Tricotomania and more

In an e-mail correspondence with Steph following her post about high-school transcripts and grading contracts (I can’t seem to link to her post right now), she asked for specific examples of how one might assess skills as well as content. I came up with a few in my reply to her but I thought that perhaps others would be interested. One thing that came to mind was teaching history. As our children get older, how do our expectations of their learning about history change? And what kinds of skills and conceptual knowledge might colleges and universities be looking for in a high-school portfolio?

I have blogged before about Myra Zarnowski’s book Making Sense of History, which sets out a conceptual approach to the teaching of history in elementary school. The concepts and general skills she outlines would be a good foundation for high-school level teaching as well. The three elements of good history teaching that Zarnowski outlines are:

1. Historical Thinking: What kinds of questions do historians ask? How do we recognize the past as both familiar and alien? What kinds of conclusions can we draw from the evidence we have?
2. Historical literature: Using good quality non-fiction literature; for high-school, one might start to include primary source documents as well
3. Hands-on experience: what I might call “doing” history; asking historical questions, searching out appropriate evidence, and presenting it

Zarnowski also sets out 5 historical concepts: Historical context, historical significance, multiple perspectives, historical truth, and historical accounts. All of this would be what I referred to at the end of the review of The Language of Mathematics as teaching the discipline of history in that dual sense of “branch of knowledge” and “the practice of training people to obey rules or a code of behaviour”.

Making the process of producing history visible to our children becomes increasingly important at the high-school level. Although young children might have a very clear cut sense of “truth” and “lies”, older children should be able to cope with increasingly complex notions of truthfulness and the limitations of our knowledge of certain facts. To return to my comments about epistemology (how we know what we know), it is impossible for us to interpret facts outside of a particular cultural context. Thus in evaluating the evidence and the arguments that are made using that evidence, we need to be aware of the context in which both the evidence and the interpretation were produced, and the context in which we are engaging with the argument. I do not mean to suggest that we cannot work to understand other contexts, but rather that we have to recognize them first before we can even begin to do so, and that our ability to truly understand another context will always be limited. We are thus seeking to approach the truth. That is where the multiple perspectives come in, along with important concepts like “corroboration” — having evidence from more than one source that supports a particular argument. A certain humility is also required though we should not be apologetic about our conclusions.

I am also in favour of being explicit about the nature of scholarly discourse. Scholars in all disciplines are engaged in debate and discussion. When they publish, they are talking to other scholars and to those outside of their field about what they have learned. When they write for children, they are inviting children into their world, introducing them to fascinating stories. What we read is never the final word on a subject but rather a contribution to an ongoing discussion. The discovery of new evidence might radically change the interpretation of what happened at a particular moment in history. More often the change will be subtle, providing a more complex understanding of events. I tend to favour an approach that treats students as novices in whatever discipline they are learning. They are not outside of this debate but need to respect the fact that they are still learning the codes of behaviour that govern it. Sometimes we learn best by participating even if that involves making a few mistakes.

One resource that I have come across which might be useful in teaching about the “doing” of history, with a particular emphasis on the nature of evidence and how it might be interpreted and used to produce historical narratives or arguments, is Freedom Roads: Searching for the Underground Railroad, by Joyce Hansen and Gary McGowan. Using the example of the Underground Railroad, the authors foreground the types of evidence that historians use in constructing accounts about the Underground Railroad. The choice of topic is important for several reasons, not least because it is one that is notoriously difficult to research historically.

The historical events that make up what is called “the Underground Railroad” are an example of such purposely hidden activities. … Over time some of the stories about the Railroad have become romantic adventures with elements of myth and legend, and it is difficult to separate fact from fiction. How can we possibly find proof and evidence of activities that were purposely clandestine? Is there any way to recover a secret past? Perhaps. (pg. ix)

The title link I’ve used is to Amazon, where there is a “search inside” feature that lets you see the table of contents and get a better sense of how the book is structured around different types of evidence, from legal documents, to diaries, to songs. Each chapter includes important details about the history but foregrounds the evidence, raising questions about its reliability while also demonstrating how historians use multiple sources of evidence to decide these questions and construct historical narratives.

For example, when discussing the use of anecdotes and oral histories collected after the fact the authors say:

Even though anecdotes like these cannot automatically be taken for fact, they become much more significant as evidence when the details are repeated in the same way by independent sources.

