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Make Space for Grace

 

The new school year is now in full swing!
Why do I feel both exhausted and exhilarated?
These two seemingly opposite emotions have been my norm in recent weeks. 

The increased screen time required to do my job (and connect with my grown children, brothers, and parents during our Sunday night Zoom meeting) is, most definitely, more draining since I spend hours each day staring at a screen. 

On the other hand, the new opportunities for collaboration with colleagues (and my weekly family check-ins) has been an exciting addition. The amount I've learned about using digital tools is mind-blowing, and now that travel time between schools isn't part of the equation, I'm able to meet with more people each day. 

See what I mean - it's exhausting, yet exhilarating!

And, it seems, that I am not the only one feeling both overwhelmed and excited at the same time. We are all still getting comfortable with the new teaching models in place across the country --- some of us are using a new online platform, some a hybrid model, and some are trying to teach with social distance rules in place --- I don't have to tell you that it ain't always easy! If that's not enough, in my district, we are using a brand new math curriculum because we needed one that would transition to remote learning more smoothly. Couple that with the fact that most of us simply prefer in-person teaching and learning where we can assess the subtleties of the whole learning process --- you know, reading student body language, building a community of learners through all of the little things we do during the school day, and providing emotional support to individuals with a simple smile, nod, or kind word. 

Recently, a colleague reminded me that I need to give myself SPACE for GRACE. I was stressed because I didn't feel prepared to support my fellow teachers as they ventured into this strange start to the school year with a brand new curriculum (the instructional standards weren't changing, so that was a relief!).  She reminded me that I needed to give myself SPACE and time to learn what I needed to know and GRACE when I overburdened myself with a feeling that I should have known it "yesterday". I then found myself having the same conversation with dozens of colleagues who, like me, were experiencing moments of stress and panic because they are fantastic teachers who don't (yet!) know how to do their best job under their new circumstances. I found myself offering the same advice: Make Space for Grace

Here are a few ideas that got me started making that Space and giving myself Grace:

1. Recognize that I do not have all of the answers - heck, I don't even have all of the questions!
2. Be open to new ideas, new learning, and new ways of doing things - this openness will likely get me many of those answers that I do not yet have.
3. Collaborate - Let's not be alone during this time of "social isolation".  I will ask for help when I need it, and I will extend my hand when others need help.
4. Assess the content more critically - Which topics can students not learn on their own and will need greater support? Which topics allow for simple exposure, which need to be further explored, and which ones require full mastery? I can't do it all in a remote or hybrid model, so I need to make better decisions to ensure effective instruction. After all, maintaining high standards is not achieved by cramming the same work load into a smaller space at a faster pace. I must look for ways to ensure engaging levels of rigor without making students and teachers feel like they were run over by a 100-car train going 150 mph!
5. And finally, embrace the silver linings of the situation - sure, our current teaching model is not ideal for many reasons, but, I have started to notice so many things that are (surprisingly) even better than they were previously. What silver linings have you noticed? Embrace them!

Learn Something New This Summer

If you've ever received an email from me, you might have noticed that my signature tagline is 

"Learn Something New Every Day" 

I truly do live by that motto. I started using that tagline wa-a-ay back in 1993 (oh my! that's 27 years ago!). I was teaching a 3rd/4th grade combination class; my class joined me on a year-long endeavor to document something we had each learned every single day (including the weekends!). At the end of each school day, we would take time to journal what we learned that was new (usually students wrote about school-related learnings, but not always). On days that I couldn't recall a new learning for myself, I would literally open the dictionary and find a word that I did not already know. I wrote the word and its definition on an index card and then tried to use it in context at least three times on the following day.  I've come a long way from the dictionary with the invention of Google, Alexa, and Siri – but I STILL "look up" something new Every. Single. Day.

Summer is a fantastic time to learn something new. I hope to get the wheels in your brain churning by offering this starter list of ideas for you to consider – but please, don't limit yourself to just the items on this list – there are so many other learning opportunities that may be just the thing that'll spark your interest for YOUR Learn Something New endeavor this summer. 

