April, May, and part of June . . . that’s it. So what are we going to do in that time?

First, we will be setting up the new small math binders so that students will be taking home some finished work as well as new assignments. That and some other changes we will be making should make our students’ homework in math easier to accomplish. At the same time, we want to say yet again that homework is not intended to be completed with total accuracy by every student. It’s a continuous assessment and planning tool — it shows us what needs review and more explanation, what is secure, and what new challenges are appropriate. Parents are welcome to help, but we really want to know what your child knows and is ready to do on the next day.

This is the time of year in which we do our “Changes and Choices” curriculum. As your child moves into adolescence (on many different timetables), there are body changes and social changes. In middle school, s/he will meet many new people whose experiences and interests are likely to come from a wider world than the one Miquon has offered. In addition, s/he will be sharing space and perhaps classes with students who are older. In addition to all of this opportunity for positive growth, we have the dreaded trinity of Sex, Drugs, and Risky Behavior. So we look for ways to prepare our kids to make good choices.

The emphasis is on independent choice. Our children need to be given information and a clear awareness of being in control. But there are potentially opposing pressures. They will want to be accepted socially in their new school. They may hear confident statements from new friends that fall into the “everyone else is doing it” category — whether it’s about drugs,tobacco, alcohol, plagiarism, misuse of social media, and countless other bad options. So we hope to help you support your children as strong and independent thinkers, enabling them to choose their friends on the basis of family values and common interests instead of perceived popularity or social power.

Our two major resources for this learning experience are a website (kidshealth.org) and a program (Our Whole Lives, or O.W.L.), and we have a large collection of print materials to add to those two primary resources.  Healthy choice education includes sex and sexuality. This is probably the most emotionally-charged thing we do at school, one that overlaps strongly with family values and practices, so parents are always welcome to ask that their child be excluded from that part of our program. However, you should consider the likelihood that an excluded child will be getting information second-hand from classmates, and that may not be as accurate or as sensitively delivered as what happened in class. Please let us know if you do want your child to be given some free reading time in place of our discussions that focus on sex and sexuality. We can’t micromanage it further than that, as student questions will have a lot of influence on the direction of our meetings, and we never know what will come up.

We will be starting our third and final topic in social studies this coming week: the foundation beliefs and rise of Islam and the history of three medieval West African kingdoms. The two subtopics are both separate and connected. As Islam spread westward across the northern part of Africa, its proponents took two routes. One group went north across the Strait of Gibraltar to conquer Spain, which remained under Muslim rule for the next 700 years. As a result, Spain became a center of higher learning for its neighbors and  a place of relative security for Jews (compared to their precarious position in Christian Europe). The other Muslim army turned south and met well-defended kingdoms with iron weapons, at which point plans for military conquest were abandoned in favor of establishing trade, especially for salt and gold. The universities and their libraries at Timbuktu, Goa, and Djenne were unrivaled, and the evolving blend of African and Arab culture was expressed in literature, architecture, mathematics, medicine, music, art, astronomy, and more. Many of the enslaved people brought to the New World were from the area successively known as the kingdoms of Ghana, Mali, and Songhai — bearers of this blended set of beliefs, knowledge, and traditions. To give our study of Islam a broader context, we will also be looking at other  world religions, including Christianity, Judaism, Hinduism, and Buddhism.

In May, we’ll start preparation for graduation. In class, students will be working on writing their graduation speech, which is a very personal and reflective document. Parents will be asked for anecdotes that our fifth grade friends will turn into skits to be presented the night before the big ceremony. Kids will argue endlessly with each other and Diego about graduation music. At home, they will be doing one more project — the “Independent Project” that is somewhat similar to the recent Life Skills 101 activity but is much more open. What would you like to learn or do or ?? We’ll send home more information about that near the end of April.

There is more, of course — wrapping up the genre and author studies, embarking on new topics in math, creating and/or selecting writing for publication in Miquon Grass, enjoying another field trip or two, camping out one more time in the woods near my house  — and suddenly they’ll be standing in their best clothes on a June day with diplomas in hand, wondering how it went by so fast.