And on pages 115-118, there is a long account of how an archaeologist went from a hunch, “It seemed like a good idea to go looking for immigrant housing under schoolyards in the inner city.”, to a rigourous investigation of maps, public records, legal documents, and tombstones, etc to unearthing a detailed history of one particular fugitive couple.

Copies of some historical documents are included so students would get a good sense of what they look like. Source notes for each chapter are at the back along with a list of additional resources. Yet the writing is geared to middle school students and thus makes a comfortable introduction to a topic not much discussed in books for children — how we do historical research.

Using this book in combination with other non-fiction books about the Underground Railroad would enable you to critically engage with the other books with your child, making visible the production of those narratives in the context of a historical debate. Zarnowski talks a bit about doing this sort of thing with historical fiction, using historical non-fiction to draw out different notions of historical truth — literal truth, artistic truth, and historical trueness. (see page 136 of Making Sense of History for details). A logical complement to this sort of critical thinking about historical fiction is to delve further into the truth of historical non-fiction. Sometimes we just don’t know certain parts of the story and we use a sense of historical trueness (with important indicators that we know that this cannot be fully verified with the evidence we have) to fill out the argument. Sometimes it is necessary to use “maybe” in an historical account but it is still important to know that this is your best possible guess based on the evidence available and to explain why you think it happened this way.

Questions for discussion (or writing assignments) based on this sort of wider study might include:

• What is the main argument of [name of specific book]?
• What evidence is used to support that argument?
• Could you interpret any of this evidence differently? Why has the author chosen this particular interpretation?
• Are you aware of other evidence that would either support the argument or raise doubts about the argument or interpretation? What is that evidence?

Sometimes this kind of questioning leads students into a rather negative position about all evidence. They begin to see bias everywhere and come close to dismissing the whole project of history as impossible. While this is probably a necessary first step, the objective should be to move students beyond this to a more complex understanding of history and its production. Critical does not mean negative. It does mean that you don’t just accept things at face value because some apparently important person said so. The fact that someone with considerable background in the discipline, who has been published by a reputable press, has said something suggests that it is probably right. But history, like most disciplines, is about debate and discussion as a means of developing better interpretations of the evidence and a better understanding of the truth. While our students are novices in the discipline, we can give them opportunities to practice engaging in the debate, respectfully.

It is also important to explain that it is perfectly okay for your historical research to raise more questions. In fact, historians expect this to be the case. So if you have a piece of your story that is only a “maybe”, or there is something about a historical account that is not convincing you, the important thing is to formulate good questions that will lead to evidence that might either confirm your best guess or help you work out what really happened. So sometimes you might want to add the following question to your list of discussion questions:

• What evidence would you need to be more convinced? Where might you find it?

For example, in Freedom Roads, the authors talk about the fact that the enactment of ever stricter laws regarding fugitive slaves indicates that there must have been a lot of slaves escaping.

We learn some basic facts from the existence of this law [the Fugitive Slave Act, 1793]. Because many of the Northern states were in the process of abolishing slavery by 1793, enslaved people had more places to run to. Indirectly from the law, we might conclude that so many more people were escaping and running away in the years after the end of the American Revolution that slave owners pressed for a law to strengthen the article in the Constitution that referred to runaway slaves.

I am convinced by their argument. No one would enact a law unless there was a perceived need for it. But I am somewhat surprised that they make no mention of how we might investigate this interpretation further. Our understanding of the situation would be enhanced by information that must be contained in debates in congress, newspaper opinion pieces, etc. in the period prior to the law’s enactment.

To return to the more general issue of assessing high-school level work, I think that you would want to provide evidence of learning that goes beyond knowledge of a particular historical period or the history of a particular place, though that is important. As your child progresses through high-school you might want to see improvement in the following historical skills:

• An ability to identify the main argument of a historical text and the evidence used to support that argument.
• An ability to recognize different kinds of historical evidence.
• An ability to discuss the strengths and weaknesses of different kinds of historical evidence.
• An understanding of the notion of corroboration: can identify the use of corroborating evidence in a historical text; can use evidence from another source to strengthen a historical argument; can use evidence from another source to raise questions about a historical argument

By the end of high school you might want to see essays or research papers that demonstrate a grasp of the uncertainty of much historical knowledge and are able to clearly express the degree of confidence their is in particular aspects of a historical account and raise questions for further study in their conclusions.

