Life Among the Elms

The Math MCAs and Prairie Creek

Caroline and I had a good conversation about math at Prairie Creek today and she asked me to write a reflection about what we're doing, what we could be doing and what this year's MCAs scores mean in the context of progressive education.

First, we do not discount these scores.

Lest, I sound defensive, I'll start by saying that I was surprised by the MCA scores and am looking forward to examining them in depth to find out how we can help individual students and where we can boost instruction to address weaknesses.  I believe that if progressive education works, students should be able to show their competence in a variety of settings, one of which is standardized tests.  Patterns in test results, even in a small cohort such as ours, can indicate areas we need to address in our curriculum.  One such area that we've addressed in the past two years was basic computation -- we'd been spending a lot of time on math concepts and had not stressed basic facts and algorithms.  We sought to balance these two poles by starting our math work with "foundation math."  This focusses on the skills that are roughly akin to decoding and literal comprehension in reading.  You can't enjoy a story unless you can read the words.  Similarly, the beauty of the relationship between fractions, decimals and percents will be lost on you if you have to spend all of your time figuring out what 100 divided into four groups is.  I believe that one of the areas we will be weaker in is estimation and another will be data handling.  Although we use the latter regularly, we don't teach graphs and graphing vocabulary discretely. Both are opportunities for our curriculum development.  As we receive more data, we'll be able to see more clearly "what happened" and address it accordingly.

The Challenge of Small Cohorts

I cringe whenever the MCA summaries come out as percentages -- even when we are well above the state average.  At Prairie Creek, our current grade level cohort is 20 students.  That means that each student represents five percentage points.  Our performance seems incredibly erratic when viewed from a percentage standpoint.  In fact, our results are from such a small cohort that most shifts from year to year are not considered statistically significant; our sample is simply not big enough.  Add to that the fact that the state does not track the scores of a cohort and their improvement as they age (following a group of third graders and then looking at their scores as fourth graders).  Instead, growth is measured by comparing this year's fourth graders to last year's fourth graders.  It is somewhat valid to do this statewide but, with only 20 kids, our cohorts can vary dramatically from year to year.  For example, many of last year's fourth graders struggled on the MCAs.  Many fewer of them struggled this year.  In fact, we scored above the state average for fifth graders meeting or exceeding proficiency.  That growth is not captured in the way the state reports scores.  Incidentally, many states have addressed this issue and have moved to following cohorts to assess growth and determine accountability for schools.  It's more complicated in terms of record keeping but much more valid in my opinion.

What Does the Test Measure?

Overall, I find the MCAs, especially the reading portion, to be a fair test.  They are untimed and they attempt to go beyond the multiple choice format and look more deeply at students' abilities.  The reading portion really does measure students' ability to comprehend texts and write about them.  The math portion assesses students' mastery of content more than pure problem solving ability.  Vocabulary and familiarity with certain ways of presenting problems affect children's scores.  For example, a student may be asked to take some data and create a pictograph of it.  If a child does not know what a pictograph is, he does not receive credit -- even if he can represent the same data in an equally appropriate way such as a bar graph.  A child's ability to comprehend data and create meaningful representations of it is not being tested, rather it is the child's vocabulary being examined.  Should kids know the word "pictograph"?  Sure.  And we do work with pictographs occasionally, but we do not spend time drilling the word or how to make them.  The word is not as important as the idea, which is intuitive for most children and does not warrant a lot of time in direct instruction (unless you make the decision to teach to the test).

