with the exception of that bout of the pesky flu when I commissioned my son to wear my watch and run laps for me, as I had a high fever and literally couldn’t peel myself from the couch).  It’s important to take care of our bodies AND our brains.

(5) Travel

All the blue pins on my mini-map show where I’ll be traveling this summer.  I’m happy to report that some pins are for “work” but most are for “pleasure”, vacationing and visiting family and friends.  I’m looking forward to riding some roller coasters (my summer OBSESSION) and soaking up some Gulf Coast rays.

(6) Crafty/Mathy Projects

I am a maker.  During the school year, most of my “making” involves designing math lessons and resources.  In the summer, my maker skills usually involve crafts, paint, and weird experiments.  Take my most recent project.  I’ve been tossing empty make-up compacts into a box under my bathroom vanity for… probably 3 years?  I took the time to count my collection (I’ve had an up-cycling art plan all along) and was surprised at how many I’d saved!

Went to the craft store to find something to attach all of these mini-mirrors to, and found a wooden square I liked.  Spray painted it, loved it.  Had NO IDEA it would end up being a 5-by-5 square… I was just trying to create a new art piece for my classroom.  Then it hit me… PYTHAGORAS!!!!  Phase 3 of this project is currently on hold until I use up a bit more face powder.  I’m all outta empty compacts.

(7) Oh Boy

My biggest goal each summer is to maintain my status (see images at the start of this post).  It’s a BLESSING to be able to have the same schedule as sonny boy.  The 2018-19 school year will be his last year of attending the middle school where I teach, so I need to soak up this time THAT I WILL NEVER GET BACK.  P.S. He’s turning 13 next month, and the fact that my son will be a TEENAGER is a bit surreal.  So proud to be his mom.  AND, I’ll be celebrating 19 years of marital bliss, blessings, and occasionally a healthy-level of bickering with the one and only Mr. Yenca.

LIFE IS GOOD!  

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

MathyCathy… from the mean streets of Fraction Town…

Posted on June 17, 2018 by Cathy Yenca

Thanks to @jennifuhs4, I was just made aware of this gem.

I hope you enjoy it at least a fraction as much as I did.

BWAHAHAHA!

Mathy Cathy makes an appearance on Bob’s Burgers

Posted in Algebra 1 | Leave a comment

An Integer Game

Posted on May 26, 2018 by Cathy Yenca

I first experienced some form of this activity with the amazing Dennis Ebersole in a workshop years ago.  When we played the game, if memory serves me, the goal was to provide a motivating way for students to practice integer addition.  (Or was it? One thing I learned from Dennis, through his constant modeling, was that the tasks he provided to teachers had layers that were up to US to discover.  When anyone asked him any sort of question, he giggled, shrugged his shoulders, and sometimes said, “I don’t know..?!?”)

Back to the game.  Here’s how we play.

The game board is simply a grid with integers and an “x” to mark the starting position.  Choose the integers you like.  Next, we need two teams.  A spokesperson who can handle the pressure of making a team decision in spite of potential disagreements is essential to classroom sanity. 🙂  One team can only make horizontal moves, and the other team, vertical moves.

Let’s say horizontal movers arbitrarily go first.  Starting at the “x”, the team gets to decide which number in that row only they’d like to have.  That number represents the points earned by their team.  (Note: Sometimes students realize in this moment that we need to establish how a team wins this game.  Most points?  Least points?  Closest to zero at the end?  They come up with a lot of creative ways to win.)

For this example, let’s say the teams establish that the MOST points at the end wins the game.  So, team horizontal chooses the 7, and earns 7 points.  Now, that 7 is used up.  Done.  Circle it and keep a running total of points earned.

Now it’s team vertical’s move.  Since the other team chose the 7, team vertical must choose an available number in that column only, and they’ll receive that number of points.

Being new to this game, that 9 is probably pretty tempting.  So, team vertical chooses the 9 and earns 9 points.  Back to team horizontal we go… and either BEFORE team vertical chooses that 9, or just AFTER they do… everyone is realizing that there’s a bit more strategy to this thing than they realized at first glance.  (Remember when I said each team needs a spokesperson for classroom sanity?  That’s to preserve YOUR sanity, teacher! 🙂  That spokesperson has to make each choice based on team feedback, so you know who to listen to for the final decision on each move.  Let’s just say this gets passionate. FAST.)

Eventually, either every number is used up, or a dead-end occurs and the game ends.  I like to play at least ONCE as a whole-class activity with a spokesperson for each team, and then have students play in pairs.

Fun Things That Often Happen

Sometimes, it doesn’t occur to either team to establish how we win.  This can get very interesting when it comes to strategy.  One team starts aiming for the biggest numbers, and the other team aims for the smallest numbers… with every turn, students confuse their opposing teammates with their point choices, and mid-game, someone finally says, “Why are you choosing those numbers?  Wait, does the SMALLEST score win?”

