“Where did the 850 cans come from?” I was in the middle of sharing the iReady enrichment lesson (14) with my fourth graders when one of them asked me this question.
Have you ever had a student ask a question in order to postpone learning? If you’re a teacher, then that’s a silly question. Of course!
This is one of the few things that I remember from my elementary and middle school days. It was a thrilling challenge to try to come up with just the right topic or question that could throw the teacher off track.
We would hope and pray for a story. Then, we would artfully flatter and ask questions that would lead our pedagogue down the rabbit hole of memories, further and further… away from the lesson at hand.
Fast forward forty years. Today’s students still play the same tricks on their teachers! This past week I was engaging some fourth graders in math enrichment, when one of them tried steering me off task. Little did they know, that I practice Pedagogical Aikido.
Redirecting Energy
Aikido is a form of martial arts that is known for using an opponent’s energy (ki) against them. Masters of this study practice redirection.
Although I have not formally studied Aikido, I love its principles and attempt to use the philosophy of redirecting thought and energy within the walls of my classroom as much as possible.
For example, the other day when my student asked about the origin of the 850 cans in our math problem, I allowed the student to think that he had derailed the lesson. I told him that this was an excellent question. “850 cans is a lot of cans. Where would a school get that many cans for a fundraiser?”
The martial art Aikido uses a triangle to teach the redirection of energy. There are three components that work together to use an opponent’s attack against them, saving your energy and neutralizing the situation. It all starts with Balance, known as tachi waza (Aloia, 2020).
“How many students does our school have?” I asked the class.
I could have squashed the student’s inquiry, telling him something like, “I don’t know where the number of cans came from. It’s hypothetical. Let’s just move on!” Or, “It came from Curriculum Associates, the authors of our math program. Don’t ask silly questions.”
If I had done that, I would have disrespected the student. A dismissive teacher or one who blocks the question head on is too hard, too strong; the lesson too one-sided. By allowing for the question in the first place, and then entertaining it, I had my center of gravity low to the ground. My metaphorical feet were spread wide apart and knees bent. The question didn’t topple my lesson. I was balanced.
In answering my question, the students were surprisingly accurate. Our school has around 700 students. “How many cans would we have if each student brought in one can?” I prompted. That was easy. “But, not every student will bring in a can… And, some will bring in more than one.” The easy back and forth of these simple concepts established a flexible, down to earth ease of thinking. It also revealed the problem. We don’t know where the 850 cans came from.
Next, it was time to Break Balance. This is the second part of the redirecting-energy triangle. “The opposite of balance is imbalance, or kuzushi. To break an opponent’s balance, one must first redirect their energy to one’s own advantage” (Aloia, 2020)
I shouldn’t be surprised, but I was very impressed, nonetheless, at how quickly my students figured out how many classrooms our school had. It was the advanced fourth grade math students receiving enrichment, after all!
I had begun the imbalance kuzushi by getting the class to come up with the total number of classes in the building. After figuring out that our school has five classrooms per grade and our school teaches six grades, if you include kindergarten, we discovered that there are 30 classes represented.
“Let’s say that our school collected 850 cans. How many cans would each class bring in?” The students had no clue where to start.
Antonio Aloia (2020) explains that kuzushi has two arms. The physical off-balancing of an attacker, parrying the opponent’s strike and redirecting the momentum of the assault, coupled with a strike of their own is what one normally thinks of when imagining Aikido. Um, of course there isn’t any literal physical contact with students, let alone “attacks,” but presenting this new problem of dividing up the number of cans by the number of classrooms was a cogitational assault of sorts.
The other arm of kuzushi is a psychological off-balancing. This is where a martial artist would “Distract a would-be opponent by bringing their attention to something else, be it an object on a building or something farther away and behind the opponent” (Aloia, 2020). Pedagogically, this happened when I changed the student’s original question from “where” to “how”: “Where did the cans come from?” turned into “How could a school come up with so many cans?”
While the martial art of Judo involves throws, Aikido keeps your opponent tight and controlled. Perhaps counter-intuitively, it is concerned with the well-being of the attacker. So, rather than toss my students aside to flounder with the problem of dividing 850 by 30 on their own, I guided them through the process of figuring out the answer.
I asked them how many cans there would be if every class brought in 10 each; 300. “Okay, maybe that was the first week of the fundraiser. If each class brought in another ten cans during the second week, how many cans would the school have collected?” We were up to 600 cans. They were starting to catch on.
One of the students used Google to divide 850 by 30. Rather than scold him, I asked him if it were possible for any of the classrooms to bring in .333333 of cans. This was a silly question. “What happens with the remainder from the division answer?” I asked. They didn’t know. “For our purposes, we will assume that the students from every classroom brought in 28 cans. The teachers brought in the rest.” My students were okay with this explanation.
The third side of Aikido’s redirecting energy triangle permeates everything. It is ki or energy. Don’t think of it as power or force, though. Ki is more like momentum.
“How big are our classrooms? How many students are there in a classroom?” I got several answers on this. We decided to use the number 20. “Let’s say that a quarter of the students don’t bring in any cans. If the rest are responsible for bringing in 28 cans, how many brought in two and how many brought in one?” My students just looked at me. I told them to try and figure it out on their own, and then I’d show them.
One student crushed it, and I had her show the class what she did. Then I modeled drawing a picture to solve the problem.
After all of this, I told my students, “Now that we have collected all of these cans, we need to put them in something to bring them to the food pantry that we are donating them to.”
“If Dylan went out and bought a bunch of boxes… Thank you Dylan! (Dylan is all smiles at this point; He may or may not have been the person to ask the question that started all of this;) And, if Dylan’s boxes are all the same size, holding six cans each, how many boxes would Dylan have to get?” I let them wrestle with that a little while.