Still, we have some 2 and 1/2 months of school to go (doesn’t that sound longer than 10 weeks?) and we’ll make the most of them.

 

It wasn’t easy to fit all of our goals for circle-related math into this week because of so many other things that we did, so we are going to continue the topic when we return from Spring Break on March 31. We’ll start with some review before we move forward. The important learning that this topic includes is the use of formulae. For some students, this was familiar ground, but others were new to it and/or were challenged by the need to understand the relationships among the variables so they could plug numbers into the right places.

The big component of this was understanding the meaning of pi. We’ve had a very long poster on our wall over the windows all year, and students have sometimes talked about it, but this was the week we dug in. Pi expresses the ratio of the circumference of a circle to its diameter. That is, the ratio of C to D is pi to 1. Why use a Greek letter? Because it is an irrational number. It is approximately 3, but — more accurately — it’s a non-repeating decimal that never ends. Through the week, we used 3 and also 3.14 as approximations. We wanted students to have not only a name (“pi”) but also a numerical value that they could internalize and use for estimates and problem-analysis. We began by measuring the circumference and diameter of lots of stuff in the room — jars, plates, stools, rolls of masking tape, round magnets, cups, and more. After they had a collection of data, they did the division: C divided by D. Although their answers varied from item to item, the general result was a bit more than 3. We agreed that it was much easier to measure the diameter than the circumference. We talked about one of the uses of pi — to give us a way to find the circumference or the diameter without needing to measure both. On Friday, we used Geometer’s Sketchpad on our computers to create a circle, measure its circumference and diameter, divide C by D (to 5 decimal places), and then drag the circle bigger and smaller to see what changed and what stayed constant. As students expected, although the numbers for C and D changed, the quotient remained the same — approximately pi.

We then moved on to analyzing the formula for finding the area of a circle (you remember — pi times the square of the radius). We worked with fraction pieces to see how a circle could be partitioned into smaller and smaller slices which would then be arranged into a parallelogram. We reviewed the area formulae for rectangles and parallelograms on the way to “discovering” the circle area formula. On the next day, we watched a short, humorous video that presented the same visual rationale for the area formula in a slightly different way.  We encourage you to watch it if you want to see our evolving process in action.

 

Essentially, when the slices are arranged in an imaginary parallelogram (imaginary because it requires an infinite number of tiny slices), the height is equal to the radius of the circle and the base is equal to half of the circumference. So the area = the radius times C/2. But we’d like to avoid having to measure the circumference because it’s difficult. We know that the circumference is equal to pi times the diameter. That means half the circumference equals pi times half of the diameter. Half of the diameter is the radius. So now we have area = pi times the radius times the radius, or pi * the radius squared.  And that’s the customary form of the formula!

 On Thursday we made 18 small apple pies in honor of Pi Day on Friday. (The connection with pi??? Well, they ARE round, and math was involved in dividing the apples as well as the pies. Several children found apple peeling to be quite a challenge, but everyone got it done.) We made enough to share with the 5th graders. One of our group suggested sharing with bridge-building partners, and that’s what we did.

 

Agents of Change was the companion activity to the conference 10 of our group attended with Mark and Jeri on Tuesday. While our travelers to the Haverford School were meeting students from more than 20 other middle schools and learning about social activism, those of us who stayed at school chose and researched a number of social activists from past and present. We deliberately offered a list of people that students were unlikely to know already. The focus issues and goals of the chosen activists’ efforts included  Native American rights, care of the mentally ill, women’s rights, child labor, saving Jews from the Nazis, Asian-American civil rights, raising awareness of deep poverty in America, rights and care of the sick (especially the poor and socially exiled), rights for the elderly, Black civil rights, care of war orphans in Rwanda, and more. The people about whom students created presentations were: Jacob Riis, Father Damien, Dorothea Dix, Anna Mae Aquash, Alex Scott, Ryan White, Joan Trumpauer-Mulholland, Maggie Kuhn, Anne Heyman, Moira Kelly, Richard Masato Aoki, Iqbal Masih, Claudette Colvin, Oskar Schindler, Mother Theresa, and Susan B. Anthony. There were connections among some of them — Moira Kelly was inspired by Mother Theresa, for example. And there were some baffling associations that needed explanation — after learning a bit about the Black Panthers, students heard about Maggie Kuhn of the Grey Panthers. That took a little time to straighten out!