I hope that some of you find this useful. I would love to hear comments and examples of things others have done, particularly those whose children are older. I am also interested in knowing about other books suitable for middle-school and high-school students that make these questions of evidence and the production of historical accounts explicit. The Underground Railroad is an important topic in both American and Canadian history, but it is always good to have resources for a range of topics. We never know what is going to really spark the interest of our children and being able to work with that spark makes the whole process so much easier.

I’m pretty sure that the Careers articles in the Chronicle of Higher Education are open to everyone. If not, please let me know in the comments. Today’s article is directly relevant to some of the discussion about how the admissions process looks. I thought it might be helpful to those of you you have never been on the other side of it.

Yet here I am, with two colleagues, about to speak to a few hundred high-school juniors and their parents: probably skeptical, jaded, and exhausted by their grand tour of liberal-arts colleges all over the Upper Midwest. Several important administrators are looking on, armed with statistics and quotations from the updated missional literature. I have just been introduced, and I am about to stand up.

What should I say? It’s always absurd to tell someone, “Just be yourself.” Which self should I be? Should I be dynamic and entertaining, or should I try to be a serious professor with big, important ideas? Should I talk about my teaching methods — my pedagogy — or should I just give them a representative episode from one of my classes? Should I be assertive about my beliefs, or should I do my best to be charming and inoffensive?

Who is my real audience, anyway: the parents, the students, or the administrators? Am I here to win converts? Am I here to scare the wrong sorts of students away? Am I auditioning for something? Will my head explode like that guy in Scanners?

Todays post over at I.N.K. is fabulous. David Schwartz reports on all kinds of class projects kids have done based on his book If You Hopped Like A Frog. Some good ideas there for writing projects….

That article by Lockhart (referred to in a previous post of mine) was linked from Keith Devlin’s page at the MAA site. I ended up surfing through his previous articles. There is a good pairing on what mathematics education should be, not at the elite level (preparing future mathematicians) but the general level (ensuring that we all have basic literacy). The main outline can be found here, but it refers to an earlier article here. That article led me to Devlin’s course at Stanford (outline and philosophy are both worth reading and can be downloaded from that link). Which, in turn, led me to his book, The Language of Mathematics. As luck would have it, it was in my public library.

As you can see it has taken me a couple of months to read it but I finished it last night. It was hard going sometimes and I can’t claim to have understood everything, but I think that I now have a better sense of what mathematics is about than I did before. And some areas were truly fascinating and really advanced my own knowledge.

A couple of summers ago, I did some work on the nature of research in the humanities disciplines. It was very interesting. And I have felt for a long time, though without a lot of knowledge, that mathematics is really more like the humanities than like the sciences. Although mathematics is very useful to scientists, mathematicians don’t really approach the world in the same way that scientists do. They are more like philosophers. Reading The Language of Mathematics confirmed this view for me. Mathematicians are a lot like philosophers. Reality does not concern them very much. Abstraction is very important to them. And finding abstract patterns really excites them. Mathematicians put a lot of value on elegance. And simplicity.

An illustration of the importance of beauty and aesthetics to mathematicians can be found in chapter 3 of Devlin’s book. Don’t worry if you don’t quite understand what he is talking about her, I’m not sure I do completely either. My point in quoting it is to highlight the use of aesthetics as an argument for the acceptance of something.

With the gradual increase in the use of complex numbers spurred on by the obvious power of the fundamental theorem of algebra and the elegance of Euler’s formula, complex numbers began their path toward acceptance as bona fide numbers. That finally occurred in the middle of the nineteenth century, when Cauchy and others started to extend the methods of the differential and integral calculus to include the complex numbers. Their theory of differentiation and integration of complex functions turned out to be so elegant — far more than in the real-number case — that on aesthetic grounds alone, it was, finally, impossible to resist any longer the admission of the complex numbers as fully paid-up members of the mathematical club. Provided it is correct, mathematicians never turn their backs on beautiful mathematics, even if it flies in the face of all their past experience. (page 135)

Throughout, Devlin is quite clear that mathematicians are not directly concerned with reality. In the last chapter he spells this out quite clearly when talking about the nature of light.

