The participating schools in Unit 111 are:
We are glad you've joined us, and are looking forward to your questions.
Also, we would like to thank Haesun Kim for doing a wonderful job of SysOp for FrEd mail, on board one. You are doing a great job.
Due to the amount of mail that comes in on board one, the Network will be using the second board for the most pan.
Q1. What does sorting buttons into different kinds have to do with mathematics?
Al. Sorting or pairing any kind of objects which can be seen as related because they have the same color, same number of holes, or go together functionally like "bread and butter," is establishing a relationship or a set of relationships. Mathematics can be defined as a study of relations, but one of my colleagues wanted to know if the relationship she has with her husband is suitable for mathematical study. I told her she might not like the way mathematicians would represent such a complex relationship, but it could be studied mathematically. However, simpler relations are better for elementary school mathematics, e.g., a tree-diagram. A tree can have many branches and branches on branches, on branches. For example, buttons can be divided into two branches by size (large and small) and then each of those branches could be divided into white and colored, and then each of those could be divided into one-hole, two-hole, and four hole buttons. Children could draw the picture of this tree, and then invent another tree to arrange the same kinds of buttons differently. (see figure 1 )--JE
Q2. What good is the study of sorting trees, when children have so much trouble learning to calculate?
A2. The standard elementary school mathematics curriculum, procedures for adding, subtracting, multiplying, and dividing whole numbers, fractions and decimals, isn't working at all well. Children forget what they have learned over the summer and it takes months to review the previous years' work before going on. Children get bored with it by fourth or fifth grade, but worst of all, they very often lose the ability they had at the beginning of first grade to use numbers in practical situations. The teaching of key words like "altogether," "more," less," etc., does not seem to be working as a way to decide which operation to use on two numbers in a story problem. Neither does practicing operations in story problem form after learning them. One usually doesn't practice thinking about the story in those problems; one only picks out the two numbers and does the current operation on them. It is even more difficult to figure out the operation by key words when there are three or more numbers in the problem. However, studying relations should help. For example, children can make up their own story problems about buttons, draw a tree of the relations, and figure out from the tree whether to add, subtract, or do something else with the numbers of buttons.
Q3. Why is it that we start on the right when we add, subtract, and multiply, but start on the left when we divide?
A3. This is a great question, and not an easy one to answer at all. One thing needs to be said at the outset, that it is not mathematically necessary to start any operation on the right. It is just a convenience in memorizing a procedure.
So, in classrooms, where calculators are used to do lots of problems, and inventing algorithms or procedures is the main activity children work at, many children invent procedures starting on the left. In some sense, also, starting on the left, with the larger digits, is more natural. If we had a lot of play money in a game, like Monopoly, we would put all the $1000 bills together, then the $100 bills, etc., and add, subtract, multiply, divide, starting from the larger categories. So, if our goal is to develop understanding of computation, so when people's calculator batteries run down, and they forget how or make mistakes in their computing, they can still figure out what they did wrong, we could de-emphasize starting on the right .
If we still want to try to turn children into speedy and accurate human calculators, it might be best to start on the right for all four operations, doing division by repeated subtraction. Why it might be difficult to start the usual division algorithm on the right when you divide is something I'd rather not try to explain, but I do suggest trying division with play money. Take a bunch of coins and bills and divide the pennies first into three equal piles, then the dimes, then the dollars, then the ten dollar bills, and so on. If that is difficult, try starting with the biggest bills first. Then try to find out how many times you can subtract a certain amount of money from what you have to start with. That can be done from either side. Division, whether done by repeated subtraction or some other way, can involve some guessing. Perhaps people who don't like to erase or cross something out, once it is written down, are the ones who invented starting on the right except for division - I don't know. - -JE
Q4. If our normal temperature is 98.7 why don't we feel hot all the time? (This question was asked by a 10-year old girl in Philadelphia.)
A4. The human body is a remarkable thermometer, it can sense hot or cold in many different places. It can sense if a beverage is too hot, just by tasting it. The body can sense the internal temperature, almost to the degree, 98.7 degrees to be exact. If the internal temperature rises or falls we feel sick, until the body can regulate itself. On the outside, the temperature is sensed by nerves on the surface of the skin. The surface temperature is usually cooler than that of the internal temperature. For our skin to feel cold, the air temperature has to be cooler than the skin temperature. We don't feel our internal temperature because our skin and fat layers act as an insulator. Also, 98.7 degrees is the operating temperature for the body, in order to feel something different the internal temperature has to go up or down. -- TN
The visit to Prospect School classrooms generated a few questions which I am recording here so they could be passed on to the review committee to see if they can be answered locally. --JH
Mrs. Hammon and Mrs. Angelos, 5th grade
Q 1. How does a hologram separate the light into different colors?
Q 2.What exactly are optical illusions, and how do they work?
Q 3.How do you make mirrors? How do they work?
Miss Thompson, 6th grade
Q 4. What are black holes?
Q 5. How do tunnels and time warps work in the universe?
This is a draft of a first message on the new board, QUEST:
Subject: Welcome to QUEST
WELCOME TO QUEST!!! QUEST has been created for the exclusive use of the Science Network with three purposes in mind: (1) to make it easier by permitting users always to sign-on in the same way, (2) to permit people in several locations to see what other questions are being asked by other participants, and (3) to permit persons in different locations to respond to the same set of questions. Please let us know how you like using it.
If you prefer to send questions and/or answers
directly to the person you intend them for that can still be done in the
usual way.
This is a draft of a second message on the new
board, QUEST:
Subject: Coding messages with the subject heading.
The first "word" of the subject heading for a question should begin with the letter Q. followed by a two-letter code for the school it came from, and a letter or digit to indicate grade level. The next word or words of the heading should identify the specified topic of the question. For example,
"QAP1 Insects" could be the heading for a question about insects from Aroma Park School (Kankakee), Grade 1, and "QPS4 Mirrors and Illusions" could be the heading for a question about how to make illusions with mirrors from Grade 4 in Prospect School (Clarendon Hills).
If there are multiple questions about the same subject from the same grade level in the same school, numbers could be appended, e.g., "QAP1 Insects2" could be the heading for a second insect question from Aroma Park, grade one.
Normally the answer to a question goes into the QUEST board with the same heading as the question it responds to.
Teachers' names normally appear as sign-ons for
each question and answer. Children's names could be added, if desired,
in the heading, thus: "QAP1 Insects 2-Billy."