EXPLORE

Mallows Bay in Charles County, Maryland

My husband is a great fan of history, so we often combine our vacation with learning something new about old things and past events. Don't judge... but when we visit an old historic town, one of the places we often end up is in the local cemetery where we look for the oldest headstone or we Google the names we find on an interesting headstone to see if we can find that person's history as it relates to the town we are visiting. If you're not into cemeteries, there are plenty of ways to explore and learn.  Last summer, for example, we kayaked in Mallows Bay to get a look at the old sunken fleet of WWI wooden ships – I definitely learned a whole lot of "something new" that day. 

BUILD SOMETHING / FIX SOMETHING

model of my next project

The truth of this story is I'm a little bit cheap and always up for a challenge. Two summers ago, our freezer was making terrible noises and we KNEW it was about a day away from just completely shutting down and leaving us with a freezer full of frozen goods that would eventually end up in the trash, so after the repairman quoted us a price tag of $80 to walk in the door and then any needed parts and labor would be on top of that, I went to the ever-informative YouTube and looked up "how to fix a noisy freezer".  I discovered a whole lot about the inner workings of freezer fans and condensation and how the two do not always get along nicely. The punch line of the story is my freezer has been working perfectly ever since and I knew just what to do last week when the freezer started making those same sounds again. 

• Repair bill: $0 
• Value of learning something new: Priceless (or at least 80 bucks plus parts and labor!)
• Next build it/fix it adventure: Learn to build an axe throwing target - yep, just for the fun and sport of it

READ

Whether it's fiction or non-fiction, reading is a great way to learn something new. It requires no suitcases to pack, no planes to catch, and you can travel around the world without even taking a day off of work. I learned a tremendous amount about the lives of elephants (which has been surprisingly impactful to my own life) by reading a work of fiction by Jodi Picoult called Leaving Time. I learned about the terrible wars of the 1980's and 90's in Sierra Leone in West Africa while reading Long Way Gone: Memoirs of a Boy Soldier by Ishmael Beah. Prior to reading either of these books, I never once thought about the powerful bonds within the elephant community or even knew about the terrible civil wars that impacted so many people in Sierra Leone (including young children).  Learn something new this summer by reading a book of your choice.

JOURNAL

How about learning something new this summer by journaling. In truth, I am not much of a journal keeper myself, but I do know that writing in a journal on a regular basis is a way that many of my friends and family learn more about their own thinking and feelings. My daughter (the writer) loves to quote one of her favorite authors, Flannery O'Connor, and I think the quote sums up the power of journaling nicely: I write because I don't know what I think until I read what I say.

PHYSICAL ACTIVITY

Photo by ZuBlu shared on GreenQueen.com

True confession: I have always wanted to learn how to climb and rappel - you know, going up mountains (or mole hills) with ropes and such and then using those ropes to bounce my way down the side of the mountain. Here's another truth: My husband is not fond of heights, so we never attempted this bit of learning. We always seem to gravitate to the water. We truly love all things water! We learned to kayak many years back and have been addicted ever since. We also love to snorkel, so we often take vacations that lend themselves to those types of events. This year, my husband is interested in learning how to scuba dive. Perhaps that will be my "something new" this summer – or maybe I'll stay home and finally learn how to make a proper crepe.

TAKE A CLASS – LEARN A NEW SKILL

Taking a class is an obvious way to learn something new this summer, but have you ever stopped to think about just how varied an experience taking a class can be? Sure, you can start working on your next degree by registering at a college, but you can also check your local Parks & Rec calendar for community classes in pottery, sign language, swimming, jewelry making, and so much more. Yes, social distancing may put a damper on those community-based classes, but you can also learn something new right from your smartphone like my brother who has been using Duolingo to learn Spanish for the past six months. You can learn to cook from Gordon Ramsay or join Chris Hadfield as he teaches you about space exploration on MasterClass.  I recently learned how to create a virtual classroom by watching a YouTube video (Thanks, Thomas Blakemore of Dubai). There really is no limit to what you can learn or how you can learn it.  In my house, for example, my trio of 22-year olds will be learning about financial literacy with the help of the book Personal Finance for Dummies by Eric Tyson; they'll also learn how to sew a button (with master instructor Mom!)

Whatever you decide to do this summer, be healthy, be kind, and be on the lookout for opportunities to Learn Something New Every Day.  