Curriculum Bias in Test Design

I taught the Everyday Math program for years when I lived in Connecticut.  I find it to be a solid curriculum that is well thought out, if uninspiring.  The curriculum is ubiquitous and I believe that it is the foundation for the math MCA.  The "In and Out" table is an example.  It's a way of presenting a functional relationship and several lessons in the fourth grade Every Day curriculum teach it explicitly.  However, it is not a standard mathematical representation the way a division sign or exponent are.  On the test, a student would be given an "In and Out" table with two columns of numbers headed "in" and "out" and no further explanation.  The question may ask for a missing number in the table.  Many children, when looking at such a table for the first time, need support to figure out that the same thing happens to the "in" number to produce the "out" number.  Children who have worked many "in and out" tables (i.e. those whose districts use the Everyday Math Curriculum) have a distinct advantage over those who don't.  Similarly, vocabulary and concepts focussed on in Everyday Math seem to be emphasized in the MCA.

So, Why Don't We Use Everyday Math?

As I said in the last paragraph, Everyday Math is a solid curriculum but it does not spark passion and curiosity in most children.  It is not progressive.  I was pushed in my thinking about math curriculum a few years ago by a speech I heard on NPR.  The author (whose name I now forget, although I'll continue to look through my notebooks) was talking about how we need to as a country move beyond creating children who are competent in computation and create a nation of kids who are passionate about math.  He believed that the number of kids (and adults) who feel comfortable stating "I hate math" or "I'm not good at math" was a real indictment of our approach to mathematics instruction.  I paraphrase, "Nobody says, 'I hate Shakespeare, I'm no good at it.'  Instead, some people appreciate it at an amateur level and some at a professional.  We could do the same with mathematics."  We redesigned the fourth and fifth grade curriciulum so that computational math was taught discretely daily for about 10 minutes.  Students worked to master basic facts and algorithms and build their foundations during this time.  Then we moved into "Exploration Math" where students worked on a concept or challenge of some sort.  We find many of these in the work of Marilyn Burns, our theme projects, and various other "challenge" math programs.  These lessons are filled with "Wows!" and "Cool!"  Children debate their ideas and sometimes even jump up and down as they figure something out.  No, Pascal's Triangle isn't on the fourth grade MCA, but an awful lot of my kids sited it as their favorite math topic for the year.  Descriptions of various explorations about can be found in previous blog entries:

Dinosaur Math (Base N)

Math Facts

Big Numbers

Writing About Math

Pi

Sieve of Eratosthenes

Algebra

Polygons

The Home/School Connection

We have very strong literacy scores on the MCAs.  This is in part because of the test design but it is also because literacy is stressed in many of your homes.  You are readers.  You read to your children.  You go to the library.  You talk together at the dinner table.  Progressive education is truly a partnership because when learning is authentic it is not confined to the classroom -- it happens all the time and a child has many teachers.  It is more difficult to be as supportive of numeracy in the home (hmmm...perhaps I'll do a workshop in the fall).  Every curriculum night I stress how important it is for children to master their basic math facts.  It is a rote skill that needs frequent work at home.  Students, especially in a mixed age classroom, master the facts at different rates and it is not an efficient use of our time to address math facts as a class (although we do work on them independently in foundation math and children are required to be able to recall facts at a certain speed before they learn multi-digit mulitplication or long division).  However, students often report that they don't work on facts at home.  It could be that our focus on intrinsic motivation makes pushing to learn math facts at home less of a priority.  Perhaps if we had "math fact tests" on Friday, parents would push students to work on them because "it counted."  I know homes are busy and that, without a deadline or a tangible reason, this kind of skill work is hard to do.  We've tried a variety of approaches and we'll continue to do so.  Beyond basic facts (the equivalent of phonetics in reading) there are so many other things we can do to support numeracy -- cook together (for older kids, make them use only a 1/3 cup measure to make a recipe), make budgets, wonder together (how many of you would it take to reach the top of that tree?  How many marshmallows would it take to make a s'more the size of your sandbox?  How much is infinity plus one? (an especially good one for bed time))  I would love to strengthen our partnership with families in developing numeracy the same way we work together to create passionate readers.

