NO.58-06 2019 DEC | 科學研習期刊目錄 本期專題 數學素養 益智遊戲易位棋中的數學思維 | 李源順 「理財素養」生活中的數學素養 | 溫世展 如何從小培養數學創造力 | 溫世展 統計與資料科學中的數學 | 王啟樺 買房裡的數—貸款的數學 | 鄧家駿 教學現場 有數學感的教與學—以周長和面積為例 | 李源順 數學奠基活動「矩形拼板」在國中數學課堂的實施與回饋 | 鄧家駿 有數學感的教與學：以雞兔同籠為例 | 李源順 隱含微積分概念的國小「圓面積」教學 | 陳玉珊 高中數學科展經驗談 —數學探究的樂趣 | 張宮明 科學新知 我們對「颱風假」應有的認知和省思 | 陳正改 臺灣地震測報的發展 | 蕭乃祺 特約專欄 全等 | 游森棚 日本月刊科學繪本初探：走讀福音館『かがくのとも』50週年紀念展 | 劉淑雯 黃明宏 STEAM課程的發展架構與教學活動設計 | 唐偉成 科普活動報導 一個『再發現』的探究歷程：2019自然科學探究式網路競賽得獎作品科學探究經驗分享 | 黃嘉郁 科學家的秘密基地 | 高瑩珊 科教館GO好玩 遊戲化核能知識卡牌桌遊推廣 | 顏慈瑤 李柏翰 蘇萬生 總召集人的話 中小學的數學教育被高度期望培養學生在日常生活中進行數字和空間思考的能力與信心，使能明辨和解決相關問題。本期特別以「數學素養」為專題。 「本期專題」單元共有五篇文章，〈益智遊戲易位棋中的數學思維〉一文介紹如何利用易位棋教學培養學生的數學解題思維。〈「理財素養」生活中的數學素養〉一文介紹數學與理財素養內涵以及理財情境下的數學素養。〈如何從小培養數學創造力〉一文介紹數學創造力的相關理論與研究、教材與教學策略以及教學實踐。〈統計與資料科學中的數學〉一文從數學角度介紹統計與資料科學背後追隨的人工智慧之夢。〈買房裡的數—貸款的數學〉一文討論向銀行「借錢」買房子後，如何「還錢」最划算。 「教學現場」單元刊登五篇文章，〈有數學感的教與學—以周長和面積為例〉一文利用小四學生學習長方形和正方形的周長與面積單元，解說該如何讓學生學得完整的周長與面積概念。〈數學奠基活動「矩形拼板」在國中數學課堂的實施與回饋〉一文介紹數學奠基活動國中組中的「矩形拼板」桌遊活動。〈有數學感的教與學：以雞兔同籠為例〉一文利用類似雞兔同籠問題，說明嘗試錯誤、有規律嘗試錯誤、邏輯推理、代數解法之間的關聯及重要性。〈隱含微積分概念的國小「圓面積」教學〉一文解說如何藉由小五「多邊形」的學習，引導小六連結「逼近」概念以及先備學習經驗，讓圓面積的學習更有脈絡性。〈高中數學科展經驗談—數學探究的樂趣〉一文分享作者多年來帶領高中生從事專題研究，進而形成科展作品的過程。 「科學新知」單元刊登兩篇文章。〈我們對「颱風假」應有的認知和省思〉一文帶領讀者面對「颱風假」課題，省思應如何看待及抱持何種態度才不致失焦。〈臺灣地震測報的發展〉一文則介紹臺灣在集集地震後在地震測報工作的進展。 「特約專欄」單元刊登三篇文章，〈森棚教官的數學題〉一文拋出有關兩個三角形全等條件的問題。〈日本月刊科學繪本初探：走讀福音館《かがくのとも》50週年紀念展〉一文分享走讀日本福音館《かがくのとも》(科學之友)月刊50周年展後對月刊科學繪本的介紹與推薦。〈STEAM課程的發展架構與教學活動設計〉一文則提出對PBL-STEAM課程發展與教學活動設計的見解。 「科普活動報導」刊登兩篇報導：〈一個「再發現」的探究歷程：2019自然科學探究式網路競賽得獎作品科學探究經驗分享〉透過2019年指導學生參與自然科學探究式網路競賽得獎作品實例，說明進行探究活動的歷程；〈科學家的秘密基地—科學好好玩，一起動手做〉報導國研院善用其強項和方式讓孩童愛上科學的展覽活動。 本期「科教館GO好玩」單元刊登〈遊戲化核能知識卡牌桌遊推廣〉一文，則介紹如何透過有趣的卡牌桌遊，讓民眾甚至年齡更小的學童曉得核災的知識。 總召編輯委員 - 李隆盛 關於本刊 出版單位：國立臺灣科學教育館 發行人：陳雪玉 總召集人：李隆盛 編輯委員： 物理科吳仲卿/陳耀榮/李柏翰/盧玉玲 | 化學科古建國/許良榮/王伯昌/林如章/周金城 | 生物科王美芬/蕭世輝/陳建志/郭淑妙 | 地球科學許民陽/王郁軒/李文禮 科技科張玉山/汪殿杰/林育沖/趙珩宇 | 數學科李源順/鄧家駿/溫世展/張宮明 | 跨領域學科李名揚/連信仲 | 特約專欄 游森棚/黃琴扉/劉淑雯 策劃：曾聰邦 主編：錢康偉 本月專題特約主編：李源順 編輯：吳郡怡 網頁設計編輯：蔡婉懿/曾怡/施曉恬 投稿規範請來信詢問：article@mail.ntsec.gov.tw