When I was prepared to let them demonstrate their math on the board, I turned to the slide that had the original question on it. They reread the word problem as I decided on who would come forward to share their work first. A few students groaned and some others called out. “That’s the problem we just did!”
“Yeah?” I feigned ignorance.
I used someone else’s name when I told the story about getting bigger boxes; Ones that held 8, instead of 6 cans. “How many of those boxes were purchased?”
As it turns out, we never got to fully explore the last question, but a couple of students tried solving it in their heads. I had completely Aikido-ed them! Lol.
Redirecting energy can be an even more effective motivator than a cool lesson. Take their energy, spin it around, and use it against them. Students will feel like they’re in charge of their own learning, and in a way, they are!
The other day my elementary school had an assembly. When it was over, a fourth grade class was left with no teacher. She had attended a meeting that was running over. Since I didn’t have a class at the moment, I decided to bring her students upstairs for her. As we waited in the fourth grade classroom for the teacher to return, I wondered what I would do to maintain a semblance of sanity. I decided on a game centered on behavior: The One-Room Schoolhouse Game.
When the teacher, accompanied by an instructional assistant (IA), entered the room, they couldn’t believe their eyes. Every student was sitting up ramrod-straight. Every single eye was trained on me. The IA verbally queried, “What is happening in here?” She was incredulous. I was in my element.
Educators are show(people). We are either putting on a performance to attract the attention of our students. Or, we are ringmasters, making sure the mayhem stays within the bounds of 42 foot diameters (the official size of a circus circle).
This is an image of the Claussville One-Room Schoolhouse, the same that my class visited on many field trips.
There are many ways to perform, but methods for maintaining order is more limited. Many years ago I came up with a unique way to do both at the same time.
When the IA, who had seen the game in action, entered the faculty room at lunchtime, she practically burst with enthusiasm, announcing to the other teachers what she’d seen. Some of the staff members wanted in on this game of good behavior that students seem to enjoy. I explained the rules to them. Since then, I’ve had a couple of teachers ask me to share with their classes how the game works. I’m more than happy to oblige.
Then, I searched my blogs to see if I’d written about The One-Room Schoolhouse Game. Unbelievably, I hadn’t! So, here goes.
It began many years ago. I brought my 3rd grade class of “Polite Pirates” (what I called my group of students) on a field trip that visited several historical sites around our area, all in the same day. It was a fast-paced adventure of a field trip, running from one stop to another, practically assaulted with information.
I made this video from photos and video of my 2016-17 class visiting Claussville.
We began the day at Trout Hall, the original house of the Allens, the family that founded Allentown, Pennsylvania. The building is staged to look like it had during the Revolutionary War era. A tour guide led us around the house and explained many interesting facts.
Students get to ring the Liberty Bell replica.Students explore the replica of a Conestoga wagon.
From there, we traveled only a few blocks away, where the Liberty Bell had been housed during a portion of the Revolutionary War, hiding it from the British. The Liberty Bell Museum has a life-size replica of the original bell, a slightly smaller than lifesize model of the wagon that would have carted the famous bell, along with several others from Philadelphia to our town. They have a nice mural and story display that they show. They also provide a favorite feature of every field trip; a gift shop! This is where I acquired my famous “One-Room Schoolhouse” bell. It is a mini replica of the Liberty Bell.
This is my 2021-22 class in front of the Claussville One-Room Schoolhouse.
The final stop of the day was an old school building that was preserved to look the way it had when it was used as a one-room schoolhouse as late as 1956. The Claussville Schoolhouse is where I learned the practices that what would turn into the rules of my One-Room Schoolhouse Game.
A tour guide walked us through what it would be like to go to school one hundred years ago. Every grade, from first through eighth was taught in that one room! Because of this, the school master had to be very strict.
I explain all of this nowadays when I introduce The One-Room Schoolhouse Game. Believe it or not, me acting like a big meanie is one of the more fun aspects of the game! Students love tempting me to pretend to yell at them. Suffice to say, this is far from my typical conduct.
The Game
Now you know where the idea for the game originated, let me explain how it’s played. I introduce the game on the very first day of school. It contrasts the comfortable social/emotional learning (SEL) environment that I foster and points out how nice I actually am.
Right off the bat, I talk about what school was like a hundred years ago. Because there weren’t any buses, schools only serviced local communities. Every kid walked to school. The building housed every grade, from first through 8th! A teacher was responsible for managing lessons for eight grades, all at the same time. And, there was only one teacher. They could not afford to have any disorder or misbehavior, so the teacher was very strict.
“There were many rules for doing things. First of all, the students had to sit up straight.” As I say this, I morph into a very serious, demanding persona. Every student whom I have ever shared this game with has always straightened his/her posture at this point. “There is absolutely NO talking.” I look around the room, daring students to even think about speaking out loud without being called on. The students are loving this. They are on pins and needles, waiting to see who might get into trouble. I have transformed into a scowl-wearing, grumbly ogre of a teacher.
Power of Role-Play
The tension mounts as I walk around the room. I might at this point explain some of the primitive punishments that would have been used during the days of the one-room schoolhouse. It’s not impossible for me to slap a ruler onto a desk to really amp up the mystery of the experience. (Of course, I make certain all of my students understand that corporal punishment is unacceptable in connection with education… but, that is how it was.)
Once I have my students good and primed, it’s time to share the rules of the game. When they are called upon, they are to stand, push in their chair, name the person or persons they are addressing, and make their statement in a complete sentence. I always make it clear that they are to “Refer to me as Mr. Weimann, or Captain Weimann if you’re classy, and you wants to be classy! If you are answering a question, and the information is pertinent for your classmates to pay attention to, you say, ‘Captain Weimann and fellow classmates…’ If there is another adult present, and your answer would benefit that grown up, you say, ‘Captain Weiman, Ms. so and so, peers and/or fellow classmates…’ You get the idea.” We practice this a bit.
