From a conceptual standpoint of the sort I am describing in this paper,it would seem that sort of practice is far more important for learningabout relationships between numbers and between quantities than the wayspoken numbers are named. There are all kinds of ways to practice usingnumbers and quantities; if few or none of them are used, children are notlikely to learn math very well, regardless of how number words are constructedor pronounced or how numbers are written. ()
Share your paper with a friendly editor, someone who has your interests at heart and who has the time to review your paper carefully and who is willing to ask questions and to challenge what you said and how you said it. This person should be a friend, but not too much of a friend. After all, you're hoping for useful criticism here. Girlfriends, boyfriends, and parents make notoriously bad editors; they think whatever you write is wonderful, not to be improved. This is no time for coddling on their part or defensiveness on yours. This person is not to rewrite your paper for you, but you can hope he or she will catch an occasional glitch in punctuation or lapse in reasoning. The main purpose of this "outside editor," though, is to challenge your argument. Does the paper really make sense, is the argument sound? After all, you know what a sentence or paragraph meant and that means you are less apt to catch a confusing phrase or momentary lapse in the argument than someone else would be. If possible, watch your editor's face for confused looks or glazed eyes as he or she goes through your paper. It might mean that clarification is called for, that you skipped over something in your development, or that you've gone too far. Before he or she goes over your paper, it might be helpful to this outside editor to have a list of the kinds of things that have given you trouble in the past or the things that your instructor is apt to look for. Share a copy of the with your outside editor or use the more extensive provided below.
The numbers of Kings and Queens should be written in Roman ..
I'm surprised how everybody is talking about password expiration nowadays and Rob talked about it 6 years ago already. :) Now everybody seems to be smart on this issue and we got customers sending us links to articles on password expiration and complaining on password changing policy. What everybody is forgetting that every single user that has credentials to important systems and data is responsible for quality and safety of their password. Password changing policy every 3 months does NOT have anything to do with less safe passwords. This policy is meant to improve password safety not to worsen it for eavesdroppers and users that write their passwords on paper and lose them. If you set similar password as before it is your responsibility and you should be aware that setting similar passwords or as some call it “password transformation” decreases your password security, so you shouldn’t do it. So instead of complaining how periodical password changing isn’t safe, everyone should start contributing to their safety, be responsible, be aware of threats and start searching for constructive solutions. Until I hear about better solutions that can also be implemented and managable, people should stop complaining & start contributing. I could start complaining about whole password logic, why do we have passwords etc., but in the meantime I am aware that there are no better solutions out there so I have to adjust and use strong passwords.
If you don’t spell numbers out ..
3) developing familiarity through practice with groupings, and countingphysical quantities by groups (not just saying the "multiples" of groups-- e.g., counting things by fives, not just being able to recite "five,ten, fifteen,..."), and, when appropriate, being able to read and writegroup numbers --not by place-value concepts, but simply by having learnedhow to write numbers before. Practice with grouping and counting by groupsshould, of course, include groupings by ten's,
When using numbers in essays and reports, ..
Then demonstrate how adding and subtracting numbers (that require regrouping)on paper is just like adding and subtracting numbers that their poker chipsrepresent that require exchanging. This is a good time to introduce, somewhatcasually, the algorithm for adding and subtracting numerals "on paper"using the "trading" or "borrowing/carrying" technique. You may want tostick representative poker chips above your columns on the chalk board,or have them use crayons to put the poker chip colors above their columnson their paper (using, say, yellow for white if they have white paper).Show them how they can "exchange" numerals in their various columns bycrossing out and replacing those they are borrowing from, carrying to,adding to, or regrouping. (This is sometimes somewhat difficult for themat first because at first they have a difficult time keeping their substitutionsstraight and writing them where they can notice and read them and rememberwhat they mean. They tend to start getting scratched-out numbers and "new"numbers in a mess that is difficult to deal with. But once they see theneed to be more orderly, and once you show them some ways they can be moreorderly, they tend to be able to do all right.) Let them do problems onpaper and check their own answers with poker chips. Give them lots of practice,and, as time goes on, make certain they can all do the algorithmic calculationfairly formally that they can also understand what they aredoing if they were to stop and think about it.