A part of our month-long exploration of measurement included “raising” Gro-Beasts. These are alligators made of a water-absorbing polymer. Students placed them in plastic shoeboxes filled with water and kept track of the changes in their mass, length, and girth. Sadly, this year’s product was somewhat defective and didn’t grow as much or as quickly as the ones we have bought in years past. (Correspondence with the apologetic manufacturer confirmed that observation, but we still were able to do the math activities that we had planned.)

Students set up a table with a place to enter data for every day from the beginning of the observations to the end. When they questioned the need for weekend days, we said they would need those spaces later. A digital scale let us find the mass, length was measured with a ruler, the girth behind the front legs needed a piece of string, and we also did a tracing of the outline at the beginning, about a week later (on the same graph paper), and at the end on a separate page..

When we decided that the gators had grown as much as they could, we started graphing our data. Students exhibited some uncertainty about setting up line graphs, so it was a good review for many and an introductory experience for a few. We discussed making a decision about the scale of the y-axis based on the range of the data. In class, we made graphs for length and mass. Making the graph for girth was a homework assignment, intended to provide us with a way to check their understanding of what we had taught. Although most came back with graphs that looked much as we had hoped, there were some wobbles that were easily resolved.

After our collected data was graphed, we discussed the idea of interpolation. Now that we had a path for the growth throughout the month, could we make some inferences about what the measurements would have been if we had been able to gather data every day? Students used a colored pencil to plot the intersections of the “empty” dates and the line of the graph. They then added that data to the table we had set up at the beginning. Those blank sections now had numbers, also recorded in colored pencil, and students understood why we had included those dates in the beginning.

The final challenge was that of finding the areas of the first and final tracings. Students were asked to make their best estimate for the large one that we made on the day we ended the project. Then we gave students a page with several polygons on it. They were able to find the areas of the rectangle and the triangles but were puzzled by the others. Some students had good ideas, such as partitioning the irregular polygons into ones they knew how to calculate, but it was harder than it looked.

At that point, we gave students a page that told them about Georg Pick, a mathematician who was born in 1859 in Vienna, Austria, and died around 1943 in the Theresienstadt concentration camp in Czechoslovakia. He was a friend and colleague of Albert Einstein when both were living in Prague (from 1911 through 1913). The friendship lasted until the start of WWII. Pick is thought to have collaborated with Einstein in some of his work. I explained that we were going to use a strategy known as Pick’s theorem to find the area of those troublesome polygons. (It’s important for students to remember that mathematics is a human construct, that there are people just like themselves behind every mathematical idea.)

The steps that Pick devised were these:

1. After drawing the polygon on a grid, you count all of the places where the outline crosses an intersection of the grid. These are called boundary points.
2. Then count all of the grid intersections inside the polygon. These are interior points.
3. Divide the number of boundary points by 2. Subtract 1. Add the number of interior points.

You now have the area. (Try it on the rectangle above — you should come up with 16 boundary points and 8 interior points, giving an area of 15 square units.)

Students applied the formula to the irregular polygons and then wanted to see if the areas were correct. We brought up Geometer’s Sketchpad on our computers, opened up a sketch that had the same polygons on it, and used some of the software’s features to find the areas. The numbers matched!

Back to the alligator tracings . . . but they weren’t polygons. We agreed that Pick’s theorem should still give us an approximate area but not one that would be as exact as we would get from figures that had straight sides. After a bit of work with colored pencils and some tough decision-making about whether the outline was really on a particular intersection or not, everyone was able to come up with a number for the area that seemed reasonable to them.

Students enjoyed using Geometer’s Sketchpad and especially liked having some free play time at the end of a couple of our classes. Sixth graders knew some things about it from last year’s math activities and happily shared their knowledge of animation and color changes with their fifth grade classmates.

We ended all of this with a few days of working with coordinates on the full Cartesian plane. (And yes, we did mention Descartes.) We showed students a page with all four quadrants drawn on it but not numbered. We placed the positive numbers on the x and y axes and then asked students about how to label the rest of each axis. Several quickly suggested negative numbers, which was right. One student observed that the concept was a lot like what we had done earlier in the year with latitude and longitude. After completing the axis labeling and discussing how coordinates were written for plotted points, we gave students a handout that contained instructions that, if followed correctly, would emerge as a drawing. With a bit of error-correction, everyone ended up with the expected picture. We gave students a homework assignment: create a picture or design, write the coordinates and connection instructions for it on a different paper, and bring it to school to give to a classmate the next day. Although a few students ran into difficulty, most came up with a plan that worked. We finished with a dice game that required, again, the use of coordinates to place the game pieces.

Graphing, finding means and medians, applying coordinate geometry, practicing the application of a formula, using interpolation to complete a data set — there was a lot of solid mathematics in this part of our measurement unit.

 

When teachers arrive at Miquon, they often bring wonderful new ideas that are likely to keep going, at least for a while, after those teachers move on. “Life Skills 101” is a multi-week activity that began in Erica’s 5th/6th grade classroom some years ago. Students are asked to consult with their family and come up with a three-week plan in which they will learn a new skill that is likely to be useful in their later lives when they are living independently. Sometimes they already have the beginnings of that skill but plan to improve it significantly. They keep a weekly journal of their activities and also a chart on which they record the time spent each day. Some students choose a task that they work on several days each week; others may work only on weekends. At the end of the time, we ask them to give us a brief presentation — a talk, a slide show, a demonstration, or whatever seems appropriate and interesting.

