Tag: thinking

Building Strategic Thinking with Dominoes

My 5th grade gifted class revisited the game of Dominoes last week. It took some review, but they enjoyed playing the game. I told them that one of the reasons I had taught them the game was because it is a classic that they could play with grandparents and other elderly people, bridging the gap between generations. The game has been in existence for over 900 years! 

In addition to the game being old, it also presents an opportunity to practice strategic thinking. In an effort to prove this to my 5th graders, I have begun dreaming up scenarios where a player might use analytic skills to make a counter-intuitive move that would benefit them in the long run. 

There are times during a game when you have more than one Bone (Domino) that you can play, but none of the plays will give you points. Sometimes, it does not matter which one you put down, but other times you can plan ahead. Much like you would in chess, you can set up future moves by arranging the Bones to meet your needs. Playing them in a particular order would benefit you more. 

I planned on showing my 5th graders what I meant by setting up scenarios of games and taking pictures. I have done that many times to teach the problem-solving aspect of Dominoes. 

Using photos as teaching tools works great on interactive devices.

Then I thought, Why not have my gifted students make up the puzzles themselves? I will give them the parameters, and they have to try to figure out how to show the need for strategic thinking through constructing an image of a hypothetical game. 

The puzzle would be an image showing Bones (Dominoes) already played, Bones available to a player (standing up so Pips or dots were showing), blank sides of the opponent’s Bones, and maybe a Boneyard (unused Dominoes). 

If you are a novice Dominoes player, some of this vocabulary might be new to you. Bones are the game pieces, named after what they were originally made out of; Ivory or elephant tusks (bones). The Boneyard is made up of the unused Bones lying face down. Face down means that the Pips or dots on the bones are not showing. All you can see is a blank Bone or the uniform design that is printed/carved on every one of the 28 Bones of the set. Bones often have something decorative on the side without Pips, so that players can identify the 0-0 Bone more easily. Every Bone has two numbers on it. There are two ends of the number side of a Bone. No two Bones have the same combination of numbers. Beginning at 0-0, the Bones go up to 6-6. 

The Plan: In order to demonstrate strategies for play, I am going to have my 5th graders come up with puzzles that point to weighted plays. In other words there will be better moves than others. People trying to solve the puzzles will have to analyze the potential moves. Which one is better and why? Puzzle-solvers will be required to explain the move they chose. 

This is from the beginning of the year.

The Work: Arrange Bones as though they had been played in a game. This means matching the ends of Bones; Six is connected to six, three to three, etc. There ought to be four lines of play that a player can connect a Bone to.

Each player has Bones left to play. One set of Bones is standing up, with the number of Pips showing. These are the Bones that the puzzle-solver has to work with. (Normally, when I am teaching Dominoes to students, I have them lay all of the Bones down, so that every student can see all of the Pips. This is so that every single play is a lesson on problem-solving. When one plays a real game, you do not show your Bones to your opponent.)

The Bones that the puzzle-solver has to work with (the ones showing Pips in the image) should have numbers that can be played. They contain the number that is present at the ends of the lines of play. One of the Bones that can be played would cause the sum of all four ends of the lines of play to add up to a multiple of five, which is how one acquires points in Dominoes. This would seem like the best choice to complete the puzzle. 

Because we want this to be a puzzle that causes Domino players to grow in their understanding of the game and not just an illustration modeling how to play, we aren’t going to make the correct answer to our puzzle be an obvious choice. A good head-scratcher will require a player to look beyond the obvious play. 

If four Bones with the same number have already been played, and the puzzle-solver has two of the remaining Bones with that same number, how likely is it that the opponent of the puzzle-solver has any Bones with that number? 

Here is your task: Make it so that playing the Bone that does NOT create a multiple of five is the better play. 

I’ll have to share this lesson with my 4th graders, as well!

How could this happen? If the opponent of the puzzle-solver is forced to draw a Bone from the Boneyard, rather than playing a Bone, not only will they not earn any points, but they will be growing the number of points that the puzzle-solver will get at the end of the round; The round that the puzzle-solver is now more likely to win because they have fewer Bones left than their opponent. 

At the end of each round the player who uses up all of their Bones first gets points from the Pips that are on their opponent’s remaining Bones. In order for the play that did not make a multiple of five in the first place (at the beginning of the puzzle-solving exercise) to be the better play, the final play must provide more points than the potential multiple of five. 

If the multiple of five would have been fifteen, and there is no way, given the Bones that are left, for the puzzle-solver’s opponent to have a total of Pips greater than fifteen (you always round up, so sixteen would go up to twenty), then not playing the multiple of five during play would not necessarily be a winning strategy. Typically, you would play the multiple of five, get the points, and hope for the best. This exercise is designed to show my 5th graders that if you plan ahead, the delay of point acquisition could very well bring a windfall of greater point tallies. Not only is this a good life lesson, but it can help them play the game better in the future. 

Now, if you want to try to figure out how to create a puzzle that fulfills these requirements on your own, without any help, go for it. You can return to this writing when/if you get stuck and need some guidance. The next section provides some helpful hints. 

If you aren’t sure where to start, or you have hit a mental block, check out these ideas.

Some Helpful Hints: 

Limit the available Bones. You can do this several different ways. One is to only give the puzzle-solver two bones to choose from. 

Another way to limit the potential outcomes is to make the lines of play long. Have most of the Bones from the set showing in the lines of play, so that the potential Bones of the opponent is narrowed to only a few possible numbers. The puzzle-solver can reverse-engineer the game to figure out what Bones are left to be played. It’s like “card-counting,” but legal;)

A very effective strategy for creating a doable puzzle is to limit the numbers in play. Idea: Make the ends of the line of play all the same number, and the puzzle-solver has the remaining Bones that contain that number. For example, there is a one at the end of all four lines of play. There are only seven Bones that have a one in them. If four of these are played, and the puzzle-solver has the remaining three, then the opponent cannot possibly play any of their Bones. 

But, the puzzle has the puzzle-solver making the next play. How can the puzzle-solver cause their opponent to have to draw from the Boneyard? See if you can figure it out.

There are a couple of ways to solve this problem. One answer is to provide the puzzle-solver with a double. A double has the same number on both sides. When this is played at the end of a line of play, it keeps that number going! 