That’s pretty much it. I throw in some variations or additional rules throughout the year to keep the game interesting and fresh. One day I might go crazy about neatness, causing everyone to clean up their desks and the floor around their work spaces. Another day I could go nuts about hearing them breathing. They love it, the more extreme and just beyond grasp the parameters are. A really fun one is pretending to be the mean one-room schoolhouse master and prohibiting all smiling. They practically burst, but work so hard to meet the requirement!
The trick is to do the game just enough, both in the number of times you play it and how long it lasts. It slows everything down; the making kids stand up, push in chairs, reanswering because they forgot to say who they were talking to or didn’t use a complete sentence.
This is the tiny bell that turns the room into a “One-Room Schoolhouse.” So little: So powerful!
The students love the game, though. They usually beg me to ring the bell, for I explain that the tiny bell that I got on that very first field trip to the Claussville one-room schoolhouse has magical properties. Whenever I ring it; and only when Mr. Weimann rings it; we are magically transformed into a one-room schoolhouse. This, of course, is a huge part of the game.
Sometimes, I will pretend to be unhappy with what is happening in the room, and “threaten” to ring the bell. The class will gasp in mock shock. If I do ring it, they all groan and moan, as if they were just strapped into straight jackets against their wills. …But, they quickly sit up straight, quiet down, and see who the big, mean school master from the past will pretend to pick on first. They are always disappointed when we return to the humdrum of contemporary time, and I turn back into fun, loving Mr. Weimann.
The Claussville One-Room Schoolhouse BellWhat would it feel like to be a student back then?
Back to the Future
This game is like “The Floor is Lava,” in that no one gets hurt, it’s all just pretend, and it amps up the excitement of an otherwise typical walk-through-the-park day. It is perfect for jazzing things up right in the middle of mundane stuff. A little ring of the bell commands everyone’s attention to both behavior and their tasks at hand.
I had no idea how different the 4th grade class that I was sharing the game with was acting, but their teacher and the accompanying instructional assistant recognized that something unique was going on. Rather than explain the game, myself, I allowed the teacher to call on students, who nearly burst with pride to show off their new skills.
It took a couple of kids to get all of the rules out, but once I felt comfortable that the teacher understood what was going on, I was free to leave the past. On my way out I whispered, “I’d wait a couple of minutes before ringing that bell. Ride it out;)”
You don’t want the game to go too long. Fatigue can set in. For the game to be fun, it has to be special, so don’t play it too often or too long. Let the students petition for it a few times, and then surprise them after returning from lunch or in the middle of a multiplication game. Use it for a transition to another lesson. Above all, have fun.
This video shows all three stops of the Polite Pirates’ Lehigh Valley, PA historical sites field trip (2018).
“I don’t know how I got it; I just know that this is the answer,” a frustrated student defends himself against the inquisition of an even more frustrated teacher who wants him to “SHOW YOUR WORK!”
You should have seen the students’ eyes bulge when I told them I was going to give them candy! LOL They were happy to gobble up the math, though.
But, what if he actually doesn’t know where the number came from? We don’t ask the toaster to “Show us how it heats up our bread.” When was the last time you insisted that the mechanic “Show you HOW they fixed your car”? (They always try to explain it to us, and I’m like, “Does it work? How much does it cost? I got stuff to do.” Ha ha;)
I recently had a math enrichment lesson with second graders where I told them what they didn’t know they did with a couple of mental math problems. We were working on comparing three-digit numbers. I had printed pictures of snacks that had prices on them. Teams of students were first asked to arrange the snacks in order from least to greatest price. Then I asked the class to compare the cost of three items to the cost of two others. The students didn’t have paper or anything to write on.
Please pardon my penmanship;)
After I received some successful answers, I asked the teams, “What did you do in order to produce those answers?” I got a variety of responses. Most teams told me the names of the operations. “We added the three numbers together, and then subtracted…”
One group explained what they did to complete the operations, and I was very impressed. While students were sharing, I took some notes on the board. I clarified what the group was communicating by drawing circles around numbers and pulling out concepts.
“You began by adding 65 cents to 55 cents,” I reiterated. Nods of heads confirmed the accuracy of my statement. What happens in a creative mathematician’s head is a little different from what one would do on paper, however, and I wanted to pull this out. These students hadn’t used an algorithm.
Here’s a post that shows 3rd graders communicating the use of compatible numbers to multiply.
“Fifty!” the group called out. We have been identifying compatible numbers, so they already knew to look for something more manageable.
“That’s right. And, in order to get to fifty, you have to adjust these a little.” I circled the 65 and wrote 15 on the side. Then I circled only the 5 from the ones of 55, and I wrote that near the 15.
If a student had paper in front of them, they might line up 65 and 55. Then they’d add the fives from the ones’ column and regroup with a “one” above the tens column… But, do we grown ups do this in the grocery store when we are comparing one item with another? No, we use mental math. We develop creative tricks that we may not even realize we use!
My aim is to unlock this mathematical creativity early in life. A secondary goal is to help students be able to communicate it.
“After adding the two 50s together, what did you do?” Everyone can see that there is still a 15 and a 5 written on the board. I wrote the sum before anyone called out, answering the rhetorical statement myself. “Now, you need to add this $1.20 to 99 cents. That sounds hard,” I teased, knowing that they’d already smashed that algorithm in their minds.
Letting students work in teams allows them more than just Social Emotional Learning (SEL). They help one another remember and recall sums and differences.
When I told them about using 100 instead of 99, several students silently shouted, “That’s what I did!” No one is going to carry a one from the tens to the hundreds column of a mentally constructed algorithm. And, we don’t always have paper. AND, do you really want to teach your students to be dependent on paper?!
Now, think about it, reader. Students are using subtraction in order to add numbers together. What 8 year old is going to be able to explain this abstract use of arithmetic in writing on a test or assessment?
