ፄӝԄຑໆࢎᄬӧ४ݤᏢಞޑᔈҔ
ഋలৃ ഋలႍ
Ѡчᑜᝳࢪ୯λ
shu6926@yahoo.com.tw lct606@mail.lces.tpc.edu.tw
ᄔा
ၗ ૻ ࣽ מ ϐ ᆶ ද Ϸ ϯ Ǵ ٬ ள λ Ꮲ Ꮲ ู ૈ ӧ ؼ ӳ ޑ ၗ ૻ ᕉ ნ Ꮲ ಞ Ǵ ၗ ૻ ᑼ Ε ௲ Ꮲ ԋ ࣁ ᇶ շ λ Ꮲ ௲ Ꮲ ޑ ख़ ा Б ӛ Ƕ ҁ ࣴ ز ᔈ Ҕ ፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ ܭ λ Ꮲ ४ ݤ Ꮲ ಞ Ǵ ځ Ҟ ޑ ࣁ ٬ Ꮲ ู ኧ Ꮲ ४ ݤ ी ᆉ ወ ૈ к ϩ ว ච Ǵ ό Ӣ ࣁ ୯ ᇟ Ў ޑ ᎙ ᠐ ૈ Κ ၨ ১ Զ ቹ ៜ ᡄ ᒠ ၮ ࡘ ޑ ࡼ Ƕ ! ௲ ी ޑ Ь ा Б Ԅ ࣁ ่ ӝ ҅ ኧ ४ ݤ ཷ ۺ ी Ϫ ᚒ ཀ ޑ ฝ Ǵ җ ፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ ڋ Ꮲ ಞ ࢬ ำ Ǵ ᐟ ᓰ Ꮲ ғ ό ᘐ ࡘ Ե а ࡌ ᄬ ޕ Ǵ Զ ᇶ շ Ꮲ ғ ၲ ډ Ծ ך Ꮲ ಞ ԋ ߏ ޑ ਏ ݀ Ƕ ၸ ௲ ኳ ಔ ϯ ޑ ी Ǵ ࣬ ՟ ޑ ௲ ϣ ё а ז ೲ ޑ ౢ ғ Ǵ а ග ϲ ಄ ӝ ΐ ԃ ೣ ૈ Κ ࡰ ޑ ኧ Տ ௲ ౢ ໆ Ǵ ᡣ ׳ ӭ Ꮲ ู ڙ Ǵ ߦ ᆛ ၡ Ꮲ ಞ Ƕ ! ! ᜢᗖຒǺၗૻᑼΕǵϕӭ൞ᡏ၂ᚒǵፄӝԄຑໆǵ ኧՏϯ௲ǵᆛၡᏢಞǵ४ݤᏢಞ AbstractAccording to the rapid progress and popularity of information technologies, elementary schools can then have suitable environments for computer integrated instruction. In this paper, we applied the compound assessment structure for the material design and implementation of teaching multiplication on elementary school students. The Mathematical potentials of students can then be promoted. The impact due to the obstacles of language while reading the materials can also be eliminated.
The main idea of the material design is to present the concept of the multiplication by multimedia and take advantage of the compound assessment structure for flow controls of study. Students are encouraged to think repeatedly to construct the knowledge. The goal of self-learning by student is then accomplished. Moreover, the design and implementation of the material are structured for rapid productions for the nine year curriculum.
Keywords: computer integrated instruction, interactive multimedia items, compound assessment, digital teaching materials, internet learning, multiplication
1.
