Showing posts with label acceleration. Show all posts
Showing posts with label acceleration. Show all posts

Friday, October 16, 2009

Math acceleration

Acceleration sometimes means to either omit things should be taught or to rush through those things. These students generally become confused, afraid, and eventually hate mathematics. Parents with money or time can hire tutors to temporarily get the students "rescued". Students without these parents will not get the same help and will fall behind to cause an achievement gap.

Those students falling behind will quickly be lost forever in mathematics. These souls will suffer through many more years of (hard) mathematics. The students who are "rescued" may start feeling that mathematics is hard and not fun any more. Many of them will "hit a brick wall" right about when they start learning algebra2.

If no acceleration is practiced from grades 1 through 8, a student could take algebra1 in 9th, geometry in 10th, and algebra2 in 11th grade. These students will have a good foundation in mathematics to further their studies in the future.

Sometime, we should visit the issue of using calculators in ES and MS.

Sunday, October 11, 2009

資優的跳級生

人生的風景何必急著壓縮 (家有資優的跳級生)

昨天應邀去上「今晚哪裡有問題」節目當特別來賓,當集的節目主題是「跳級生」。
主角人物是兩個跳級生的家長:蔡爸爸與蔡媽媽,我和另外一位媒體人、還有在建中任教超過三十年的陳美儒 老師,則是搭配的來賓。


整場錄影,簡直是讓我有「傻眼」的感覺。
蔡爸爸與蔡媽媽本身都是相當高水準的知識份子,蔡爸爸是光武工專電機助教、留美高材生,蔡媽媽本身是家管,師範大學公民教育系畢業。
三個孩子中,老大佩真今年以十六歲的年紀,拿下大學指考第四高分,錄取台大電機系,在就學過程中,她兩度跳級,國小跳一次、國中跳一次。老二也是跳級生。
蔡爸爸、蔡媽媽與大家分享他的「學齡前教育法」。
他們說,兩個大的一出生,24小時內就抱回來餵母乳,還未滿月前,她就開始「字卡教學」。
蔡媽媽手繪各式各樣字卡,還有由圓點點組成的「數目圖卡」,從1到99,在每次餵奶前,寶寶哭鬧、最有精神時,在寶寶眼前晃過卡片,告訴寶寶相關的字、數目,然後再餵奶。
蔡爸爸說,三歲前的寶寶有大腦有百分之七十的未開發區域,先給予字卡再給予喝奶,就是教導他「學習」跟給予「獎勵」。接下來,寶寶還未學會走路,家中牆壁就貼滿了數字、九九乘法表,以及國小國語課本裡的課文。
家中所有的家具都貼上中英文字卡,隨時隨地不忘教學。


因此,在蔡媽媽的耐心教育下,蔡佩真一歲就已經識得數字及國字,會用手指出正確位置,兩歲會說話時,就已經會背完九九乘法表,三歲已經可以自行閱讀中英文故事,並在鄰居教導下,學會基礎日文。
她中班以前已經把小學一、二年級的課程上完。
於是,她小學二年級就隨著媽媽到師院附小上六年級的數學課,四年級時跳級至五年級。
國二下再跳國三下,隨即考上北一女中。
蔡爸爸並分享孩子們生活的點滴,包括喜歡打球、打撲克牌,以及他自創的「十分鐘預習法」及一些聯想記憶術等等。
節目結束後,他並送我一張他個人印製的「學齡前教育」的演講DVD。
我當場只能不停的搖頭讚嘆。
我看到的是,一個優秀的媽媽,將所有的精力都放在兒女的教育上,將所有自我的成就都擺在成就兒女上。


但是,我也看到,蔡家父母將所有的心力放在智育的教育下,三個孩子在優秀課業表現的同時,顯然在人際關係上都有極大的問題 不斷的跳級,導致的是在學校裡的寂寞,沒有朋友,還有,人生閱歷顯然較同年紀的孩子貧乏 陳美儒 老師對於這樣的教育行徑十分不贊同,在錄影現場就不停的開砲,導致對方有點小尷尬,因此我的角色其實比較像潤滑劑一般,偶爾開個玩笑,嘲笑自己很懶,沒有辦法這樣教小孩。不過,私底下,我很認同美儒老師的看法。
美儒老師在建中任教三十年,得天下英才而教之,她說了一個故事我覺得很有趣。
她說,有一年建中將所有數理資優的孩子集中在一個班上,那年,那個班上考上了六個台大醫科,十幾個台大電機。
其中有一個「考壞」了的孩子,考上台北醫學院醫學系,放榜當天人就消失不見,大家嚇壞了,後來陳 老師在碧潭橋畔找到了他。