Here, I’m having the group of 2nd graders “play” with numbers by lining their teams up in order of least to greatest, having constructed the largest number possible with the loose number cards I’d given everyone in each team. Get-up-and-move-around-math.
And, we (myself included) expect them to “Show their work!” I’m happy if they know what they are doing and get the correct answer. I’m nearly 50, and I only just learned how to show MY own work! LOL
What I found myself doing in the past was asking students who had performed mental gymnastics to achieve a remarkable mathematical feat to write down the steps they took. In other words, if you added up three numbers (65 + 55 + 99), and then subtracted a fourth from that sum, write it all down…
Even if you can’t describe the exact process of creating the sum or exactly what you did to subtract. Just tell me what you did with the numbers. I, like every other math teacher in the world, wanted to see more than just an answer!
I think that having students use mental math, and then having them explain what they did VERBALLY is helpful in sharing the mechanics of the creative math. It’s easier to verbalize than it is to write. I bet there are books written about this. (If you know of any, please share. Thank you.)
Didn't she do a great job. I love how every kid does it differently. One girl wrote on the screen, while she explained. As a T, I am thrilled to witness these Ss talking about their #ReadyMath. I can write comments and give #StandardsBasedScores in @Flipgrid #EastPennPROUDpic.twitter.com/Kux2rJbZTm
A tool I’ve enjoyed having students use to verbally communicate their creative math skills is Flip (formally known as Flipgrid). Kids can make videos of themselves talking about the math. They can also write on their screens to show what they did while talking about it. If they did the math on paper, they can take a photo of their work to include in their video. Finally, they can watch each other’s videos, get ideas for future creative math projects, and leave encouraging replies to each other. The platform is easy to navigate and teacher-friendly for leaving feedback and assessment info.
In conclusion, while I always instinctually knew that forcing a kid to write down everything they did in their head could squash their creativity, I never knew how to bridge the gap between teacher and student; The chasm between the answer (what the student produces) and the process (what the teacher cares most about) before now. I’d tried varying techniques with varying results. My new thing is to verbally walk them through tricks I’d use to do mental math. Through this process, they recognize some of what they are already doing in their minds. They are learning how to communicate it. And, some students are learning creative ways to play with numbers.
How do you challenge yourself as a teacher? I’ve been working on making my pedagogy more powerful by pushing lessons forward with STEAM. Originally known as STEM (Science, Technology, Engineering, and Math), STEAM introduces the Artistic element to the closely related fields. When you are teaching a STEM subject, it is common to integrate more than one letter of the acronym (Hertz, 2016), but one of my modus operandi is to try to incorporate as many of the letters as possible into any given lesson. Powering my teaching with as much STEAM as possible is an art form to me.
I sometimes use art as a reward for completing work. “Once you finish solving the math, you may draw the aliens you encounter on your adventure!” I told enrichment students at the beginning of this math lesson.
Some lessons are more successful at incorporating all five letters of STEAM than others. A recent math lesson got my creative juices flowing, and turned into a beast of learning for my 4th grade gifted students. It all began with an enrichment lesson from Ready Math.
4th grade gifted students use art to get even more out of STEM.
Fourth graders had been reviewing place value as well as adding and subtracting large numbers. This is the perfect example of a math concept becoming boring for advanced students, those who have shown mastery of the subject matter. Once these kids conquer the use of algorithms, plugging in numbers to get sums and differences becomes mindless. Adding and subtracting is like riding a bike. Why make them pedal a stationary one when we could take it on a trip, instead? This is where I come in.
My first stop on developing math enrichment lessons is to check out the iReady Teacher Toolbox for ready-made resources that I may build upon. Curriculum Associates, the makers of Ready Math, has developed an enrichment assignment accompanying nearly every lesson. These are worksheets that can be printed for students to work on independently. You can push the assignment out digitally via Google classroom, too. The Ready Math team has provided a “Teacher Version” that contains answers; Even potential answers to open-ended questions, so that teachers know what to expect!
For this lesson, I took a screenshot of an iReady enrichment assignment, and used it as the background of a Google Jamboard. I like Jamboards because my students can draw and write on their iPads. They can create new blank slides, as well as duplicate the one with the instructions on it. It is easy for me to make a template, and then create a copy for each student through Google classroom.
This zany lesson, “Planning a Trip,” had students pretend to explore an imaginary planet, Zanyville. It introduced gigantic numbers and was very open-ended. I included some more instructions that I shared orally, when I initially rolled out the project. “You must tell me the number of miles from the beginning of the trip where each of the stops happen. Also, you have to provide the distance between the stops.” Students were instructed to use “sticky notes” in Jamboard to share this information. They showed their work on other slides.
The 4th graders worked hard and were engaged in making their maps. Only, the maps were grossly disproportionate. Some students made the third stop only “one mile” from the end of the trail, but placed it a fifth of the distance from it along the route they drew in their Jamboard. In actuality that distance would represent tens of thousands of miles! It is true that I did not instruct students to partition their maps with accuracy, but when I witnessed the misuse of proportion, I saw a fertile opportunity for learning. Enter, STEAM!
My vision for math enrichment is to dig into each concept, finding riches that deepen the understanding of my students.
The next time that I met with the 4th grade math enrichment students, I taught them proportionality. There weren’t any Ready Math lessons on this, but it fulfilled my mission for the enrichment group perfectly! My vision for enrichment is to deepen students’ understanding on math concepts. We do not rush ahead or necessarily “do more” math. I try to present novel ways of using the concepts that students are learning in the classroom. Sometimes, lessons include real-world problems, using the math that they are learning to perform a task they will most likely encounter some day. Other times, we may play a game that requires students to view the numbers in a unique way. In this instance, I wanted my enrichment students to learn about the relationship (ratio) between numbers.