ق
ፐ ௲ Ꮲ ኳ Ԅ ࢂ ᅿ ന ޔ ௗ Ǵ Ψ ࢂ ന ද ၹ ޑ ሀ ޕ Б ݤ Ƕ ၗ ૻ מ ೌ ޑ ጲ ࠁ ว Ǵ ٬ ள ႝ တ ᆶ ᆛ ၡ ཇ ٰ ཇ ද Ϸ Ǵ ᔈ Ҕ ႝ တ ᆶ ᆛ ၡ ܌ ፍ ғ ޑ ኧ Տ Ꮲ ಞ ԋ ࣁ ঁ ߐ ޑ ᖿ ༈ Ƕ ! ൩ ኧ Տ Ꮲ ಞ Զ ق Ǵ ӵ Ֆ ஒ ၗ ૻ ࣽ מ ᑼ Ε Ꮲ ಞ ሦ ୱ Ǵ а ߦ Ꮲ ಞ ԋ ਏ Ǵ ࢂ ख़ ा ޑ ୢ ᚒ Ǵ ځ ύ Ѹ ࢰ ჸ ൞ ᡏ Յ Ǵ ӝ ௲ Ꮲ ፕ ᆶ ၗ ૻ ࣽ מ ٰ ൨ ँ ઇ ϐ ၰ \5^Ƕ! ค ፕ ࢂ ௲ Ꮲ ܈ ຑ ໆ ܌ ୃ ख़ ޑ ᔈ ࢂ ӧ Α ှ ک ቚ Ꮲ ғ ޑ Ꮲ ಞ Ǵ Զ ό ࢂ ຑ ۓ Ꮲ ғ ޑ ᓬ ӍǴፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ \6^่ ӝ ຑ ໆ ᆶ Ꮲ ಞ ޑ ᐕ ำ Ǵ ᐟ ᓰ Ꮲ ғ ό ᘐ ࡘ Ե а ࡌ ᄬ ޕ Ƕ Ӣ Ԝ а ၂ ᚒ Б Ԅ և Ꮲ ಞ Һ ୍ ᇶ а ฝ ᇥ ܴ ࢂ ᅿ ӳ ވ Զ Ξ ૈ ߦ Ꮲ ู Ꮲ ಞ ޑ ӭ ൞ ᡏ ௲ ी Ƕ ! ᙖ җ ႝ တ ᆶ ᆛ ၡ ᇶ շ Ꮲ ғ Ꮲ ಞ Ǵ а Ҟ ޑ ၗ ૻ מ ೌ Զ ق ς ࣬ ԋ ዕ Ƕ ᆛ ၡ Ꮲ ಞ ܌ ॐ Ϫ ሡ ޑ ࢂ ε ໆ ᓬ ፦ ޑ ኧ Տ Ꮲ ಞ ϣ Ƕ к ჴ ᆛ ၡ Ꮲ ಞ ϣ Ǵ ࢂ ኧ Տ Ꮲ ಞ ख़ ा ޑ π բ Ƕ ! ҁ Ў ග р ঁ ᔈ Ҕ ፄ ӝ Ԅ ຑ ໆ բ ࣁ Ꮲ ಞ ࢬ ำ ڋ ޑ ௲ ी Б ݤ Ǵ ၸ ϕ ӭ ൞ ᡏ ၂ ᚒ Ǵ ڈ ᐟ Ꮲ ู ࡘ Ե Ǵ ᙖ җ ฝ ӆ ᄽ ᛢ ᚒ ཀ Ǵ ᔅ շ Ꮲ ғ ᕇ ள ԋ ф ޑ ᡍ Ƕ ך ॺ а λ Ꮲ ४ ݤ ௲ Ꮲ ࣁ ٯ Ǵ ᇥ ܴ ௲ ी ޑ ࢎ ᄬ ᆶ ࢬ ำ Ƕ ! !2.
ၗૻᑼΕ
൩ ᆛ ၡ ኧ Տ Ꮲ ಞ Զ ق Ǵ ၗ ૻ ࣽ מ ᑼ Ε ௲ Ꮲ ܌ Ї ว ޑ ࢂ ௲ Ꮲ ܈ Ꮲ ಞ ࠠ ᄊ ޑ ᙯ ᡂ \5^ǶԶ ࣁ Α ߆ ௗ ཥ ਔ ж ޑ ࡷ ᏯǴஒȨ ၗ ૻࣽ מ ᑼ Ε ௲ Ꮲ ȩ Ψ ԋ ࣁ ж ௲ ػ ܌ ᜢ ݙ ޑ ፐ ᚒ \3^Ƕӕ ਔ ၗ ૻ ᑼ Ε Ψ ࢂ ཥ Ш ж ௲ ৣ ೢ ค ࡙ ޑ Һ ୍ \7^Ƕၗ ૻ ޗ f Ш ж ޑ Ꮲ ғ Ψ ය ఈ ள ډ Ȩ و ޑ ୷ ҁ ૈ Κ ȩ \2^Ƕ ! ҁ ࣴ ز ܌ ໒ ว ޑ ϕ ӭ ൞ ᡏ ၂ ᚒ ࢂ Ҕ ٰ բ ࣁ ᆛ ၡ ኧ Տ Ꮲ ಞ ޑ Ꮲ ಞ ϣ Ǵ ځ Ў ӷ ᚒ Ҟ ࢂ ௦ Ҕ ς բ ၸ ၂ ᚒ ϩ ޑ ᚒ ҁ ࣁ ᙔ კ Ǵ ᙖ җ Γ ޑ ࣴ ز ϩ ่ ݀ ஒ ၂ ᚒ ႝ η ϯ ࣁ ᒧ ࠠ ᄊ ϕ ӭ ൞ ᡏ ၂ ᚒ ᆶ ᓉ ᄊ კ Ў ၂ ᚒ Ƕ ! Զ ໒ ว ኧ Տ Ꮲ ಞ ϣ ځ ၸ ำ Ь ा ϩ ࣁ Ѥ ໘ ࢤ Ǵ २ Ӄ ࢂ ၂ ᚒ ϣ ϩ ᜪ ǵ ځ ԛ ࢂ ࡰ ۓ ӝ ޑ ΐ ԃ ೣ ૈ Κ ࡰ ǵ ௗ ࢂ ी ၂ ᚒ Ӆ Ҕ ኳ ಔ ǵ ന ࡕ ࢂ ໒ ว ᄽ ᛢ ၂ ᚒ ޑ ฝ ϣ Ǵ ӵ კ ܌ Ң Ƕ ! ! კ ໒วኧՏᏢಞϣϐࢬำ
3.