機車排放廢氣是我們在路上隨處可見的空氣污染，許多機車騎士都有戴口罩，但戴口罩到底能不能真正阻隔機車所排放的廢氣？便是本研究想探討的重點。我們借用環保局檢測機車排放廢氣的儀器－HORIBA 來進行實驗，結果發現：活性碳口罩確實比一般棉布口罩的阻隔效果來得好。但因活性碳口罩較貴，又不能洗滌，使用期限短，我們便用便宜的棉布來自製口罩，並加上生活中隨手可得的物品以增加其阻隔廢氣的功能。結果竟發現了咖啡渣的棉布口罩其阻隔效果竟比活性碳口罩來得好，這個利用泡過的咖啡渣做成口罩還很環保呢！選用口罩除了考慮阻隔力以外，還應考慮透氣度。本研究發現活性碳口罩不論在阻隔力或透氣度上都有很好的表現，紙口罩雖然阻隔力佳，但透氣度差。以上結果可供消費者在選擇口罩時作為參考。

二氧化鈦是光觸媒中最常被使用的，雖然合成方法很多，但如何提升其產量及分解效果，一直是學界及業界的熱門議題。\r 在此篇報告中，我們發展出一種新的方法來製造二氧化鈦，利用控制合成時溶液的pH值、使用幾丁質當作新的保護劑，並且改變加熱的溫度和時間來得到二氧化鈦奈米顆粒。在降解實驗中亞甲藍光的分解反應速率級數為一級，降解亞甲藍液的半生期在2.9~7.0分鐘，比一般文獻的數十分至數小時以上的速度高出許多。\r 另外，在幾丁質未燒去的實驗中，我們發現亞甲籃分子會被吸附在幾丁質的表面上但不被分解，燒去幾丁質時奈米粒子又無法完全分散，為解決這一個問題，我們使用了分子篩，分子篩可以吸附許多有機物質，再加上其為具有許多中/微孔構造的鋁矽酸鹽礦物，奈米粒子可以分散在其表面而不生團聚；在光降解的實驗中發現光觸媒結合分子篩後可大幅提高染料的分解效果，在短短一分鐘之內便將亞甲藍分解掉一半以上！\r 這個實驗提供了很好的方法，可以快速有效的合成二氧化鈦奈米顆粒，作為光觸媒使用。我們相信這個方法可以推廣到其他有機汙染物質，以降低工業進步後對地球環境所造成之污染危害。