Last Words

I'll close, although I still have some reflections on the impact of the multiage classroom on math scores (our fifth graders often report how much more confident they feel as mathematicians compared to their year as a fourth grader -- and their scores historically reflect that confidence), the math recovery program being implemented in Australia, the best way to develop mathematical thinking in all students...  Know that we're still striving to improve our approach to mathematics and to create students who are competent and passionate about math, something which, sadly, the MCA cannot measure.  I look forward to continuing this conversation informally via e-mail ([email protected]) and formally in a committee this coming fall.  I hope you'll join me.

So Long but Not Goodbye

I wish I had images from graduation -- alas, I am very focussed on making sure everything goes smoothly and I forgot to deputize someone to take some pictures.  I did take a few pictures at our alumni bonfire.  It's such a joy to see students back again -- transformed physically, to be sure, but the same kids at their cores.  A few high school juniors (fifth graders the first year I worked at Prairie Creek) stood in the gym and pointed out their contributions to the mural that hangs on the wall.  Some younger alums had a spirited game of "bop," the swim noodle strategy game they invented when they were in fourth and fifth grade.

At graduation, I have to remember that this is a send off but not a final goodbye.  We'll see everyone again, whether its at May Day or a bonfire or to help at Village.  When alumi come back, they always share what they remember -- projects, forts, unfortunate cooking experiments.  At Prairie Creek, so much of the year is memorable, in a way that I don't feel is true of a traditional school.  When something is real, when something is authentic, it stays with you.  For alumni, Prairie Creek is a place that belonged to them, a place where they were known and are still known.  The same is true for this year's graduates.

And so, bon voyage and best of luck.  But visit us soon and keep us up to date with your adventures.

The Celebrity Life

Today when we got our literary magazines, two third graders stood up and asked if the fifth graders could all sit along the stage so that "we won't miss getting any of them to sign."  The area was jammed with students and a lot of the fifth graders said they felt like rock stars.  While I got to sign a few books, I certainly wasn't mobbed like the fifth graders.  It made me reflect upon their special place in our school.  They take on a lot of responsibility when they reach fourth and especially fifth grade.  They are expected to help the audience be respectful during all school gatherings, they are to set the tone on the bus, they are to help out the younger students at recess.  We even expect them to incorporate younger students in their play, even if it's a competitive game of football.  They uphold the mission of Prairie Creek and communicate it to their younger peers in a way that is much, much more powerful than then droning voices of us teachers.  They are our rock stars.

So Many Questions, So Little Time

This week, I was invited to visit Cathy's class at Carleton to talk about Prairie Creek and progressive education.  I got to go last term as well and have really enjoyed the questions and challenges that are posed.  Of course, there's never enough time, but Cathy asked her students to write down their questions on index cards and I'll have more leisure to address them here.  Some of the questions are based on "The Case for Working with Your Hands", an article in a recent New York Times magazine.

"Isn't is possible to prepare all students for college without advertising it as the only worthwhile path?  Don't schools have the obligation to prepare students for college so that it at some point down the road they decide it is a path they would like to pursue they are able to do so?"

This question was based on the Times article.  Alfie Kohn would (and has) called it an excuse to claim that one must teach a certain way at a certain level in order to prepare kids for the next level.  For him, the fact that most colleges don't teach progressively is their problem and we as progressive educators should not bend to their edicts.  He would urge us to question the system instead of submitting ourselves to it.  I think that all educators at all levels have a responsibility to teach in a way that engages students.  Whether you work with first graders or graduate students, it's not enough for a teacher to say, "Learn it because it's on the test."  Why is it on the test.  How will the learner use the information?  Why should someone learn it?  If the answers to these questions aren't evident to the learner, the information will not be retained.

"Do kids at Prairie Creek have more diverse interests/possible career paths?"

I sometimes say that at Prairie Creek my class is full of quirky kids.  I think that the environment allows kids to pursue their true interests instead of grouping with peers or conforming to media norms.  I think all kids are interested in almost anything until they're taught that it's uncool to be interested.  We actively work against this.  I'm not sure if Prairie Creek alumni continue on their independent path.  Anecdotally, I hear of many who are teaching or involved in the arts or social work but I don't have any longitudinal data to back that up.