४ݤཷۺ
ӧ Ꮲ ಞ ኧ Ꮲ ၸ ำ ύ Ǵ ी ᆉ ૈ Κ த ࢂ Γ ܌ ᜢ ݙ ޑ ข ᗺ ϐ Ƕ Ѥ ߾ ၮ ᆉ ύ Ǵ у ݤ ǵ ෧ ݤ ឦ ܭ ୷ ҁ ޑ ी ᆉ ૈ Κ Ǵ ४ ݤ ǵ ନ ݤ ߾ ॶ ୷ ܭ ॊ ୷ ҁ ૈ Κ Ƕ ඤ ѡ ၉ ᇥ Ǵ у ݤ ǵ ෧ ݤ ࢂ ४ ݤ ǵ ନ ݤ ޑ ୷ ᘵ Ƕ ! ܌ ᒏ Ȩ ४ ݤ ȩ ࢂ у ݤ ϐ ݤ Ǵ ࣁ Ȩ ४ ኧ ȩ ᆶ Ȩ ४ ኧ ȩ ϐ Ȩ ᑈ ȩ ޑ ၮ ᆉ ၸ ำ Ǵ ځ ύ Ǵ ܭ ४ ဦ Ѱ ᜐ ϐ ኧ ࣁ ४ ϐ ኧ ᆀ ࣁ Ȩ ४ ኧ ȩǴ ܭ ४ ဦ ѓ ᜐ ϐ ኧ ࣁ ܌ ४ ϐ ໆ ᆀ ࣁ Ȩ ४ ኧ ȩǴ Զ ၮ ᆉ ܌ ள ϐ ่ ݀ ᆀ ࣁ Ȩ ᑈ ȩǶ ! Ꮲ ู வ Β ԃ ભ Π Ꮲ ය ໒ ۈ ௗ ४ ݤ ཷ ۺ Ǵ Ԝ ਔ д ॺ খ ڀ Ԗ у ෧ ݤ ޑ ཷ ۺ ୷ ᘵ Ǵ ჹ ܭ ४ ݤ ޔ Ԗ ኳ ጋ ޑ ཷ ۺ Ǵ ௲ Ꮲ ޣ ᆶ Ꮲ ಞ ޣ ค ݤ ਔ ଛ ӝ Ǵ ࢂ Ҟ ४ ݤ ௲ Ꮲ ঁ ख़ ा ޑ ୢ ᚒ \4^Ƕ ! Ҟ λ Ꮲ ኧ Ꮲ ሦ ୱ ჹ ߃ Ꮲ ४ ݤ ޑ Ꮲ ู Ԗ Ο ঁ ໘ ࢤ ޑ ा Ǵ а Π а ঁ ٯ η ᇥ ܴ ϐ Ƕ ! ٯ ӵ Ǻ ! ! 2 ଫ ټ η Ԗ 5 Ѝ ဌ Ǵ 7 ଫ ټ η Ԗ ൳ ଫ ဌ ǻ ! ! ಃ ໘ ࢤ ࢂ ࢂ ൂ Տ ໆ ޑ ᙯ ඤ Ƕ Ꮲ ғ ѝ ा ૈ ஒ เ ਢ ᇥ р ٰ ջ ё Ƕ Ӣ Ԝ Ꮲ ғ ѝ ा ૈ ӣ เ р Ǻ ! ! 