A big thanks to Jamie Forshey for inviting me to be a guest blogger! Check out Jamie’s blog, which is packed with great technology integration ideas!
Using @thinglink_edu as a pre-teaching tool bit.ly/1375fhB @mathycathy #edtech #mathchat
— Jamie Forshey (@edutech20) April 15, 2013
Actually “doing” math is a highly effective studying strategy… who knew? 😉
Kind of reminds me of an epiphany one of my former 7th grade students had years ago. The conversation went like this:
Him: “Mrs. Yenca! I finally figured out the secret to doing well in your class!”
Me: “Really?”
Him: “YES!!”
Me: “What’s the secret?”
Him (serious as a heart attack): “Pay attention!”
We are roughly a month away from the STAAR Algebra 1 E.O.C. exam, so I hope my students have been paying attention, and have bought into my mantra:
Me: “How do you study for math?”
Them, in unison: “You DO MATH!“
Here is a ThingLink I created to facilitate the “DOING” of math. It would be great to add other resources that are printable or iPad-friendly. Suggestions?
A fun aside… I encountered this doozy in a problem set from the Algebra textbook my students and I currently (rarely) use, and Tweeted my amusement…
For once, my (c) 2007 textbook is ahead of its time! How did they know about Minecraft in 2007 with this problem? twitter.com/mathycathy/sta…
— Cathy Yenca (@mathycathy) April 13, 2013
…to be met with pure poetry, over which I am still giggling as I type (you must click the link to Christopher’s wp blog to truly appreciate the poetry aspect):
Exothermic fauna: A surface area poem h/t @mathycathy, @absvalteaching wp.me/pAG7Q-HV
— Christopher (@Trianglemancsd) April 13, 2013
This annotating message is one I have heard loudly and clearly from my math students this year.
The 2012-2013 school year has been our first year with 1:1 iPads. As a matter of fact, as of this past week, every student K – 12 in our district now has an iPad! However, before we pursue pure paperlessness (is that even a word?) I must say that mathematics students are still pretty passionate about having at least SOME paper.
I have never made it an iPad goal to go paperless because my students still favor paper and pencil for most mathematics. I have to agree with them for some writing-intensive topics, such as solving multi-step equations. I asked my students today if I should have any “teacher-guilt” that I am not diving into the paperless workflow realm with their assignments and assessments. In unison, every class said, “NO!” If writing on the iPad slows students down, distracts from the objective at hand, or frustrates them, then it’s not being used effectively – and let’s face it, there are LOTS of ways to use an iPad beyond a vehicle for paper substitution (see, for example, my previous posts about revolutionizing assessment or problem solving with iPads). However, there are instances in my mathematics classroom where annotating PDFs is mathematically favorable.
1) Graphic Organizers
Any topic for which a graphic organizer is helpful is a great time to annotate. The ability to zoom in and out of a PDF makes smaller spaces on an organizer easier to write on and easier to see. Plus, purposeful color-coding beats a greyscale worksheet any day.
2) Quick Intro Activities
Sometimes I just want to make a quick point to my students. Sure, I could write it on the board or have students copy it down in a notebook, but such menial tasks can detract from an “A-Ha!” that I’m trying to facilitate. Most of these motivators have been one-page copies in the past. These aren’t meant to be collected or graded, so sharing a quick PDF gets the point across without the copies.
3) Extra Practice Resources
I like providing students with an abundance of resources, even if I never officially “assign” them. Giving students extra practice resources (often with answer keys) is a great way to share boatloads of information without killing trees (NO MORE “PACKETS”)!!! Students that choose to use the extras can do so on the iPad, or by referencing the PDF on the iPad and working the problems on paper. Or, as many do, they can completely ignore the fact that I just gave them some rockin’ resources and wait until they get a not-so-great test grade to start caring. But that is an entirely different blog post… 😉
4) Topics Requiring Less “Work”
Some math topics have a little less work than others. Perhaps these are opportunities to help students gain comfort with annotating a math PDF. For instance, we were adding and subtracting radical expressions today, and students had no complaints about annotating a PDF because the work they showed was minimal. When problems increased in difficulty, it was appropriate to mentally sort through what “simplest radical form” looked like – written work was at a minimum, and appropriately so.
