Concept Maps of Math

August 24, 2011

Introduction to algebra.

While it’s nice to have the math concepts arranged nicely based on their presentation in the textbook. Since my plan is to give just a few overview lessons and let students discover the details I’ll be presenting things a little differently based on my own conceptual organization. So I’ve created a second graphic map, which looks a bit disorganized, but gives links things by concept, at least in the way I see it.

Concept map for an introduction to pre-Algebra based on the first chapter of the textbook, Pre-Algebra an Accelerated Course, by Dolciani et al., (1996).

This morning I presented just the first branch, about equations, expressions and variables. The general discussion covered enough to give the students a good overview of the introduction to Algebra. Tomorrow the pre-Algebra and Algebra topics will start to diverge, but I think today went pretty well.

We’ll see how it goes as we fill in the rest of the map.

Citing this post: Urbano, L., 2011. Concept Maps of Math, Retrieved July 27th, 2017, from Montessori Muddle: .
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Standards, scope and sequence

September 18, 2010

Curriculum alignment graphic. Still very much a work in progress.

The Montessori middle school curriculum we use is designed to meet the Texas state standards, so there are some interesting lessons about Texas history that I’ve had to drop or adapt, and some other topics that needed to be supplemented or replaced. Trying to represent this all in the same place has been quite the challenge. I’ve been working on the graphic above for some time.

The graphic is set up with the Tennessee Department of Education’s standards in mind, but I’m using the free, mind-mapping software, VUE, to make it easily adaptable. This way I can update any small annual changes fairly fluidly, and plug in the national standards when I get around to it. Aligning all the standards can be a bit of a pain, because the graphic really should be broken down to show the individual assignments that meet specific standards, but the figure is busy enough as it is.

In case it might be useful to anyone else, and so I can keep track of it myself, in addition to the image above I’m also posting a pdf version as well as Full-overview.vue here, with the strong caveat that it is very much a work in progress.

Citing this post: Urbano, L., 2010. Standards, scope and sequence, Retrieved July 27th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Learning science

May 1, 2010

al-Hassan Ibn al-Haytham (b. 965-1039) (Image from Wikipedia)

Science is, at its core, hypothesis testing. To learn science learn the scientific method: figure out the precise question to solve (as best you can); come up with an answer you think might work (hypothesis); test it; and repeat as necessary while modifying the hypothesis. Almost all science experiments for middle school through college involve following a set of instructions in the lab manual. Only in independent research projects do students actually go through the scientific process and then it’s difficult because they don’t have the experience.

Part of the problem is that it takes time. Time to muddle through the though process of trying to figure out what exactly is a tractable question to solve. Time to come up to with a reasonable, testable hypothesis. Time to figure out how to test it. Time for iterating through the process again, although, once you’ve set up your experiment the first time doing it again and again is not that hard or time-consuming.

With our Montessori Middle School’s six-week cycle of work, and even with the two weeks dedicated to the Natural World, students should be possible to get through this process for at least one problem. They would probably have to dedicate the two weeks to a single problem/experiment and it would probably be terribly slow in the beginning.

To discover the truth about nature, Ibn a-Haitham reasoned, one had to eliminate human opinion and allow the universe to speak for itself through physical experiments. “The seeker after truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them,” the first scientist wrote, “but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration.” – Steffens (2008) (Ibn Al-Haytham: First Scientist)

Citing this post: Urbano, L., 2010. Learning science, Retrieved July 27th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Daydreaming …

April 15, 2010

Focused work. We like to see our students focused on their work and we give them long blocks of time to do so. It is hard, however, for anyone to stay on task for two hours straight. You have to allow for a certain amount of mind wandering and daydreaming. What a lot of neurologic research is uncovering is that zoning-out is an essential part of putting the pieces together and helps with learning.

When we are no longer even aware that our minds are wandering, we may be able to think most deeply about the big picture. – Zimmer (2010)

Daydreaming by Edward Harrison May (1876) (from Wikimedia Commons).

While we sleep the brain assembles information into coherent patterns, helping us learn and process emotions. Carl Zimmer has an article in Discover Magazine on how unfocused daydreaming accomplishes the same thing.

Citing this post: Urbano, L., 2010. Daydreaming ..., Retrieved July 27th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Leadership and competitive games

March 11, 2010

“Treat a person as he is, and he will remain as he is. Treat him as he could be, and he will become what he should be.”
Jimmy Johnson

As much as I want to offer my students near-autonomy for at least a small part of the day, I am finding it necessary to reinforce the lessons of the classroom during PE. Physical education is an important part of a holistic education not just for the fact that healthy bodies lead to healthy minds, but because it offers another domain for students to develop their leadership skills.

I’ve found that not everyone who is great in the classroom will be great on the playing field, so students who are often learning from their peers when they’re inside, get a chance to teach and lead others. Often however, because they are unused to it, they need a little guidance to recognize the reversal of roles.