7 ଫ ټ η Ԗ 35 ଫ ဌ ! ! ջ ё Ƕ ! ! ಃ Β ໘ ࢤ ࢂ ૈ इ ᒵ ှ ᚒ ၸ ำ Ƕ Ԝ ໘ ࢤ Ꮲ ғ Ѹ Ҕ ฝ კ ܈ у ݤ Б Ԅ ஒ ၮ ᆉ ၸ ำ ቪ р ٰ Ƕ ! ಃ Ο ໘ ࢤ ࢂ ٬ Ҕ ४ ဦ ᆉ Ԅ ඔ ॊ ှ ᚒ ၸ ำ Ƕ Ԝ ਔ Ꮲ ғ Ѹ ૈ ௗ ڙ ४ ݤ ಄ ဦ Ǵ ٠ Ъ ૈ ٬ Ҕ ४ ဦ ᆉ Ԅ ඔ ॊ ୢ ᚒ ٠ ள เ ਢ Ƕ Ӣ Ԝ Ꮲ ғ Ѹ ૈ ቪ р Ǻ ! ! 5!Y!7!>!35! ! ω ᆉ เ ჹ Ԝ ᚒ Ƕ ! ! Ꮲ ู ૈ ԋ ф ޑ а ४ ݤ ၮ ᆉ ൂ Տ ໆ ᙯ ඤ ޑ ୢ ᚒ ࡕ Ǵ Π ঁ Ꮲ ಞ Ҟ ߡ ࢂ ७ ኧ ୢ ᚒ Ƕ ! ਥ Ᏽ \8^ ճ Ҕ ୢ ᚒ ޑ ნ ஒ ҅ ኧ ४ ݤ ୢ ᚒ у а ϩ ᜪ ࣁ Ǻ ಔ ࠠ ǵ ޔ ᑈ ࠠ ᆶ К ၨ ࠠ Ο ᜪ ޑ ४ ݤ ୢ ᚒǶԶ ӧ \9^ޑ ࣴ ز ύ Ψ ஒ ४ ݤ ୢ ᚒ ϩ ࣁ Ο ε ᜪ Ǵ ϩ ձ ࢂ ໆ ኧ ӕ ᄬ ǵ ໆ ኧ ४ ᑈ Ϸ ӭ ख़ К ٯ Ƕ ೭ ٤ ϩ ᜪ ൩ ᇟ ཀ Զ ق Ԗ ౦ Ԕ ӕ π ϐ ֮ Ǵ а Π Ҕ Ο ঁ ٯ η ϩ ձ ᇥ ܴ ϐ Ǻ ! ! Ȩ 2 ଫ ټ η Ԗ 5 ଫ ဌǴ7 ଫ ټ η Ԗ ൳ ଫ ဌ ǻ ȩ ࢂ ឦ ܭ ໆ ኧ ӕ ᄬ ܈ ಔ ࠠ ޑ ४ ݤ ୢ ᚒ Ƕ ! ! Ȩ ۊ ۊ Ԗ 5 ҹ Պ Ǵ 7 చ ဵ η Ǵ གྷ གྷ ࣮ Ԗ ൳ ᅿ ಔ ӝ Б Ԅ ǻ ȩ ೭ ᜪ ޑ ᚒ Ҟ ࢂ ឦ ܭ ໆ ኧ ४ ᑈ ܈ ޔ ᑈ ࠠ ޑ ४ ݤ ୢ ᚒ Ƕ ! ! Ȩ ঢ ঢ Ԗ 35 ᗭ ቸ ੧ Ǵ Ԗ 7 ᗭ ቸ ੧ Ǵ ፎ ୢ ঢ ঢ ޑ ቸ ੧ ࢂ ޑ ൳ ७ ǻ ȩ ೭ ᜪ ޑ ᚒ Ҟ ࢂ ឦ ܭ ӭ ख़ К ٯ ܈ К ၨ ࠠ ޑ ४ ݤ ୢ ᚒ Ƕ ! ϩᜪᏢಞન ीӅҔኳಔ ۓ ΐ ԃ ೣૈΚࡰ ໒วฝϣ4.
