Saturday, December 16, 2017

Library Workshop: Montessori Mathematics Materials Part II

I'm leading a workshop series at my local public library on progressive education. The sessions will take place on Tuesday evenings from October 3 to December 12 (not including Halloween).

Some of the sessions are on Montessori and some are on Waldorf. Here I will put a corresponding series of blog posts listing what materials I took with me, both to help out other people who may be leading similar workshops and to help me out if I do another set of workshops like these in the future!


Montessori Mathematics Materials Part II

This, the final workshop in my series of ten, was by far the simplest to set up.

This workshop included miscellanous math topics such as Fractions, Reading an Analog Clock, Algebra (coordinate graphing), and Geometry (area). I also brought materials for the Montessori Fifth Great Lesson, the Story of Numbers, which helps inspire children to choose different math lessons throughout the school year. This brought us full circle from the very first workshop in the series, the Montessori First Great Lesson. Here are photos of some of the materials, which I arranged along the long conference table.



from Nienhuis Montessori:


from Great Extensions:


from Hello Wood:


from Clocca Concepts:


I also had some math supplies arranged among the books for the Fifth Great Lesson, including a material I made to help children understand the difference between the solar calendar and the lunar calendar (which involves 12 foot long finger knitted string circle and a pile of small white buttons), a clock rubber stamp and the Thermometer Stamp from Montessori Services.



The History of Counting

by Denise Schmandt-Besserat


The Story of Clocks and Calenars

by Betsy Maestro


Twelve Years, Twelve Animals: A Japanese Folktale

by Yoshiko Samuel


The Story of Money

by Betsy Maestro

Ideas About Choosing
by John Maher and S. Stowell Symmes


How We Learned the Earth is Round

by Patricia Lauber


The Librarian Who Measured the Earth

by Kathryn Lasky


Mathematicians are People, Too: Stories from the Lives of Great Mathematicians, Volume 1

by Luetta & Wilbert Reimer

    Thales
    Pythagoras
    Archimedes
    Hypatia
    John Napier
    Galileo Galilei
    Blaise Pascal
    Isaac Newton
    Leonhard Euler
    Joseph Louis Lagrange
    Sophie Germain
    Carl Friedrich Gauss
    Evariste Galois
    Emmy Noether
    Srinivasa Ramunujan


Mathematicians are People, Too: Stories from the Lives of Great Mathematicians, Volume 2

by Luetta & Wilbert Reimer

    Euclid
    Omar Khayyam
    Leonard of Pisa (Fibonacci)
    Girolamo Cardano
    Rene Descartes
    Pierre de Fermat
    Maria Agnesi
    Benjamin Banneker
    Charles Babbage
    Mary Somerville
    Neils Abel
    Ada Lovelace
    Sonya Kovalevsky
    Albert Einstein
    George Polya


Ada Byron Lovelace and the Thinking Machine

by Laurie Wallmark


Agnesi to Zeno: Over 100 Vignettes from the History of Math

by Sanderson Smith


Math and Science Across Cultures: Activities and Investigations from the Exploratorium

by Maurice Bazin, et al.


The Man Who Counted: A Collection of Mathematical Adventures

by Malba Tahan


You Can Count on Monsters: The First 100 Numbers and Their Characters

by Richard Evan Schwartz (see the poster of 1 through 100, factored)


This post contains affiliate links to the materials I actually use for homeschooling. I hope you find them helpful. Thank you for your support!

Thursday, December 14, 2017

#7 The Endocrine System

Main Lesson Book
We began, of course, by reviewing the previous lesson, The Ear. Students completed their summaries and illustrations for their main lesson books.


Day One Topic & Exploration
The Endocrine System is actually another office in the Department of Communication, with signals sent via chemical messages as opposed to electrical ones (which is what The Nervous System uses).

These chemical messages are called hormones, a term which most of the kids had heard before.

I used the paragraphs of explanation from the Unlocking the Endocrine System lesson plan, and we briefly discussed a few specific examples, such as insulin, epinephrine (also known as adrenalin or adrenaline), and growth hormones. I have a cousin who stopped growing when she was about four years old as a child and didn't get any taller for several years until my aunt and uncle decided to give her growth hormones. Then she grew taller. The children found that really interesting.