“Does it?” say I (and Dennis would be SO proud of that response).

It’s also really cool when teams make up unusual rules for how to win.  The other day we played, and several students had an idea.  They thought we should find the mean of the two final team scores at the end.  Then, look at how close each final team score was to this mean value.  The team whose score is closest to the mean score, wins…

… and so we follow this victory rule… and the teams TIE!  Not with a nice value, but each team is exactly the same convoluted decimal distance from the mean!  It’s a miracle!  How did this happen?!?  The class goes BONKERS and wants to play again, under these same circumstances.

And I am biting my tongue and practicing my best poker-face.

We play again, and AGAIN, a perfect tie!  This time, the distance each team’s score is from the mean is less obscure, but it’s the SAME! Again!  Are we amazing, or what?

Wait for it…

“… wait, Mrs. Yenca.  Will this happen EVERY time?!?”

What do *YOU* think?  

How do you know?

School’s out for summer for me… but is it for YOU?  Give this integer game a try, and share any new strategies you or your students come up with!

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

Desmos Pet House: A Linear {and Not-So-Linear} Project

Posted on May 20, 2018 by Cathy Yenca

It all started with this tweet, and the rest is mash-up #MTBoS history.  Thanks to all who shared and shaped the final draft of this project!

Math 8 students set a firm algebraic foundation for linear concepts.  Included in Math 8 Texas TEKS are the following Readiness Standards:

  • 8.4(B) Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship
  • 8.4(C) Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems 
  • 8.5(I) Write an equation in the form y = mx + b to model a linear  relationship between two quantities using verbal, numerical, tabular, and graphical representations 

Mom Brag: My colleague also used this project with his Math 8 students. Here’s my son’s creation!

To prepare Math 8 students for future linear studies in Algebra 1, Desmos Pet House, a math-meets-art-meets-coding project, began as a seemingly simplistic graph paper sketch.  However, the open task proved to be a “low floor, high ceiling” experience that whisked students into the world of linear functions, linear inequalities, restrictions on the domain and range, and even animations!  Desmos provides a platform for instant visual feedback for the algebraic “code” students wrote.  

The Project in a Nutshell:

  1. Students sketch a “pet house” rough draft using graph paper, labeling the slopes of all line segments on the sketch.
  2. After draft approval, students gain access to a Desmos activity where brief tutorials help them explore new graphing skills.
  3. Students recreate the draft “pet house” using linear function “code” in Desmos.

As my Math 8 students explored and discovered how the mathematics they wrote impacted the math-art they created, their hunger for more math extended the due date for the final project repeatedly.  They didn’t want to stop!  Thanks to the teacher dashboard in the Desmos “Activity Builder” platform, students could view one another’s projects in progress as they worked during class, creating a constant collaborative atmosphere of, “How’d you DO that?”

After exploring restrictions on the domain and range of linear functions using Desmos, students met the linear expectations of the “pet house” quite quickly.  However, the project didn’t end when students met the minimum requirements.  Rather, students wanted to include nonlinear elements in their houses, shade various regions with color, and even animate their pets!  Essentially, students had created their own “problems” when they designed their houses, and through research and experimentation, they solved the problems that they, themselves, had created.  Ownership win!

To access the project description, rubric, and Desmos Activity where students will ultimately create a “pet house”, visit this link.

To see project showcases for each class, check out the videos below!  Each video showcase was created exclusively on my iPad using Apple’s Clips app.  I took screenshots and screen recordings of student work from teacher.desmos.com, right on my iPad, and used this media to create the #ClassroomClips.

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UPDATE! Desmos has added the ability for students to add an image to a full-screen graph in Activity Builder! I still like the idea of giving students a folder of pets to start with, but adding the element of choice will surely up-level student projects, moving forward! Maybe they’ll even use photos of their *actual* pets! 🙂

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

Desmos Breakout “Escape Room” Activities = Amazing Review

Posted on April 28, 2018 by Cathy Yenca

At several teacher workshops over the past few years, I’ve experienced “Escape Room” tasks that married the novelty of “breaking out” with academic content.  SUPER FUN!  This idea was on my never-ending “TO DO” list of things I’ve learned and would like to try with students.  And there the idea sat, on my list…

…until RECENTLY when I learned about Jay Chow (@mrchowmath) and the way he connects the idea of “breakouts” with math content using the Desmos platform.  Already made.  Ready to go.  Boom.