Ꮲಞࢬำڋ
ፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ ࢂ ࣁ Α ှ Ꮲ ғ ཷ ۺ ϩ ݔ ᗺ Զ ी ޑ ෳ ᡍ ࢎ ᄬ \6^Ƕҁ ࣴ ز ஒ Ԝ ࢎ ᄬ ᔈ Ҕ ܭ ४ ݤ ཷ ۺ ޑ ᆛ ၡ ௲ Ꮲ ύ Ǵ Ҕ а ڋ Ꮲ ಞ ࢬ ำ Ƕ ࢎ ᄬ ύ Ь ा х ֖ ϕ ӭ ൞ ᡏ ᒧ ࠠ ᄊ ၂ ᚒ ᆶ ᓉ ᄊ კ Ў ᒧ ࠠ ᄊ ၂ ᚒ \6^Ǵ ϩ ձ ᇥ ܴ ӵ Π Ǻ ! ϕӭ൞ᡏ၂ᚒ ϕ ӭ ൞ ᡏ ၂ ᚒ Ǵ ӧ Ў ӷ թ ᚒ և ࡕ ኧ ࣾ Ǵ ջ а ฝ ޑ Б Ԅ ᄽ ᛢ ᚒ Ҟ ޑ ֖ ཀ Ǵ ٠ ी ࡪ ່ ๏ ڙ ၂ ޣ Ծ җ ᗺ ᒧ ᕇ ڗ ၂ ᚒ ׳ ޑ ૻ ৲ ܈ ख़ ࣮ ᄽ ᛢ ᚒ Ҟ ֖ ཀ ޑ ฝ Ƕ ! ᓉᄊკЎ၂ᚒ ࣬ ჹ ܭ ϕ ӭ ൞ ᡏ ၂ ᚒ Զ ق Ƕ Ў ӷ ᆶ კ Т ܭ թ ᚒ ਔ ӕ ਔ և Ǵ ค ฝ ޑ Б Ԅ ᄽ ᛢ ᚒ Ҟ ޑ ֖ ཀ Ǵ ҭ ค ी ࡪ ່ ๏ ڙ ၂ ޣ ᗺ ᒧ ᕇ ڗ ၂ ᚒ ׳ ޑ ૻ ৲ ܈ ှ ញ Ǵ ڙ ၂ ޣ ჹ ᚒ ཀ ޑ ှ ૈ ၸ ᎙ ᠐ Ў ӷ ܈ კ Т Ǵ ᆶ ર ෳ ᡍ ޑ ၂ ᚒ ᜪ ՟ Ƕ ! ፄӝԄຑໆࢎᄬ ਥ Ᏽ ࣬ ᜢ ࣴ ز ่ ݀ ፕ Ǵ Ꮲ ғ ё ૈ Ӣ ᇟ Ў ᎙ ᠐ ૈ Κ ၨ ৡ Ǵ ค ݤ Α ှ ᚒ ཀ Զ ค ݤ р ҅ ዴ ϸ ᔈ Ƕ ႝ တ ӭ ൞ ᡏ ෳ ᡍ ߾ ૈ ග ٮ ၨ ӭ ޑ ૻ ৲ Ǵ Ꮲ ғ ׳ ૈ మ ཱ ᕕ ှ ᚒ ཀ Զ ૈ к ҽ բ เ \6^Ƕፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ ၮ Ҕ ᓉ ᄊ კ Ў ᒧ ࠠ ᄊ ၂ ᚒ Ե ᡍ Ꮲ ғ ૈ Κ Ǵ ঃ ऩ Ꮲ ғ ค ݤ ҅ ዴ ϸ ᔈ Ǵ ӆ а ϕ ӭ ൞ ᡏ ᒧ ࠠ ᄊ ၂ ᚒ ϸ ᙟ ግ ಞ Ǵ ӵ კ Β Ƕ ! კ Β ! ፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ \6^! !5.