Then I took out a large envelope which was filled with messages written on colored 3 x 5 index cards. I created the set of cards in advance, writing messages on them and then cutting each one into two pieces, curving the cut lines so that the pieces went together like a puzzle. I explained that this is like a hormone matching up with its hormone receptor. There MUST be a match. Only then will the body be able to read and follow the message. (This is why the mis-directed letter to Mr Hatch -- below -- would end up being confusing. It's not really true that any old receptor site will work.)

I passed out several card parts to each person and they had to work together to match up their messages and then complete the task.

Here were the task cards I created:

    Run around the house three times.

    Do four jumping jacks.

    Quack like a duck.

    Water the bonsai.

    Ask Ms. Renee if she would like a cup of tea.

    Pet the rabbit.

    Count to 10 in ASL.

    Give the dog a treat.


Day Two Story & Exploration
Start by reading "The Letter" chapter from Frog and Toad are Friends, then ask the children, "What does this have to do with The Endocrine System?"


Nearly any story which involves a mailman delivering a letter would be fine. This one works well because the message is delivered slowly, a good contrast with the speed of The Nervous System. Somebody Loves You, Mr Hatch is one of my favorite books but wouldn't really work for this topic because it is about the accidental delivery of a mis-directed letter.

Review The Endocrine System. Look at the side of several milk cartons for the notice about bovine growth hormones. Bovine somatotropin or bovine somatotrophin (abbreviated bST and BST), or bovine growth hormone (BGH), is a peptide hormone produced by cows' pituitary glands. Discuss that some people worry that bovine growth hormones might negatively affect humans. Point out that, as the milk label states, "The FDA has determined that no significant difference has been shown between milk derived from artificial growth hormone treated and non-artificial growth hormone treated cows."

We also talked about the hormone seratonin and how people who have trouble sleeping, or people who travel and have to adjust to a radically different time zone, can take seratonin.

For students who want to delve into The Endocrine System in more detail, and learn the specific names of some of the glands and where they are located on the body, I suggest using the nomenclature three-part cards from ETC Montessori.

Note: there are sexual body parts and hormones included in this set of nomenclature, which may be an issue for some families depending on the age of the child. You could always adapt the set by removing some of cards (testes, ovary) and leaving others (pineal gland, pituitary gland, thyroid gland, adrenal gland, pancreas).


Main Lesson Book
Students began to draft their summaries and illustrations for The Endocrine System.

Pass out colored index cards and markers and scissors and let the children create and cut task cards to use as their MLB illustrations. There are three options. Cards can be written, cut, matched back together, and glued in readable pairs on the page. They can be written, cut, left separate, and glued down scattered around on the page. For kids who want to include an actual activity in their MLB, they can write and cut several task cards which can then be put into an envelope and the envelope can be glued to the page.


This post contains affiliate links to the materials I actually use for homeschooling. I hope you find them helpful. Thank you for your support!

Wednesday, December 13, 2017

#6 The Ear

Main Lesson Book
We began, of course, by reviewing the previous lesson, The Vestibular System. Students completed their summaries and illustrations for their main lesson books.


Day One Story & Exploration
I took my story for The Ear from Linda Allison's book, Blood and Guts: A Working Guide to Your Own Insides.


The chapter is called "Ears: Receivers for Vibes from the Outside." I required that the older students take notes during the lesson.

It may seem incredible that we are STILL doing stories for The Department of Communication, but I reminded the children of the bearded mussels we observed. They are such simple organisms and they don't need a complex nervous system. We, on the other hand, are very complex organisms and capable of amazing things (and we talked about Albert Einstein and Stephen Hawking and Wilma Rudolph and other famous people), so it is only logical that we would have an incredibly complex Department of Communication to help all those moving parts coordinate smoothly with one another.

I think it really helped to bring those mussels into the classroom! When I ask the children to think of a simple animal, they have something to picture.