This year, as in previous years, students selected many different things as their life skill. Family members were often quite involved in teaching skills and providing supplies and transportation, which we appreciate very much. Five students worked on house-cleaning in some form. Bathroom cleaning was decidedly unpopular but acknowledged as necessary. One chose to clean and de-clutter his room in anticipation of having his house go up for sale, and he also worked on designing the room he hopes to have in his new home. Six students chose cooking. One of those noted that he was specializing in learning the kinds of things he will want to eat when he is away at college “because my father won’t be able to drive there and cook for me every day.” One student painted her young cousin’s bedroom, working with her grandfather as her mentor. Another student decided to learn to travel independently to several useful destinations, taking on the challenges of dealing with buses and trains as well as using an app to track the schedules of both. A couple of students learned to do the laundry. One remarked that he not only learned to fold but also put his own clothing away for the first time. One learned to plan meals,  set a spending limit, make a shopping list, and go to the store for what was needed.

When students made their presentations, we talked about some of their insights and opinions as well as their skills. Ones who had tackled a very messy room observed that it would be much less of a job to keep things neat and clean now that the big cleanup was over. Several spoke of enjoying time spent with family members as they learned from them. Several expressed new-found appreciation for the time and effort that their parents spent when they were tackling these jobs. Many thought they would go on doing these things because they could see how important they were to family life.

The presentations were uneven, but we could see progress in many ways. All of our students talked to their audience instead of reading from the screen or from a detailed page of text that they had prepared. The slide shows that some students chose to create were highly visual and served as a structure for their talk without having many (or, in some cases) any words. Some had organized their talk well, telling us without any prompting what they chose and why, what they did during the three weeks, and what they learned in the way of new skills and perhaps some new insights.

We could also see that there is still some work to do. It was obvious that some students had not reviewed their journals carefully (or at all) to remind them of some of the details of their activities. Some had not practiced their talk aloud and found themselves groping for language and fluency. One had photos of his efforts but didn’t know how to get them into his slide show and didn’t ask for help. Some had forgotten that there was a presentation expected, even though a note about it was written at the bottom of their daily time sheet and should also have been recorded in their student planner when the project began.

We reminded everyone that there was at least one more presentation in our plans before we will have reached the end of the year, which is their personal project. That self-selected learning activity takes place in the month of May and, like Life Skills 101, is shared at the end with their classmates. Students were urged to think about what went well with the presentations we just completed, in their own sharing and/or those of some classmates, and what would need more thought and preparation next time. Our emphasis was on learning from this experience and using that learning to move forward. We expect to see many wonderful presentations when the personal project ends, based on the growth that we were able to observe this time around.

One of the professional pleasures of working at Miquon is that teachers are not locked into a rigid curriculum that remains the same, year after year. Although the learning goals are well-established, the ways those goals may be reached are flexible, are likely to change from year to year for many different reasons, and are under constant evaluation by individual teachers, teaching partners, and the staff as a whole.

One of the core programs in the fifth/sixth grade groups is one we call Changes and Choices. This program includes making healthy choices of many different kinds (including diet, drug and alcohol use, smoking, and peer pressure); navigating the social and informational world online; and understanding the changes that are a part of puberty. This year, we decided to do the program in a very different way.

In prior years, we have often worked on Digital Citizenship as a separate topic. Students have learned about engaging with social media, doing internet research efficiently and wisely, considering ways to protect their own identity and privacy, and dealing with personal safety and cyber-bullying. Changes and Choices generally encompassed the rest of the topics listed above. These explorations have usually spanned several weeks and have been done along with the rest of our program and the specialists’ classes.

This year, at Diane’s suggestion, we decided to try a different format. We put all of our other topics on hold (including those of the specialists) and spent all four days of this past week on Changes and Choices. We divided the topics into three major parts:

• Digital Citizenship (1 day) — led by Mark and assisted by Jeri
• Healthy Choices (1 day) — led by Jeri and assisted by Mark
• Human Development (2 days) — led by Diane and Lynn

We blended and then divided our 31 students into four groups. Two pairs of groups stayed together throughout the week, rotating through those three topics. During the week before, students had the 3-part program explained to them. Then they were asked to write on a slip of paper any topics or questions that they hoped we would explore and drop them into our 3 collection boxes. Teachers later looked at those papers and made adjustments to their plans in order to incorporate as many of those wishes as possible.

Although the first two topics listed above were done in ways similar to our past practice, Human Development was initially intended to take us from conception to death. As we planned our time and activities, however, it became clear that we were not going to have enough time to explore death and dying, although it was clearly a subject that interested many of our students. We will take that topic up before the end of the year, but it could not be fitted into the four days that we had.

All four teachers wrote a summary of each day’s activities and included some general notes about students’ engagement with them. Those summaries were shared with parents at the end of each day. Parents were urged to continue the topics in conversations at home.

Below are some excerpts from those daily summaries. Because the conversations were greatly shaped by the students’ questions and degree of interest throughout each day, not every group had precisely the same experience with each topic. The excerpts represent what some families received; others got slightly different descriptions.

From Jeri (Healthy Choices): Today, our group worked on learning to make healthy choices on a daily basis and in life in general. There were several activities and lots of group conversations in each.

We started the day in half groups. Mark worked with a group doing with an online activity, “All Systems Go” and its worksheet. This helped the kids learn to identify the various parts and systems of the human body. The other half group took a close look at information about nutrition and exercise. Specifically, what should be included in a balanced diet, and how much exercise should kids get every day? We also looked at sugar and its effect on the brain and body, how the labels can be tricky to understand, and how sitting too long is bad for you. The kids were really surprised to learn how much sugar is in so many products and also that sitting too long has so many bad effects on your body.