她想說的是,一路順遂、超人一等、資賦優異的孩子,並不見得是快樂的孩子大家在一味追求學業的資賦優異過程中,不該忽略的是孩子的體能教育、品格教育、愛情教育、財物教育、人際關係、以及各種各樣生活中的歷練。
最好笑的,是二十年後, 陳 老師去參加這班同學的喜酒。
在喜宴兼同學會上,眼看當年資賦優異、人人稱頌的這一群大男孩,分坐了兩桌,變成醫生、工程師,並為人夫、為人父,喜酒的菜一上,大家不約而同,紛紛低頭不停的剝蝦。
其中最優秀的那一個男生,自顧自的吃蝦,結果被老婆狠狠的踢了一腳之後,也開始低頭幫孩子剝蝦殼!
哈哈!我在一旁,忍不住大笑!
陳 老師的意思是,「資優又SOWHAT?20年後,他跟一般頭腦普通的男人,並沒有兩樣!
他仍然要在社會上生存,跟家人相處,結婚生子、養兒育女。」

今天我去上MOMO親子台時,忍不住跟現場兒童心理師分享昨天的錄影經過。
他說了一句話我覺得超棒!

他說:「人生的風景有多少?值得我們慢慢享用,何必急著把它壓縮著過完?」



沒錯啊!就是這種感覺!
我並不否定蔡爸爸、蔡媽媽的心血,也認為他們全心為兒女的付出非常值得讚美,但我相信,以他們夫妻倆資質的優秀,即使不在寶寶滿月前就開使用「閃卡」、「字卡」,奮力的教學,他們的孩子一定也可以順利考上北一女、台大電機!我相信,優秀的父母培育出的孩子,在學業上絕對不會差到哪裡去!只是或許多用了一、兩年的時光。
但是,童年的時光何其珍貴?
與其辛辛苦苦的製作閃卡、字卡、數目圖卡,為何不用這樣的時間多跟孩子去溪邊散散步、看看美好的晨光?



與其花費時間教他「媽媽起床、爸爸讀報」的國語課文,為何不多講幾個好聽的故事、讀幾篇優美的詩歌?

與其花時間背九九乘法表,為何不帶孩子看一場好看的電影,看一齣有趣的話劇?


與其讓孩子先讀他還不需要知道的知識,何不帶孩子一起粉刷油漆、擦地洗碗、種花除草,
或是去一趟育幼院、幫忙照顧其他失去父母的幼兒,讓他懂得關心這個社會?
與其在十五歲時就在大學選修課程,為何不鼓勵她多交幾個閨中好友,去逛個街、打個工,讓她培養正常的社交關係?
在全力追求智育的時刻,我看不到的是強調孩子品格的教育、藝文的欣賞與正常的社交培養。
最重要的並且是:生活的歷練缺乏一個十六歲的女孩,正是最甜美的時刻,她應該要有她這個年齡所該有的青春、愛情,擁有運動與社交、懂得追求自己所愛,享有秘密與夢想。
我期望我的女兒十六歲時,除了唸書之外,看到人會主動的打招呼、微笑,對於長輩展現出應有的禮貌,進退得宜,而不是當別人向妳問好時,只知道直楞楞的瞪視對方、沒有任何反應。
我希望我的兒子十四歲時,對於沒看過的環境充滿好奇,到了攝影棚會問東問西,而不是呆若木雞。
我希望我的孩子能夠爬山涉水,懂得探詢世界,求知慾不僅僅限於學業。
我希望她在苦讀ABC時,除了用來看TIME雜誌,更能領略毛姆、莫伯桑筆下的人生縮影。是的,生命何其珍貴?求知何其快樂?我並不急得他們跳躍度過,也不在意是否速成有效,我只希望他們慢慢享受、領略其中美的世界。
看信的好處是可以『增廣見聞』,穫取您平凡的生活不會去想的東西。
如果您收到別人分享給您的好文章,不要吝嗇,您也可以繼續分享給好友,請別忘記我這一份喔 ! !
當我們用心對人時,有心人將以熱情回報您,希望我們都是用心的人,也是有心的人。

Wednesday, June 17, 2009

Math acceleration

Just Saying No–to Accelerated Math
June 10, 2008 by SwitchedOnMom

Last week the Washington Post ran a story on the a topic I’ve blogged on before: the uneasiness many parents are feeling about willy-nilly math acceleration in MCPS. You can read the story, “Accelerated Math Adds Up to a Division over Merits,” (yuk, yuk) here.
While parents support rigor and the opportunity for acceleration, many are uneasy that it’s being approached backwards, being carried out by fiat. The word has come down from on high that students who complete algebra before high school are more “successful.” Thus it should be so–regardless of whether there are/exist numbers/percentages of students to meet these targets (20% of 6th graders, 40% of 7th graders, 80% of 8th graders taking algebra in 8th grade). To make it so, the math curriculum is being back-mapped into elementary school, with acceleration starting abruptly in 2nd grade. As the article notes, concern seems to be greatest in the less affluent “red zone” schools.