I modeled partitioning a space on the whiteboard. With students’ input, I placed numbers in appropriate places on the makeshift number line. After a short lesson on this, I had students revisit their “Planning a Trip” lesson from the previous week. They were to make a number line and show where each stop would happen. Their Google Jamboards showed excellent progress in understanding this concept.
From Enrichment to Gifted Instruction
This is where the lesson took a turn from enriching math understanding to present problem-solving and higher-order thinking through gifted instruction. In order to illustrate the disproportionality of the original maps, I’d have the gifted 4th graders use one of their own to display an accurate account of the journey.
How would we do this? I would lift the trail from the map. The trail would become a rope that could rise up off of the map. This would allow my gifted students to account for extra mileage and figure out how someone may have covered the distance of tens of thousands of miles, but look, from only glancing at a two dimensional map, as though they had only hiked a handful of miles. My plan was for the fourth graders to learn about topography.
I gave my students a rope that was about 50 feet long. Their initial task was to tie pieces of yarn onto the rope symbolizing stops on the trip. They used what they had learned from the previous math enrichment lesson to do this.
“If the entire trail was 498,013 miles (this was on the planet Zanyville, remember), and the first stop was only 35K miles from the start, you couldn’t mark it halfway along the journey!” I reminded them.
We brought the rope into the hallway, so that we would have plenty of room to #STEAM. The first thing my students did was section the rope into five equal parts. It being a 50 foot rope, each of the five sections was ten feet. As it turns out, the tiles in the hall were one foot wide, so each one symbolized ten thousand miles, nicely. Once we had some reference points, we figured out where each stop would be and tied a piece of yarn to represent the place.
I then took one of the disproportionate maps that one of the gifted students had drawn, and I enlarged it onto poster paper that covered a large portion of the classroom floor. Next, we placed the rope showing our well-proportioned stops onto the map. We taped the pieces of yarn to the stops drawn on the map. There were huge portions of extra rope between some of the stops, and it was too short in other places.
I asked my students to “Imagine that this rope isn’t a rope, but a journey. Someone actually did travel these miles, and they traveled along the route that is represented on this map,” I told them. “How could this be?” Their first idea was that the “journey” coiled around and around; As in, the traveler had actually walked in circles. “There is a loop drawn on the map,” I pointed out. “You should assume that the line drawn on the map is the exact path the person traveled.” I wanted them to discover the concept of elevation on their own.
“The journey (they were very keen on calling the rope ‘journey’ and yelled at me when I mistook it for ‘rope’;) goes up!” several students shouted in unison. Feigning surprise, I encouraged my students to show it. I told them to make it happen. “Elevate the rope to show traveling up off of the paper.”
Watch the time-lapse of my 4th grade gifted students creating a model of their journey.
The students started grabbing everything within reach to raise their “journey” off of the paper. I gave them a few parameters: They could use anything in the room, other than my personal things. It had to follow the line of the map. The journey has to stand independently. “It can’t need you to hold it.” I heard the students mentioning how much fun this was several times, as they stacked Rubik’s cubes, built structures out of KEVA planks, and draped rope Journey over the 4’ high faux pilings I’d made for another project.
After finishing, I asked “How could we show these mountains on a two-dimensional map?” This is where topography enters the scene. Before exploring the topic, I had the gifted students brainstorm ways to display three dimensions on a flat piece of paper. They came up with drawing small images, like triangles symbolizing mountains. Information in a key was paramount. I showed them some maps that had varying colors used to illustrate elevation. They liked that idea. Finally, I introduced contour lines. These are drawn around the mountains, and show the incline of the slopes.
Once I did my best to explain how contour lines worked, I showed my students a video (above) made by HikingGuy.com. In the film, “Hiking Guy” takes a two-dimensional, topographical map and imports it into Google Earth Pro. He overlays the topographical map onto the exact geographical area that it represents. With Google Earth in 3D mode, the Hiking Guy swivels the view, so that you can see the depth of the mountains and valleys. We were in awe of the effects. I could have told my students that a contour interval is the amount of elevation between two contour lines on a given map, but seeing it displayed via three-dimensional modeling drove the concept home.
Next, it was time to collect some data to use in our map-making. We used yardsticks to measure how tall our mountains were. (I would have used centimeters as the measuring increment, in order to keep with everything scientific using the metric system, but since the Ready Math assignment had started the project off with “miles” on Zanyville, we kept to the standard system.) Before clearing away all of the materials elevating our journey, we marked the beginnings and ends of each mountain along the route on our map. In this way we would know the edges of the bottoms of our mountains for drawing contour lines.
Prior to drawing our contour lines, we needed to figure out what our contour interval would be. The first thing we did was figure out the height of each mountain, according to tens of thousands of miles. If a mountain is only nine inches high, as was Mount Rubik’s (we named all of our mountains), and a foot (12 inches) represents ten thousand miles, what is the elevation of the summit? We figured out that nine inches is 3/4 of a foot, so we concluded that our nine inch mountain was 3/4 of ten thousand; or 7.5 thousand miles high. The taller mountains required us figure out how many feet fit within the total number of inches. Some rounding was used, and we came up with some valuable summit information that was transferred to the paper map.
Now for our contour interval. How much elevation should each space between contour lines represent? We want the lines to be meaningful, but too many would make the map cumbersome to produce as well as read. We took each of our summits and found a number that was doable.
STEAMing Up Your STEM
Believe it or not, including art with the traditionally scientific fields of STEM has been mildly controversial. “The focus of STEM is developing rigorous math and science skills through engineering. How can you focus on other subjects (such as art) without losing the mission of STEM or watering down its primary purpose?” (Jolly, 2014). People who think this way are trying to isolate the left side of the brain (Pietrangelo, 2022). They imagine that opening STEM up to the arts would allow right-side brain activity to infiltrate and weaken STEM, but Jolly (2014) points out that this is viewing it all backwards. Art is already used in engineering, product design, creative math, and out of the box science. Strengthening our artistic use of STEM will make all four subjects so much more powerful.