The mid-section of the day focused on a variety of drugs and their effects on the brain and other parts of the body. Together we walked through an online activity, Drugs and Your Body. This activity includes information about the effects of abusing drugs such as tobacco, cocaine, methamphetamine, steroids and vaping. It goes through the effects on six different body parts – the brain, skin, lungs, mouth, heart –  and how they can lead to death. This activity was particularly shocking to the kids and grossed them out a bit. We also noted that not all drugs are bad, such as aspirin, but that they all need to be used cautiously and on short term, unless prescribed by a doctor.

In the last portion of the day, we focused on friendships and peer pressure, both good and bad.  The kids were asked to describe each and we talked through a few examples. A few of the kids acted out different scenarios that demonstrated both good and bad peer pressure situations. And finally, each child completed a “Decisions, Decisions” sheet, on which they ranked the values they hold and goals they aspire to, identifying ones that could not be swayed by friends and other peers.

From Mark (Digital Citizenship):  Today we started our morning with “Digital Life 101” from commonsensemedia.org, where we learned about the ways digital media fits into our everyday lives. We explored the 24/7, social nature of digital media. We began simply with what is media and how does it differ from digital media? We investigated our digital lives by questioning the way we communicate with and share with others over digital media. Because we’re connected in a more social and interactive way these days, we discussed online relationships and how to navigate them safely. We talked about ethical and appropriate ways to communicate online. We gave our students some tools to communicate effectively, avoid misunderstandings, represent themselves in a professional and thoughtful way, and engage respectfully when interacting with other online users. We ended our afternoon with robust debates about how to judge the intentions and impact of people’s words and actions online. We talked about ways to remain safe when online relationships turn into inappropriate online behavior and crosses the line into cyber-bullying.

From Diane (Human Development, day 1): Today’s work began with an animated conversation about the nature of development — how it happens in stages, how age boundaries on those stages are approximate, how it suggests growth that occurs across the lifespan, and how aging is something that can be understood to be happening from the beginning of our lives. Development also exists on many planes at once — physical, cognitive/language, and social/emotional.

We watched video clips of a 6 week old and then of a 21 month old child and observed for development in each of the areas above (physical, cognitive, emotional/social). We noted the clear and demonstrated development that was visible and connected it to other observations or experiences we had in our lives. The kids were astute observers and made reasonable inferences about what they noticed. We also briefly noted and roughly ordered a variety of developmental milestones. We talked about all of this as giving us insight (and therefore sympathy or even empathy) into others. The children then spent ten or fifteen minutes examining a chart of developmental milestones and descriptors for 9, 10, 11, 12, and 13 year olds taken from the book Yardsticks by Chip Wood. They were encouraged to find themselves reflected in those descriptions and to appreciate how their uneven development can mean they are on several charts at once. Attached to those sheets was a growth chart — the type one would see in a pediatrician’s office — and many of the children chose to chart their height on the chart. Tellingly, few charted their weight.

Every child then had an opportunity to observe a child in the nursery or kindergarten for  a short time, looking for development in those areas again. While those observations were happening, the other students were reading about the developmental milestones of particular age ranges (birth through age 5). Using that information, they drew outlines of appropriately-sized children and, with a partner, labeled those milestones in relevant places on the drawings (such as putting walking on the legs or feet). Those drawn and labeled figures were then hanging around us as we reconvened for a review of the morning and what we had learned/observed.

The afternoon was filled with work in gender-separated groups about the developmental stages in which these children find themselves, focusing specifically on the nature and challenges of puberty. Mark met with the boys and Diane with the girls.  (Lynn assisted Jeri, since Mark was needed for the boys’ meeting.) Both groups had open, free-ranging discussions as they learned about the body changes that puberty brings (to both boys and girls), about the reproductive system of men and women, and much more. Parents were sent a more detailed account of what their child’s discussion group asked about and explored, as the meetings were not identical in content.

Lynn (Human Development, day 2): Today Diane and I completed our 2-day study of Human Development with your child. We started with a teacher-created game show that we titled “More on Puberty and What Lies Beyond.” As students played the first part of the game in small teams, they learned about changes during puberty and adolescence that were not about sex and reproduction, such as growth spurts, cognitive maturation, and possibly needing eyeglasses. The second part of the game was about physical, cognitive, and emotional changes and experiences that are characteristic of the many stages of adulthood. These included strength and mobility gains and losses, career and family decisions, and changing financial obligations, among other things.

We watched “Life’s Greatest Miracle” from PBS, the amazing story of a child’s journey from conception to birth, featuring the amazing photography of Lennart Nilsson. Students asked some good questions afterward.  We talked briefly about the many ways that a child might enter a family (including ways that were chosen because of fertility issues, being a single parent, or being a same-sex couple — adoption, surrogate mothers, in vitro fertilization, sperm donation, etc.).

We spent about 45 minutes talking with Tony Hughes, Diane’s mother-in-law, Betsie, and her father-in law, Richard, about getting older. Students had generated questions and topics for them last week, and we had a very good conversation today about many different aspects of aging.

Finally, we looked at Thomas Armstrong’s concept of 12 Stages of Life and the “gifts” that come with each. There were a lot of good vocabulary discussions as students tried to figure out such words as benevolence, ingenuity, and enterprise. Children tried to pair the stages and gifts on their own, then got an explanatory handout of his view, and created a mobile with 3 by 5 cards.

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All four of us will meet soon to review how the revised program went, make sure the resources and activities are clearly described and annotated for use in future years, and consider adjustments to the format and time frame. We will also make sure that death and dying will be explored before the year is over.

Too busy with other school work to get a blog post up this week, but there will be lots to share next week.

“How did it get so late so soon?” ― Dr. Seuss

An article appeared in the NY Times Review of Books recently: “Pause! We Can Go Back!”   It discusses a book by David Sax called The Revenge of Analog: Real Things and Why They Matter. The analog examples cited in the review did not include clocks, but I hope they are discussed in the book. At some point, I plan to read it and find out . . . when I have the time.