One last thought – I think writing with a stylus on an iPad is a learned fine-motor skill that takes some practice and patience. Resistant students (and teachers) may find that, with time and practice, annotating PDFs even for math isn’t SO bad. Perhaps it’s just another small piece of the iPad learning curve?
Before moving to Austin, I had the pleasure of working with a team of teachers in the Bethlehem Area School District in eastern Pennsylvania that knocked my socks off. At the time, I was a Middle School Math Coach who spent time co-teaching with this amazing team of teachers on a daily basis (what a blessing!)
During the spring of 2011, we decided to conduct a “PSSA BOOT CAMP” with the 40-some students on the “team” (yes, this was before deep budget cuts that obliterated the middle school teaming model). Our “boot camp” consisted of four teachers, each of whom represented a branch of the military, and roughly ten students per military branch (so each teacher closely monitored ten-ish students). We dressed the part (see photo above) and really hammed it up, referencing students as “cadets” and ourselves as “Sergeants” – and those 7th graders ATE IT UP. Boot camp lasted for 5 days, and was structured as follows each day (one 45-minute class period per day):
* A physical warm-up (think push-ups or jumping jacks, done to a military tune)
* A “mission” (a test-taking strategy) which we modeled, both “effective” applications, and “ineffective” somewhat humorous non-examples
* Time to do a brief problem set to immediately apply the day’s “mission” (I believe we set a timer for 7 minutes, and monitored our 10 cadets closely)
* Accountability that the mission was accomplished (gathering student work samples to anonymously display to the class via doc cam for discussion)
At the week’s end, we had an awards ceremony, where every student was presented with a certificate. During the final week before testing, we focused on test-taking strategies and novelty, and hoped that our “missions” would stick!
Fast-forward to this past week – I’m teaching in Austin now at Hill Country Middle School, and have the pleasure of working with yet ANOTHER fabulous team of teachers who embraced the “boot camp” idea to prepare 8th graders for STAAR testing. It is so fun to work with students and staff who are willing to embrace a little role-play and fun! Our daily agenda has included an objective and a “mission” (strategy). Since every student has an iPad, we’ve conducted live-data daily homework spot-checks using Socrative as well as individual quizzes using Thatquiz.org. We used a TAKS Prep workbook as our resource for practice problems. Our daily agenda has been:
Objective 1: Numbers & Operations problem set (only had half the period to explain that we were beginning “STAAR Boot Camp” so Day 1 was cut short with no test-taking strategy “mission”. We did, however, play loud military music, wear camo, and march while distributing the TAKS workbooks to set the tone!)
Objective 2: Algebraic Reasoning problem set; Mission “Scrap Paper”
Objective 3: Geometry problem set; Mission “Multiple Choice”
Objective 4: Measurement problem set; Mission “STAAR Chart”
Objective 5: Probability & Statistics problem set; Mission “Key Words”
Objective 6: Math Processes problem set; Mission “Griddables”
Every day started with a Socrative Teacher-Paced (formative) homework quiz. I would call out a specific problem number, and students sent me their answer choice for the multiple-choice problem at hand. I connected my iPad to the projector and kept the “live results” bar graph hidden from view until all students had weighed in. When I displayed the live results, we crossed our fingers and hoped for that beautiful picture of a unanimous, tall bar above the correct answer choice! Sometimes we got it… other times, we cringed at the sight of a bar graph nearly evenly split between all four answer choices. This instant data provided great discussion and brief-reteaching opportunities.