Slow cookers like crock pots use lower heats to cook food over longer periods of time, deepening flavors and breaking down meat muscles, so that food becomes soft and tender (2022). A pressure cooker, on the other hand, cooks meals much faster. This mechanism has a seal that helps maintain the pressure within it. Steam builds up and pushes into the meats and other ingredients, breaking down the foods to make them tender, as well as infusing the flavors. You may not have tons of time to teach a STEM lesson. Use art to make the learning more memorable.
Saunas are small rooms that are heated up to 160 Fahrenheit. The health benefits of sitting in one of these hot beds for a short amount of time include clearing the pores of your skin, relaxing muscles, and burning calories, as well as increasing blood circulation (Hussain & Cohen, 2018). Add some water to the hot rocks in these wood-paneled spaces, and you have yourself a steam room. A steam room can help clear ones sinuses, loosen joints, and repair broken skin tissue (Johnson, 2023). [One thing to watch out for in a steam room is dehydration. It may seem ironic to dehydrate when surrounded by so much water, but the heat will cause moisture to leave ones body. Make sure to drink plenty of water and keep your time limited.] Using art in your lessons can add health benefits to your teaching. Students who favor their creative right side brain work might remember the lesson more. The artistic element could clean out misconceptions for visually-oriented students.
The difference between STEM and STEAM is as subtle as sauna vs steam room and slow cooker vs pressure cooker. I’d say that teachers are most likely using some art in their STEM lessons… I can also imagine a STEM teacher feeling pressure to utilize art which could lessen the lesson. Does titling teaching “STEAM” allow for art, promote its use, elevate art to STEM prominence, or simply point out the fact that it was there all along?
I like to think of art as the glue that holds the Science, Technology, Engineering, and Math together. I’m surprised we could see out the windows; There was so much STEAM happening in our classroom!
Enriching the Enrichment
A lesson that I began in the middle of this long mapping of a “Journey” project involved slope measurement. I thought that figuring out the value of the angles of the mountains would be useful. As it wasn’t helpful in completing the drawing of our map, I dropped it after spending only a little time on it. The information was very interesting, however, and I can foresee using it in on a slightly different angle of the lesson; Switchbacks.
Our Journey would not have gone straight up the sides of the mountains. A switchback is when a trail travels at an incline, but also more parallel than perpendicular to the mountain’s rise. After a short distance, the trail will “switch” directions and zig zag up the side of the incline. This means that the hiker will walk a much longer distance in order to get to the top of the incline, but it is an easier hike. What does this mean for our Zanyville trek? The journey, being its given length, will not go up as high; This will lower the peak or summit of each mountain. But, by how much?
Students can explore steilhangs, learning more about earth’s geography. Furthermore, they could research the differences between Earth and other planet’s geographies.
I had students conduct a scientific examination through dropping small plastic cubes on top of one another to form a miniature naturally formed mountain. They were not allowed to touch the mountain with their hands. What was the angle of elevation? We placed a ruler parallel to the side of the slope and used a protractor to measure the angle of elevation. It was about 15 degrees.
It will require some advanced geometry to recalculate the distance from the base of the mountain to the summit, given new measurements of switch back angles and lengths between directional changes. I might incorporate these elements to the lesson when I do it next year. It’s time to wrap this up.
Finally, I would like to see my students graph the elevation of the trip. Between zero miles and 498,013 miles, where did the trail rise and fall, and how much?
I use a running app that uses GPS to track my progress. It calls out my splits at five minute intervals. It also provides charts showing variations in my speed, cadence, and elevation. I want my students to create an elevation chart similar to the one from my running app. It ought to display where the traveler would begin and end hiking up/down mountains, as well as how high the peeks were.
What if you could produce a dessert packed with protein and healthy nutrients; I’m talking even more beneficial than a typical meal. Would you serve this delectable dish for dinner every day? My conclusion may surprise you.
Last week was Parent-Teacher-conference-week at my school. Students had half-days, and families either visited the building or used virtual conferencing tools to converse face to face with educators. This was the very first time that I bounced around from teacher to teacher, visiting the conferences of my gifted students’ parents. While there are many ideas that I could comment on, the one that stands out most was from the parent of one of my math enrichment students.
The family has a third grader who is gifted, and that is why I was attending the conference. But, his little sister, who is in first grade, attends my math enrichment lessons, and it was something that she said that got me thinking. Her parents told me that they asked their daughter what she did in math enrichment class, and she told them, “We play games.”
“Is that all?” I imagine them pressing, being the good communicative parents they are. Yup, is the first-grade answer:)
This is a recent pic of 2nd grade learning to play Dominos.
I laughed when I heard their tale. I explained to the parents that I was teaching the first graders Dominos. After defending the fact that there is a lot of mental math and problem-solving, there was some light banter between parents and the regular ed teacher about only knowing the stacking and tumbling side of Dominos.
Because their gifted third grader had already experienced lessons showing the critical thinking development of Dominos, it wasn’t necessary to get too defensive. They were “on board” with my use of games for strengthening math skills. But, the idea of my lessons being categorized definitively as nothing more than games gave me pause. Initially, I was perfectly okay with tricking students into learning through having fun. What teacher would turn down that strategy? “Can we have some more math enrichment, please!” the students whine. “Um… Yes!” every math teacher in the world would utter.
Then I thought about the idea of turning everything into a game. Wouldn’t that be wonderful for the students? But, would it be healthy? Hmm…
This is where the thought experiment at the top of this blog originated. I was musing over my math lessons being perceived as games, and I dreamed up the analogy of only eating dessert. Prepare to enter a rabbit hole of research. I’ll try to keep it palatable😉
History of Dessert
Asking “Why does dessert even exist?” feels a little like questioning the purpose of gold or jewels. Isn’t it obvious? It’s awesome!