Diane and I have talked about the value of analog clocks off and on for several years. The conversation was intensified this year by a workshop she attended that encouraged teachers to help students learn to manage time by understanding it better in a spatial sense.

In the blog entry for November 14 (part 1), I wrote about our children’s understanding of time in connection with the Terra Nova testing that we were doing. Below is most of that essay, reprinted here because the book review got me thinking about it again. It continues to seem like an important part of every child’s education, one that may be getting overlooked.

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Because so many of [our students] are surrounded by digital clocks and wristwatches, they have not developed a visual/spatial grasp of the units of time or the passage of time. I said on Friday that we were changing to a different activity at “a quarter to twelve.” I heard one student turn to another and ask, “What’s a quarter to?”

Every classroom at Miquon has at least one analog clock. To what is it analogous? To the circular nature of time and the infinite number of units that exist between the hours, minutes, and seconds that are marked on the face. A digital timepiece jumps from one unit to another — however small and precise its numbers may be — skipping the endless number of fractional parts in between its programmed units. An analog clock’s hands move smoothly around the circle, touching all of the infinite number of fractions between, for example, 3:04:27 and 3:04:28. It models the continuous rate of change that is part of the nature of time.

An analog clock gives us a visual representation not only of what time it is now but also what time it was and what time it will be. It is [also] a pie chart that shows the customary fractions of an hour that we reference when we speak of quarter after, half past, and quarter to. A digital clock displays a single, constantly changing set of numbers in isolation. It’s an entirely different and very sparse way of communicating about time.

This year, we did something new and very successful during the Terra Nova testing. Diane had gone to a professional development workshop that included some strategies for helping students with time management and planning. In response to what she learned, she brought to our two classrooms four clocks that had a metal rim (something that took her most of a weekend afternoon to locate!) and a clear plastic cover on the face. The metal rim was needed to hold a magnet, and the face could be written on with a whiteboard marker. Before we started each timed sub-test, we colored in the amount of time the test allowed and placed a colorful magnet approximately at the halfway point.

 

Now students could see the amount of time they had as something visual — not just a number that would come up sometime in the future.They could also readily see how close they were to the halfway point in their allotted time and compare it to where they were with the number of questions that remained. One student commented that the magnet made him anxious at first, but then it made him less stressed because he found that he was usually where he needed to be when the halfway point was reached.

In recent years, we have sometimes had a few students in fifth or sixth grade who have never learned to read what some of them call a “face clock” — something that would have been very unusual before those digital clocks came along. Learning to “tell time” from an analog clock was a skill we learned at home, along with tying our shoes . . . before the age of Velcro.

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We still need to know how to tie a knot or bow that can be easily undone, however our shoes may fasten these days, and we still need to have a deep understanding of time, despite the increasingly-digital world in which we live.

This is the first of several weeks in which we will have stepped away from our small math instruction groups that are blended with students from Diane and Jeri’s class so the two classrooms can do some different work with their whole group. In our class, the main focus is on measurement. We are working with both metric and “common” or “English” units — separately, not together. We’ve discussed and will continue to talk about the differences between the two systems, the need to memorize an arbitrary series of relationships in the English system, the base-ten organization of the metric system, and the way that metric prefixes apply  across the units that measure length, mass, and volume.

Students have all made a personal copy of a wonderful sign hanging in Diane and Jeri’s kitchen that shows the relationship among cups, pints, quarts, and gallons:

Our afternoon bingo games have focused on vocabulary and relationships. How many teaspoons in a tablespoon? What does the metric prefix “kilo” mean?

Students have also started working in the “Key to Measurement” booklets, starting with units of length. After completing one or more pretests, some are doing the metric series and some are doing the English series. In both programs, students are doing a lot of actual measuring as well as learning to convert among the units (inches to feet, for example, or centimeters to meters).

With everyone, we are doing some additional practice with fractions. Students have measured many things around the classroom using inches and have recorded those measurements as inches, feet and inches, and feet and fractions of a foot:  62 inches = 5 feet and 2 inches = 5 and 1/6 feet. This has led to some review of fractions and fraction simplification for some students who found this last step difficult.

Estimation has been part of our work as we try to help students internalize some of these measurements. For example they were asked to measure only things that they thought were more than a foot long. On Friday, before we delivered the sandwiches to classrooms, they were asked to estimate the mass of each kind of sandwich, based on their very limited experience with their alligator Gro-Beasts (explained below). A few students were able to come quite close to the actual weights, and many were right in the relationships (one sandwich being about twice as heavy as another one) even if the actual numbers were far from the mark. We’ll be doing more of this as opportunities come up.

The alligators are providing a lot of fun as well as lots of practice with measuring. Most students have named them and speak to them in a friendly way when they arrive in the morning. Some have set up partnerships to ensure that their alligator will be looked after on days one of the partners might be absent. We’ll be writing about the ‘gators this coming week.

Students started by finding the mass, girth, and length of their alligators before they went into their tubs of water. They have a folder in which to keep the records. “Girth” was a new vocabulary word for just about everyone. They also did a tracing of the outline of the alligator on graph paper and will be doing another on Monday. The next day, they repeated the measurements and also calculated the difference in the mass. We’ll be doing this daily until we are convinced that they have absorbed all of the water that they can. Then we’ll take them out of the water and track their changes as they dry out. We’ll be doing some graphing of the data, and we’ll use those graphs to interpolate and record approximate numbers for days that we did not measure, such as weekends.