We asked students to try to find out if the people they selected had always (or ever) worked peacefully, if they had paid a price for their activism, and if they had been successful in their work. Students were encouraged to look for a quote from their subject as well as any criticism of their goals and outcomes. One of the things students realized (we hope) as they made their presentations is that they should never present information they don’t understand — they need to ask about the meaning of unfamiliar words, the location of cities and countries, the references to events that were connected to their topic. And they need to know how to pronounce all the words when they read their text aloud. This is a gradual process, of course, but we hope that most students will be much more clear about those responsibilities by the end of the year.

On Thursday, we got the whole class together to hear about the conference and to start sharing the research presentations, which finished up on Friday. It was a very meaningful part of our week that we expect to extend its influence far into our children’s futures.

We wrapped up our Life Skills 101 project. Students printed out their journals and worked with a partner to explain each other’s goals and how it went. Many students worked on cooking in some form, mostly preparing meals for their families, but there were other projects as well, including dish-washing, laundry, dog walking, and grocery shopping. Some expressed interest in continuing their work beyond our classroom culmination. All acknowledged that what they were doing was usually done by their parents. We hope they at least have a new-found appreciation of that parental support, even if they can’t wait to hand the jobs back to them again!

Our Friday Lunch Sales . . .

A few weeks ago, we had a rather embarrassing lunch sale. Here’s how it works — we process orders on Thursday and deliver food on Friday. Students are paired and have responsibility for each of the 8 classrooms as well as the specialists and other staff. Two are mainly responsible for managing our supplies as students pick up sandwiches, juice, chips, and more for the classroom that is waiting for food.

Thursday is the critical day. That’s when we collect the orders and record them. They report the numbers to me and then open the envelopes and check the money. Errors of amounts up to 25 cents are usually allowed to pass, on the assumption that some other parents will give us a five dollar bill for a $4.75 lunch.  But Mark and I don’t check the students’ count. If the totals they report say we need 12 cheese hoagies, that’s what we order. Although we usually over-buy on things we can save for the next sale (chips, juice, pudding, etc.,), we usually cut the sandwich order pretty close.

Although this week went really well, the previous hoagie sale was not great. I made a mistake while adding up some classroom totals, students recorded orders in the wrong column on the form for their group, one class lost some orders in the classroom and never handed them in . . .  and we felt pretty bad about it. But that was okay. Why? Because it’s real work. We have real customers, and we are selling (and, we hope, delivering)  a real product. If we get it wrong, it’s a lot more serious than a spelling mistake. And getting it wrong makes us want to work harder and better next time. (Mark now checks my addition, and our kids are taking their double-check routine much more seriously.)

Our children need real responsibilities at school and at home. The children become important, accountable, and committed. When a couple of errors surfaced in this Friday’s lunch delivery, students were intent on finding out what had happened. As it turned out, one mistake occurred when a sandwich was recorded by a team in the wrong category. One was a result of a second grader’s paying for an applesauce but not writing it on the his/her order form. We took care of both mistakes. We agreed that one mistake that we owned was not bad — an acceptable level of customer service, especially since we did have the correct sandwich to replace the wrong one.

We see the same growth in pride and commitment as the “Life Skills” project moves along. Children who are learning to cook meals, do laundry, do the grocery shopping, take over care for a pet, and the like are doing “real” things. We appreciate the time parents are spending in supporting this growth. We know it takes longer to teach a child to do something than to do it yourself, but that time will be more than balanced when the child becomes independent at the task.