Another solution requires more work, and could therefore be trickier for the puzzle-solver to find. Make it so that all of the Bones that the puzzle-solver possesses have numbers on them that can’t be played. You have to position every bone that has any of the other numbers on them within the lines of play. No need to worry about your puzzle-solver using up their Bones because every one of theirs contains the same number as the ends of the lines of play. 

Stack the Pips. Create lines of play that have low numbers, thus ensuring that the Bones that the opponent possesses are more likely to have higher Pip counts. In this way, even if the puzzle-solver would make a fifteen or twenty with the false-solution-Bone (the one that would make a multiple of five and seems to be the better choice for the puzzle-solver to choose), the total Pips that the opponent would have must be greater than the multiple of five. This number work is truly statistical thinking. Out of all of the Bones still available, how likely is it for the opponent to have a high enough number of Pips for the counterintuitive play to benefit the puzzle-solver more? 

This puzzle would allow for the opponent to make a play or two before the puzzle-solver is out of Bones. My student would have to work through all of the possible outcomes to ensure that the puzzle-solver would come out on top. 

3rd graders learn to play Dominoes

Try it out, and make the puzzle fool-proof. When making the puzzle, turn all of the Bones over so that the Pips are showing. Create a model of lines of play. Give the puzzle-solver the Bones they will work with. Now, look at the Bones that the opponent could have. Adjust the lines of play, so that there is no possible way for the opponent to have a way of winning. You also have to double-check that there are only Bones that would cause the opponent to have more Pips than the false-solution. Then turn over the Bones that form the Boneyard, and stand up a couple that represent the unknown opponent’s Bones. 

Conclusion:

Normally, I will do a lesson like this, and then write a blog about it. This is different. I have used my writing to think through what I want to have my 5th graders do. 

My aim is to have them build their understanding of the game of Dominoes and learn statistical analysis through the process of constructing their own puzzles, rather than just solving mine. Hopefully it will be successful, and I can write a follow up blog about how wonderful it went… or the lessons I learned through its execution, pun intended;) 

If you try this idea or one like it, please share your results. I’d love to learn feedback and improve future teaching. 

Sources:

Marcus, M. (2020). How to Play Dominoes . Cool Math Games. https://www.coolmathgames.com/blog/how-to-play-dominoes

Average Salt Consumption: 5th Grade Math Enrichment

In the excitement of beginning a 5th grade math enrichment club I created a math problem that may have been a bit extreme. I wanted to use something from real life, make it challenging, and leave my students thinking. 

Photo by Castorly Stock on Pexels.com

The topic I settled on was sodium; specifically, our salt intake. What 5th grader can resist paying attention to a life and death lesson? They may have already heard about salt consumption severity, but if not, they will! This should make the lesson stick. (see “Explanation” of The Power of Contrast.) As it turned out, I was right. Not only did a few of the 5th graders understand the dangers of salt, but some knew that too much can negatively affect your blood pressure. 

In order to increase the cool-factor of the lesson, I explained the importance of salt in conducting electricity throughout your body. I did this by asking them which is more dangerous during a lightning storm, swimming in a chlorinated pool or a salt water pool. Salt is a much better conductor of electricity than regular, clean water. They were energized by this new information. (For a very easy to read article about salt’s necessary functions in our bodies, check out “Pass the Salt: Sodium’s Role in Nerve Signaling and Stress on Blood Vessels” by Abbey Bigler-Coyne. And, here is an awesome, short read about salt’s dangerous properties during lightning storms: “Ask the Physicists: Swimming in a Lightning Storm“)

I knew that the 5th graders had been working with decimals. I thought it would be fun to make a problem that had them wrestle with decimals in more than one way. We would average our salt intake. 

First, I did some research. According to the American Heart Association, humans would ideally consume 1,500 milligrams (or less) of salt per day. Written in decimal form, this translates to 1.15 g.

American foods are loaded with salt, and our favorites are the worst! For lack of time, I did not burden my math enrichment students with too much detail. They had no trouble understanding what foods are super salty. They mentioned French fries, hot dogs, and chicken fingers. Then, we discussed foods that didn’t seem salty, but definitely had some, like ice cream. 

This set me up for presenting my word problem: While the human body needs some salt (only around 500 mg), too much of it can be harmful. It is recommended to consume around ½ of a teaspoon or less per day. A half of a teaspoon of regular table salt measures about 1.15 grams. 

Some foods are notoriously more salty than others. In the interest of being healthy, one might try to consume less salt on days surrounding heavy intake periods. 

Look at the data to the right. How many days will this person need to consume only 1 gram of salt in order to bring their average down to 1.15 grams per day?

How It Works

Before going over the problems with my 5th grade math enrichment students, I taught what it means to find the average of a few numbers. I pretended that the students had taken a quiz, and I wrote some fake scores on the board. What was the average score? It isn’t necessarily the middle of the range (distance from smallest to greatest). I had written 10, 8, 5, 6, 8, 4, 0. (They insisted that someone get a zero; Rude! I suggested that the zero was probably due to the person failing to put their name on the quiz, and couldn’t get any credit;) 

There were two 8s. That might pull the average up. “You use an algorithm to find the average, and it can adjust,” I explained. I showed them how you add all of the numbers together, and then divide by the number of scores. “There’s more than one 8, so that should cause the average to weigh heavier on the higher end of scores. But, then the zero is going to drag the average down.” 

“It is like tug of war,” I explained. “The higher the scores, the more the rope gets pulled in that direction. If there are more low scores, the rope begins to go to that side.” 

We played with the numbers, changing them a few times. I showed how, when you raise a few grades, the average goes up. I had students make predictions. 

Next, I showed the 5th grade math enrichment team our word problem for the day. I read it to them, and then asked them our Ready Math questions that help us understand word problems:

  1. What is this problem about? A. Salt; Adjusting the average consumption.
  2. What are we asked to find? A. The number of days necessary to significantly decrease our average amount of salt consumption.
  3. What is the important information? A. The amounts of salt we consumed over the weekend, our goal, and the amount of salt we will allow ourselves to eat until we reach our average goal.
  4. And finally, what are you going to do? A. Continue figuring out the average of the three weekend amounts, combined with ones (1 gram per day) until you reach an average < 1.15 g.

They understood the story of the problem. We ate way too much salt over the weekend. Now, we feel the need to eat extra healthy to make up for it. 