On several days, as students emptied, rinsed, and refilled their tubs, we asked them to use the cup or pint containers to do the refilling and count how many it took. Again, we expect that this kind of experience will help with the internalizing of what those measurements really mean. Anything parents can do at home to provide measuring experiences of any kind — cooking, building, sewing, and the like — will add to the knowledge gained in our classroom activities.

Even our hydroponic tomato garden is getting some measurement attention. Students have been amazed by the rate at which our seedlings are growing.

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Lots of other things went in class, of course. We started literature groups that are going to meet on Thursdays for the next several weeks. After students looked at a lot of different books and indicated interest in at least three of them, we ended up with Un Lun Dun by China Mieville, Fourth World by Kate Thompson, Mockingbird by Kathryn Erskine, and The Wordsmith by Patricia Forde. Vocabulary and syllabication will be part of our work along with discussions of the novels themselves.

Our study of Ireland has passed through the Bronze Age and brought us to the Celts. Students are enjoying developing their skills with a board game commonly called brandubh. Is what we are playing a truly authentic version of this ancient pastime? Probably not, but it is likely to be reasonably close to the game as it continued to evolve and be played in more recent times for which we do have some written references.

The start of Donald Trump’s presidency has given us a lot to explore as we use it to continue our year-long involvement with the Constitution, the structure of our 3-part federal government, and current events. We have looked into executive orders (a practice that goes back to George Washington), including the one issued by Franklin Roosevelt that forced people living on the West Coast who had even a small amount of Japanese ancestry into internment camps during World War II. (Students know that this will be our final topic for the year in our exploration of migration and immigration.) We will be finding out more about the Supreme Court and the ways justices apply and interpret the Constitution during the coming week of school. These are, indeed, interesting times.

And as all of our parents know, we began our 3-week adventure with “Life Skills 101.” We’ll share more about that next week.

Teachers spend a lot of time planning activities, observing children as they engage with them, making adjustments for the group or individuals, and applying what they’ve learned when they do something similar. Rarely does any activity go exactly as planned, and sometimes we encounter the same challenges over and over, despite our best efforts to improve our plans and strategies.

One teaching resource we often use is video. Seeing things in color and in motion and hearing authentic voices brings many topics to life in a way that text and still photos can’t do. But the narration is often important to understanding, and our students generally find it difficult to listen carefully. They make comments (on or off the topic) to the people sitting nearby, get lost in their own thoughts, and miss a lot of the intended content.

As we were about to watch a 20-minute video about the neolithic structures in the valley of the Boyne River in County Meath, I did something we haven’t done for a while, and it was a roaring success.

First, students sat in groups of four to discuss a list of words and phrases that they would hear in the narration: shrouded, artifact, cairn, excavate, decipher, megalith, pay homage, modest, ritual, symbolic, motif, winter solstice, heritage, and several others. They tried to come to some agreement about what they meant and made brief notes on the page. We then went over the list as a group.

The next step was to watch the 20-minute video without the narration (something Tony often did when he showed a video in the science room). Students were invited to make all of the on-topic observations and voice all of the questions that occurred to them. (On-topic excludes such things as “That man’s hair is really weird.”) What began to happen, much to the teachers’ delight, was that students began looking for opportunities to use the vocabulary list:

That’s an interesting artifact. That’s a modest house. I think he’s doing a ritual. That river is shrouded in fog. Is that a megalith?

       

It became almost a game as they playfully competed with each other for finding places to use the words. That was an unexpected and spontaneous engagement — a wonderful way of reinforcing their mastery of the new vocabulary.

Later in the day, we watched the video one more time, and we turned on the sound. Needing just one reminder about the importance of the narration, the whole class watched in silence. They heard every word. As they listened, they were clearly thinking about the accuracy of the observations they had made the first time and the explanation of the things they had wondered about. We had an excellent discussion afterward in which that reflection was evident.

Can we do this every time? Realistically, no. Some of the things we watch require several days because of the length and density of their content. It would also lose some of its effectiveness, I think, if we did it too often. But it’s important to keep in mind that our middle-school-age students need their intellectual, social, and physical energy accommodated with flexibility and good humor as we plan their learning experiences.

 

Working backward from the end . . .

We spent Friday afternoon’s half-group time with our buddies in Bree and Rich’s class. This is a high-energy group of first and second graders that help our own students see how much they have learned and grown since they were that age. The focus of the afternoon was on math games. The teachers in both groups offered games that were not beyond the skill level of our younger friends but had enough luck involved that our partnerships could play fairly equally.

In a few weeks ahead, as we begin to talk about human development with all of the young people in our building, they will be able to draw on their experiences and observations about readiness, diversity of learning styles and maturational pace of their buddies, and more. (We will share more about those plans in an upcoming message to parents; right now they are still being fine-tuned.)

We’re moving deeper into our Ireland unit. A video about Ireland from the public television program Nature is showing us how human migration and other natural forces (such as the most recent ice age) have helped to change the landscape. We have moved in a very sketchy way through the Mesolithic and Neolithic times and are moving toward the Bronze Age. We are enjoying the luxury of having multiple copies of several age-appropriate books that cover the same periods, so we can compare, find conflicts and (in)consistencies, and discuss the reasons that the same material might be presented in different ways or with different levels of detail.

When students were doing research in earlier grades, the idea of using multiple resources for the same set of facts was sometimes difficult to appreciate. Students in third and fourth grade — when exhorted to use more than one source — may use one for one part of the information, another for a different part, and so on.  By the time they get to fifth/sixth grade, we expect them to go to more than one source for the same bits of information. How do we resolve a conflict? How do we evaluate and compare the credibility of our sources — online, print, and/or interview? This is a challenge that will not be resolved by the time our students graduate, but we hope to lay a strong foundation.