The result–at least what I’m hearing anecdotally–is kids who are rushed through a compacted curriculum, who are stressed out, and who have decided that they aren’t good at math and in fact hate it. Down the line, there are reports of a watered down algebra and kids with weaknesses who fall apart when they hit Algebra 2 in high school and lack a truly solid footing in math.
Last night I had dinner with a good friend. She told me she had informed the “math content specialist” that her 4th grader (who has been doing combined 5th and 6th grade math this year) was going to repeat the same level math class next year. (Her child was in agreement and parents have ultimate say on placement.) The content specialist said it should be no problem.
A few days later, however, the mom got word that the principal wanted to see her. She went into a meeting with the principal, vice principal and math content specialist. To her surprise, the principal was under the impression that it was the mom who had requested the meeting. She told the principal that no, they were the ones who had requested to meet with her. The principal then asked why she wanted her child to repeat math next year, as the grades on the cumulative unit tests (which he had in front of her/him) were quite good. (It should be noted that the school thinks “mastery” is earning a “C.”)

To the prinical’s astonishment the mom said that in her opinion the scores were essentially meaningless. The tests were given over two days, and her child had confided that she had been told by the teacher which questions were wrong–and which he/she needed to answer correctly the next day in order to get a higher grade. The principal sputtered that the mom had just robbed her/him of any argument against the mom’s decision. The principal was clearly not pleased and as the mom was leaving told the others present to stay behind.

The only question is, was the principal angry that the testing was being manipulated? Angry that she/he didn’t know that the data was being manipulated? Angry that there would now be one less child on the accelerated math track? Angry that a parent had discovered this? Some of this? All of this?

Monday, March 9, 2009

Math practices

By ERIC WALSTEIN BrookevilleSunday, March 1, 2009; Page C07 Washington Post

As a teacher in the Montgomery County Science, Mathematics, Computer Science Magnet program, I have the privilege of teaching some of the best young minds in the United States. But even as standardized test scores have risen and the county has claimed great strides in math instruction, our program has had to offer a week of remedial math classes during the summer for our entering ninth-graders.

This past summer, the teachers administered a test of concepts we thought the students should know coming out of algebra, geometry, and algebra II. I constructed the test, and the other teachers reviewed it. We grouped the students into four levels based on their magnet qualifications. We gave them one hour to complete the exam. We did not let them use calculators. It had 27 questions and yielded eye-opening results.

I was assigned to the top group, which averaged only 15 questions right. The other groups scored commensurately lower, some as few as three or four questions right. Students found many of the ideas of algebra and geometry foreign, reporting that many core ideas had never been taught. This process of giving summer math help has been going on for five years now, and the knowledge trend has been down each year. This is a direct consequence of policy decisions of the Montgomery County Board of Education to eliminate course objectives, to push students to take algebra earlier -- often before they are ready -- and to rely heavily on calculators.

Cumulatively, these decisions leave students in an untenable position. They lack the rich math background to fully understand their current work. So, to get their work done, they have no option but to memorize the current work and punch unfamiliar buttons on a calculator. This technique masks their lack of connection between current tasks and previous concepts they supposedly know.

Calculators used incorrectly enable children to "solve" problems they don't actually understand. They not only hide the intellectual connections between ideas that mathematicians seek to have students understand, but they also impair math strategy, long a staple of math curriculum design. Used correctly, calculators can be an important tool. Used incorrectly, they subjugate mathematical progress and reasoning to a list of questions with a corresponding list of answers.
A Montgomery school official once told me that calculators are important because they give more students "access to math." That's wrong. They give students access to answers disconnected from math concepts. Many of my current students complain that curriculum acceleration made them move too quickly without proper understanding. Take the calculators away, as we did, and even the county's brightest bulbs now get a failing grade on material they supposedly have learned with top marks.

Our magnet program students bring to the table a significant amount of mathematical knowledge and talent. Their work ethic is impressive; they make extensive use of the additional materials that a school with real resources can provide.

The students have the ability, but the school system is not matching their commitment.