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.
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.
Sparking curiosity with the Toilet Paper Timeline, then following up with the beautifully drawn Cartoon History of the Universe seemed to work pretty well to keep students interested and engaged in their work. However, in putting it all together in their presentations we needed a simple graphic organizer to point out the highlights.
The History of Life on Earth timeline I put together to start with gives the broad overview, but we need to telescope the Cambrian to observe the really interesting, broad patterns in the evolution of multicellular life.
There are two key ideas I want students to get from these exercises. The first is what the Montessori lessons call the Gifts of the Phylum, which boils down to the fact that different Phyla represent major milestones in evolutionary development. For example, Cnidaria, the phylum of jellyfish, are important evolutionarily because they mark the emergence of organisms with endoderms and exoderms.
The second important concept regards the cycles of extinction and diversification that can be found in the fossil record. Dinosaurs emerge after the Permian-Triassic extinction event and diversify; large and small species, carnivorous and herbivorous, land based and ocean based. Similarly, after the Cretaceous-Tertiary extinction wipes out the dinosaurs, mammals take over and diversify to fill all the empty niches; elephants and mice, tigers and gazelles, rinos and whales.
The cycle of work. Within each subject area there are different types of assignments designed to provoke learning in many different styles.
The lessons, the individual works, the different group works, the reading; they’re all set up in this elaborate combination so that different students with different learning styles can get the information they need in the way that’s most meaningful to them. But the students also get to experience a wide range of learning styles so that they can become acclimatized to the different styles while actually figuring out which ones work best for them.
The logic behind this approach comes from Howard Gardner’s ideas on multiple intelligences. He argues that we have aptitudes for different ways of learning, and learning is easier and faster if students take advantage of their preferred learning styles. Whether we acquire these preferences through nature or nurture is an intriguing question, but by middle school I’ve found that it does not take long to recognize that some students have rather strong preferences.
[T]here exists a multitude of intelligences, quite independent of each other; that each intelligence has its own strengths and constraints; that the mind is far from unencumbered at birth; and that it is unexpectedly difficult to teach things that go against early ‘naive’ theories of that challenge the natural lines of force within an intelligence and its matching domains. – Gardner (1993)p. xix.
The learning intelligences have been defined in a number of different ways (see Smith, 2008 and BGfL for examples). We parse them like this:
Linguistic intelligence – learning from the written word or hearing words (auditory).
Logical/Math – using numbers and logical reasoning.
Bodily-kinesthetic – learning from doing.
Visual/Spatial – emphasizes images and relationships in space.
Interpersonal – learning from/with others.
Intrapersonal – introspective learning.
Musical – rhythm is important
Naturalistic – comprehending of the environment.
I prefer students to discover their preferred intelligences via the variations convolved into the curriculum, however, the BGfL has an online, multiple intelligences test that I’ve used in the past. However, as with standardized tests, you don’t want to stereotype students or have them stereotype themselves. All the intelligences interact. Different challenges force us to take different approaches, using different combinations of our intelligences to best effect. As always, a growthmindset is best. With their mental plasticity, adolescence is the best time to explore different learning approaches.
This year the theme is life. My central organizing structure is the timeline of life on Earth. I plan to link all of the discussions of taxonomy, phylogeny and genetics to this timeline over the course of the year.
The timeline above will be the first lesson. As with these things the trick is deciding how much detail to keep in and how much to keep out.
What I like is that it gives the general overview of when important things happen while leaving a lot of space for students to investigate. Most of what we’ll be seeing this year happened in the Cambrian and this timeline conveys that this is a very small part of the whole history of life. In fact, it’s only when we cover the biochemistry of genetics that we will be talking about the origins of life.
The Earth's magnetic field protects us from the solar wind. Image from NASA.
Having a magnetic field protects the Earth from the charged particles spewing out of the Sun, the solar wind. This makes life on land a lot easier since the solar wind’s particles are quite damaging to DNA. However, prior to the magnetic field forming all this damage to DNA may have also accelerated mutation and thus evolution.