We are also continuing to read folk tales and legends. We plan to turn some of them into skits to share with our buddies. They may also form the basis for a larger dramatic production in the spring, but there are other possibilities, too. Our students will help us decide.

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On Friday, we talked for a while in our morning meeting about the inauguration of the new president. Our emphasis was on the importance of our fundamental commitment through the Constitution to the “peaceful transfer of power.” It is clear to us that most (but not all) of our children’s families supported a different candidate. Many of our families are involved in protest demonstrations and other actions to express their concern and dissatisfaction with the result of this historic election. But we are working on the idea of respecting diversity within our community and making sure that what appears to be a minority political view is not swept aside. Respect for diversity is sometimes a bit of a tightrope walk — seeking balance while moving toward a shared goal. Embracing true diversity challenges us all. Where are the boundaries? Violence? Exclusion? Ideological dismissal as indefensible by logic, evidence, and/or science?

Clearly, there is not enough time in our day to address all of these questions to the extent they deserve, and our students are at many different places in terms of interest, information, family involvement, and more. We hope that all of you will convey your values and concerns to your children while also expressing your support for the respectful inclusion of those who did not vote as your family members may have done.

We talked about the “100 days” benchmark. What are the powers of the president? Does it matter what has been done it 100 days? 125 days? 200 days? We took some time to figure out when the 100-day mark would be reached. It took a bit of review of the monthly calendar to get us to the 1st of May, give or take a bit. We’ll be talking about goals and actions, process, and outcomes in the many weeks between now and then.

We discussed what was unique about this president. With some wobbling around, we arrived at the fact that he had no previous political experience or military experience, unlike every past president — who has had at least one and often both. One student said, “He’s a businessman.” Yes. Is running our government in any way like a business? Do we have money to spend, profits to make? Are there competitors? Where does the government’s money come from? How do we decide how to spend it?  Who decides how it is spent? Does the president make all of those decisions? We hope you will keep this complicated conversation going at home. Our children are growing up in a politically-historic time. We’d like them to be informed witnesses to it when they are talking about it with their grandchildren.

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Learning to play the pennywhistle is a challenge for some students and easy for others. Among all of the  other ways it connects with our learning goals for our children, one of the major ones is realizing that repeated practice leads to success. For that reason, we spend a little time playing music together more afternoons than not. We take apart the tunes and the fingering — what do we need to practice again and again until our brain-memory of the tune and the muscle-memory required to play it come together?

On Friday, in response to several students’ requests, we wrote out and distributed The Wren Song,  which was our entry and exit song for the mummers’ play we performed at our Winter Assembly. Because they knew the tune already, it was easy for most of them to play it at a good speed the first time they tried. We listened to an Irish band (The Cassidys) playing the very first tune we had tackled (“The Kerry Polka”) and agreed that we were not yet ready to match their speed. The connection between the music and our larger study is easy to make. One of our map-enthusiast students had been giving a close look at a map of a small region in the west of Ireland and was able to point out the town of Lisdoonvarna on that map — a town whose name features in both a jig and a polka that we’ve been learning.

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Coming soon — Life Skills 101, Changes and Choices, new literature groups, a new weekly schedule, and more. Please check in here often.

 

 

We got properly launched with our Irish unit this week, the second part of our migration study. Students had and will continue to have blocks of time in the classroom to read from our collection of folk tales. This is a good beginning point for learning about any culture. Stories tell us a lot about the people who made them. What did people value, admire, fear, and seek? Who were their heroes, and why? What are their creation stories, deities, and spirits?

In the course of several afternoons, I read them a very short version of The Book of Invasions, which is a pseudo-history of Ireland written sometime around the 11th century. It combines elements of Greek mythology, old Celtic tales, and other narrative sources. At the end of the book, the world has been divided between the fairy folk and the humans, who sometimes cross into each other’s territory — especially at the two turning points of the year, when the boundary is thin. Most of our Halloween traditions come from this. The sixth graders remembered the novel we read as a chapter book last year, The New Policeman,  in which a time leak between our world and Tir na nOg (the Otherworld, in which no time passes and no one ages) was causing trouble in both locations and had to be located and fixed.

We gave out several maps for students to keep in their classroom binders so they could become familiar with place names. A single combined page with the maps we have distributed so far is here:  maps.

At the same time, we looked at another kind of beginning — the geological formation of the island. Students looked in their atlas to see the location of tectonic plates today. We saw a fascinating video that took the earth back in time some 240 million years, showed the drifting of the continents to the present day, and then went forward in time about the same amount to project what the earth might look like long after we are gone. For many students, a lot of this was new, and they had a lot of good questions. They learned that Ireland had, at one time, a tropical climate because of its drifting; it contains fossils today of plants and animals from that period. Students added a map to their collection that showed the extent of glaciation in Ireland, part of the set on the page above.

Talking about millions of years is a very challenging conversation because the numbers are so large. One of our resource books written for young Irish students, Historopedia, has a 2-page spread that tries to convey the kinds of changes that might occur in 100 years. (This book has no connection with the website of the same name.) The authors selected the period from 1900 to 1999. Some of the events, people, and inventions are at least somewhat familiar to our students, including the sinking of the Titanic, World War I and II, and the first cloned animal. Other things in their list raised a lot of questions, some of which we discussed this week and some of which will need to wait for our Irish history study to catch up with them. Your child may be coming home with questions that this short timeline has engendered.  The oversized book is organized first as a chronology and then in thematic sections, such as music and inventions.

We gave each student a copy of another book that we will be using throughout our study: The Story of Ireland. This book begins in the Mesolithic period and takes its readers to the present time. Like many of our books that have been published in Ireland for students there, it has a delightful blend of humor and cartoon-like illustrations along with the much drier facts.