This experiment mainly aims at three kinds of solution - Dextrose, Saccharose, and Fructose. By changing its temperature, density, length of tube, as well as different wave length factor of polarized light, we observe the influence of the direction of polarization by those factors. The experimental result showed as follow. The Dextrose and the Saccharose can cause the polarized light with the rotary direction of clockwise, so both are ‘dextrorotatory’. The Fructose can cause the polarized light with the direction of counterclockwise, so it is the ‘laevorotatory’. For the Dextrose, when the\r temperature is lower than 20℃, the direction of polarization has changed observably, but doesn’t have any rule. When the temperature is higher than 20℃, the direction of polarization increase slowly. For those three kinds of solution, when\r density increased, the polarization increased observably. When the polarized light passed through the solution with longer path, the direction of polarization has more change. When the wave length of the polarized light changed, the direction of polarization has been changed observably. When the wave length of the polarized light is shorter, the direction of polarization change increased.本實驗主要針對葡萄糖、蔗糖、及果糖等三種旋光性溶液，改變其溫度、濃度、容器管長、以及不同波長的偏振光等因子，觀察這些因素對偏振方向所造成的影響。實驗結果顯示：葡萄糖與蔗糖會使得偏振光的偏振方向以順時針旋轉，屬右旋性之光學異構物；果糖會使得偏振光的偏振方向以逆時針旋轉，屬左旋性之光學異構物。若溶液為葡萄糖，當溫度低於20℃時，偏振光的偏振方向會有明顯的改變，但無規則可尋；當溫度大於20℃時，偏振方向旋轉角位移則以非常緩慢的方式增加。當此三種溶液之濃度增加時，偏振光的偏振方向有明顯遞增的現象。此外，當容器長度越長（即偏振光在介質中的行程越長）時，偏振方向的改變亦越明顯。當偏振光的波長改變時，偏振光的偏振方向有明顯的變化，且當偏振光的波長越短，偏振方向的改變越大，似乎與波長呈反比，但此結果與理論值（即旋光度與波長平方成反比）仍有一些差距。

On account of the rapid development of human activities, much more fossil fuel is burnt and thus a greater amount of greenhouse gases are emitted to the atmosphere including carbon dioxide (CO2). CO2, is considered as the major cause of the exacerbating global warming. “Geo-engineering”, literally, means the options that would involve large-scale engineering of our environment in order to combat or counteract the effects of changes in our atmosphere. As a carbon neutral CO2 scrubber is proposed to be a large-scale scheme to fix carbon globally through reducing the CO2 emitted to the atmosphere and our ultimate goal is to implement the CO2 scrubber scheme to the whole globe, that is, a large-scale scheme to our environment, it is a project of geo-engineering. The procedures of the project are as the following: (a)Investigating on the absorption of CO2 produced by calcium carbonate (CaCO3), using different basic substances at different temperatures (b)Investigating the absorption of CO2 in car exhaust produced by combustion of petrol in car engine using basic solid (c)Feasibility of using a prototype of CO2 scrubber in exhaust pipe of car (d)Feasibility of fixing carbon by turning CO2 into dry ice and stored in deep water (e)Feasibility of growing plant in used basic solution Results: 1.The CO2 scrubber prototype had an average CO2 removal ability over 50%, which was considered to be efficient. The concentration of CO2 (561ppm) was even lower than that in the ambient air (CO2 612ppm). During the experiment, the prototype was closely attached to the exhaust pipe and did not fall down. Thus, a CO2 scrubber was feasible to be used in the vehicles. Besides, our prototype was more energy efficient than LM2500 PE simple cycle gas turbine (consumed 21MW electricity) though our prototype had a lower CO2 removal efficiency. The cost of our prototype would be much lower than membrane technology as the production cost of the membrane was high. 2.Unlike existing CO2 scrubber prototype installed in open area (with electric fan installed), our CO2 scrubbers installed in the chimneys of power stations and exhaust pipes of cars are carbon neutral as exhaust gas has high kinetic energy and would pass into the scrubber. 3.dry ice would not evolve carbon dioxide gas at high water pressure such as at the bottom of the ocean. 4.Plants grew well in alkaline environment, it was feasible to grow plants in basic solution. Conclusion: CO2 scrubber is a suitable choice in combating the climate change through absorbing the excess carbon dioxide, with the utilization of the carbonates produced in the reaction, it is hoped that the climate change can be relieved using an environmentally-friendly device.