Learning UNplugged (screen time alternatives)

These are just a handful of the headlines I came across when I searched for articles related to screen time and our current pandemic situation. My district, like nearly every other district in the nation, relies on an online platform to deliver instruction and instructional materials during this learn-from-home emergency. We are producing some great activities that is helping to maintain continuity of learning, but I do worry that students are being asked to spend too much time in front of a computer – which comes with its own laundry list of concerns: eye strain, inactivity, passive engagement, etc....  In these uncharted times, let's embrace opportunities for whole families to engage in mathematical discussions and "thinking outside the (internet-connected) box". 

REFRIGERATOR DRY ERASE CHALLENGE

When I started this activity with my kids, all three of them said something to the effect of "Really, mom, you're not serious?"  But you wanna know what happened before I even left the kitchen? – they stopped rolling their eyes, slowly gravitated toward the numbers written on the refrigerator door, and became fully engaged in finding solutions. Getting started is as easy as 1-2-3!

1. Post 3 number cards on the refrigerator (I used randomly selected cards from our Phase 10 deck)
2. Write the numbers 1-20 with an equal sign and line following each one.
3. Put some dry erase markers nearby and watch the magic happen!

RULES for PLAY: You can only use each of the three numbers once per equation. You do not have to use all three numbers. All mathematical symbols are permitted. Proper notation for Order of Operations is, of course, required when needed. 

If your refrigerator is textured or filled with artwork, try the front of the washing machine!

Do you notice how this activity is well-suited to many readiness levels working together at the same time? I have played this with 7 year olds and 7th graders. For this home version, my college-aged son contributed to the board with square roots and factorial notation. I love that this activity has no time limits and isn't a competitive event (unless you want it to be). It reminds me of doing jigsaw puzzles with my auntie at the beach. Each summer, one of my aunts rents a beach cottage for several weeks where members of our family come and go throughout the week. She always has a jigsaw puzzle set up on the coffee table that we add pieces to as the week goes on. These refrigerator problems have the same sense of relaxed collaboration. When I put problems like this one on my refrigerator, my kids add answers as they think of them throughout the day/week until the puzzle is completed – and the refrigerator is the perfect spot with all the snacking happening these days. The first few equations are added very quickly, but as we get to the tougher numbers (like 19!), we find ourselves gathering around the refrigerator contemplating possibilities together – sometimes leaving it and coming back later, often times discovering the final solution together. Today I found my son (one of the original eye rollers), camped out in front of the refrigerator – he pulled a stool over and was all in. He is determined to find the last two solutions, 16 and 19, before the end of the day [update: It's 9pm and still no solution for these two remaining values].  

Maybe you know a solution for 16 & 19. Frankly, we're stuck.... Tweet your solution and tag me @HelloMrsCaine.  We'd love to see what you discovered. 

23 STEPS

A simple concept. Try to guess which things are 23 steps away.

The steps can be of any size, but all 23 steps must be the same size. So if you take "tiny mouse steps", all 23 steps must be "tiny mouse steps". 

This activity builds the mathematical understanding that when we change the size of the measurement unit (tiny steps vs. giant steps), the number of units needed changes (2.MD.A.2).

Once you've mastered this version of the game, try a modification. You might change it to a "how many steps" activity. Players guess how many steps it will take to get to the end of the driveway using regular-sized steps. Whoever gets the closest to the actual value wins! 

SIDEWALK MATH

Take your math play outside! Each week, I look forward to the Twitter posts of @traciteacher.  Traci Jackson has been engaging her neighbors with some sidewalk math since mid-March when most of the country's school buildings closed and we were advised to practice social distancing. When her neighbors emerge from their homes to get a bit of exercise, they are greeted with her sidewalk art as they pass her home. What fun it must be to live in Traci's neighborhood! To see the whole collection from @traciteacher, visit bit.ly/mathwalks2020.

EGG CARTON 10-FRAME

Another simple idea (this time focused on our youngest mathematicians) involves unitizing. 

Unitizing is an essential skill that extends well beyond primary school – beyond all formal schooling, actually. Think about the retail giant Amazon. Do you think they count items one by one? No. They unitize them on pallets and efficiently count the inventory in groups of 10, 120, 1000.... Learning how to unitize begins at a very young age and, like any other skill, it needs to be taught and practiced. 