A study that spans this kind of time in a few months is necessarily brief. However, we hope that it will also contain enough variety that at least some parts of it will catch every student’s interest. We’ve had a very brief discussion of two sports: hurling and Gaelic football. We’ll be watching some videos of these games as they are played today; several of the group are very eager for that to happen.

Right now, however, we are still in ancient times. The natural environment is an important part of our study, and we’ll be learning about the wildlife, the rivers, and the bogs that are such an important part of the landscape. What were the raw materials from which people could build houses, make clothing, manufacture weapons and household articles? What did they eat? What was their primary fuel? We’ll look at their burial practices and the building of monumental structures, such as Newgrange. We hope you’ll be hearing a lot about this at home. A few of our students have connections with Ireland and know some of the stories as well as having been there with family. Their knowledge and experience enliven our reading and discussions with personal observations.

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Several of our math groups are working with geometry right now. Triangles are one of the topics. What follows is a description of what one of our groups has done so far, mostly in the past week.

We started with defining the word. Just what is a triangle? What do tri and angle mean? Then we got out a math tool called AngLegs. These plastic sticks of different lengths snap together to form angles and polygons. We asked students to find sets of 3 sticks that would make a triangle and sets of 3 sticks that would not. We asked for a rule or generalization that they could base on the physical relationships. What was true about all the sets that worked, and what was true about the others? Forming generalizations is an important part of learning, not just for mathematics but also for many other areas, such as grammar, reading, and spelling.

For this particular group of students, this was not an immediately-easy task. They could work with the sticks to find both kinds of sets, but getting the concept into mathematical language was harder. After several tries, they came up with a clear explanation: for the sticks to make a triangle, the two short legs had to have a combined length that was greater than the longest leg. They could demonstrate why with the sticks. The word leg took on a new meaning from this experience. Vocabulary is always easiest to acquire in contexts in which it is needed and can be applied over and over until it is familiar and secure.

Then we worked with a diagram that classified triangles: acute, obtuse, right, isosceles, equilateral, and scalene. Students discussed the definitions and recorded them in their graph paper math journals.

We got out our Geoboards to see how triangles and rectangles of the same dimensions were related. These boards — with their pins and rubber bands — allowed us to create a triangle with a base of 3 units and a height of 5, for example, and then to surround it with a rectangle that had the same base and height. Gradually the rule emerged: the triangle’s area is half of that of the rectangle. The relationship was easier to see with some kinds of triangles than others, but repeated experience and table conversations made it clear to everyone: the formula for finding a triangle’s area is base times height divided by two.

Students were asked to draw several different triangles that had the same area. We needed to define different and its opposite term, congruent. Suppose you are making triangles with an area of 12 square units. How many different sets of dimensions are possible? How do you know you’ve found them all? This let us review factors and methods for finding all of the factors of a number. And just which number are we talking about? Oh, right — we are looking for factors of 24 if we want an area of 12 . . . another opportunity to review that formula.

Why bother with all this hands-on work and ? Why not just present the formula and practice with it until it is memorized? The primary reason is that math should always be experienced as something founded on chains of reasoning and connected to physical experience. Rote knowledge is fragile — there is no way to re-invent it for yourself if you forget what you have memorized — and it doesn’t lead to making connections with learning that came before or will come after.

We did some investigation into the formula itself. Must it always be done in that order — first multiply the base and the height and then cut the product in half? We looked at a number of sets of dimensions and tried it several ways. For example, take a base of 6 and a height of 16. Well, 6 x 16 requires a little thought, but we end up with 96. And half of 96 is, ummm, 48. What if we found half of the base first? Now the equation is 3 times 16. Still not a quick calculation. How about half of the height first? Do we know what 6 times 8 is? Yes — it’s a familiar multiplication fact. Taking a few minutes to consider the numbers in the equation and select an efficient sequence is an application of good mathematical reasoning. Solving the equation in different ways is a bit of basic algebra experience that will be even more useful later on.

At this point, that math group has just started working with finding the areas of triangles drawn on blank paper. The grid pattern of the pins on the Geoboard and on the graph paper we used to record our work made identifying the bases and heights and collecting the measurements easy to do. But now we’re going to have to find the measurements with rulers. Which leg is the base? Can any leg be the base? How do we make sure that the height is really perpendicular to the base? Is there a tool that will make that easier? Although we will be working with protractors soon, right now we are giving students a set square. It has taken considerable discussion, experimentation, and explanation to enable everyone to use it to correctly draw a height that is at right angles to each of the possible bases.

Whenever we work with mathematics in a physical way, we see how much time and experience it can take before a student has a solid understanding of what s/he is really doing and learning. It establishes much firmer ground on which to build subsequent skills and concepts than simply presenting and drilling on a formula. It’s always worth the time.

 

 

 

We ended our westward migration study on a sad note which provided an authentic contrast to the joyful arrival of our pioneers in Hacker’s Valley last month. We looked at two different resources to learn about the Trail of Tears — the forced movement of most of the Cherokee tribe (as well as many of the Creek, Choctaw, Chickasaw, and Seminole people) from several southeastern states to the “Indian territory” — most of which is Oklahoma today.

We read a short play aloud from a Junior Scholastic publication. It said very little about the details of the actual journey made by various groups (including the most famous one that went with John Ross), but it did give a good explanation of the divided response within the tribe to the federal migration order and its eventual outcome. A minority of the Cherokee people were willing to accept the money that the government offered for their property and signed a treaty that sealed the contract. Congress approved treaty despite the fact that the group signing it had no positions in the tribal government and were not authorized to represent their people. Those Cherokee made the trip west in relative comfort in 1835.