"Crawford mentions in his NYT article that, 'Academic credentials do not guarantee this [a field of action where you can put your best capacities to work and see an effect in the world].' How does progressive education address this?  What is the value of secondary or post-secondary education?  Is it not extremely important?  Is it okay, then, if students don't want to be at school?  How do you confront?"

I agree that academic credentials don't guarantee you'll see the effect of your work in the world.  I think that we as educators have a responsibility to create learning environments where students see that they can have an impact on the world and learn how to make a difference.  Their work, from the earliest age, should have meaning.  If more schools held meaning and agency as the gold standard of teaching then, perhaps, "academic credentials" would be more of a guarantee that one's work would make an impact on the world.  For me, it's not okay if a child doesn't want to be at school but it's my job to find the root of the issue and address it directly.  The more they feel that their work is real and has meaning, the more they will want to be at school.  I end the year with twenty students who are sad that the last day of the school year has come.

"How does Prairie Creek evaluate the performance of teachers?"

We set yearly goals in four different areas:  curriculum, professional, environment, and communication.  We meet with our director about these goals at the beginning and end of the year.  She observes established teachers informally and offers cognitive coaching to anyone who is interested.

"Are students ever held back to repeat a grade (beyond the two years they [spend in a classroom]?  If so, is it for academic or maturity behavior reasons?"

The decision to retain a student is always made with careful thought and long deliberation.  It very rarely happens in any school including ours.  When it is considered an appropriate course, it can be for either academic or developmental reasons -- most often, these go hand in hand.

"What do you think is the best way to dispel the myths of progressive education?  (Especially since information about it does not often reach parents of kids attending public traditional schools.) (Or is that assumption wrong.)"

I think, most frequently, people simply have never heard of progressive education.  Even people who are involved in education often don't have a clear idea of what progressive education is or is not.  I start with my classroom parents, using my blog to explain not just what we are doing but why we are doing it.  Mixing pedagogy with the typical class newsletter fare has helped parents feel more connected to what happens in our classroom and why.  We make an effort to do this school wide and have been somewhat successful.  The wider community is much harder.  We conduct a lot of open houses and work to communicate our mission and approach in the media.  We invite education studies students and student teachers into our classrooms.  We urge our parents to talk about the school and progressive education.  The myths persist, however.

"What do you think about artificial learning environments?  Do you think that students can learn without always having hands on experiences?"

I think that all schools are artificial learning environments but authentic learning can still occur in them.  Hands on experiences are a great way to learn and often create deep understanding.  However, they are not the only way to learn.  Especially as students get older, they are able to learn in a much wider variety of settings and through a much wider range of methods.  I still remember the first time I read about constructivism, "Yeah, great, but how do you learn about Pluto using a constructivist approach -- we're not all Mrs. Frizzle."  But, of course, any educational approach taken to an extreme has fatal weaknesses.  And, actually, I could now create an experience which would include a way for students to construct an understanding of Pluto.

"I think there are things that ALL students must know...do you think there are things everyone must know?"

This was one of my favorite debates with a former colleague.  My answer probably doesn't come straight from the progressive playbook.  I have found, for example, that students are able to explore and see the wonder of mathematics much better when they have a solid grounding in the basic facts and computational algorithms (addition, multiplication etc.)  They are able to see patterns and don't spend as much energy on the more mundane aspects of their math work but can get right to the heart of a problem.  They're much more flexible as mathematicians.  In addition, we use a framework called the Habits of Mind that help concretize the things that successful learners do.  These are things like "Responding with Wonder and Awe,"  "Applying Past Knowledge,"  "Working in Groups," and "Communicating Clearly."  While I don't think the list is definitive, I would count these skills among things everyone must know about and cultivate.  I also think that everyone needs to know how to be a critical reader who is able to synthesize various texts. Finally, I think all students need to have a basic financial understanding and an understanding of statistics and probability.  These last few stem from my belief that the primary mission of public schools is to produce a citizenry ready to make good decisions about its leadership.