In what sense is this rapidly moving entity a wave? Strictly speaking, what the mathematics gives you is simply a mathematical function — a solution to Maxwell’s equations. It is, however, the same kind of function that arises when you study, say, wave motion in a gas or a liquid. Thus, it makes perfect mathematical sense to refer to it as a wave. But remember, when we are working with Maxwell’s equations, we are working in a Galilean mathematical world of our own creation. The relationships between the different mathematical entities in our equations will (if we have set things up correctly) correspond extremely well to the corresponding features of the real-world phenomenon we are trying to study. Thus, our mathematics will give us what might turn out to be an extremely useful description — but it will not provide us with a true explanation. (Devlin, page 311-312; emphasis mine)

In some ways this is quite freeing. What we are being introduced to in this book is a new way of thinking; a way of viewing the world through mathematicians eyes. At times this kind of makes your head hurt a bit. And if you really wanted to understand everything he was saying, you would get frustrated very quickly. But if you are willing to let some of it flow over you a bit in an attempt to grasp something of that way of seeing, then it is well worth a read. I suspect that if one was really interested, this book would take several readings. A bit like philosophy really.

Indeed, as noted above, I discovered The Language of Mathematics when investigating Keith Devlin and what he did. He uses this book as the core text for a course he teaches. And it might be the kind of thing that is better taken slowly, over 3 months, pondering each chapter and engaging in actual mathematical work as a means to develop understanding. I’m not sure how easy that would be to do without the guidance of a professor, the structure provided by a course, and the opportunity for discussion in a seminar. But I’m sure it would be worthwhile.

However, for those of us who do not have the time or energy right now to take on that kid of commitment, The Language of Mathematics is still useful book. Individual chapters would be worth reading to get a sense of the bigger picture in some specific field of mathematics. The Prologue gives an overview of the discipline. Chapter 1 “Why Numbers Count”, opens our minds to new ways of thinking of numbers and what we can do with them. Chapter 2 ” Patterns of the Mind” introduces us to mathematical logic and proof, the “discipline” of mathematics not in the sense of “a branch of knowledge” but in the sense of “the practice of training people to obey rules or a code of behaviour” (OED). (These two senses of the term are not unrelated.)

Chapter 3 “Mathematics of Motion” gave me a much better sense of the calculus and what it is trying to do. It is interesting that this topic comes so early in the book and perhaps that has had some influence on my plan to introduce it earlier in Tigger’s education than is usually the case in the school scope and sequence. It is followed by “Mathematics gets into Shape” (Chapter 4) a fascinating discussion of geometry that begins with Euclid and moves on to demonstrate why Euclidean geometry, though terribly useful in everyday life, is not actually the geometry of the “real world”. The 3 angles of a triangle only add up to precisely 180 degrees in the imaginary Euclidean plane. We live on a sphere. For most everyday purposes, even of scientists, the piece of the sphere we live on is so close to a plane that we can ignore this fact and work as if it were in fact a plane. But if we were flying an airplane, the difference makes a difference.

Now if you are the kind of person who likes things to be True and can’t see the point of studying anything that is only approaching the truth or approximating the truth, this might be terribly disturbing. For someone like me who has long embraced a sort of epistemological uncertainty, this just brought mathematics and the sciences into the same set of discussions that the humanities and social sciences have been grappling with in a different room. That’s a lot of big words, sorry. “Epistemology” is just the study of how we know what we know. So the central issue here is not “is there a Truth?” (big T) but “can we know it?”. I have become less concerned with the Truth, and more at ease with approaching it, approximating it, and generally learning. This book takes very much that approach, as the quotes above demonstrate.

Back to the chapters… “The Mathematics of Beauty” (Chapter 5) deals with symmetry, tiling the plane, sphere packing and related issues, introducing the mathematical concept of the “group”. Chapter 6, “What Happens when Mathematics Gets into Position”, introduces topology beginning with the very useful, but not at all to scale, London Underground Map and leading on to the concept of “networks” and some very funky ideas about n-dimensional universes. (I did warn you that mathematicians are not concerned with reality.) “How Mathematicians Figure the Odds” (Chapter 7) is obviously about statistics but introduces some interesting connections among gambling, insurance, and global finance.

Devlin closes with a discussion of light and the universe, “Uncovering the Hidden Patterns of the Universe”, that includes a very simple explanation of Einstein’s theories of relativity that makes perfect sense. (Or maybe it only makes perfect sense once you have read the whole book and come to terms with epistemological uncertainty.) Approaching the problem of the nature of light from a different angle, Einstein developed his theory of special relativity

Building on Lorentz’s theory, Einstein went one significant step further. He abandoned the idea of a stationary ether altogether, and simply declared that all motion is relative. According to Einstein, there is no preferred frame of reference.