Here's a simple idea for building skill in unitizing:

• Get an empty egg carton and cut off two of the sections to make a 10-Frame.
  I like to leave the lid on the egg carton when I cut off the last section allowing me to close the lid and hide the contents inside.
• Place objects in some of the spots - the items should be large enough to be seen easily (blocks, pom pons, etc.)
• Open the lid for 2 seconds. Close the lid. Ask "How many did you see?"
• After an answer is given, follow up with "How do you know there are (7)?"
• Child explains how they saw the seven (perhaps they used subitizing skills and saw 4 and 3 or 5 and 2 or maybe they saw that 3 spaces were empty and since 3 + 7 = 10, there must be 7 objects). 
• Reveal how many are in the carton. 
• Discuss.
• Play another round.

What variations could you make to expand this activity? 

Image Source: https://www.schooltimesnippets.com/

BEDTIME STORIES

Bedtime stories (or "anytime stories" for that matter!) are not reserved for building literary knowledge.  The next time you read a storybook, think about what mathematical ideas could be supported by the story or the pictures? There are many ways to incorporate mathematical thinking into story time. One approach would be to read the story all the way through, THEN go back to the beginning of the story and have a mathematical scavenger hunt. As you peruse the pages a second time, ask questions that support mathematical thinking, like "how many" and "which is more". When my children were small, they always begged to have books read again (and again and again). By approaching the second reading of the book from a mathematical standpoint, we interact with the book in a different way. 

Another way to bring math into the discussion during story time is to stop along the way. As you are reading, stop on interesting pages and ask a mathematical question about the story or the picture. These questions can be easily tailored to the child's readiness level – even when reading to a multi-age audience. 

Let's imagine that we are reading the book Where the Wild Things Are by Maurice Sendak. As you may know, this book was not written for the purpose of supporting mathematical thinking (like Even Steven and Odd Todd by Kathryn Cristald used in many 2nd grade math classrooms), but that shouldn't stop us from using Where the Wild Things Are to focus on numbers and patterns. Consider how these questions support mathematical thinking: 

• How many teeth does this Wild Thing have? Let's count.
• How many claws does this Wild Thing have on each hand? 
• Is that more or less than the number of fingers that you have on your hand? 
• Let's skip count to see how many claws the Wild Thing has in all: 4, 8, 12, 16.
• Which is more? The number of teeth the Wild Thing has or the number of claws? How do you know?
• What shape are the Wild Thing's teeth? 
• How many more buttons does Max need on his pajamas to have ten buttons? 

...So many possibilities - Have fun with it!

DAILY CALENDAR

One of the best things about the whole world moving to a learn-from-home instructional model during our current pandemic situation is that many educators and educational company's are sharing resources like never before! Most of them are free. I recently came across Zorbit's Math daily calendar. Honestly, I had never heard of Zorbit's Math before learn-from-home teaching forced me to seek alternative resources, and one of the things I found was this daily math calendar of simple things that families can do at home to support mathematical thinking. 

Click HERE to see the full May calendar of daily mathematical activities from Zorbit's Math Home-Learning Kit

GAMES THAT REINFORCE MATH CONCEPTS

On March 23rd, Mick Minas and his sweet child Nash started posting daily math games. The father-child duo demonstrate how to play each game. The games are great for building essential basic math skills. I look forward to the new game each day! You'll love his collection of videos; check them out on YouTube and follow him on Twitter @mminas8 or look for his Facebook page.

I just love the math practice that young Nash is getting every day playing games with dad. What an amazing opportunity this is for Nash!

• Go Fish! (Near Doubles)
  I have played Go Fish Make Ten and Go Fish Doubles, this version focuses on near doubles, too
• Combo Dominoes
  I just love this creative version - even played it with my nearly-grown children!
• 100 Laughs
  This one is delightfully challenging and requires participants to laugh once they make a sum of 100

NOW GO AWAY and PLAY!

I hope you found several great ideas that you want to try at home or share with others, but even more, I am hoping that you were inspired to look around and to find ways to incorporate math and math discussions in places that may, at first, seem unlikely. And yes... I get the irony of you reading a blog post on your online device that encourages you to get off your device to do more live-action math – so get offline and go find some UNPLUGGED opportunities! 

So You've Just Become a Math Teacher

...or perhaps you’ve been one for years!

With nearly every child across the globe working from home during the COVID-19 pandemic crisis of 2020, many parents are now working more closely than ever with their children in an effort to maintain a continuity of learning as best we can under the current circumstances. 