Believe it or not, dessert did not always exist, however. Similarly to gold and jewelry, it was discovered, and has evolved over time. The French are responsible for turning entremets into dessert (Gerson, 2019). Before there were sweets to end a meal, entremets were served as “interval” dishes, literally “between-foods” courses (Teppen, 2015). They were meant to cleanse the palate. They may be sweet, but not necessarily.
Eventually, a final course of fruit, called le fruit, was formalized (Gerson, 2019). Only, before serving it, the table must be completely cleared. This cleaning of the table was called desservir, the French verb for “to clear.” More than tasting wonderful, the original final course of fruit developed into something lovely to gaze upon. Some desserts even consisted of “Elegant metal and glass structures holding whole apples or plums. Other times, meticulously crafted sugar figures became the center of dessert displays, and might not be eaten at all. Dessert specialists in the eighteenth century were supposed to understand architectural design and be capable of replicating it in sugar paste” (Gerson, 2019).
These creators of dessert, as it came to be known around the time of the French Revolution, when the Bourgeois assimilated the term, were originally more like artists than chefs. Maryann Teppen (2015) writes of an entire battle scene, complete with tiny sugary soldiers with guns and canons, that told the story of Louis XV’s demise crafted out of sugar. It is hard to imagine your dinner table being cleared; plates, napkins, silverware, and foods being “dessert-ed” away; only to be replaced by an elaborate, sugary scene of violence that you feast your eyes upon but don’t touch!
Modern dessert serves a different purpose. BreezeMaxWeb (2022) suggests it psychologically signals the end of eating. Consuming a small, sweet treat at the conclusion of a meal might communicate to the body and brain that we are all done, and there is no need to nibble superfluous snacks. The End.
A practice that I began a couple of years ago has helped me lose some weight and become more healthy; I will eat an apple at the end of every lunch. Many years ago I heard that apples help clean your teeth, and apparently there is some truth to that (Apples: Dental Hygiene Facts, 2017). Once I’ve eaten my apple, I cannot/will not eat anything else. I don’t want to undo my teeth cleansing. This has helped me de-snack my afternoons.
Let me reintroduce the concept of math games, here. Could a game be used to transition from one course of subject matter to another? Would playing a game cleanse the cognitive palate, and prepare students for something completely different? Of course! Would this be an appropriate way to signify we are done with the subject? I think so.
Delayed Gratification (Deferred Satisfaction)
How many parents use dessert as a reward for finishing a well-balanced meal? That treat is the ribbon at the end of a race. Some contests require more work and take longer, but when getting to the game of a lesson is the goal, students may trudge longer, work harder, and persist through all kinds of problems. Those students who finish first might learn patience through having to wait for their peers to catch up with them before the whole group can consume the dessert of a lesson together.
Self control. Training. Conditioning. “If I let you eat this piece of cake, do you promise to gobble up all of your peas and carrots without complaining?” doesn’t just sound silly. I probably don’t have to tell you that this is an ineffective reward model;)
These are this year’s 3rd graders (math enrichment), learning the game, Cribbage.
But, what if the dessert is carrot cake? What if the dessert is healthier than the dinner? Then what? “Eat all of your cake, or you won’t be given any peas…” Wait, what?!
Is there something to be said for learning to crunch through cardboard in order to earn cake? According to a longitudinal study spanning 40 years (Casey et al., 2011), learning and practicing self control early on in life can lead to better academic performance, less behavior problems, and even higher SAT scores. Casey and company (2011) describe in their paper, “Behavioral and neural correlates of delay of gratification 40 years later,” some ways kids can curb the pull of stimuli by learning cognitive control. There are mental strategies and tricks that people can use to provide buffers, dampeners, and walls to contain and maintain self sovereignty. Students may never learn or develop these important skills if they are never asked to wait for anything.
Through reading this research I wondered if teachers, themselves, are bypassing the delay of gratification when they jump right into games to teach. What educator looks forward to grumblings from their students? I propose that most would prefer praise of pupils happy with pedagogical practices over the squabbling of scholars required to earn a fun activity. Are we educators partaking in dessert before dinner when we teach with games?
Before we beat ourselves up too much, let’s bring our metaphor along with us as we explore a couple of Jamarillo’s fun list of 11 Reasons to Eat Dessert First (2023). This may initially seem like a self-serving exercise, justification, or defensive maneuver, but hold on. Jamarillo raises the point that food can sometimes be a serious psychological hangup. “When we have disordered eating, we can often develop food or meal fixation. Dessert is one of the most common food items restricted. This can lead to binge restrict cycles and disruption of hunger cues” (2023).
Is it possible for students to develop “learning disorders” by experiencing “binge-playing” with learning games after enduring unnecessarily long restrictions? Just as Jamarillo (2023) suggests that dessert-first-eating can help overcome eating disorders through stimulating hunger, tapping into nostalgic memories, practicing navigation of bodily needs versus wants, and learning to respect cravings, beginning a lesson with a learning game can help students who struggle academically to open up to pedagogy.
One thing more, and this might be a great way to end this blog, Jamarillo (2023) ends her short article with the fact that dessert is an ambiguous course. It can be a sweet, but doesn’t have to be. Fresh, raw fruit could serve as dessert. Pies, pastries, a tiny chocolate or candy, sweetened veggies, and yes, of course cake can all constitute desserts, whether eaten at the beginning of a meal, middle, or end.
In conclusion, my first grade student may imagine all she does is play games during math enrichment time, but this learning dessert is rich with problem-solving proteins, mental math nutrition, and healthy higher-order thinking! With the short amount of time I have with my students, I have to make my challenges tasty. And, I’m okay with that;)
Ready Math has an enrichment activity for nearly every math lesson. These are usually accompanied by a worksheet. The papers can be printed, photocopied, and distributed for students to complete during independent time. The worksheets have thorough instructions on them, sometimes with examples, so that students can manage the assignment without teacher help.