The theory of general relativity is an extension of this. I think now is a good time to go back and look at the Einstein exhibition the American Museum of Natural History put together (which I saw when it toured here). As I recall there are some very good illustrations of this principle.

Of course that gets mathematicians back into n-dimensional universes, and the shape of them. That whole curvature of space-time notion is a bit weird from our place on a sphere that looks very like a plane most of the time. But at the end of a book which has thoroughly demolished any idea you might have had that mathematics is some sensible discipline about the real world, it is quite fascinating. Which is the point, I think. Utility, especially immediate utility, limits the pursuit of knowledge so much. Many of the weirder things that Devlin talks about do eventually have some utility but sometimes it takes hundreds of years and several mathematicians to develop these ideas to a point where they can relate to some problem in the “real world”. That isn’t what motivates them to keep working on the ideas though. Mostly, mathematicians keep working on these problems because they are fascinating.

And this brings me back to where I started, wondering about how we teach mathematics. Reading Devlin has opened my mind to a different way of seeing the whole subject. And has confirmed that the objective of mathematics teaching should be to fascinate our students. We must also discipline them: train them to obey the rules or code of behaviour of mathematics as a branch of knowledge. But part of that is just giving them the tools to understand what mathematicians are doing.

And thus even if you can’t face reading The Language of Mathematics, I would strongly urge you to read Devlin’s thoughts on the goals of a mathematics education. Many of them seem perfectly in line with the kinds of things that homeschoolers discuss. In fact, his first goal, the one he says is least common, seems to be a primary goal of the Living Math crowd.

By the way, we should be teaching our children that the rules and codes of behaviour are different in different disciplines. That’s what distinguishes the disciplines as branches of knowledge. The point of learning how to write an elegant mathematical proof is not that this is a “transferable skill” but that this is the way that mathematicians go about demonstrating the truth of something. Although some of the logical principles are also used in other disicplines, practitioners of those disciplines will use them differently, being concerned with a different kind of elegance, perhaps.

On that recurring theme, someone on the LivingMath Forum posted a link to a talk by Ron Eglash on fractals in the design of African villages and other aspects of African cultures. Very interesting. I might have to go find some of his books. There is an article available online about the origins of binary code in African patterns, something he talks a bit about in the video.

He also has a website with tools to create designs using African fractals. And one specifically designed for kids as well as a set of tools specifically designed to relate to specific cultures. Hmmm. Lots of possibilities.

I also found a carnival for Canadian homeschoolers in my travels yesterday. It seems to be pretty new and small so I thought I’d post here about it in case anyone is interested. It aims to be weekly so I’ll try to post to it.

So despite the fact that I agree with Ron that the best way forward is portfolios and I should stop worrying and just get on with it, I spent some time futzing around on the internet yesterday looking up high school stuff.

I started with the Ontario Ministry of Education website just to find out whether the high school curriculum guidelines are as weird as the elementary school ones. They aren’t. But those kind of documents still freak me out. I can see how I could have a list of the objectives for the various courses, though, and just tick stuff off as we accomplish it (in a different order).

Though I know it is common, I’m still not clear why you would hit velocity and acceleration 3 times in high school — grade 9 science, grade 11 physics, grade 12 calculus. I guess I can’t figure out how you hit it differently each time. And if you’ve done it a couple of times without the need for calculus, no wonder it is hard to convince students of the importance of the calculus for science…

But then I decided to see what was available out there that specifically related to the situation where I am. I love my American homeschooling buddies, but I don’t live in the US. And Canada is a different country even if it doesn’t look like it on the surface. Well, I’m in luck because there is a woman who maintains a whole website and blog about getting into college from alternative routes (including homeschooling). * And just to boost my confidence that I’m not the only one thinking what I was thinking the other day about grades and transcripts she has a great post about homeschooling “diplomas”.

The family unit does have the power to confer some honor or privilege upon a child who has, in the family’s mind, successfully completed high school.

But, the family unit does not have the power to confer upon said child an award that others outside the family are forced to acknowledge.

It is misleading, I believe, to represent yourself as having earned a “high school diploma” because that phrase carries with it the understanding that a government-approved organization assessed and granted diploma status. In other words, if it came off your own printer, how “official” can it really be?