Video Literacy . . .

Another thing we did this week was take a second look at the final scene in Bridge On the River Kwai. We had a good discussion about nuances of dialogue, camera angles, the role of various characters, and the same kinds of plot “signposts” that we have been using for reading. See our blog post from January 13 for detailed information. We saw quite a few “aha!” moments and agreed that they often occur at the end of films and books.  If you enjoy movies, we encourage you to think about how ongoing conversations while watching as a family can help make your child more aware of how a good story is put together and interpreted, whether in print or on the screen.

This is the second film we have watched in which the two central characters represented strong and opposing views. The first was I Shall Fight No More Forever  — the story of Chief Joseph’s doomed struggle to avoid the placing of his Nez Perce tribe on a reservation. The army officer who pursued and ultimately defeated him was General Howard, a Civil War veteran of the Union army and, later, founder of Howard University. His “tough questions” were about his duty to the army and its orders, which were in direct conflict with his own values and wishes. Chief Joseph’s “tough questions” were about how much loss he was prepared to see his people suffer in order to try to get to Canada and freedom.

Math . . . 

As many of you know, we have been doing a lot with ratios in math recently (and some students have extended that understanding into problems involving rate as well). This is some of the most challenging work we have done this year, and we have seen tremendous progress in our students’ understanding. At the beginning of the year, we did a lot of work with proportional reasoning in the context of fractions and also percentage concepts and problem-solving. This connects strongly to that. As we noted last week, most students are quite solid on the necessary computational processes — it’s analyzing the problem situation that is difficult. And, for many parents, the homework  looks like problems that can be solved only with high school algebra because — like Mark and me — they were not taught any other method for working with such tasks. But the bar modeling technique that is a core part of the Math in Focus program takes a different approach that is visual, logical, and entails no complex equation-based strategy. If you’d like to see another set of solved examples such as we posted last week, go here:

math_problems2_for_blog

If you are trying to help your child with math homework and seem to hit a wall together, please keep a couple of things in mind. First, the purpose of homework is not only to provide practice in things that have been learned in order to build fluency and mastery. It is also to point up what may still be wobbly and in need of ongoing instruction and practice in the classroom. It’s quite all right for work to come back unfinished and for the student to say “I need some help with this.” That’s a healthy request that gets us all ready to move forward. Lately, we have been having students who were given the same assignment sit down in pairs or threes at the start of math class to go over the work together. Sometimes we have indicated on their worksheets which things were correct, but sometimes we have not. (There is often more participation if students aren’t sure who, if anyone, got something right.) As they talk with each other, they share strategies, realize that they aren’t the only ones who are getting some things wrong, and often figure things out together that didn’t go so well the night before. When a pair or threesome become totally stuck, they call a teacher over, and we help them sort it out. We’re very pleased with the amount of independence, reasoning, and careful explanation that we can observe in those student-led discussions. You learn a lot by teaching someone else. You also find that two or three heads are often better than one, so collaboration is valuable. The second thing to keep in mind, please, is that email is not a good way for students or parents to try to get homework help at night. A phone call is always better. We can have a two way conversation, remind the student of classroom instruction, and — if necessary — agree that we need to sort it out in the classroom the next day.  Third, if a student is totally stuck on one problem, s/he should move on to a different one instead of feeling frustrated for most of 30 minutes. That’s one of the reasons we send more problems home than we expect students to complete in half an hour.

The SAT is changing — will the SSAT follow?

Many of our students took the SSAT exam as part of their school application process. We all agreed that the test was extremely difficult, at least partly because it penalized students for guessing by taking off points for a wrong answer but none for a problem that is skipped. We have a lot of doubt about whether most 6th graders are ready to make a determination about their level of confidence in their answers. In addition, skipping problems is a good way to get out of place on the answer sheet, as it’s easy to skip #12 and then put the answer to #13 in the row for the skipped question. We continue to believe that “standardized” testing tells little about a student now or in the future other than how s/he does on this kind of test. At the same time, we know that failing to give students the opportunity and experience of taking such tests (including the Terra Nova test that we do in October) could make things difficult for them and their families as they move on to secondary schools, both public and private.