It is also interesting to note that some students who are great at peer-teaching the academics can get really riled up on the field and loose all sense of perspective, forgetting those carefully taught collaboration skills. This is particularly true when we play competitive games and they have to balance competition and collaboration. Fortunately, there is a well established term (even if not gender neutral) that sums up appropriate behavior in competition, sportsmanship.

Citing this post: Urbano, L., 2010. Leadership and competitive games, Retrieved July 27th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

The Clinton Library

February 27, 2010

Inside the Clinton Library

I have one student who intends to be president. He already has the date picked out. So the Clinton Library in Little Rock was a great stop on our immersion. It took a little coaxing to get him all the way through while some of the others, who were not as enthusiastic, waited patiently. I’m fairly sure he would have been happy to spent the entire day there.

The library is located on the Arkansas River. In fact, while it’s mostly built on the bluff overlooking the river, one side of juts out over the embankment, out over the flood plain. I suspect that if the river were to flood (which is perhaps unlikely with all the locks on the river), the supports for that wing of the building would be under water.

Inside the museum are displays about Bill Clinton’s eight years as president, a small theater with a video about Clinton’s life and some other odds and ends of the Clinton presidency (the limo, the replica oval office). The highlight was the replica of the cabinet room. Everyone enjoyed sitting at the table. After the initial rush for seats, it was discovered that they were all labeled for the different members of the cabinet, which was interesting enough as the all took at least a second to consider what their role might be if they were actually in the government.

There was also an exhibit with a number of Madeleine Albright’s pins, which she used to send messages to her diplomatic counterparts while she was the UN ambassador and as Secretary of State. You might not think that would particularly interesting to adolescents, but there were some spectacularly beautiful, jeweled insects that attracted the attention of some students, and an interesting RPG pin (from Pakistan) that attracted the attention of others.

Since we’d been doing museums and tours all day, everyone was tired by the time we’d finished the museum. It would be another hour before we got back to Lake Catherine so instead of just jumping into the van I offered them the chance to run around on the steep, grassy embankment, down into the floodplain. Instead they (mostly) opted to roll down. Fun was had by all.

The museum was a decent stop, worthy of an hour or two, but, with our current study of civil rights, and the age of our students, it could not match Central High.

Citing this post: Urbano, L., 2010. The Clinton Library, Retrieved July 27th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

Seeing history through food

February 19, 2010

Spices in a Moroccan market. Image by Donar Reiskoffer, found on Wikipedia Commons.

Montessori elementary programs approach history from the perspective of the basic needs of human beings. They look at how humans have satisfied the needs for food, shelter, spirituality and so on over time.

A new book by Tom Standage called, “An Edible History of Humanity” looks at human history through food, from how agriculture lead to the beginning of civilization, to the role of spices in the European discovery of the Americas, to how food production shaped the rise and fall of Napoleon, to the effects of the Green Revolution on the world today.

it concentrates specifically on the intersections between food history and world history, to ask a simple question: which foods have done most to shape the modern world, and how?

Spiked Online has a nice review of the book that touches on many of the key points. This book certainly open up a wider discussion of world history. A simplified version would likely be a great addition to the middle school curriculum.

The vivid colors, heart-rending smells and sheer mass of the pyramids of spices in Moroccan markets are a vivid reminder of the importance of the Arab spice trade. The spice mixes I remember in particular, they can consist of over twenty different spices coming from all around the world.

Citing this post: Urbano, L., 2010. Seeing history through food, Retrieved July 27th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

A reason to draw

February 18, 2010


Why do we use our hands? Milton Glaser (above) uses his to think, and he cites Frank Wilson who argues that the hand and the brain are so connected as to be a single almost indistinguishable system. In fact, Wilson extrapolates this connection to education where, he makes the arguement, “less rigid more individualized approach to education will yield a student with a unified body and mind” (according to The New Yorker, 1998).

“The hand speaks to the brain as surely as the brain speaks to the hand” – Robertson Davies in The Cornish Trilogy

Drawing is thinking for some people at least. Perhaps that’s one of the things that defines kinesthetic learners? It certainly is something to bear in mind when designing and implementing the curriculum. Teachers tend to use teaching methods that fit their learning styles, so it is important to bear in mind we will have a variety of students. It’s certainly something about which I have to keep reminding.

It is also important to remember that all students benefit from experiences with different modes of learning. Students, especially adolescents whose brains are rapidly developing new neural pathways and pruning others, need to experience variety, because once we are set in our ways, it becomes a lot harder to learn new tricks.

This is where preparing the environment becomes so important. We want student to have choices, but we want them to try new things, and sometimes these two objectives conflict. The video above does make a persuasive argument to me about why we should draw and practice drawing. Perhaps it will do the same for our kids.

Citing this post: Urbano, L., 2010. A reason to draw, Retrieved July 27th, 2017, from Montessori Muddle: .
Attribution (Curator's Code ): Via: Montessori Muddle; Hat tip: Montessori Muddle.

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