I walked the class through one or two tries: “If you consume only one gram of salt during the day after the weekend, what happens to the average?” We added up the number of grams, and then divided by the four days in question. 9.61 ÷ 4 = 2.40, still too high.

I had placed the word problem in a Jamboard. When I pushed the lesson out to my 5th graders via their new 5th Grade Math Enrichment Google classroom, I made a copy for each. I let them wrestle with the numbers on their own for a few minutes. I showed them how you can “duplicate” a slide in Jamboard, so that all of the important numbers and word problem get carried over to another clean workspace. I wanted them to try the math a few times, showing me their work. 

I caught a few of them trying to average the three days of the weekend. I told them that this was unnecessary, because we already know that every single day of the weekend was way over our end goal of 1.15 g! “You can go ahead and practice averaging, but this won’t get you to our goal: Finding the day we don’t have to limit our salt intake to only 1 gram.” 

After a while, I wrote the weekend numbers on the dry erase board: 2.56, 3.08, and 2.97. Then I said, “What if you eat only one gram of salt for the next ten days?” I drew ten ones next to the first three numbers. “In order to find the average, you first add all of the numbers together.” I drew plus symbols between every number. “Next, you divide by the number of weights.” I walked them through dividing 18.61 by 13. “The average intake would be 1.43 grams per day. This is still too high, so we have to continue eating only one gram per day a little longer.”

We hadn’t found the answer by the end of our time together, but that was okay. This time of math enrichment was meant to provide teaching that they can bring back to class and use on their own during independent work time. I had hoped that some of the students would continue working on their salt word problem throughout the week, when they finish their other work. 

A few students seemed excited about finding the accurate number of days as they left the classroom. They told me their tries and expressed surprise at not finding the answer yet. I told them to keep going. It was out there!

I found out later that a few students expressed to their math teacher that the problem was a little too hard. This inspired me to include the next part of this blog; The explanation. 

I chose 1 gram to be the new amount that the person consumes each day because you could eliminate one of the steps from the algorithm for solving averages, if you used increments of ten days. More than erase the step, you do it mentally. We already did ten days in class. That wasn’t low enough. Next, try 20 days. If you remember that the three days from the weekend is 8.61 g, all you have to do is stick a two in front of it! Then put a two in the tens place of the number you are dividing by; 23 (twenty more days + the three weekend days). At this point, it would be best to use a calculator to figure out the long division. (I never said that you couldn’t. I modeled using long division, but once you leave the classroom… 😉 Just show your work!! Write down what you did. Document each try, the answer you got, what you did. Be a scientist about it. 

Once you find between what two tens your answer falls, you can begin narrowing your work further. 28.61 ÷ 23 = 1.24 (twenty days of 1 gram of salt per day); 38.61 ÷ 33 = 1.17 average grams of salt per day; close, but not there yet; 48.61 ÷ 43 = 1.13 We made it! …But, we only ate one gram of salt for more days than necessary. We overshot our goal. In order to figure out the exact day, we could go back one or two days at a time. Maybe try the middle; 35 days. 

One student messaged me within the 5th Grade Math Enrichment Google classroom, seeking clarification. She had taken notes on my example of ten days, and couldn’t remember why we added the ten to 8.61. I messaged her back, and a couple of days later, she had it! This student not only figured out the answer, but showed me all of her work. It is beautiful and impressive. 

In addition to this incredible success, however, I am pleased to share that some of the students were still mentioning the problem to me in the hall, days later. A student whom I see riding his bike when I monitor the crosswalk in the mornings queried if anyone had solved the problem, and we talked about possible solutions. I told him that it was more than 30 days. He couldn’t believe it. 

Congratulations to this amazing student! She did it. Great job!

Out-of-the-Box Thinking w/ Dominoes

This is a screenshot of the last paragraph + picture from my last blog, with the question of the day above it. I presented this on our Google Jamboard at the beginning of gifted teaching time for students to wrestle with.

I’m back with some more Dominoes word problem work. At the end of my last blog about Dominoes I dreamed up what I thought would be a good problem to get students thinking. It seemed not only doable to me, but I worried that it might be too easy. Not so.

I asked my students, “What is the highest score possible in one play of Dominoes?” I put 28 bones (one whole set) on each table, and encouraged students to move them around looking for the best combination.

This is a screenshot of photos that I used to show students how to connect Bones, adding up all of the ends, and analyzing which Bone would make the best play.

A game of Dominoes proceeds until one player or team acquires 150 points. It takes several rounds to accumulate that many points. During each round the players add Bones (Domino pieces or tiles) to an existing cross of Bones. You have to connect the same numbers, so a 6-4 Bone could not be added to a 5-1 Bone. It could be added to a 4-4 or a 6-6 Bone. When you connect a new Bone to the Line of Play, you add the last number from each end. Your goal is to have a sum that is a multiple of five. Only multiples of five get recorded as points, pushing you closer to the goal of 150; victory.

The first group that I met with are 5th graders. They are still learning the game. I thought that providing the question of figuring out the very best play would create a goal; “This is what I can aim for.” Instead, my students began building towers with the bones and grumbled, “Why don’t we just play Math 24?” Upon self-reflection, I now realize that my word problem was like asking someone who is just beginning to learn how to construct an airplane to calculate how fast it will go. “Dude, let me get the wings on this thing, already!” Ha, ha. Sorry, students.

Before wasting too much time, fostering further frustration, I decided to scrap the 5th graders’ warm up and move on. I made a mental note on the idea of a Math 24 preference, though. This gave me much to think about; More to come on that, soon.

My 4th graders were at their wits’ end.

I didn’t even try the problem with my 2nd graders, who are also novice Domino players. I thought I’d wait and see how my experienced 4th graders, the students whom I taught to play the game last year, would do. These guys would love the challenge, and should have all of the conceptual tools necessary to tackle this problem. They’re the ones in the picture on the Google Jamboard, for crying out loud!

My 4th graders jumped into “Problem-Solving” mode right away. Their biggest hangup was trying to play the game from the beginning. They kept trying to build the arms from the center of the game, forming a cross they way they always do. That won’t work when attempting to find the highest possible score, though. They would have already used the Bones with the greatest number of Pips (that is the technical term for the dots on the Dominoes) on them. Those need to be saved for the ends.

Finally, success!
Frustration.
Start over, and over, and over, again.