我們從化學課本及參考資料了解到製備乙烯的方法，再從已知的方法中設計並改良出較佳收集乙烯的方式。製出的乙烯先用點火燃燒證明氣體的可燃性，再用溴水褪色證明的確是乙烯。最後利用強氧化劑(過氧化氫，過錳酸鉀)，與乙烯做非勻相反應，可以觀察到高濃度的乙烯和強氧化劑間的反應有明顯的變化，利用此變化的觀察及數據的收集，作為此次研究的指標，來印證乙烯和水果熟成的相關性，進而希望藉此指標(簡單又方便的檢驗方式)作為水果保存的依據，並希望日後能找出簡單又有效的方式提高水果的保存期限。我們選用常見又易於觀察的水果－香蕉，並將上述的兩種強氧化劑(過氧化氫、過錳酸鉀)，分別放在密閉容器中，在室溫下，希望氧化劑能反應掉香蕉所釋放的乙烯氧體，或降低乙烯濃度，以期達到減緩香蕉外表熟成(香蕉外表變黑)的目的；沒想到過氧化氫超出我們意料(並沒有如預期減緩香蕉熟成)反而是整個外表熟成加速(香蕉外表變黑速度更快)，而兩組實驗組(香蕉釋放的乙烯分別在過氧化氫和過錳酸鉀的反應下)與對照組的外表熟成和香蕉內部甜度關係也有些連帶變化，雖超出我們預期，卻又有令人意想不到的結果，因為過錳酸鉀在開始實驗一天後香蕉內部甜度就有明顯增加，而後甜度增加率卻逐日下降！我們再將相同環境下，皆放入氧化劑(分成有香蕉及無香蕉兩組)經香蕉外表熟成後，再分別對剩下的氧化劑做滴定，先排除氧化劑在空氣中自然反應的變因後，發現有香蕉的實驗組與沒有香蕉的對照組的確有些差距，也間接證明了氧化劑的確是有與水果所釋放的乙烯反應。

一、介紹一個簡單好玩的小遊戲。二、小遊戲進行時，有人先下；有人後下，但先後兩方對下的勝算卻不同！三、研究分析小遊戲先後兩方對下的勝算為何不同？四、根據研究分析小遊戲先後勝算所得的 4 個發現來推算先後兩方對下真正(實際)的勝算！

The main reason for the creation of the project was looking for the uncondutuinal support for the entire handicap people that reside in the whole world. \r In all the communities there are barriers that oppse the total development of these people, and what currently exists can not help achieve a full lige for example: it's hard to have a basic education, a productive employment, or in their case to have a simple normal life.\r at the present time there is a serious problem of inequality, this is presented beacuse there has not been a mechanism that has been albe to please 100% of its real demand. That's way what we seek with this prototype, to be able to help them to have and live a better quality of life, it has the function of warning them when an object is near or before them emitting a brief sound that dose not cease until the way is completely free of obstacles, it is also sought to prevent accidents lkie falls, trips, among other, and also to help create more accsess possibilities to help any people that suffer any kind of handicap.\r This is a prototype that is able to help blind people, by heping them become able to move from one place to an other more faster and more securely, these is trying to make them more sure and reliable on them self, also the project is very economical and it was created due to the high quantity of blind men and women that exist in the whole world

