My 3 year-old asked to play a round of “Go Fish.” Apart from his tendency to ask if I have any sharks every time — whether he has any sharks himself or not — he has gotten the general idea of the game by this point.
As we started to acquire matching sets, I deliberately modeled 1 to 1 correspondence as I counted out my sets (ie, “Onnnnnnnnne” [while laying out the first card], “Twwwwwwwooo” [while laying out the second], etc).
And with probably excessive satisfaction, I watched as he reciprocated 1-1 counting with his own sets.
While starting to count one of his subsequent sets, I noticed that he missed the correspondence of naming “One” while simultaneously laying out the first card. And of course, as 1 to 1 correspondence requires us to understand that we can only count one number per object, I was ready to jump in to supply correction.
But, in that brief moment, sensing he was still working things out, I decided to bite my tongue and hold back. And I observed his quiet thinking: “Oh…wait, no…Onnnne” [while firmly laying out that first card again].
He’s already recognizing 1-1 correspondence for himself, thank you very much!
And I realized that I almost missed the whole thing with premature intervention — and more importantly, that he almost missed the opportunity to let his thinking catch up with his hands.
Sometimes, we just need time. I am reminded of this by the many teachers in my PLN who are choosing to slow down as they start the school year, allowing their students to settle into all the new routines, absorb all the new concepts, and build all the new relationships.
It seems to me that when we are too hasty with our learners, we’re often making it less about their learning and more about our fears (falling behind, failing to preempt problems, etc).
Most importantly, making a shift from hurried problem-solving toward reflective observing/questioning, we leave much room for inquiry, curiosity, and quiet thinking.
Think having students self-grade and reflect is fluff?
Think again.
Over the course of a 15 year study, John Hattie analyzed over 800 meta-studies to identify effects that have the strongest impact on learning (and he is constantly updating this list through continued studies). Self reported grades is almost at the top of the list of over 150 effects.
It beat out motivation. It beat out home environment. It even beat out “decreasing disruptive behavior.”
The truth is, students know a lot more about their own learning process than we so often give them credit for.
Which brings me to the issue at hand: When a student claims he/she “sucks at ___.”
When I hear that claim, I hear a student that has become convinced that their personal rate of learning is inferior to classmates. That because their progress has not looked identical to their peers, it must mean they are defective. That their learning is fixed, hopeless, and beyond theirs or anyone else’s reach.
Now, discouragement is normal for all learners from time to time. But when said discouragement is also rooted in learning that feels irrelevant or imposed, we’ve got problems.
Enter student ownership.
Any time we empower students with tools to take their learning in their own hands, we are giving them ownership.
Self-assessments are one such powerful tool.
Michael BondClegg recently wrote about giving students the opportunity to write their own report card comments, encouraging teachers to help students identify “ways in which learners can identify their strengths and areas for growth” and “plans for improving.”
This may seem trivial, but really, it turns the whole “I suck at” model on its head.
When a teacher fills out the comments, it perpetuates the whole “this is out of my hands” notion.
When a student is encouraged to fill out those comments in this way, it places the learning back in the students’ hands.
A student in diagnostics mode is student on her way toward a stronger growth mindset.
Many of us have spent just as much time in math courses as we have spent wondering the point of those math courses.
However, today, what makes mathematics most fascinating — that is, visual representations — are more widely shared and distributed largely thanks to social media. And perhaps this is how math teachers everywhere will at last be able to help their students understand “the point.”
Being more spatially-challenged in general, I always had trouble as a child comprehending concepts like mirror images, rotations, and geometry nets.
Fortunately, as a grew older, I learned that these are all just facets of broader concepts of scale and perspective. I’ve also benefited by recognizing their applications beyond mathematics–from art to city planning to interpersonal relationships.
So this week consists of a provocation to help our young learners begin with the big picture of scale and perspective, hopefully encouraging them to draw their own connections and conclusions.
The first is a fascinating video that lays out the entire history of the earth on a football field.
The second is a photo series by artist Matthew Albanese. He creates stunningly realistic landscapes using forced perspective, using materials from nutmeg to steel wool to fake fog. Head over to his site to view the collection of images, along with the incredible behind-the-scenes images and information on his process.
Provocation Questions:
How do people use scale and perspective to help us see “the big picture?”
How does technology allow us new possibilities to show scale and perspective?
How do scale and perspective change the way we see the world?
What is our responsibility to use perspective in our lives?
How are scale and perspective connected?
How does perspective help us understand other people?
If you, like me, have ever waffled on the debate of whether we “just teach them the trick” for math before, take a careful look at this side-by-side comparison of students showing their math thinking.
Example A:
These two samples are from the same student. Makes me think about what we prioritize, and about who else is hiding. pic.twitter.com/ePCfiEVVWK
My question is this: even if teaching the trick gets students to pass the test and ace the class and get into the college–have we, as educators, truly done our jobs?