I must have told them to, “Focus on the ends of all four arms. Don’t play a whole game. You don’t need the center of the cross in order to calculate the largest point accumulation possible,” a dozen times. I began to feel like a broken record.

This is a picture of the notes from my journal that led to this “Wonderful Word Problem.” I only focused on the ends of the Line of Play. I’d hoped that this is what my gifted students would do.

Finally, I stopped them and taught them a new vocabulary word: Hypothetical. “This is a hypothetical situation. If you could have the ideal play; The absolute best play ever, what would it be? Don’t worry about what was already played. What Bones would give you the very highest points?”

This is truly Out-of-the-Box Thinking. I wanted my gifted students to leave the box of the game and imagine only the very last play. All previous plays are fog. They don’t matter. You can only see the tips of the Lines of Play, and they have huge Bones… Doubles, every one of them; The highest Doubles, even! Eventually, I had to just tell them the answer.

I had one last group to try out my wonderful word problem. I started the Domino difficulty by sharing with my 3rd graders that the 4th graders could not do this. That got their competitive juices flowing! Next, I did not allow them to put any Bones in the center of the cross. “We are NOT playing Dominoes,” I explained. We are figuring out a hypothetical question: “What if you had an opportunity to make a play that gave you an enormous amount of points? How many points would be the greatest possible in one play of Dominoes?”

Believe it or not, the 5-5 Bone is worth more than the 6-5 Bone, because it can be played differently.

I guided their thinking toward the Bones that represent the greatest numbers. Even though a 6-5 Bone has more Pips than a 5-5 Bone, it does not present the greatest value when played at the end of a line. Why? Because, you don’t add the 5 and the 6 from the 5-6 Bone. Only one of the numbers would be available for adding. However, if you played the 5-5 Bone sideways, you’d have ten. Gasps, sighs, intake of breaths… Doubles were explored. I forced them to put the Doubles at the ends of the lines of tape I’d stuck on the tables to guide Lines of Play.

“Place the Doubles at the ends of Lines of Play.”
Afterward, we explored what Bones may have been played previously, working backward from our hypothetical best play.

Letting the 3rd graders figure out answers to my guiding questions, I led them through Out-of-the-Box Thinking. In the end, they felt like they had solved the problem, and they had (with a little guidance from their teacher). Lesson: People can be taught to Think Outside of the Box. It is not necessarily natural.

Wrestling With the Beginning

When preparing to bring the original “Scarlet’s Superpower” from 13 pages to 26, I was thinking of ways to beef-up the story. While I liked the simple story line, the text needed a little more meat to it. Should I develop characters more? Could we include additional ways that her superpower was utilized? My favorite idea was to show ways in which Scarlet’s ability to shut out noise by removing her coils could benefit her. 

One morning, several years ago, I was driving Scarlet to her before school daycare when an idea hit me: What if Scarlet used her superpower to avoid hearing bullies belittling her? We could begin the book with her wanting to take a nap. She could query about sleeping on a mat in the infant room of her daycare, at the end of the first day of school. Older kids; kids Scarlet’s age; could see and hear this, and they would tease, “Look at Scarlet. What a baby.” 

Scarlet would NOT hear this teasing, though. She would have already removed her coils. She can’t hear anything–nothing–when she takes her coils off of her head. So, exhausted Scarlet lies down, innocent and thankful for peace and quiet. 

The teacher, on the other hand, hears these older kids teasing Scarlet. Because the facility has a “Zero Tolerance” (no teasing) policy, the teacher reports the miscreants to the person in charge of the daycare. They get in trouble. 

I’m not sure if Scarlet finds out about the bullying behavior or not, but by the end of the book she helps these kids, using her superpower. They admire both her ability to forgive and the power to NOT hear. 

Here are a couple of the problems with this beginning.

Scarlet’s mom and I looked at tons of daycare facilities to determine which would be best for our only child. In addition to staffing, cleanliness, and the usual concerns, we had to consider how noisy the place was. Luckily, our area had many to choose from.

While I like using more than one setting for the story, having Scarlet attend a daycare could paint her as privileged; Her family is wealthy enough to send her there. 

I could explain that Mommy and Daddy make just barely enough money to have her attend, and need her to, so that they can work the jobs that pay for her attendance, basically breaking even. This circumstance would explain away the idea of private child care being a symbol of wealth; It is a shackle (Fetters, 2020). A surprising 57% of the working population of America pay more than $10,000 a year for child care (30+ Essential US Child Care Statistics [2022]: Availability, Costs, and Trends – Zippia, n.d.). 

Additionally, Scarlet attending a daycare categorizes her as lucky. According to 30+ Essential US Child Care Statistics [2022]: Availability, Costs, and Trends – Zippia, “51% of Americans live in communities classified as child care deserts“ (n.d.). I do not want someone to come across “Scarlet’s Superpower,” and think to themselves, what an entitled, lucky, rich brat. 

Obviously, I am totally overthinking the situation. Some kids go to daycare. Some don’t. The kids who don’t go to daycare know about others who do. Is the situation relatable? That is the question. Can readers visualize kids making fun of Scarlet for wanting to take a nap? I think so.

Sources:

30+ Essential US Child Care Statistics [2022]: Availability, Costs, And Trends – Zippia. (n.d.). 30+ Essential US Child Care Statistics [2022]: Availability, Costs, and Trends – Zippia. Retrieved January 10, 2023, from https://www.zippia.com/advice/us-child-care-availability-statistics/

Fetters, A. (2020, January 18). The Working-to-Afford-Child-Care Conundrum. Working to Afford Child Care so You Can Work – the Atlantic. Retrieved January 10, 2023, from https://www.theatlantic.com/family/archive/2020/01/working-afford-child-care-so-you-can-work/605206/

U.S. Department of Education, National Center for Education Statistics. (2021). Early Childhood Program Participation: 2019 (NCES 2020-075REV), Table 1.

Not All Online Learning Is Created Equal

IMG_6437
Scarlet is a pro when it comes to imaginative play. 

Along with every other kid in the world, my 8 year old daughter Scarlet is experiencing at home, online learning during the “Stay at Home” novel Coronavirus Pandemic. She is receiving daily assignments of online activities. As I’ve been witnessing hers and preparing my own, I am evaluating what makes the most effective distance learning tools.