Whether you are a teacher in the classroom or a parent who is reading this during our current reality of learning-from-home, it is important to know that the way we respond to the math answers given by children plays a critical role in how they think about their own reasoning.

When learners make mistakes, it's almost a reflex to say, "No, that's not correct" – not because we are trying to shut down thinking, but because it's efficient. It saves time and energy and we do it as a way to prevent the learner from going down the wrong pathway of thinking. Saying "NO" is a great strategy when we need to prevent someone from touching something hot or walking across a busy road without checking for traffic, but... when it comes to learning, it is important to invest a few more moments of time encouraging learners to evaluate and justify their ideas.

Here's the interesting part: 
We can assess learning by asking the exact same questions whether the given answer is right or wrong. 

By asking questions that are reflective, learners engage more deeply with the problem and will often self-correct their own thinking when it's needed (this is powerful!).

Perhaps you're thinking, "Well, that's not very efficient at all – isn't it faster to just tell them that the answer is wrong and ask them to try again?"  Well, yes, that IS faster – asking reflective questions is not the most efficient path to let a child know that the answer given was wrong, but it is the ONLY path for helping to develop a true understanding of the math that is in front of them. 

The next time your child/student makes a math mistake, rather than saying, "No, that is not correct", try out one of these replies to promote deeper thinking and greater problem solving – We may be surprised at how much we can learn from a wrong answer.


Some reflective questions to try when discussing math with a child:

Exciting sidenote: I talked to a parent this week who couldn't wait to share that she tried this strategy of asking reflective questions instead of saying, “wrong”. She told me that she was nervous because she didn’t really understand the work her child was doing and wasn’t sure how she would be able to help. By the time mom and child were done, the child had a full understanding (and so did mom!). So... you don’t actually have to know the correct answer or understand the strategy that was used before asking reflective questions to gauge your child’s level of understanding (and that is just another brilliant feature of reflective questions!)

Closing Learning Gaps and Increasing Rigor Through Reasoning

If you've been following this blog, then you already know that I'm likely to tell a little story before jumping into the good stuff – I promise, I'll take you to the practical, usable stuff just as soon as I can.

THE STORY –  The way my math teachers taught me (back in the day) as compared to the way I teach young students today are very different models of instruction. One of the primary differences with the way we teach today is the emphasis on reasoning and not just focusing on correct answers. As I think back, I remember so many of my math teachers grading papers by simply laying a template over our papers and looking for the penciled in shading peeking through the punched out holes to determine if our answers were right or wrong – I also remember my very clever friend Mary sometimes marking two answers if she was unsure which was correct; she knew one of the two circles she shaded was bound to turn up in the grading hole on the teacher's template.

The problem with the method of instruction I experienced as a young learner of mathematics was – well actually, there are many problems with it – but two that come to mind immediately are (1) how could my teacher possibly use the powerful instructional strategy of error analysis to help me refine my thinking if all he was doing was looking for shaded dots and (2) how could he possibly know why I thought the answer was "C" if he didn't ask me to justify any of my responses? If you're thinking, "he couldn't", you're right!

By emphasizing increased instructional rigor through activities that require students to reason, we do a better job of closing learning gaps and can better prepare our students for the type of math they will do throughout their lives – after all, math in the real world is rarely multiple choice! 

The Department of Education in my state has recently refined the expectations for student-reasoning in mathematics. These newly designed reasoning standards do a nice job of reminding us to use a variety of task types to help students develop their mathematical reasoning skills. As I continue my own journey of learning how to better teach students to reason, I came across a quote from Michael Battista (Reasoning and Sense Making, 2017) that reminds me why helping our students to make sense of the math is so important to their mathematical development:

Students who achieve understanding and sense making of mathematics are likely to stay engaged in learning it. Students who fail to understand and make sense of mathematical ideas and rely on rote learning will eventually experience continued failure and withdraw from mathematics learning. 

Okay, so here comes the practical, usable ideas I promised you when you started reading....

Transforming Basic Operations into Reasoning Opportunities!

Below are specific examples of how we can transform a rote-type of mathematics question into one that requires students to use reasoning. For each of the four new MCAP reasoning standards, I have included one example of how to change "THIS" to "THAT". 

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Math Relies on Generalizations!