A recent NY Times article, however, says that the SAT (for college admissions) is about to stop the points-off for a wrong answer and also make many other changes to tie the question content and test format much more closely to typical high school curriculum. The essay will become optional. (How many essays did our 6th graders have to write for schools as well as for the SSAT?) The article can be found here.

We can only hope that this change will trickle down to the SSAT as well. Even those changes would be an improvement.

One of the big events of this week (aside from the fact that it was a FIVE DAY WEEK) was that we finished testing the last of the bridges. This year, every single bridge held the target mass of 2 kilograms. What a success! There was a lot of learning that went on in the course of this blended group project that took a lot of weeks and a lot of work. Does every bridge need to succeed? No — sometimes we need to face and accept failure and disappointment. But it’s easier if we aren’t alone. So, if a bridge fails the test, we always hope it isn’t the only one. Success, misery, and hard effort all love acknowledgement and company. We will be giving the bridge journals (which will include some photos of the teams at work) to parents when we meet with them for conferences.

  

We started our short Life Skills project this week. What’s a life skill? It’s something you need to have when you have moved out of your parents’ sphere of support and need to fend for yourself. Clear the trap in a clogged sink; plan and cook a healthy meal for your family; put buttons back on some clothing that used to have more; take over pet care that includes some stinky jobs; pack your own lunch instead of expecting someone else to do it;  take a grocery cart and fill it with what’s on the list; do the laundry properly, including sorting, folding, and maybe even some ironing’; and whatever else looks like something you should know how to do before you leave home. We always get a few thank-you notes from parents when this starts, and we often see a new light of confidence in students’ eyes when they report on fixing breakfast or learning to use a major appliance.

We completed the Math in Focus unit on fractions and decimals this week. The most challenging thing for them was analyzing the many “word” problems that we wrestled with at the end of the chapter. Everyone knows how to multiply and divide fractions when given the task as a pure computation. The challenge came when students had to read the description closely, understand the relationships among the numbers, choose the right operation, and interpret the answer to the calculation(s). This, of course, is the work that a calculator cannot do and is therefore the most important learning goal. For many children, this was both confusing and frustrating (for some parents, too, perhaps!) and it something that we need to keep working on as we move into units on ratio and rate. Using concrete materials, acting it out, drawing useful diagrams, and checking the answer for reasonableness are all part of that ongoing instruction. For a detailed explanation of a solution strategy for two of last week’s problems, click here:  math_problems_for_blog

A few students who are already secure with a lot of the skills and concepts that the majority of the class are developing have been working more independently. Using the first year text of a program called Interactive Mathematics Program (IMP). We have given them explorations from the book without a lot of instruction or coaching, encouraging them to work together as they explore patterns, sequences, probability, and now ratio and rate.

We watched “Bridge on the River Kwai” in several installments through the week and finished it on Friday. (We’ll watch the last 5 minutes or so again this coming week, as a lot of students had questions about what the various characters were doing and thinking during the dramatic conclusion and what became of them.) It gave us another opportunity to talk about the “signposts” that we have been using to get to a deeper understanding of the books we have been reading and discussing in small groups. The film is filled with contrasts and contradictions, aha moments, and words from the wiser — three of the narrative elements described in “Notice and Note” — a wonderful book we talked about in an earlier blog post. A discussion earlier on Friday led students to ask for a definition of irony. The film is saturated with examples, and we think everyone had a good understanding of the word by the time we finished recalling examples. When parents and children watch a film together at home (especially if you can pause it to talk) is a good way to develop many of the things that we hope children will bring to the novels they read — especially understanding nuances of language and action, interpreting the motives and feelings of the characters, making predictions founded on the story so far, and much more. We hope you find time to do this occasionally.