Recently, Scarlet was asked to log into a math website and complete a task geared toward teaching coin-counting. This cartoon animation had her making 25 cents with nickels and dimes. 

I try to let Scarlet do her online learning with as little distraction as possible, but this got to be too much for me! She was dragging coins to a spot on the screen until she accumulated 25 cents, and then it would celebrate her accomplishment with a silly jingle. I felt like my daughter was turning into a chimpanzee. 

IMG_6461I closed the device she was using and drew a grid. “I’m going to teach you a homonym; a multiple-meaning word,” I told her. “This is a table; not the kind you eat on. You use this to make sense of numbers.” 

We made a few tables with varying totals and different coins available. She made many different combinations of coins to show the same amount.

IMG_2567
Manipulatives help kids visualize math. 

While filling in a row of varying coins totaling a dollar, Scarlet made a slight mistake. The table already had one half dollar and one quarter. She wrote “5” in the nickels column which made me happy, but then she wrote “2” in the dimes space. I knew what had happened. She equated the value of one nickel with the number to be written in the field. No biggie. As it turned out, we happened to have toy coins that I had dug out of the closet. I presented the actual coinage on the carpet. Scarlet almost didn’t let me get out all five nickels, having realized her mistake. 

IMG_6466
If/Then problem solving; Cause & Effect relationships

Eventually, I made some puzzles where I would fill in certain coin fields and have Scarlet solve the missing number. “If you are making one dollar out of pennies, nickels, and dimes, and you have 8 dimes & 3 nickels, how many pennies will you have?” Not only did Scarlet solve the problem easily, but when I asked her to describe what she had done in her head, she walked me through her thinking. 

 

Thinking.

 

This is what was missing from the chimpanzee-producing online practice. The software allowed Scarlet to drop coins onto a spot on the screen and either rewarded her with a jingle or delivered a negative noise. It was up to Scarlet to figure out what worked best for getting the jingle to happen: Pull the lever to get the banana. 

IMG_3130
Follow Up Blog: “How Coding Can Be Taught Through Solving An Empty Field In A Math Table”

I’ve witnessed software programs that stop a kid after a few wrong answers and reteach a concept before allowing the student to continue an activity. Another way to check for thinking is having students type or video-record their reasoning for an answer. Then the educator can interact with the thinking, praising accurate steps, guiding ideas, and correcting missteps. 

The closer to simulating the tailored responses of a human teacher an online program can produce, the more thinking it will stimulate in the student. How can you make a program applicable to the most practitioners, while simultaneously being tailored to the most personalized outcomes/answers?

Visual Thinking is Classy

screen shot 2019-01-13 at 8.06.15 amThe exciting and informative live chat #MasteryChat that takes place on Twitter between 8 and 9PM on Thursdays discussed the topic of “Visual Thinking” on January 10th, 2019. I’ve always held the belief that the more connections students make to a lesson, the more they will remember. Also, the more emotionally attached they become to their learning, the more they will get out of it.

Teaching nonfiction text can seem like a boring topic. Here is a way I get kids creative about their learning: They make mini booklets about the text features that help them navigate through nonfiction texts.screen shot 2019-01-13 at 7.15.24 am

This is great because it gives them a reason for listening: They need to know what to include in their books. Each page models and defines a different text feature or part of a nonfiction book.

The learning tool becomes a toy. Students love looking through their creations all year long. They are proud of what they produce, and show them to their peers and parents.

screen shot 2019-01-13 at 7.15.48 amHere’s how it works. First, I spark the class’s excitement by showing telling them they are going to make books. Then I show them a mini book. Everyone loves that! They begin screen shot 2019-01-13 at 7.16.04 amantsing to make one. That is when I share a unique style of nonfiction text; The “instructional text” that tells how to make a mini book. I point out the sequence words, and we picture in our minds what is happening to the paper.

After students display good listening skills, it is time to hand out paper. I walk around and model as well as help make the folds. The cutting from fold to the center of the paper is tricky. There is always, without fail, a couple of kids who mess it up and have to start over.


Once they have their booklets made, students number the pages. This year, to get everyone back on track, listening carefully, I made this process hilarious by acting like the students couldn’t possibly guess what the next number was going to be. For some of them, I made up riddles and algorithms. Even though the kids obviously knew that the numbers were simply chronological order, they loved it. They were recreating my jokes days afterward in new contexts.screen shot 2019-01-13 at 7.16.17 am

The next thing that we do is put the vital information on the cover of the book. The project usually takes several days to complete, and I don’t want any books to get lost. The “Locating Info Mini Booklet” by (name of student) is placed in “Unfinished Work” folders, to be continued later.

screen shot 2019-01-13 at 7.16.43 amWhen we work on the mini booklets again, I have students label each page. They look at the list that I post on the board for them. Then we make a “Table of Contents”. Finally, students write explanations for each text feature on its page. Some of them, like the “Title Page”, are virtually self-explanatory. Others, like “Graphic Organizers”, require many examples. Students are only permitted to decorate, which they are all iching to do, AFTER all of the information is completed.

This project is more than just visual. The crafty nature of creating your own learning tool is sure to coat axons with much myelin.

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Image from Wikipedia

To Evaluate is Classy

“Kira – Kira” by Cynthia Kadohata

The title of this Newbery Award winner intrigued me. I read it in October of 2018. I havescreen shot 2019-01-10 at 7.50.39 pm struggled to blog about it. What angle do I want to use? How can I talk about this novel’s impact on me without giving too much of its plot away? I loved it, and I hated it; like something so bad that it’s good. And, I don’t mean poor quality–It won a Newbery Award!

Right after the new year, I was scrolling through Twitter, and I came across a tweet from the American Library Association that got me thinking. I replied to the idea, but haven’t stopped thinking about it since. I haven’t stopped thinking about it because I disagreed with it. The tweet suggested getting rid of books that don’t bring you joy. My reply communicated my dissent. I have loads of books that are only sad and some that are downright scary, quite the opposite of “joyous”.

It didn’t take long for someone to rebut my reply. Don’t think of joy as “happiness” the person suggested. After a few more back and forths, I began to understand it to mean “emotion”. As in, if a book does not “do something for you emotionally” (bring joy), toss it. This was still difficult for me to swallow, for I adore books. I love them the way I love students. Would I “toss” a student?! Of course not!! You can learn something from every single book and, in one way or another, help every single student.