First, I worked through his linear and quadratic escape tasks, filling pages of notebook paper with work I’d anticipate my students might do.  I love how Jay addresses paths in his activities for those who might make a mistake along the way, as well as the variety in the tasks themselves.  SO FUN.  I decided to use the quadratic activity with my Algebra 1 students, and the linear activity with my Math 8 students.

I created student groups, and generated several Desmos activity codes so each group in each course had a different code.  I didn’t want student groups to know that they were all doing the same task… at least initially… I also didn’t TELL them what the code was for.  To add a bit to the “drama” of introducing these “Escape Room” tasks, I stuffed envelopes with old, one-sided worksheets (to be used for scrap paper, not to do the worksheets… would students actually just start working on random worksheets that didn’t even align with any math we’d been learning?).  Also in each envelope was an index card with student group members’ names, and that mysterious “code”.  I wrote the name of one group member on the outside of each envelope as well as #BREAKOUT.

On launch day, I started class by standing at the front of the room, announcing that some students “got mail”.  I called the students to the front to receive the stuffed envelopes, and the buzz was immediate.  What is Mrs. Yenca up to?  What is this “mail” she’s giving to us?  Is she going to call my name?  They know me, and started grinning and hypothesizing.

Students with envelopes were instructed to wait until I gave the word, and they were to open them simultaneously.  They found the index card with student names on them, and realized that #BREAKOUT was a huge clue about what we were about to do… 🙂

Then, just like that, student groups got together, started typing the mysterious code into various apps, eventually trying it in student.desmos.com with success.   And… some groups just started doing the math worksheets!  I didn’t let this linger long… I stopped by their groups and said, “Some groups found a code in their envelopes… did you get one too?”  “NO WONDER! I WAS WONDERING WHY YOU’D PUT WORKSHEETS IN HERE THAT HAVE MATH ON THEM FROM YEARS AGO!!!”  I let them know to use the back of the worksheets to do any figuring and they chuckled and got right to work!

Can I capture the energy in the room and convey it accurately to you here?  Nope.  I wish I could.  It was REALLY SOMETHING!  All I can do is encourage you to work through these awesome tasks yourself, launch them with your kiddos, and get ready for high energy, determination, and JOY!!!

P.S.

How does Mr. Jay Chow create this Desmos magic?  I think it may have something to do with this… and boy, do I have a LOT to learn!


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Posted in Algebra 1, Pre-Algebra | Tagged , , | 7 Comments

Play Kahoot! and Downplay the Time Factor

Posted on March 6, 2018 by Cathy Yenca

Lisa Bejarano and her apprentice teacher Eric recently shared insight on work-arounds while students play Kahoot! for math.  I loved reading these ideas, as those of us who have used Kahoot! in math class may have experienced the following:

  • Students making a fast choice without reading the choices at all
  • Students getting caught up in the leaderboard MORE than the MATH
  • Students feeling unnecessary pressure because the clock is ticking

However… I’d be willing to bet you may have ALSO experienced the following:

  • Students communicating mathematics, arguing and justifying their choices
  • Students realizing and fixing math misconceptions in real time
  • Students engaged and having a whole lot of fun

For me, the positives outweigh the negatives here if we’re intentional and strategic… as we should be for every tool, high-tech or no-tech, eh?  Lisa and Eric’s clever work-arounds make Kahoot! an effective platform in math class, and I’d love to piggy-back on their ideas with a few more, including Kahoots! that you can use or tweak for your own students.

Build in reflection time

I like to pose more in-depth math questions by using TWO questions in the Kahoot! platform.

QUESTION 1: Consider giving students the maximum time allotted (120 seconds) and creating answer choices that aren’t ANSWERS, but are reflection statements about confidence in one’s solution, or method choices for solving the problem.  Make this initial question worth zero points.

Then, in QUESTION 2, provide a shorter timeframe for students to choose an answer for the VERY SAME QUESTION.  Since the teacher ultimately controls the pacing, even when students need more than 120 seconds, delay advancing to the next question as long as needed.  Consider having discussions before providing students with the opportunity to see the answer choices.

Example: Algebra: Write a Linear Function

Example: Algebra: Solve Linear Equations in One Variable

 

Keep the math visual

Visual math ideas work BEAUTIFULLY within the Kahoot! platform.

Asking students to identify and interpret attributes of graphs can serve as a great pre-assessment, mid-lesson check-for-understanding, exit-ticket… you name it!  Students feel confident that they can complete visual tasks in a shorter timeframe, so they work well within the platform.

Example: Algebra: Graphing Linear Systems

Example: Algebra: Attributes of Quadratic Functions

 

Use Socratic Questioning to TEACH concepts

Rather than use Kahoot! as a “quiz” or “assessment”, consider using it as a platform for posing questions that guide students to understand concepts incrementally.

Here’s an example that helps students visualize the difference of two squares by asking strategic questions, combining the questions with meaningful visuals, and scaffolding concepts along the way.  Teach by asking questions that include EVERY student, and have discussions before advancing to the next question.

Example – Algebra: Difference of Two Squares 

 

Use multiple questions to “chunk” multi-step concepts

Rather than ask students to cut-to-the chase and solve a problem within the Kahoot! platform, ask about one concept at a time, making each question a building-block toward a greater goal.

Example – Algebra: Systems of Linear Inequalities

Example – Algebra: Solve Quadratic Equations

 

Do you use Kahoot! in math class?

What are some additional tips you have to use Kahoot! more effectively?

Please share in the comments!

Check out other creative strategies for effectively using Kahoot in math class shared by Laura Wheeler here.

AND… Scroll up to check out TEKS-aligned math Kahoots in the sidebar for both Algebra 1 and Math 8! —>

Posted in Algebra 1, Pre-Algebra | Tagged , , , , | 35 Comments

Using Socrative for… You Guessed it… Socratic Questioning

Posted on January 21, 2018 by Cathy Yenca

My Math 8 students have discovered and applied the Pythagorean Theorem.  Our next move this week was to address the following standard:

8.7(D) Determine the distance between two points on a coordinate plane using the Pythagorean theorem.

“The book”, being a static resource, included diagrams where a diagonal line segment already had perpendicular reference segments… and the step-by-step work… which, of course, had the Pythagorean Theorem as the first step.  Static resources can inevitably provide static lesson spoilers too.

I wanted to create a journey for students, providing information incrementally, asking questions along the way, while giving EVERY student a chance to weigh in at each step.

Socrative was my tool of choice here.  The super-clean interface for asking questions and eliciting responses is often my go-to.  I love their Teacher-Paced option, so that I can pose and display one question at a time from the front of the class, and I can hide responses until everyone has weighed in.  If I want to know the specifics about who-answered-what, I have a detailed report for that later.  In the moment, I’m often less interested in knowing who said what, and more interested in seeing the variety of responses, and overall progress AKA class percentages.  Sometimes too much detail in the moment makes the lesson experience feel clunky.

So, students entered class, joined our Socrative “classroom” and began by answering two “low floor” questions (graphs created using Desmos.com).  Piece of cake… except some students DID count incorrectly, and commented on how, next time, they’ll consider coordinates and/or look at a nearby axis to confirm their counting abilities.  THEY came up with these little tips.  Sweet!

I could hardly wait to send out the next question.  I anticipated the looks on their faces ahead of time… but their reactions are generally even better than I anticipate.  Furrowed eyebrows, various thinking sounds like, “Huh…”  “Wait… what?”  and a handful of students who transitioned to… “I think I know what to do here…” and “OH! I totally know what’s going on!”  Scanning the classroom and just watching and listening… I mean… SO FUN.

Some students simply estimated, others guessed correctly, others tried relating this experience to finding the slope of a line, and others knew EXACTLY why the distance was 5.  We’d also experienced Pythagorean Triples in class (as well as THIS particularly emotional YouTube video) and I strategically chose the most familiar triple so that the students who made the connection could do so mentally.  The big idea here wasn’t necessarily about showing WORK or needing to grab a CALCULATOR, but seeing RELATIONSHIPS.  Simple dimensions were important for that.

Students who had made the connection celebrated quietly – they knew a secret that others didn’t yet.  Rather than encourage a class discussion at this point, I quickly moved to the next question.

At this point, some students were about to burst with excitement, and others were super curious… what did these confident students know that they didn’t know yet?

Next question…

My typical “curse of knowledge” surprised me a bit here.  In every class, the correct answer choice percentage ranged from 79% to 85%.  I thought I’d nearly spoiled the lesson at this point, but in every class, some students were still working through why I’d provided this additional visual information…

During this mushy spot in the lesson/warm-up/whatever you want to call this 15-minute Socrative experience, I heard a lot of what I call “The Sound of Learning.”  Lots of grunts and a-ha’s… all happening at DIFFERENT MOMENTS.  I get the privilege of actually seeing and hearing each student go from not knowing to making connections.  Such a JOY!

To be sure I didn’t miss anybody, I provided another experience just like this one, using 5-12-13.  Question 1: What’s the distance? Question 2: How confident are you about your answer?  Question 3: Right triangle time.  SWEET.  Check out THAT percentage.

And just for good measure, I asked once more.  No Pythagorean Triple this time.  No guiding questions.  Just find the distance.

Much more meaningful than a lesson spoiler!  If you would like to use this Socrative resource, here’s the link:

https://b.socrative.com/teacher/#import-quiz/32367596

What other math concepts do you think lend themselves to Socratic Questioning rather than spoiling-by-telling?

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