I'd love to hear how you would answer the questions above and any more questions that may have come up.

A Capitol Day

We had a wonderful time at Fort Snelling and the capitol today.  Senator Dahle, Senator Pariseau and Representative Garofalo were able to meet us.  We were also able to visit the rooftop quadriga and the governor's reception room, both of which have always been closed when I have visited before.  The students were unanimous in their wish for more time at Fort Snelling.  I hope that you'll be able to visit this summer.

May Day 2009

The sun shone, the temperature climbed, the prairie walked (which kept making me want to paraphrase Macbeth but I refrained).  I hope you were able to take a moment and look around at our community, our growing community, and appreciate your role in it.  I know I was touched by how many families were able to join us and celebrate the coming of spring.  

At least for me, days like May Day re-connect me to our mission.  To take time for such traditions is a way to remind ourselves we are different than most other schools -- we are a community school and we are progressive (as an aside, I think that most schools are child centered and have a service component, the other parts of our mission).  I don't tend to be an overly sentimental person but I always tuck away a mental picture of our families, old and new, eating together while the alumni play with our current students and toddlers, including mine now, wander in the woods they will someday lay claim to.  It helps you get through an MCA practice test or two.

It's a bittersweet moment for our fifth graders who often get a bit contemplative before running off to play capture the flag.  They're in the process of tucking away these bits and pieces of their time at Prairie Creek, tiny moments to bring out in the years ahead.  I'm glad I share the memory, too.

What's Going on in There?

Today the Elms headed outside to find buds to dissect.  It always amazes me to see their wonder when they explore outside, "Woah"  "Look what I found!"  "What's this?"  "C'mere, c'mere!" echoed though our little woods.  We took our finds back inside, sketched them, and then took them apart and sketched some more.  Students reported finding "tons of tiny leaves" in their buds.  Others found the bud scales that protect the bud throughout the winter.  Many went on to do close up examinations of some of our epiphytes (air plants) and dandelion flowers that are already popping up.

Yesterday, we examined the bean sprouts that we grew and labeled their various parts.  Students this age like to know the "real" names for things and we practiced getting words like "cotyledon" and "hypocotyl" to flow off our tongues.  Their sketches were beautiful.

When we looked at the beansprouts today, we noticed  something interesting.  Having been liberated from their dark closet growing place and placed on a sunny window sill, their first leaves had turned from a yellow white to a spring green.  Chlorophyl!  Today we talked about photosynthesis and even got a chance to look at the chemical formula.  Students discovered for themselves why plants release oxygen -- "Wait!  It uses the 6 carbons from CO2, 12 hydrogens and 6 oxygens from H2O...that leaves 6 O2s!!  That's where our oxygen comes from!"  (I'm not kidding, they figured it out.)  As S.H. said, "Hey, nature math!"

Use only a #2 Pencil

Well, it's silent in the Elms right now -- something that rarely happens when we're learning.  The GORP fueled students are bent over their MCAs, working hard and trying to remember that, this once, it's not O.K. to ask a neighbor for help.

At Prairie Creek, we don't focus on test preparation for a month or two before the MCAs.  Our first conversation about it was last Friday.  I think it is our responsibility to help students feel comfortable in test taking situations and to help them understand the format and purpose of this particular test. 

We explain that a standardized test is an efficient way to get a snapshot of a student but is not an effective way to get to know a learner or to see everything that learner can do.  We talked about our recent 4th grade and honors projects and how much more information that provides to us as teachers.  We also help the students understand that the state couldn't afford to send someone to watch their projects or interview so this is one way they can try to make sure that schools are successfully teaching students -- or at least get an idea of what schools might be struggling.