In the “Teacher Toolbox” you can find an array of tools for each lesson for every grade. I like to start off with checking out the “Extend” ideas and adapt them to meet my students’ needs.
The idea is for students who’ve attained mastery of the subject to apply their skills to slightly more challenging tasks. It’s nice for the teacher to have something concrete to look at after the student is done. This evidence of work and proof of advanced mastery can be shown to parents and back up grades on report cards.
One problem with this is that students aren’t always thrilled about being rewarded with a worksheet when they understand and are good at a math concept. It’s helpful for a teacher to introduce the worksheet. They can spice up the assignment with some extra enthusiasm. It might be helpful to pave the way for success with a check for understanding of the assignment. Perhaps the teacher could introduce a twist to the pre-made project, including an additional step or task.
When I am preparing an enrichment activity, I try to provide an opportunity to use the math concept in a real world scenario. We all remember the age-old question, “When will I ever see this in real life?” uttered with a groan and eye-rolls. This is my aim: Show students situations where their math lesson would actually be found.
This amazing 5th grade student figured out the last two digits of one of the missing numbers from our #Grinch Escape Room. #Math#MathEnrichment#MathTalk
Another goal of mine is to help students grow their thinking muscles. Perhaps there isn’t a clear use of Pythagorean’s theorem in everyday life, but it can be used to sharpen geometric and algebraic understanding! Puzzles are great for this.
I recently used one of Ready Math’s enrichment assignments to challenge a group of fifth grade students. The lesson/worksheet looked a little like busy work; It involved adding and subtracting four-digit numbers with decimals. You needed to be handy with the math to complete the task with accuracy, but I didn’t see any way that the student would be richer having completed the assignment.
One of the first things I do when attempting to turn a pre-made assignment into an enrichment activity is see if there is some bit of information or number that can be taken away. Can I remove something, and the students still figure out the answer?
The assignment that I was looking at was a three by three grid with some boxes filled in and others blank. Every row and column, as well as the diagonal lines crossing the center square, all add up to the same number. The worksheet tells the students what the shared sum is. Can I remove that final answer and students still figure out what numbers would go in the boxes?
I tried it out in my journal. The way I saw it, there’s no way around having at least two unknowns. I could ask the students to figure out multiple correct answers; sums of every row and column, but this kind of activity stretches beyond enrichment and requires gifted thinking. That is a topic for another blog; the difference between enriching math and providing gifted instruction.
I tried playing around with the numbers in my journal.
Still liking the idea of removing the sum that all of the numbers share, and making students really dig for the gold of their lesson, I decided to limit the unknowns by providing parameters. I began writing these into hints or clues. Then, the lesson morphed into a type of riddle. I left gaps in the clues, so that students would have to address a few empty boxes in order to solve the entire grid.
As the project evolved, it struck me that I could pretend the problem was a lock that prohibited the class from leaving the room; It facilitated an escape room sensation. This would be the way that I presented the whole problem! I’ve been wanting to explore the use of escape rooms at school. This could be a great start.
I prepared some more clues for bits and pieces of the four digit numbers within the grid. I put an image of the grid into a Google Jamboard. Then, I copied the riddles and pasted them into “sticky notes” that got spread out around the grid. I themed the whole thing with Grinch, and it was ready for “production.”
The fifth graders loved it. When I told them that they were stuck inside the Grinch’s lair, their faces lit up! “The Grinch, that big ole meany went and scribbled over the sum that we need to solve this grid. He left us several riddles to figure it out. You can’t leave the room until you do.”
Everything was going great… Until… One of the students had actually completed this particular worksheet in the classroom, as an extension activity. My heart instantly sank. Did the Grinch steal my Christmas? Luckily, I’m pretty good on my feet, and I told them that we can still use this whole activity in order to learn how to make up our own riddles and clues, so that we could develop another, future escape room that other students could have to solve. Everyone was cool with this new plan.
I wrote an equation on the board, using as much information as was available. Then we filled in missing pieces with information from the clues. I showed them how they could do this on their own in the future! It was still fun.
We continued exploring the clues, now with a new purpose. Granted, we were working backward, since we already knew the final answer, but that was okay because the students were able to see how the clues functioned. I showed them the way you can start with an answer, analyze the number’s attributes, and make up hints that color and shade the number, without giving it away. They seemed to like it, and we still had to do some adding and subtracting of four digit numbers containing decimal points!
This lesson wasn’t over when this group of students left, however. The way fifth grade math enrichment works in my school, I meet with a different group of advanced math mastery fifth grade students in afternoon. I told the AM students to not tell the afternoon math students the answer, just in case none of them had completed this particular assignment. Then the Grinch let them out;)
Between the groups, my fourth grade gifted students painted a giant Grinch face to hang up over the door. That was fun.
When the afternoon students entered the room, I pitched the escape from the Grinch’s Lair idea the same way I had with the morning crew, but with the understanding that they may already know the answer, like the first group. One student of the eight or so kids had done this assignment and knew the answer, but he was a good sport about keeping it a secret.
Since I had thoroughly examined the entire riddle with the first group, I was well-versed in the clues and could easily present them to this final class. I let them wrestle with the ideas. As it turned out, you could figure out the final answer before getting all the way through the final clue. That was interesting to learn. The experience was pretty fun, and they got plenty of practice adding and subtracting numbers containing decimals.
I’m definitely looking forward to making more lessons containing clues and using the escape room scenario to encourage tension and motivation! It was really nice to have a pre-made template from Ready Math to build from; or, more accurately take away from. But, in the future, I’ll have to be careful about assuming kids hadn’t used the lesson before.
The Captain of Class 