I continued to wrestle with this concept for a while. I was trying to decide whether I agreed with this definition of joy, and whether it was a good enough reason to get rid of any books. One idea I had was that some books can actually be dangerous. I own books that I not only disagree with philosophically, but that have been shown to contain falsehoods. These books are actually hurting the public who read and believe them. Why would I own or keep them? (My wife is constantly trying to purge our library of them.) They serve as reminders and warnings. As the saying goes, keep friends close, but enemies closer.

Another thought I had concerned the books that I have read that didn’t do anything for me. They ended up being time-vacuums. I did not gain a thing by reading them. Could I get rid of those? Well, I did actually learn something through reading them: That they were pointless and a waste. This is a very important lesson. They could be kept to simply remind me of that danger.

I am aware that this could come off as a defense for keeping every single book, but what I am aiming to show is the process of “evaluation”. In this case, it looks more like “justification”, but simply thinking about each text from my library with the question, “Can I part with this one?” instigated a process that caught my attention. Evaluating is a higher-level metacognitive skill that is very valuable; And therefore extremely classy.

Each one of my books was evaluated on several different criteria. Did it evoke emotion? Did I learn a lesson from it? Was my life or world-view changed as a result of reading it? Would I recommend this text to a friend, and why?blooms-taxonomy-650x366

Eventually, I came to “Kira-Kira”, the book that I have wanted to blog about, but couldn’t quite bring myself to sharing why I liked it… or warn people of its harm. Of course, it elicited emotion! There were a few things in the book that could be potentially dangerous; concepts that immature minds may not be ready for. Obviously, I wasn’t going to part with it… But, wait a minute. What was I doing? I have mulled over this one book, that was probably my least favorite so far, in the way of bringing me the traditional definition of joy, more than any other! Through my “evaluation” of the text I am getting even more out of it.

The tweet that I originally disagreed with also caused me to evaluate. I had to look at the word joy from many perspectives. It drove me to look at a thesaurus, for crying out loud. I didn’t like the tweet. But, in the end, it was one of the most powerful, because it caused me to think the deepest. And, finally, I find myself doing the only metacognitive act higher and classier than evaluation: creation.

e56baeb7-646c-4020-a07d-b536633ee8c6
“Kira – Kira” by Cynthia Kadohata: Loved it/Hated it (healthy kind)

How are you using evaluation in everyday lessons? What do you have your students evaluate?

Sources:

American Library Association. (2019, January 4). Retrieved January 10, 2019, from https://twitter.com/ALALibrary/status/1081299680535998464 %5BThis is a link to the original tweet that sparked the thought for this blog.]

Armstrong, P. (n.d.). Bloom’s Taxonomy. Retrieved January 10, 2019, from https://cft.vanderbilt.edu/guides-sub-pages/blooms-taxonomy/

Infectious Thinking: Chess

IMG_1618 2I was glancing around my classroom before I unplugged the Christmas lights and took off, yesterday, and I saw this: A chess board had been “put away” by being placed on the Red Bin. The Red Bin is the place where notes, money, messages, etc. for the office are placed first thing in the morning. They then get sent down to the office with our lunch count in the green envelope seen under the chess set.

IMG_5301We are just beginning our school chess club, this year. I accepted too many members, and don’t have enough of the nice big vinyl boards with 3 inch plastic pieces for everyone. (Christmas idea;) So, we have been using a mishmash of different sets. The one in the picture is magnetized, that’s why the pieces can stay in place.

What struck me about this pic is the concept of actually sending the board to the office! Did a student think that this was a message for the secretaries? Should we move a piece and share the board with another class? There is a buzz around the school of students becoming increasingly interested in this “thinkers game”. I have been working on populating a webpage from my classroom website with chess related information that could be helpful not only to the members of our club, but any beginning player. Mr. Vitale, my third grade teammate and partner in running the chess club, and I have made several videos to post on this website. My dream is for the whole school to become interested in playing chess. I wouldn’t be upset if other elementary schools caught this vision. Wouldn’t it be great for our district, state, country to learn, practice, and master thinking strategically, analytically, as well as creatively?

Mr. Vitale and I began a chess game this past week during lunch. We couldn’t finish it, so it remained set up in Mr. Vitale’s room. He couldn’t help but show and talk to his students about it. I took pictures and shared them with my class. By Friday, we were able to complete the game, but only after both of our classes worked on analyzing the following images to help with potential moves. It was fun, exciting, motivating, and infectious. By Friday, my students were sneaking onto Chesskid.com whenever they could. I found iPads with chess games begun, hiding under notebooks.

Here is an idea: Teachers sign up for the Chess Challenge. The magnetic board travels around the school, visiting learning spaces (not just classrooms). A chess enthusiast, either chess club member or one of my students or myself, can visit participants, if desired, to help with some chess instruction. (In other words, teachers shouldn’t feel like they have to be good at the game to participate.) A paper with notation will accompany the board. This will also be posted on the website for classes to keep up with the game, virtually. The color a class is responsible for will depend on which is moving at the time the game arrives at their doorstep. If it is Black’s move when Room 205 gets the board, then they are part of the black team. When a class captures a piece, they get to keep it until the end of the game. They can display it as a chess trophy. Much of the game is strategy, so rooms could even display thinking by posting writing or drawings of the ideas that prepared their move. Perhaps awards could accompany the moves that displayed creative, analytical thought.

My aim is to not only spread the love of chess, but inspire thinking, especially an affection for analytical reasoning. Lets get kids excited about using their cognitive abilities as much as they are pumped to tackle, shoot hoops, hit home runs, etc. The brain may not literally be a muscle, but it should definitely get exercised!

Sources:

Editorial Staff. (2013, October). Treat Your Brain Like a Muscle: Exercise It. Retrieved December 1, 2018, from https://www.toyourhealth.com/mpacms/tyh/article.php?id=1885

Is The Brain A Muscle? (n.d.). Retrieved December 1, 2018, from https://www.top-health-today.com/general-health/is-the-brain-a-muscle/

Automation Might be Convenient, But Is It Classy?

My daughter Scarlet and I visited a restaurant the other morning to purchase some bagels. I ordered a “Baker’s Dozen” of various styles; plenty of Scarlet’s favorite, the oneIMG_0519 with sugar piled on top. When I asked the person behind the counter to slice and toast two of the bagels, so we could eat them then and there, I was told that I’d have to buy two more bagels, outside of the baker’s dozen. “The Line, where they assemble sandwiches and cook things, would have to toast the bagels,” it was explained.