The purpose of this project is to control the Aphis craccivora Koch. on the cow pea Vigna unguiculata (L.) by using two predators, the earwigs (black) beetle, Proeus simulans Stallan and the ladybird beetle, Micraspis discolor (F.). The experiments were carried out in the closed system in the laboratory and in the opened field with various ages of Proeus simulans Stallan and Micraspis discolor (F.) from the 1st - 4th stage of embryo to the adult form. Prior to the study in the field, the capability of the predators, Proeus simulans Stallan and Micraspis discolor (F.), that can eat the Aphis craccivora Koch. within a period of time was set up in the laboratory. The result showed that the 1st-4th stage of embryo of Micraspis discolor (F.) can eat 8.46+1.25 – 12.50+0.60, at 95% confidence, Aphis craccivora Koch. per day, while its adult can eat at the average number of 43.66 + 0.78, at 95% confidence, per day. The 1st–3rd stage of Proeus simulans Stallan embryo and the adult form can eat Aphis craccivora Koch. at the average number of 2.37+0.33 – 3.74+0.29 and 9.84+0.36, at 95% confidence, per day, respectively. This data showed that Micraspis discolor (F.) was more efficiency as predator than Proeus simulans Stallan. The insecticide activity of these two predators in the closed field (8 m x 9 m) was then determined. The number of Aphis craccivora Koch. on the plant was randomly counted everyweek for 10 weeks. It was found that the number of Aphis on the experimented and control groups were 16.20+4.30 and 2,582.00+102.40, at 95% confidence, per plant, respectively. The result support the efficiency of the two predators in controlling the pest. When the experiment was set up at the two opened field (6 m x 30 m, each field), 27.51+2.74 and 52.11+5.21, at 95% confidence, of Aphis craccivora Koch. were found on the plant of experimented and control groups, respectively, at the 10th week. The lower number of Aphis on the control plant might possilbly due to the interference from natural predators. From this study, the biological control of Aphis craccivora Koch. on the cow pea Vigna unguiculata (L.) could be achieved by using Proeus simulans Stallan and Micraspis discolor (F.). To avoid the use of chemical insecticides, biological control should be trained to farmers to help reduce the environmental problem.

每天上厠所的時候，最怕的是衛生紙常常被擦破，我的手就弄髒了。是我使用的衛生紙太少張呢？或是衛生紙的質料太差呢？還是使用衛生紙的方法不對呢？.......我也問了同學，他們也有同樣的困擾。衛生紙用太多張，操作不方便；太少張萬一拉肚子或大便太稀的話，衛生紙又會破掉，把手弄髒了。我建議媽媽買好一點、貴一點的衛生紙，一可是也有同樣的煩惱。到底怎麼辦呢？我在這次的科學研習活動中提出來，老師就請我們每一位同學，買不同牌子的衛生紙來試驗看看，找出衛生紙破掉的原因？同時，也可以知道那一種衛生紙比較耐用 · · · · ，下面是我們對衛生紙的研究。

以發光二極體(LED)設計組裝作為植物生長箱的人工光源，利用其低耗能特性，達節省能源之目的。金線蓮及嘉德利亞蘭組培過程，以不同光波長，搭配不同照度，與一般燈源作比對，就環境因子：溫度、波長、照度，對生長情形的影響。金線蓮用頂芽微扦插、嘉德利亞蘭以小芽分割直接育苗，以一般燈源為標準，比對LED組之白、紅、藍、綠及紅藍混光組?本進行實驗。試驗量測各光源之溫度及照度，觀察葉、莖、根生長之顏色與形態且量測重量作為指標。實驗結果，所有光源皆能促進生長，以LED白光處理之組培苗的質與量最佳，且最低耗能下有最高照度值，以LED白光2.9klux取代傳統光源，每一植物生長箱，每年至少省721度電，達到節省能源且可得到健壯組織培養苗之目的。

從自然與生活科技課本的第四冊第三單元「空氣的秘密」中，我瞭解到空氣是聞不到、看不到、摸不到的氣體。它的組成份以氮氣(78.08%)和氧氣(20.95%)為主，另外還有二氧化碳(0.03%)、少量的惰性氣體(氫氣、氦氣等)，以及水蒸汽和懸浮微塵等混合組成。因此我們針對混合在空氣中令人看不見的水蒸氣進行研究。但該如何製作攝取空氣中水蒸氣的實驗裝置呢？在老師的指導下，我們設計由抽氣機、U型管、漏斗和橡皮管連接起來攝取空氣中的水蒸氣。經過冷凝後，U型管內的水蒸氣會凝結成為水。如照片所示。實驗器具製作完成後，我們先在校內不斷嘗試，運用熟練後就到校外，如住宅區、公園、市場、十字路口等地區攝取水蒸氣液化水，並比較各地區的液化水量，同時利用化學試藥來檢測這些液化水中所含有的物質，及這些物質含量的多寡。由於液化水的檢驗，讓我們瞭解各地區的液化水中含有二氧化碳、硫化合物及有機物等，這些物質的含量如果過高，會造成空氣汙染，進而危害我們的身體健康，由此可知清淨環境中的空氣是非常重要的。