Image from the Art Renewal Center.
May 31, 2009
May 29, 2009
Summer Math Workshops: Houston, TX Area (Repost)
Does your child need review in particular areas of mathematics?
Would you like to give your child a better understanding of mathematical concepts and how they relate to real-life situations?
Are you wondering if your children really grasp what they’ve learned in their math courses this year?
If so, my Summer Math Workshops are just what you and your children need. (For information on my credentials and background, for testimonials, or for my teaching philosophy, see my Website.)
These workshops will cover specific areas of mathematics, giving students the opportunity to develop a deeper understanding of particular concepts and to lay the foundation for future academic success. A workshop will consist of four classes meeting on four separate days over a two-week period. Each workshop will be offered in three summer sessions: one in June, one in July, and one in August. Students may sign up for individual workshops or attend the entire day.
But what is the value of my methods and classes? Mrs. Helene Galloway says: “My son, Ryan, has participated in Mr. Gold’s algebra class this past year and has thoroughly enjoyed learning not just the mechanics of problem solving, but also why concepts are applied and how they relate to everyday life. He has been learning a great deal from Mr. Gold in private geometry classes, too — the mechanics, the ‘why,’ the ‘how,’ the applications.”
In order to better serve the needs of the community, four different workshops at two levels, (1) upper elementary/lower junior high, and (2) upper junior high/high school, will be offered each session. A minimum number of 8 students is needed for a workshop to “make”. If the minimum number is not met, arrangements can be made for holding the desired workshop — cost would be on a sliding pay schedule depending on the number of students.
I. Workshops to be offered include:
Learning From Thomas Edison
In “Thomas Edison Lit Up America With His Bright Ideas” (Investor’s Business Daily, 5-21-09, 5:53 PM ET), Marilyn Alva said:
Though Edison’s top achievements were in electricity and sound, he innovated in other fields ranging from radio-wave telecommunications to iron-ore mining and rubber.
He did solid research followed by experiments and prototypes.
“He wasn’t an expert in the beginning, but once he got interested in something he found a way to become an expert,” said Kelley, a founder of the Stanford Institute of Design, or d.School. “He was the best proof that if you’re good at innovating, you can apply it to almost any field and make a contribution.”
Fossil/Archaeological Dig Opportunity
Diana said on TAFFIE-ANNOUNCE:
This is a great Learning opportunity…we have gone the past few years and learn allot and get to dig for fossils and artifacts. You even get to bag, analyze and caterogize what you find. Wear a hat and sunscreen it gets hot out there! contact info in below, all I know is what is posted here. Just wanted to share!
Come dig with us! Rancho de las Cabras Floresville, Texas
It’s FREE!!!!
Join archaeologists from the UTSA Center for Archaeological Research and the San Antonio Missions National Historical Park at this 18th century Spanish Mission Ranch just outside San Antonio
When:
May 28, 2009
On Hierarchy in Education
Here is an excerpt from an email I wrote:
The general idea of developing the hierarchy of a subject or concept is critical. Take even something simple like handwriting. The breakdown of skills Montessori has for teaching the skill of handwriting is ingenious. I remember learning handwriting in school, by non-Montessori methods. It was hard to learn. All of a sudden I had to hold this big damn pencil in my hand, when I had no preparation for anything like that. (But I think another factor toward the difficulty was bad fine motor skills.) The experience was traumatic — maybe mildly, but still traumatic. Instead of getting encouragement, or, even better, a slow breakdown and build up of the skill, I got berated. At least, that is what I remember. Montessori, in contrast, has the young student do sensorial activities such as button a shirt, tie laces, make things with beads — to learn eye-hand coordination and muscular control and to develop muscle strength, as the student learns useful life skills; has the student trace letters on sand paper and felt — to learn the motor skills needed for tracing letters as he/she trains herself to make distinctions in touch; has the student put knobbed cylinders of various dimensions into the correct hole in a wood block — to learn the motor skills needed for holding a pencil (by grasping the knob) as he learns about volumes.
There should, of course, also be a hierarchical development for the core subjects. Algebra and geometry, as taught today, usually hit students over the head like a wood rolling pin. (”Why do we use letters in math???”) Montessori has students learn about and work with geometric shapes (in 2-D and 3-D) from an early age. Students reach a point in arithmetic where they study squaring and cubing — following the pattern laid out by the ancient Greeks — as geometric ideas. When you square a number you make a square that has sides of length, for example, 6
A Good Paleo Breakfast
That is: Breakfast by Science and Capitalism
A delicious breakfast (last week) of walnuts; raspberries and blackberries; half an avocado with some Napa Naturals extra virgin olive oil in the center and with some Adam’s Reserve ground chipotle pepper sprinkled on; and some shrimp with cracked pepper and extra virgin olive oil.
Thanks to Art DeVany and Dr. Loren Cordain for the good ideas on diet and foods — ideas based on an integrated view of diet and exercise. By integrated meaning based on facts and principles from evolution, biology, genetics, archeology, anthropology, chemistry, biochemistry, physics, biodynamics, etc.