Rather than schooling the employee on customer-service or being difficult, I opted to have two of the baker’s dozen sliced right there and forego the toasting. I felt a little

food breakfast fork bagel
Photo by Jaymantri on Pexels.com

cheap, but it was a principle-thing. I had purchased the baker’s dozen to save money. Buying two additional bagels would have canceled that, and then we would have too many bagels to eat over the course of the next couple of days.

You should know that there were, maybe, three people sitting and eating in the restaurant, and there was one person behind me in line. In other words, it was not rush hour. It seems to me that the main reason for the toasting needing an additional purchase was because the computer didn’t have a way to send an automated message to “The Line” when a baker’s dozen was being purchased. The only way for this worker to communicate that two bagels were to be toasted was by producing a separate order… Or, she could have grabbed a couple of the thirteen and asked the people working “The Line” to toast them… verbally… perhaps with hand gestures or signs.

Empathy: This deserves a whole series of Classy Blogs, but let me start here. In every single situation, I try to empathize with each person involved, because I believe attempting understanding motives is classy. When you know where someone is coming

photo of black flat screen monitor
Photo by Fancycrave.com on Pexels.com

from, it is easier to behave classy. In this instance, the girl taking my order could very well have been new. Perhaps she was told to only use the computer. Maybe she was specifically told to avoid extra transactions, outside of the automated system. “If a customer wants his bagel toasted, you HAVE to press the toast icon on the keypad,” a manager may have said to her right before I placed my order. It isn’t impossible for there to even be an unseen difficulty for this girl to walk the ten feet and talk to “The Line”. Her ex-boyfriend could be working over there, and they just broke up. Who knows? The one thing that I did know was that this girl could not see through the automation of the ordering system before her.

It reminded me of a movie that I do not recommend you watch. It isn’t the drug use and profanity that keep me from suggesting you see “Idiocracy”. The movie has gone from satirical comedy to frightening realism. Its preface is a world 500 years in the future that has become idiotic due to people’s intelligence devolving. While there are several ways this is depicted, one is the use of computers with nothing but icons on them. When I first saw it, I thought it funny, but watching it a year or so ago made me dangerously depressed.

Here is some more empathy: I understand why automation exists. The people at the head of companies want to make as much money as they can. This is only natural. I would like to have more money, too. By lowering the steps necessary to take care of customers,

party glass architecture windows
Photo by Negative Space on Pexels.com

limiting the amount of time a living human being is needed for communicating with people, the companies can hire fewer people, thereby spending less on employment. Also, automation can lessen the amount of trivial needs that their paid employees have to deal with. When there is bad weather and I call my gym to see if it is still open, I am surprised to talk to an actual person. I apologize for simply wanting to know if it is open. “Yes, we are open,” a courteous receptionist assures me. I feel badly for how many times that person is probably going to have to deal with my question throughout the morning. An automated system could help them.

On the other hand, when I have a pressing need or question that I know won’t be

person holding smartphone
Photo by rawpixel.com on Pexels.com

addressed by an automated system, it is infuriating to have to jump through a million hoops to talk to a real person. Sometimes I mask myself as a person seeking to begin a new account just to get to talk to a live person. When I get “transferred” to a person who can “help with my specific issue,” my cynicism makes me wonder if my lengthy wait is just part of meeting the company’s hold-time-quota: “You’re going to wait, whether you realize/want to, or not.”

In the case of my morning bagel customer-service crisis, it was sad to see a young woman be boxed into an algorithm that didn’t allow her the ability to show the classic “customer-first” concept that makes the service industry classy. Doctors are equipped with an awesome amount of valuable information via the Internet, which can make their work of diagnosing patients’ ailments more effective. Who would be okay with the doctor texting you what they find? The 2009 movie “Up In the Air” gets it. George Clooney plays a businessman who is hired in order to fire people. When his job is threatened by an online career-termination skeem that a fresh, young mind thinks up, Clooney’s character insists that the inventor travel with him to witness the class necessary for handling this delicate procedure properly.

Fighting automation is a losing battle. “Let the robots take the jobs…” Kevin Kelly (2012) thinks robots should win the jobs that can be automated, “And let them help us dream up new work that matters.” There will be hiccups along the way, and Scarlet and I might have to eat a couple untoasted bagels, but it’s worth being able to type this on a computer instead of being busy with farm chores; one of the many ways robots have rescued Americans.

man watering the plant during daytime
Photo by Pixabay on Pexels.com

 

Judge, M. (Director). (2006). Idiocracy [Motion picture on DVD]. United States: 20th Century Fox.

Kelly, K. (2012, December 24). Better Than Human: Why Robots Will — And Must — Take Our Jobs. Retrieved July 27, 2018, from https://www.wired.com/2012/12/ff-robots-will-take-our-jobs/

Reitman, J. (Director). (2009). Up in the Air [Motion picture on DVD]. United States: Paramount.

 

5 Classy Elements of “The Story of Mankind” (1921)

It is interesting that the American Library Association (ALA) would choose a history text IMG_5131for its first-ever children’s literature award winner. Was the organization making up for only just now (1922) beginning to honor kids’ books? Were the organizers thinking they’d catch everyone up to speed? “This is what has happened in the past; Now, lets award one book each year.” I’ll tell you one thing: This is one classy history book. Here are 5 features I found to be extraordinarily classy.

1. Figurative Language: What struck me first and foremost was a combination of beautiful prose and mountains of metaphor. To begin at the end of the book, on page 482 Van Loon refers to the world as a “workshop”. He sees the steam, gas, and new-to-his-era electric machines forging a global factory. The story of Hendrik’s history ends a few

New_Street_Station_Iron_Horse_sculpture_,_Kevin_Atherton
New Street Station Iron Horse sculpture , Kevin Atherton.jpg (with “Iron Horse” on rails behind it)

years after The Great War. He concludes the new world is a  place where political lines are as important as the edge of a concrete slab under a picnic pavilion (my metaphor;) Van Loon sees the “Iron Horse,” machinery in general, as the true victor of the First World War, running wild over, across, and through the entire world, regardless of man-made borders. Was he right? What would Van Loon make of today’s robots, not to mention the Internet!? The previous nearly 500 pages are teeming with as many metaphors.