We began with page 97 (How the Ear Hears) and I had a little drum available to show to the children. It is hollow (open at the other end, opposite the head) and so I could put my hand inside it, which I recommend. It was helpful when we came to the part about the Eustacian tubes later on.

We looked closely at the diagram of the outer, middle, and inner ear on page 98 and then read the rest of the page (Silent Dog Whistle?) and looked at the diagram of sounds. I reminded the students that the retina in the eye translates the visual images into electrical signals which get sent to the brain; the cochlea in the ear does the same with sound vibrations. Both systems have a piece whose role is simply to translate events into a language the brain will understand: nerve signals.

We read page 101 (Eustachian Tubes) and did the activity Meet Your Eustacians, which is a little uncomfortable so I wouldn't recommend it with students who have sensory issues.

Then we did the activity Are Two Ears Better Than One? on page 102 and read the rest of the page (Sound Source). We read page 103 (Musical Bones [or, Bones and Overtones]) and I demonstrated how a tuning fork works. We then struck a tuning fork and put it in a glass of water. It makes the water splash out in quite a dramatic fashion! The kids loved it and they wanted to do it over and over. I got this idea from Torin Finser's School as a Journey: The Eight-Year Odyssey of a Waldorf Teacher and His Class.


We did the Turning Fork Test activity at the bottom of page 103 and students reported that they could hear the sound vibrating in their teeth. Then we did the "Making Cutlery String Chimes" activity from page 51 of Roberto Trostli's Physics is Fun: A Sourcebook for Teachers. This is another dramatic, and very beautiful, experience. I let each child take his or her 2 foot piece of string home so that they could demonstrate this to their parents.


We ended with page 104 (The Inside Story on an Old Wives' Seaside Tale, Amazing Facts).

One student asked me if it was possible to be both blind and deaf, and so I told the children the story of Helen Keller and her early years and the peppermints and then the arrival of Anne Sullivan and the pump and water and learning what a word was. We also talked about Ludwig van Beethoven and how he lost his hearing later in life and was quite deaf by the end of it. They understood why he would lay down on the floor and try to feel the vibrations of it. They also asked me questions about hearing aids and Cochlear implants. For my older students, I gave them an assignment. I asked them to each choose a disease which was related to one of the body systems we were covering in this first block and to research its causes and its treatments. They will work on this at home all week and will add their final essay to the end of their MLB. They each went home to choose a topic.


Day Two Review & Exploration
We began by reviewing the parts of the ear which are used for hearing (ear drum, hammer, anvil, stirrup, cochlea) and then we read The Music of Life: Bartolomeo Cristofori & the Invention of the Piano. This is a great tie-in on several levels. First, it is about an inventor so we used it as an example for our Virtue of the Week, Determination. Second, it laid the perfect foundation to the story of Beethoven which we will read tomorrow. Third, it is about the different volumes which sound can be, as well as the musical terms for them. Fourth, it is about a musical instrument which plays by a tiny hammer striking something, just like the bones in the ear!

After the story we listened to a recording of the 1720 pianoforte, which is located in the Metropolitan Museum of Art in New York. Then we listened to David Wong play Beethoven's "Ode to Joy" on the piano. There are more links to music on Elizabeth Rusch's website; she is the author of the book.


My seventh grade students each chose a topic to research in more detail for this MLB. One picked asthma (The Respiratory System), one picked glaucoma (The Eye), and one picked Cochlear implants (The Ear).


Main Lesson Book
Students began to draft their summaries and illustrations for The Ear.


Additional Notes
We read two additional books related to the students' interest in people who lost their sense of hearing. I spread them out through the course of the final week of our main lesson block and, again, considered them to be books which highlighted the virtue of Determination. I presented these picture books in chronological order: The 39 Apartments of Ludwig Van Beethoven and Helen's Big World: The Life of Helen Keller.


My daughter Becca also read Helen Keller's autobiography, The Story of My Life, and watched the wonderful 1962 film called The Miracle Worker.


This post contains affiliate links to the materials I actually use for homeschooling. I hope you find them helpful. Thank you for your support!