I encourage you to read the whole thing, but the point is that a diploma is, fundamentally, a government approved document. And also that you don’t need one to get into college. Many universities will take other evidence of being prepared, including parent prepared transcripts, a portfolio of work, and results of standardized tests.

I also discovered, that in Ontario it is probably easier for homeschooled kids to get into university than into community college. This is because Ontario universities now have policies (or are developing policies) for admitting homeschooled kids as non-traditional entrants. They have even had workshops at their collective gatherings, apparently. Community colleges, on the other hand, haven’t got there yet. I noticed, for example, when leafing through the course offerings at our local college in the library a week or so ago that they require a high school diploma though there is a statement that those who don’t meet the requirements as laid out can approach someone for special consideration.

I think I have done enough worrying for now. I’m going to just relax and do what we are going to do at the level that seems appropriate (which, yes, means calculus alongside velocity and accelleration the first time through unless a good reason not to do that crops up in the actual doing of it). I need to deal with my own inability to keep good records so that when we need to demonstrate to someone that she knows these things, I can do so. But otherwise, we are back to our generally unschooling approach.

If any of you are similarly challenged in the record keeping department and have found ways to keep track of things that work (more or less), do shout out in the comments or post and let me know about it. (No, Angela that is not you. You are wonderful in many ways but I suspect you can’t even begin to understand the problem, being a natural record keeper and planner.) I’ve started jotting things in a day-planner and I think that might be a good basis. Other ideas more than welcome.

* The site is specifically about getting into Ontario universities. She does have some links to information on other provinces. But even if you live in another part of Canada, Ontario has the lion’s share of all the universities in the country, so the info is likely useful for all Canadians. (I found out about a year ago that something like one third of all graduate degrees granted in Canada are granted by the University of Toronto, for example.)

Ron’s comment reminded me that I really should post the full photo. I had Tigger stand in front of the bush for scale. It is a pretty impressive bush.

I decided that I had too much stuff in the sidebar for a 2 column theme and went browsing around looking for something new. If you’ve dropped by at all in the last 12 hours you’ve probably seen a couple of changes. Took me a while to work out how to get my own photo in the header. I looked in my iPhoto library for something that would crop to that shape nicely but the first thing seemed inappropriate to the season (ice; I’ll maybe change it in 6 months time).

I think I’ve settled on this for now. I like the font colours. I like the lilacs (a photo taken yesterday at the Fletcher Wildlife Garden). And I like that there are two sidebars so you don’t have to scroll down forever to find things. I also really like those 3 drop downs at the top so I don’t have to have the pages, categories and archives in the sidebar.

Now I just need to be on the lookout for photo-ops that would make good headers. And maybe figure out how to use the wide-angle option on the new camera.

Someone declared a photographic emergency the other day and bought a new digital camera to replace the one out of the stone age that we’ve been using. Tigger monopolized it for a bit but I’ve managed to get my hands on it. In addition to the knitting photos in the previous post, I have a few of the front garden. Although it warmed up pretty quickly once the snow melted and the tulips and daffodils came out very fast, it then cooled a bit. We have had tulips in bloom for a good long time this year. Here are the end of mine and the first blooms on the iris.

first a photo from ground level of the bed to the right of our front path. This is not the same bed where the crocuses and snowdrops were. And that is my neighbour’s house.

I love the colour of these. It was only when I downloaded the photos that I realized that that stripe was almost purple. If you look right down the middle of them, they are yellow inside (sorry no photo of that).

  I’ve had lots of comments on these ones. They are very dark purple but look almost black. Very dramatic mixed in with those other ones. I’m pretty sure that it was serendipitous that this dark purple and the dark stripe in the others are so close in colour.

  And these are the irises. I got these from my neighbour (other side) a few years ago when her daughter-in-law was dividing them.  We have some others that are darker shades of purple (almost like that tulip) and red but they flower later.

The back garden is mostly vegetables though we do have a lovely show of alliums right now. And the lilac is in full bloom. We are eating baby lettuce, mezuna, radishes and arugula out of the garden already along with some green onions and herbs. The broad beans are up as are the peas. The strawberries are in blossom as is the apple tree. Cucumbers, tomatoes and the like have been planted out though peppers and eggplant are still in pots on the front porch. Pole beans have been planted out (started from seed indoors) and bush beans have been sown directly.

This year we have an annex at a friend’s place in the country where we’ve planted potatoes, onions, carrots, beets and other stuff that doesn’t need to be harvested daily once it is ready.