I also think it is important for students to be "good test-takers."  Unfortunately, standardized tests are a way institutions use to measure our abilities and students will be asked to show their learning this way for many years to come.  I keep test taking advice simple:

1. Have fun - smiling releases chemicals that enable us to think better.  I give the students test taking nick names on their GORP cups (ala World Wide Wrestling)-- "The Bubbler," "The Eliminator."  This kind of silliness helps students relax and feel comfortable as they are taking tests. 
2. Get interested - you do much better on tests if you're paying attention.  We talk about our "Wonder and Awe" habit of mind and how it can help us be better readers and thinkers as we're moving through new material.  I always share that I once had to take a two hour reading test that was entirely about the history of buttons.  If I would have been bored, I would have been sunk. 
3. Be prepared - know the format of the test and its purpose.   I encourage students to always take a pre-test if it's offered so that they can feel very comfortable when they are sitting down to the test.  They know what to expect.
4. Take your time - I am almost always the last person to finish a test.  We teach that "check your answers"  means "think through the answer from scratch."  For open ended questions, we urge students to write more than they think they need to, to be clear in their response (marking the different things they were asked to provide), and to be obvious ("as it says in the article").  This type of specialized writing takes time to develop but we do introduce the frameworks for successful standardized test writing.

  Simon and I used to have disagreements about test taking in the progressive setting.  Personally, I think that if a pedagogy is successful then students should be able to exhibit their abilities in a variety of ways.  I do think that progressive teaching allows students to excel in many, many more ways than can be measured with a multiple choice or limited written response test -- but when asked, I'd like my students to be able to perform on such tasks.  Simon, I think, saw test preparation as simply training students to jump through hoops, hoops that had no meaning and no value in "real life."  Perhaps.  Perhaps.  For right now, I'll have another handful of GORP and marvel at our silent, diligent students who have learned that no matter what you do, you should do it to the best of your ability.

Collecting Data with All of your Senses

Yes, Emma and Milly are licking the maple tree in front of the school (as all of us did.)  The Elms participated in a quick but very memorable lesson on xylem and phloem on Friday.  For those of you who don't do crosswords regularly, xylem and phloem are the botanical name for the "straws" that run through plants.  Xylem typically brings water from the roots to the leaves.  Phloem brings the sugars produced by photosynthesis back to the roots for storage.  Only in spring time does the xylem transport sugars, this time from the roots where it's been stored all winter to power the growth of the buds, leaves and new growth.

After learning about the process, the Elms got to observe it first hand, licking trickling sap off of our only maple tree.  All in the name of science.

Honoring Week

One of my favorite weeks of the year is upon us.  The fourth graders get a chance to try their hands at presenting -- learning very valuable lessons about how much preparation they need to do to feel truly comfortable.  The fifth graders get to see the fruition of their months of work.  I'm always amazed by the questions students ask and their ability to sit for hours and watch the projects.  They are interested in everything.  They celebrate each other in such a genuine way by admiring the work of their friends and being fascinated by what they're learning.

This year, I was excited to hear several students include sections about new questions they have after studying their topic.  In a few cases, the new questions out numbered the original questions by a fair margin.  It's an illustration of the winding path most true research takes.

Thank you for all the support you've given your children as they work through these projects.  Fourth grade parents, your children have been working through the process largely independently.  We'll reflect with them about what they've learned and what parts of their work were the most difficult.  We allow fourth graders to make some mistakes such as not practicing as much as we'd like or trying to write a paper without organizing one's ideas first.  Only through such stumbles do they truly come to understand the process and its rationale.  The hope is that next year they'll be able to motivate themselves to ask for help or spend more time on the things they found difficult this year.

Each child will be writing a letter to a fifth grader about his or her work.  These letters are carefully drafted and we stress the importance of honoring the work of one's friends by thinking deeply and sharing details one notices.

I hope you'll come and join us at Honoring Night to see the fruit of, really, six years of learning. mm