If you've met me in person, then you already know that I not only write about mathematics instruction, but I also love to talk about mathematics instruction (a lot!). With that said, it is very possible that you’ve heard me share this exemplum of my own experience before: 



When I was in 5th grade, I was asked to find the quotient of 8,024 ÷ 17. 

Would you be surprised to learn that I have never been asked to solve that same problem again -- not even once! (Probably not surprised, are you?). Back when I was learning about multi-digit division, I could have practiced and rehearsed to memorize the solution, but that would have used up precious storage space in my brain that could have been available for something else.

The truth is, we do not ask students to solve, memorize, and store things like the quotient of 8,024 ÷ 17 because good mathematics instruction focuses on the patterns and relationships of numbers, not just isolated specific elements. Good mathematics instruction is not about specializing, it is about GENERALIZING. 

Let's connect this idea to something a bit more universal in nature to illustrate the importance of generalizing even more: Every day, we turn on lights and open doors without much thought or effort. Opening the front door to your home is much like opening the front door to your friend's home, or the door at your favorite bookstore, or even the refrigerator door. We recognize value in generalizing the process of opening a door in order to apply that information to other doors that we encounter. The doors do not have to be in the same location or even open in exactly the same way. If we had to learn, memorize, and store information about how to open each individual door we encountered each day, we would spend most of our time just figuring out how to get inside.  


The importance of generalizing mathematical concepts is often an undervalued lesson. We either expect our students to automatically generalize information or we simply overlook the essential role that generalizations play in learning mathematics. We should introduce students to mathematical concepts beginning with things that are simple and then move toward the underlying generalizations in order to help our students better understand the patterns and relationships behind what they are learning. My own 5th grade teacher recognized (so many years ago) that the value of the lesson was not simply knowing that the quotient was 472, but rather, the value was in understanding the relationships of the numbers and generalizing both the process and my conceptual understandings so I could go on to divide any pair of values.

Before I share specific examples illustrating the importance of mathematical generalizations, I’d like to thank my wonderful thought partners and share a bit about our recent idea sharing session:

Every now and then I hear people talking about how they had an idea and scribbled their thoughts on a bar napkin. Well, my notes for this month's post are scribbled on a cardboard coaster with mathematical models and notes weaving in and out among the water rings caused by the condensation of my drink -- actually from my colleague's ice tea. I am at an educational conference this week and was thrilled to be surrounded by like-minded colleagues who were willing to talk about instruction as we tossed around ideas over a three hour dinner. Ideas were flying and I didn't want to lose a single one of them -- the napkins were cloth, so I reached across and grabbed Julie's drink coaster  😊 Thank you for being thought partners with me. I am grateful for the specific examples that stemmed from the wonderful academic conversations I had with Julie, Jason, Candace, Kristin, and others at the table. 


So let’s call this next segment "The Coaster Notes”
Below are a few of the ideas we discussed as we shared each of our ideas about the critical importance of mathematical generalizations. 

When we teach early skills in decomposing numbers, we are actually preparing students for subtraction with regrouping in later years. For example, students learn that 47 = 40 + 7 but 47 also equal 30 + 17. It is this second decomposition of 47 that will be essential when we are later asked to solve 47 – 28. The model shown below shows the progression of how 47 – 28 might be approached across various grade levels until students are simply using what we've come to know as the standard algorithm. Why didn't we just start with the standard algorithm? Well, it is important that student have a conceptual understanding of the process, so they can work more flexibly and fluently when using these types of calculations for real-world applications.

The work we do at the elementary level has far-reaching implications as students enter higher levels of mathematics in middle school, high school, and beyond. 

With every lesson we teach, it is critical that we help our students discover the generalizations that create the patterns and relationships of the mathematics they are doing. When a student notices that the sum of an even and an odd integer always results in an odd integer, for example, that student is generalizing. Generalizations allow students to think about computations independently of the particular numbers that are used. Without this, and many other generalizations made in mathematics from the early grades, all work in mathematics would be cumbersome and inefficient [CA Digital Chalkboard].

Assess how much you talk with your students about the generalizations of their math work. If you are spending a large chunk of instructional time discussing specific solutions, you are most definitely missing the proverbial boat! Mathematics is about the patterns and relationships of numbers - to see these, we must look for the generalizations that create them. Set a goal to increase the amount of time you dedicate to discussing the generalizations and less time focused just on correct solutions.