Next came the day’s objective and mission. We’d ask students each day to first provide examples of the day’s mission, such as multiple choice test-taking strategies, effective uses of scrap paper, defining variables on the STAAR reference chart, and identifying key words in problem statements. Each of the three of us teachers would then chime in with additional tips and examples of the day’s mission.
Then, a problem set was assigned to the class. Students were given 5 minutes to work silently and individually, then 5 minutes to continue working with a partner. Students were also expected to apply the day’s mission specifically as they worked. After 10 minutes, we brought the class back together and used the Random Name Selector app to select “random reporters” to share problem solutions.
To hold students individually accountable throughout the week, I created brief quizzes using Thatquiz.org. Every other day, students had a quiz on two objectives (objectives 1 and 2 served as a quiz, objectives 3 and 4 served as the next quiz, and so on).
As students quizzed individually, we teachers watched their live quiz scores from the teacher login side of thatquiz. We could click on student scores and see which problems they were missing. After all students completed the quiz, we were able to briefly address the mistakes we observed behind the scenes on Thatquiz. Careless errors in arithmetic and reading comprehension were repeat offenders!
The iPad was a tremendous help during Boot Camp! While we didn’t always like the data we saw… its real-time-ness helped us address concerns and guide our students very specifically and intentionally. We’re hopeful that the errors that happened during “camp” help students be more careful during STAAR testing next week!
My Algebra students will begin a mini-unit on square-root functions after their exponential functions test on Monday. Here is the “anchoring activity” they will explore when finished with the test.
I can’t stress enough how helpful it is to have a tool like ThingLink available for those weird class times when some students are finished, others are still working, and a new unit is on the horizon. Creating ThingLinks helps “pre-teach” so I can do justice to a new lesson the day after a test. It’s a “mini-flipped” lesson, and I plan to continue creating and utilizing ThingLinks this way.
Added bonus: students return to each ThingLink as an interactive study guide toward the END of each unit, and can cumulatively review all ThingLinks to prepare for end-of-the-year exams.
Here you go – Square-Root Functions 101!
And when your students are ready to tackle “Simplest Radical Form” here are some resources to help them with fluency and to facilitate communication and collaboration!
Simplest Radical Form “Bundle”
Curious about ways to use ThingLink in the classroom?
Check out this doc for more ideas!
Several weeks back, I had the pleasure of eating at Chipotle and consuming every bite of my usual chicken burrito with white rice, black beans, fresh tomato salsa, and “a little bit of cheese and sour cream”… and then I noticed the cup containing my beverage with a beautiful counting principle claim that there are “60-some thousand flavor combinations at Chipotle”.
I posted the cup picture on Twitter as a teaser, and my brother, who is a Chipotle aficionado, immediately chimed in, sending me a screenshot of the menu he sees when placing his daily lunch order online. He sent the menu image because it was much more comprehensive than the menu typically displayed in the restaurant. I could see a math story unfolding, so I created a Keynote slide with images of my cup, a Chipotle menu as displayed in the restaurant, and the online menu image my brother sent to me.
Enter 8th grade students who are ready to learn about the Counting Principle.
To assess prior knowledge on the spot, I asked students to solve a simpler problem that I fabricated. They clearly had an understanding of the topic, and decided the claim made by the “Build-Your-Own-Sub Shop” was fair – no suing for false advertisement this time. 😉
But could we sue Chipotle (well, not REALLY sue… but that 60,000+ claim seemed a little bold to us!)
Students got into pairs and small groups, and scanned the QR code shown below to access the Keynote slide I designed. My question was posed quite simply – is Chipotle telling the truth on my cup? (They would have preferred to add… if Chipotle is not telling the truth, can we sue for false advertising?)
Groups assembled and conversation ensued. Everyone in the room was craving a burrito. Students initially came to me with all sorts of questions, but my answer every time was posing their own questions back to them. After awhile, they gave up on seeking me as some seemingly all-knowing-question-answerer and owned their own problem-solving. Students used their iPads and an assortment of drawing apps and calculator apps to defend their claims.