If we’ve never heard their creative approaches to making sense of math because we’re too busy telling them the right way to “borrow,” have we joined them in their learning journey, or are we scripting it?
If we just keep focusing our energy in helping them memorize, are our students ever going to see themselves as competent mathematicians?
Many of us have a love/hate relationship with math. And depending on your students’ ages, they may have thoroughly convinced themselves that they hate it or are no good at it. If that’s the case, we have all the more responsibility to help our students see the bigger picture and the true beauty behind the numbers, starting with our own attitude.
via Network Osaka
This is easily the most phenomenal mathematics video I’ve ever watched. Share it with your students to provoke inquiry and appreciation for math–and at only 1:41 minutes, don’t be afraid to play it again and again as the conversation deepens and understanding sinks in.
The Daily 5 and 3 for literacy and math: perfect for addressing some questions I’d had on inviting more student choice and ownership. Unfortunately for me, my school adopted it the very year I began my extended parental leave. However, I was thrilled when I was invited to mentor a student teacher that fall, allowing me to still test out the Daily 5/Daily 3 waters for myself. And after a few weeks, the students and I agreed that it was a worthwhile change.
Meanwhile, not everyone at the school welcomed the transition with such enthusiasm. Some worried about not spending enough time on spelling. Others worried about students squandering time. Others were simply entrenched in their existing routines. If you are considering either program, here are some tips to keep in mind to foster a smooth transition.
Allow a LOT of training time
This is no joke. Most students have learned “school” pretty well, but that tends to be more of a teacher-directed perspective. The autonomy of evaluating how they need to spend their learning time is going to be quite novel for most of them. Take each Daily 5 or Daily 3 choice one at a time, emphasizing not only stamina, but metacognition to support their ability to reflect upon their own strengths and needs.
Use status of the class–especially starting out!
One of the recommendations in the current Daily 5 book for monitoring which Daily 5/3 choices students make is roll call or status of the class. It enabled me to track their choices and to offer brief feedback so they could learn to really plan their time well.
Many teachers I spoke with felt it would be too time-consuming to call out each student’s name for their response. However, after a period of training on this process as well (we even timed ourselves to make it a competition), we were able to finish in under 2 minutes. Especially for older students, over time, you may be able to eliminate this step and let students simply move their name or picture on a choice board (such as the example below).
via Sarah’s First Grade Snippets
However you decide to track their choices, avoid the temptation to regularly assign them to stations. This eliminates one of the fundamental purposes of Daily 5/3, which is to foster students’ ability to determine how they need to spend their learning time.
Make the schedule work for you
Don’t be intimidated by the way blocks of time are outlined in the book. Interruptions to the school day are almost always a package deal, but the good news is that Daily 5/3 are designed to be flexible.
If the time you have available for student choices time is a bit shorter than ideal, add one more Daily 5 block (without any whole group time) during the day for them to choose another station to revisit and catch up on. See the example schedules at the bottom.
Don’t skimp on wrap-ups
Despite the flexible nature of Daily 5/3, don’t skip the wrap-up! This moment of reflection is invaluable both for you and students to gauge the progress, problems, and successes.
Stagger the mini-lesson one day and assignment the next
If you don’t have enough student choice times for all students to get to a station that includes an assignment based on the mini lesson, simply give the assignment the day after the corresponding mini lesson.
Make an assignments board
Simplify where students should look for Daily 5/3 assignments (and possibly a reminder on essential agreements) by designating a bulletin board or a corner of your whiteboard. See below for a great example.
via The Daily Cupcake…A Kindergarten Blog
Don’t drown their choices with teacher-centered worksheets
It may be especially tempting in Math Daily 3 to make each of the stations different kinds of worksheets from the lesson manual. However, keep in mind that one goal for Math Daily 3 is to foster more hands-on learning experiences. Both “Math by Myself” and “Math with Someone” are intended for games and exploring math manipulatives (see next tip). “Math Writing” is appropriate for students to show their understanding on paper.
Create a running bank of games/activities for math
As students learn each new game or math manipulative activity, write down the title on a sentence strip. Then, for Math by Myself & with Someone, you can just pull out familiar games for new concepts (or for review, especially at the beginning of a unit). Examples:
This teacher has prepared gallon ziplock baggies of games ahead of time for partners to play together. Her examples are geared toward grades 2-4, but the concept is great because it reinforces having a bank of games the kids are familiar with. This would be a great parent volunteer activity!
Play with which Daily 5 and Daily 3 stations you use
Feel free to adapt which stations you use. For older students, you may want to eliminate “Listen to Reading,” and if your students blog, maybe they would like to add a “Math Blogging” station for them to create Educreations to display their math understanding online.
Get strategic with noisy “With Someone” stations
If the noise level is reaching a distraction for students in independent stations, seek out solutions as a class. For instance, they might find limiting the number of partners that can work during a block to be helpful.
EXAMPLES OF SCHEDULES/CHOICES FOR 2 DIFFERENT CLASSES:
