 |
| 玩玩Venn's Diagram 數學真的不僅僅只是算術 |
 |
| Venn's Diagram的概念俯拾即是，圖為《I Spy》這本書的某一頁。 |
在去年151109〈關於「最佳學習時間點」這件事……〉的文章裡，我說了現階段學齡前我最在意的三個面向──閱讀、數學、語言，這三個面向在進入學校之後，就變成了三個學科──國語、數學、英文。如果我的理想能夠實現的話，對噗們來說，英文並不會是一門獨立的學科，和中文一樣，只是工具，任何的精進都只為達到更好的吸收及表達效能，所以對學齡時的噗們來說，做為媽媽的我會「盯」的就是語文和數學兩科。
為什麼是這兩科？因為這兩科是任何學習的工具、基礎，少了語文和數學能力，自主學習是緣木求魚。
語文，沒有爭議，它是人類文明最大也最重要的載體，重要性不在話下，但我認為語文的學習是比較開放的，不管是注音不注音、自然發音還是音標這類選擇的問題，還是先注音後國字、先聽說再讀寫這類順序的問題，都不是重點，我傾向「全語言Whole Language」的觀點，在一個「非用不可」的環境裡「實戰」，而且「以戰養戰」越用越精。
數學，完全就是另外一回事了。
數學很重要，但數學不僅僅只是算數，數學是一種邏輯的、推理的思惟，數學的訓練讓人的腦袋可以用來解決問題；數學也是一種語言，定義、邏輯和推論越清楚的語言越能達到溝通的目的，更惶論在這個CPU主宰的世界裡，人們或多或少地要和「非人」溝通，能夠使用定義、邏輯和推論清楚的語言的能力越形重要。
我說過我不吃那套什麼具有「完整的系統性架構」的「套裝知識」，但我必須承認，數學有它的架構；往前行的每一步都深深地倚賴著過去所建立起來的「先備知識」，就像是疊磚起樓，底層哪怕是一點點的不紮實，樓都會塌；有洞，唯一的辦法就是打掉，回到有洞的那個點重新練起。
節錄一段《Family Math(ISBN: 0912511060)》裡的文章〈Doing Mathematics at Home〉，並畫上我自己的重點
- Let your children know that you believe they can succeed.
- Be ready to talk with your children about mathematics and to listen to what they are saying. Even when yourself don’t know how to solve a problem, asking a child to explain the meaning of each part of the problem will probably be enough to find a strategy.
- Be more concerned with the processes of doing mathematics than with getting a correct answer. The answer to any particular problem has very little importance, but knowing how to find the answer is a lifetime skill.
- Try not to tell children how to solve the problem. Once they have been told how to do it, thinking usually stops, Better to ask them questions about the problem and help them find their own methods of working it through.
- Practice estimation with your children whenever possible. Estimation helps the thinking about a problem that precedes the doing, and is one of the most useful and “sense-making” tools available.
- Provide a special place for study.
- Encourage group study.
- Expect that homework will be done. Look at the completed work regularly. But try to keep your comments positive. Don’t become a drill sergeant. Praise your child for asking questions, and look for places where you can ask questions about the work. To be successful, your child will need to study 30 to 60 hours a week in college, at least an hour and a half each day in middle school, and probably 20 minutes a day in elementary grades. The experts tell us that there is a high correlation between success in mathematics and the amount of homework done.
- Don’t expect that all homework will be easy for your child or be disappointed that it seems difficult. Never indicate that you feel your child is stupid. Sometimes loving, caring parents unintentionally give their kids the most negative messages.
- Seek out positive ways to support your child’s teacher and school. Join the parent group. Offer to help find materials or role models. Accompany field trips. Avoid making negative comments about the teacher or the school in front of your child –your child needs to maintain a good feeling about the school.
- Ask the teacher to give you a course outline. See Mathematics Generally Covered at Various Grade Levels and Resource List for Parents and Teachers.
- Find time to sit in on your child’s classes.
- Look carefully at the standardized test results, and ask about any test scores that may indicate a skill deficiency or a special talent. But do not use these test scores as your primary means of assessment. The teacher’s observations and your own will be much more valuable. Some of the most important attributes, such as sticking with a problem, or having many effective strategies to use, are not tested with paper and pencil.
- Ask the teacher at the beginning of the term how placement decisions are made.
- Try not to drill your child on math content or create hostilities by insisting that math work be done at any one specific time or in a specific way. Don’t use math work as a punishment. Parents and adolescents have enough things that may create friction without adding math to the list.
- Model persistence and pleasure with mathematics. Include enrichment, recreational mathematics in your family routine. Try to introduce math ideas with a light touch at the dinner table, or while traveling, even to the grocery store.