Initially, most students came up with totals well below 60,000. Many students simply multiplied 4 • 6 • 2 • 3 • 3 • 9 to get 3,888. They referenced the digital menu and counted the white square “bullets” next to the menu items, multiplied them together, and voila – most popular first answer of 3,888.
After seeing this total numerous times, I pointed out the heading above the “Toppings” list… “Choose MANY Toppings”… OH!!! Students started realizing that they weren’t limited to choosing just one of the nine toppings, and totals started increasing.
I’ll be honest – at this point, I’m not sure what the final answer is supposed to be. And I am not alone (see here). Some other folks talked about doing a similar activity but never mentioned a final answer such as a post here. My purpose was never for students to get ONE definitive final answer anyway. I wanted to help facilitate a real-life discussion on a mathematics topic that every student could relate to, and have them thinking and defending their mathematics. Perhaps the mathematics needed to truly solve this problem surpasses a simple counting principle lesson, but the lesson students learned was that real-life math can be messy, takes persistence, and can be quite rewarding to defend! Check out a quick video to see some excerpts from my classroom.
Just a quick blurb to share my excitement! My very first Nearpod Authors presentation is currently available in the Nearpod store!
Download it for free on a mobile device near you!
Thanks also to Nearpod for the mention on the Nearpod Community blog here !
Up to this point in my career, I haven’t really questioned my procedures for grading homework. This year, our staff has been challenged to think about assessment in terms of learning… are we assessing student learning, or student behaviors?
I am still working this out. I need help from others to continue to gain perspective. My hope is by the fall of 2013 I will have a solid homework system in place. Right now, I am still bobbling around, seeking opinions and research, all specifically with mathematics content in mind… because I believe when it comes to grading (or not grading) homework, the content area, specifically with respect to mathematics, can’t be ignored.
I started some dialogue several months ago here, and really enjoy reading different ideas from other math teachers in the trenches. Some of us seem solid in our systems, not questioning whether homework is assessing learning of content or behaviors. Yet, I wrestle with not only *how* to “grade” homework, but whether “grading” homework in math is even fair at all. So, here are my “before and current” homework grading procedures. I’ll follow up with “potential future” methods I’m tossing around.
“Before & Current”
Up to this point, I have graded homework primarily based on completion. There. I said it. And it goes a little somethin’ like this:
3 points: Student legitimately tried every problem, with evidence of work, even if there are errors (This is the first chance to practice a new skill or concept, after all… are we expecting perfection at this point? This is part of the reason I think “grading” homework in math seems inappropriate).
2 points: More than half but not all problems legitimately attempted
1 point: Less than half of all problems legitimately attempted
0 points: Homework not done or not present at due date/time
To encourage math communication, students get into a “homework huddle” at the start of each class (small groups or pairs of students comparing and discussing homework answers, seeking resolutions for discrepancies). While students “huddle” I take a lap around the classroom, glance at student work and listen in on dialogue, recording scores as mentioned above. We come together as a class, I either ask for answers verbally, display the answer key, or use a tool like Socrative or Nearpod to spot-check specific problems. Generally, questions are minimal after a “huddle” since students help one another talk through and correct errors or misconceptions. This process helps me know if I need to do a little reteaching before moving forward as well. To put the homework “grades” in perspective, my current district chooses to weight homework as only 10% of students’ average… which tells me, whether I choose to “grade” it or not, it’s not worth very much. At only 10% we don’t seem to value homework as a “grade”, do we?
So why “grade” it at all? (Am I being devil’s advocate, or posing a legitimate question?)
“Potential Future”
A feasible method to “grade” homework in such a way that scores reflect learning of math content, not behaviors, could be as follows:
* Assign daily homework, as in the past.
* Facilitate a daily “homework huddle,” spot-check work, and listen to conversations.
* Display answer key, or use an app to do a quick check of specific problems.
(So far, nothing in the plan has changed… wait for it…)
* Don’t assign a homework score for each and every assignment. Rather, give a weekly homework “quiz”, perhaps every Friday. Problems on this quiz would be inspired by homework problems, but wouldn’t be the exact same problems. Allow students to use the homework they completed throughout the week as a reference during the quiz (this would hopefully provide incentive to do it, now that actually recording a score for every assignment has been taken away).
* “Grade” the “homework quiz” knowing that students have been practicing on a daily basis, have communicated with one another about the concepts, and have had reteaching classroom opportunities.
Ultimately, if I opt for the “homework quiz” philosophy, I’d like to utilize an app to help with the actual grading or scoring. Socrative could help, but because students can accidentally press the wrong answer choice, it’s not ideal for graded assessments in my experience (I REALLY REALLY hope they change this issue soon because I love their instant color-coded data reports so much!) I am looking into The Answer Pad as an option, and Infuse Learning looks promising, though I prefer apps that don’t require the teacher to manually enter student/class info.
What are your thoughts? Is the “Before & Current” plan acceptable? Should we aspire to assess mathematics over behaviors and embrace a plan more like the “Potential Future”?
Please discuss, and thanks in advance for reading and for your input! 🙂
This post was also shared here.
Happy Pi Day!
At 1:59 my inbox was flooded with Pi Day greetings from my students… who are currently on spring break! Some students sent e-mails from destinations with differing time zones. Most students aimed for 3/14 at 1:59, and a few chose to send me greetings around 3:14.
Before break, I held to my tradition of giving every student this Happy Pi Day greeting card. Students inevitably attempt to memorize the digits of Pi… and the winner this year memorized a whopping 65 digits in no time at all! Though we all understand that this task is highly impractical 😉 it was fun and impressive to see how quickly students could memorize SO many digits! Too bad they didn’t see this video beforehand (how clever is he?)
FOLLOW-UP!
An inspired student studied pi over spring break – check out this amazing feat!
To see additional resources I’ve used to celebrate Pi Day over the years, check out this post. Cheesy Pi Day videos with cheesy Pi Day songs are included. 😉
I didn’t learn about ThingLink until a few months into this school year… and now, I’m hooked! Every unit of study since, I’ve created an interactive ThingLink for students to reference as an anchoring activity, study guide, and “pre-teaching” tool. As my students are currently basking in spring break relaxation, I’ve been preparing this image to help them get focused on the morning that dreaded alarm clock sounds after 9 days off!
I love that ThingLinks can provide instant differentiation too. Some students may prefer to read the text I’ve included, while others go straight for the video and Prezi links. Certain students may benefit from tutorials and the follow-up problems that hold them accountable, while others may find the visual images on the Keynote slide itself helpful, especially the graphs… which brings me to a huge shout-out to Desmos! Not only did I use Desmos to create the graph and table images here, but I also graphed the 4 functions (color-coded to match the ThingLink images) and included a direct link to my graphs for students to explore! Usually when folks ask about a good graphing calculator for the iPad, I say, “Be careful, kids can’t use the iPad for testing so they need to know how to use a *real* graphing calculator…” BUT… there is SERIOUS value in using Desmos for instruction! Color coded graphs… iPad-friendly… AND, you can graph things ahead of time and create an instant URL great for sharing the graphs quickly! Go Desmos!
My hope is that the brain-friendly strategy of showing students information in multiple ways helps prepare them for actual instruction and assessment… which hasn’t even happened as of their first interaction with a ThingLink such as this. As a matter of fact, I allow students time to explore the image, then go around the room asking each of them to tell me one thing they learned… inevitably, students practically teach quite a bit FOR me!
Any great iPad-friendly links that would make this ThingLink even better? Send ’em my way!
Curious about more ways to use ThingLink in the classroom?
Check out this document which is jam-packed with ideas!