Here is a fun passage for discussion:

And now that I have almost finished I discover that certain chapters gallop, that others wade slowly through the dreary sands of long forgotten ages–that a few parts do not make any progress at all, while still others indulge in a veritable jazz of action and romance. (p. 446)

Present Hendrik Van Loon’s self reflection prior to reading the text and then categorize the readings. Which chapters or sections would you label “gallop”? Are there any that were “jazzy” with action? Romance?

2.  Evidence-Based: The forever swinging pendulum seems to have exorcised more than 14219487807_6eabf4c50a_bjust public prayer from schools. A friend of mine told me recently that she was pointing out the similarities between the Greek myths and the story of Moses from the Bible. Her students had no idea who Moses was. Whether you are religiously-minded or not, this should alarm you. I am pleased to report that Van Loon mentions Moses, Abraham, and even Jesus in his history of mankind. He does this in a classy way. Rather than telling the reader what the Bible says, Van Loon provides outside sources. For example, a letter from AEsculapius Cultellus (Roman physician) to his nephew, written in 62 A.D. tells of a first hand account of treating Paul (the apostle) of the New Testament (p. 119).

3. Provides the People’s Perspective (a little): In addition to hitting many of the main events of history, Van Loon pauses to describe what life was like for a common person. Napoleon, his feats, the land his army conquered are all important facts to know. These

Eastlake_-_Napoleon_on_the_Bellerophon
What was life like for the guy holding the board Napoleon is leaning on?

events affect the course of history. Van Loon provides more than just the basics in his blitz of history. He paints a picture of life for the Frenchman who was proud to take up arms to help Napoleon. The way the Roman Empire gradually usurped land and people, assimilating other cultures into its own is a lesson in and of itself, but learning about the life of a slave under Greek and Roman rule brings the everyday life of thousands to light. What was life like for them? It is easy to project attitudes onto others, yet the author of “The Story of Mankind” gets into the character of his subject illuminating everyday struggles and fears, helping the reader empathize with the characters in the story of history.

Here, I have a criticism. Of course with any history project it is going to be “The Story of Mankind” according to the author, who in this case is a Dutch-American professor from Cornell University. In his view Holland and England were heroes to the natives of the Americas in the seventeenth century (p. 324). With sympathy, he provides the mildly racist annotation, “During their first relations with weaker races, all European nations have behaved with shocking brutality.” Although it is interesting to read about France exploring and fortifying the Mississippi River, cutting English and Dutch settlement off from westward expansion early in the new world exploration, absolutely no attention is given to the “mankind” that already inhabited the Americas. Of course space is limited, but an entire chapter is devoted to the relationship between Russia and Sweden! One of the best books I have ever read, devoted to the people’s perspective, is “A People’s History of The United States” by Howard Zinn. Before reading this text, I did not realize that in the year 1491 the Americas were more populated than Europe and that the largest city of Europe paled next to the Aztec capital, modern day Mexico City. There is a youth edition.

Discussion Point: Page 449 suggests that “Athens and Florence, during the hey-day of their glory, had only one tenth of the population of Kansas City.” The larger-than-life influence of Greece and Italy on our culture makes it feel like these peoples must have had infinite populations. It was a bit of a paradigm shift to realize that a tiny group of people could have such a large influence over a vast amount of time.

IMG_83534. Thought-Provoking: An informational text is naturally going to be educational, requiring cognitive engagement, but Van Loon has a knack for skipping the boring stuff of history and presenting ideas that get the neurons fired up. He assumes the reader already knows the basics of the American Revolution. Instead of covering the main points, Van Loon attempts to shine light on the unique angles. In the United States we focus very much on the ground battles led by our hero, General George Washington. How much attention is given to the weakening of the English army by its enemies from the European mainland, and how much that affected the outcome of our revolution?

Van Loon does an excellent job pointing out that there is always many factors that contribute to a single historical event. The famous Congress of Vienna, that ended The Great War are referred to as “reactionaries” in the chapter on “National Independence” (p. 381). 

Caricature_of_CongressVienna
Caricature of Congress (of Vienna)

5. Opinionated: Here is a topic deserving of its own blog. It is not classy to believe what everyone else believes, just because everyone else believes it. Believe something based on the evidence available and how much sense it makes. The classiest people possess their own independent opinions. With knowledge of subject and contemplative thinking, they form cognitive constructs that they then share with others. Additionally, they are prepared for varying opinions. An example of Van Loon’s “opinion writing” can be seen in the chapter “After Seven Years.” He explains that the men who were responsible for ending the First World War treated the, at that time (1921), modern situation as if it were colonial times (1719), rather than recognizing the rise of the industrial age and accepting a more global perspective. He points to the way they sat around a map and drew arbitrary lines dissecting land with little regard for the people and industries that lived there. It is heart-wrenching for me to read text written between the two world wars: “Meanwhile in their agony and distress the people will turn to the cure-alls offered by Bolshevism and Fascism” (p. 480). Was Van Loon a prophet? No. He simply took what he saw happening around him and formed an opinion. If only we can be so classy.

 

Watch out for…

  • Violence–Can’t really talk about war or humanity without mentioning murder. What was the French Revolution without mention of the great invention of the guillotine? What little kid needs to picture heads rolling on the floor? –none. I would sticky-note and smooth over or couch the violence in age-appropriate concepts. For instance, “Learning history can be a way to help avoid mistakes made in the past. One bad thing that happened a lot, is war. Sometimes people and countries avoided war by getting together and talking. But, not always.” How to Talk to Kids About Violence

Here is an online version of the entire original text, complete with illustrations and hyperlinks from the index items to the “pages” containing the relevant information.

Sources

Child Development Institute. (n.d.). How To Talk To Kids About Violence. Retrieved July 16, 2018, from https://childdevelopmentinfo.com/how-to-be-a-parent/communication/talk-to-kids-violence/#.W0CQJzNKhE4

Van Loon, H. (1921). The Story of Mankind. Garden City, NY: Garden City Publishing Company.

Zinn, H. (2007). A Young People’s History of the United States: Columbus to the War on Terror (For Young People Series). New York, NY: Seven Stories Press. [This was accessed for free via Overdrive through my public library. I read it on my iPad.]

Zinn, H. (1980). The People’s History of the United States. New York: Harper Collins.