I should say my breakfast is based on their ideas only as far as I have learned and have understood their ideas and the facts and principles behind those ideas.
May 27, 2009
Texas Highway Emergency Numbers
A member of TAFFIE-ANNOUNCE posted some good information (subject title: “Texas Highway Emergency Numbers”) on May 26th (10:14 PM CDT). She said:
If you are traveling on Texas highways this summer, be aware that Texas has a free courtesy patrol on major freeways in major cities. They will change a flat tire, give you gas, help start your car, or call you a tow truck. It is paid for by our taxes. Good phone numbers to have in your car. These hours seem to change, so if you have a problem, try a call anyway.
HOUSTON
6 am to 10 PM – Mon- Fri
TX Dot Courtesy Patrol
Mon, Tues, Wed, Sat, Sun – 10 PM to 6 am
713 225-5627AUSTIN
6 am to 10 PM Mon.-Fri.
512 832-7310.DALLAS
4:30 am to 10 PM – Mon-Fri
9:30 am to 6 PM Sat-Sun
214 320-4444
214 512-2726 – Beeper
Montessori on the Educational Value of Complex Multiplication
Dr. Maria Montessori said — after discussing how to introduce and develop the concept of number (with materials like beads and rods) and the concepts of addition and subtraction (again, with Montessori materials like beads and an abacus (a “counting frame”)) — that once a child gets to complex multiplication and has done some basic multiplication (yup…beads and abacus):
When there is a number to be multiplied by more than one figure, the child not only [already] knows the multiplication table, but he easily distinguishes the units from the tens, hundreds, etc., and he is familiar with their reciprocal relations. He knows all the numbers up to a million and also their positions in relation to their value. He knows from habitual practice that a unit of higher order can be exchanged for ten of a lower value.
To have the child attack this new difficulty successfully one need only tell him that each figure of the multiplier must multiply in turn each figure of the multiplicand and that the separate products are placed in columns and then added. The analytical processes hold the child’s attention for a long period of time; and for this reason they have too great a formative value not to be made use of in the highest degree. They are the processes which lead to that inner maturation which gives a deeper realization of cognitions and which results in bursts of spontaneous synthesis and abstraction.
(p. 228 of The Advanced Montessori Method, Volume II by Maria Montessori (Clio Press, Oxford England, ISBN 1-85109-233-1, (c) 1965 Montessori-Pierson Estates))
Math develops a person’s ability to think conceptually and abstractly, and develops a person’s ability to think through complex problems. And helps develop the child’s power and patience to engage in sustained mental effort.
Paleo Tacos
Delicious. Shrimp, Adams’ Reserve chili pequin, pignoli, minced red onion and sun-dried tomatoe, all doused in Napa Naturals extra virgin olive oil and served in whole Boston lettuce leaves. And sprinkled with Parmesan flakes. Good for the body, good for the brain (which is made up of a lot of fat, and needs lots of fat fed to it to function).
May 26, 2009
Brief Notes on a Geometry Tutoring Session
I tutored some students in geometry recently. Here is a note I sent to their parents to let them know what their children were doing and how their children were progressing (I will call one student A and the other B):
A and B did good in tutoring today. A and I covered six proofs — that’s a first. We have not done that many proofs in one sitting before. He’s doing good! We also discussed the nature of definitions (as having a genus and differentia, which we had discussed weeks/months ago) and their importance; we discussed and analyzed the definitions of polygon and triangle, and from there discussed quadrilateral and pentagon, midpoint and bisector, and, to discuss the concept “genus”, capitalism, democracy, communism (genus political system), and then dog and cat (genus mammal). And we discussed how, in learning a subject, it is important to review material that came before what one is doing now; A had forgotten what a polygon was, what a midpoint was, what a definition was, and what some of the axioms were, and so could not use them when he needed to. This was a great discussion for learning how to learn and how reason works. And we discussed Mill’s Methods of induction: the method of agreement, the method of difference, the joint method of agreement and difference, and the method of concomitant variation. These are very important for science — and every day life.
B and I analyzed four theorems in the book, and went over one proof (two proofs?). The proof was several steps more complex than others he had done, so it was one I needed to help him on. We had to do a bit more reasoning and add more to the diagram than what he’s used to. Most diagrams so far had given him all the information he needed. One theorem we covered proved that the hypotenuse of a right triangle (with a 30 degree angle) is twice the length of the leg opposite to the 30 degree angle. This triangle is one that we build on and use in trigonometry — which fact I pointed out to B. We find 30 degree angles and 60 degree angles used around the unit circle; now B will know why we use those angles in particular.
Very good sessions today. A and B are both making clear and definite progress; they have come a long way.
Geometry is used — as it should be — as a means of teaching reasoning. These students are learning how not just geometry but all knowledge has structure. They are learning to make connections, i.e., to integrate knowledge, and are being trained to take integration as the norm. They are learning how to think independently.
A good teacher is invaluable; a good teacher opens a student’s eyes to connections and heights the student would not see himself or herself. And if reasoning is important in life then so also is a good teacher important to a student’s adult life.