When they arrived in Oklahoma, they set up a tribal government, ignoring the government that had already been created by Native Americans who had been moving into the territory in the decades before the Indian Removal act was passed in 1830. Those earliest migrants included many Lenape from our own area. When the forced migration of the larger group of Cherokee took place — involving those who had refused the government offer of money for their land and disavowed the representation of the so-called Treaty Party — they, too, set up a tribal government, and there was a lot of internal conflict among those various factions. In the end, the three principal leaders of the Treaty Party were assassinated, as they had grimly predicted would occur. Were they right or wrong to have signed the treaty? Would more lives and family wealth have been saved if the tribe had united behind them? What would have been lost as well as gained in that theoretical transaction? These are difficult questions, and our students were challenged by their complexity.

We then watched parts of a documentary made by a Native American film company. The great-great-granddaughter of John Ross told part of the story. We saw the beautiful, mountainous Southern lands they left behind, and we heard a young man tell us in Cherokee (with subtitles) about the deep attachment the people had to their ancestral home. We also learned a lot about the forced march west that began in the winter of 1838. By the time the unwilling emigrants completed their 1,200 mile journey, a fourth or more had died of exposure and disease.

One of the important pieces of information that the documentary included was the early history of the bad relations between the Native Americans along the Eastern seaboard and the colonists during the Revolutionary War. Because the British promised to protect and recognize the rights of the local indigenous people and because they had a long-established trading relationship, most Native Americans assisted the British instead of the rebels. When the war ended, many acts of violence were directed against them by the now-independent colonists bent on revenge.

The earliest leaders of the new United States, including George Washington and Thomas Jefferson, believed that, if the indigenous tribes could become civilized, peace would prevail. Ironically, the five tribes that were forced to go west in the 1830s had done exactly that. They spoke English, lived in houses, farmed the land (and, in some cases, owned slaves if they had enough land), ran small businesses, educated their children in white schools, and lived much like their white neighbors. Sadly, it wasn’t enough to protect them. It came down to racism and envy, and the “civilized” people were pushed off their prosperous lands by the uncivilized behavior of the United States government under President Andrew Jackson and many of its citizens.

We then moved forward in time to 1877 and learned about the travails of the Nez Perce tribe in Oregon under the leadership of the man generally called Chief Joseph in official documents. We watched a partly-fictionalized film called I Shall Fight No More Forever. Once again, we saw that the indigenous people were deeply attached to their lands, had signed treaty after treaty with representatives of the American government that promised them ownership of their ancestral territory in the Northwest, and were still ordered to move to a reservation when settlers wanted what they had.

Chief Joseph led a doomed effort to escape the order, taking his people hundreds of miles in rough, mountainous country, engaging in skirmishes with the pursuing federal troops, and finally giving up just 40 miles from the Canadian border, where he had hoped they could join Sitting Bull and the Sioux that had moved there.(I pointed out that it was about 40 miles from school to my house, a connection our children could understand.)

The film raised a lot of questions about duty, values, oaths, and honor. The general leading the forced removal of the Nez Perce was Sam Howard, an ex-Civil War soldier and founder of Howard University. In the film, he had many {fictionalized) conversations with a young adjutant throughout the pursuit in which they debated what the ethical choice should be when an oath to serve and obey was in direct opposition to one’s own values and sense of what is right. It was a lot for our young people to think about and might be a conversation worth continuing at home.

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As we now start to take up our study of Ireland, we have begun to learn to play the pennywhistle. Every student has one and will be encouraged to take it home when we are finished with this unit. (The pennywhistles were bought with money available from the Tony Hughes Fund. Established in Tony’s honor when he retired, it has supported our workbench activities, our classroom music in many ways, and other music/woodworking/science/technology projects throughout the school. We are very grateful to the donors who made this funding possible.)

We have a lot of budding and accomplished musicians in the group. Several are enjoying the chance to figure out and share tunes that are not part of what we are doing — currently some of the musical themes from The Lord of the Rings films. As they did with their dulcimers, a few of the boys have set up a shared Google doc in which they are writing instructions for playing things they have worked out on their own.What a wonderful idea!

I can see the benefit of the years of recorder instruction that our students have had from Diego. Although the fingering is not the same on the whistle, it is actually simpler, and many students have moved comfortably into the beginning work. A few were delighted to learn that it didn’t matter which hand was placed above the other, although most have chosen to stay with their left hand above their right, as is required on the recorder.

As we learn and practice tunes and songs, we’ll also be talking about Irish history and culture as well as incorporating some basic music skills. Most of the written music will be presented in 2 forms, usually on the same page — in standard notation (along with accompaniment chords designated by letter name much of the time) and also as a simple tablature that indicates the finger position but not much else. For example, the note G is played with the top three holes covered and the bottom three holes left open, so the number 3 is used to represent that. Although it’s not my intention to teach everyone to read music better than they may already do, we will be referring to the standard notation often for information about time signature, key, note duration, and the like. In truth, folk instruments (such as the dulcimer and the pennywhistle) can and should be played by ear and from memory more than from written notation in any form. We will be encouraging that throughout our lessons.

We’ll be finding time for pennywhistle lessons just about every day for short blocks of time. I have found that this is much more successful than meeting once or twice a week and expecting students to practice at home in the intervals. Students are welcome to take their whistles and books home, too, but we have tried to be very clear about how important it is to have them at school every day.

There is an excellent site for exploring Irish tunes here: The Session. Music can be downloaded and printed in standard notation and also in ABC notation, which is a format that can be use to print music and to hear the tunes played through your computer.  Visit the ABC site for more information if you don’t know about it already.