ኧՏᏢಞ௲ޑ໒ว
௲ Ꮲ ύ Ǵ ค ፕ ࢂ ௲ ਢ ी ܈ ၂ ᚒ ी Ԗ ᝄ ᙣ ޑ ໒ ว ၸ ำ Ǵ ӭ ൞ ᡏ ᆛ ၡ Ꮲ ಞ ௲ Ψ ό ૈ ٯ Ѧ Ƕ ҁ ࣴ ز а ᗦ ֖ ᒧ ۓ )Jefoujgz* ၂ ᚒ ޑ Ь ᚒ ܈ Ҟ ǵ ी )Eftjho*၂ ᚒ ǵ ຑ )Fwbmvbujpo*၂ ᚒ ǵ ᆶ ϩ )Bobmztjt*၂ ᚒ ޑ JEFB ኳ ࠠ \6^բ ࣁ ໒ ว ኧ Տ Ꮲ ಞ ϣ ޑ ࡰ Ꮴ Б ଞ Ƕ ! 5.1 IDEAኳࠠ JEFB ኳ ࠠ ࣁ ၂ ᚒ ी ޑ ࢬ ำǴЬ ा җ Ѥ ঁ ᡯ ܌ ᄬ ԋ Ǵ ٩ ׇ ࣁ Ǻ ᒧ ۓ ၂ ᚒ ޑ Ь ᚒ ܈ Ҟ Ǵ ी ၂ ᚒ ǵ ຑ ၂ ᚒ ǵ ᆶ ϩ ၂ ᚒ \6^Ƕ၂ ᚒ ी २ Ӄ ᔈ ዴ ۓ ၂ ᚒ ޑ ຑ ໆ Ҟ Ǵ ዴ ҥ ၂ ᚒ ܌ ట ຑ ໆ ޑ ૈ Κ ቫ ԛ ᆶ Ꮲ ಞ ϣ Ƕௗ Ǵ ी ኧ ᅿ ߄ ၲ ၂ ᚒ ޑ Б ԄǴ ҁ ࣴ ز ϩ ձ ी Α ϕ ӭ ൞ ᡏ ၂ ᚒ ᆶ ᓉ ᄊ კ Ў ၂ ᚒ ٿ ᅿ և Б Ԅ ᄒ ฅ ό ӕ ޑ ၂ ᚒ Ƕ ฅ ࡕ ᔈ ຑ অ ҅ ၂ ᚒ Ǵ ന ࡕ ϩ ၂ ᚒ ᜤ ࡋ ǵ ᠘ ձ ࡋ ǵ ෳ ࡋ ឦ ܄ Ǵ Ԝ ำ ׇ ӵ კ Ο ܌ Ң Ƕ ! ! კΟ IDEA ኳࠠ[5] 5.2 ४ݤኧՏᏢಞϣ ҁ ࣴ ز ज़ ܭ Γ Κ ނ Κ ޑ Ե ໆ Ǵ Ӣ Ԝ ᒧ Ҕ ಄ ӝ JEFB ኳ ࠠ ܌ ी р ٰ ޑ ၂ ᚒ ϣ բ ࣁ ໒ ว ኧ Տ Ꮲ ಞ ௲ ޑ ᙔ კ Ǵ а Ԝ ᓉᄊ၂ᚒ ࢂߚᚒ ࢂߚᚒ Πঁ ᓉᄊ၂ᚒ ӭ൞ᡏ၂ᚒ เᒱ ߄ Ң Ꮲ ғ ჹ Ԝ ཷ ۺ ό Α ှ Ǵ ᔈ ่ ״ ෳ ᡍ ံ ௱ ௲ Ꮲ ܈ Չ Π ঁ ཷ ۺ Ե ᡍ เᒱ เჹ เჹ เჹ เჹ เᒱ เᒱ ϩ၂ᚒ ຑᆶঅ҅ ჴሞࡼෳ ी ᓉ ᄊ კ Ў ၂ ᚒ ी ϕ ӭ ൞ ᡏ ၂ ᚒ ी ۯ ՜ ၂ ᚒD
ी ۯ ՜ ၂ ᚒ ᒧۓ၂ᚒʳ ຑໆҞI
E
A
୷ ᘵ Չ ࡕ ុ ޑ ฝ ी ǵ ᇙ բ Ƕ ܌ ᒧ Ҕ ޑ ᚒ ҁ ࢂ ၸ Ⴃ ၂ অ ҅ ၸ ޑ ҅ Ԅ ᚒ ҁ Ǵ ٠ ς ϩ ၸ ၂ ᚒ ᜤ ܰ ࡋ Ϸ ᠘ ձ ࡋ \4^Ƕ ! ҁ ࣴ ز ၮ Ҕ Gmbti ೬ ᡏ ໒ ว р ϕ ӭ ൞ ᡏ ᒧ ࠠ ᄊ ၂ ᚒ ᆶ ᓉ ᄊ კ Ў ᒧ ࠠ ᄊ ၂ ᚒ Ƕ ځ ኧ Տ Ꮲ ಞ ϣ а ಄ ӝ Ꮲ ู ޑ ४ ݤ ཷ ۺ Ꮲ ಞ ࣁ Б ଞǶᒥ ൻ \8^ޑ ϩ ᜪ ݤ ߾ ϩ ࣁ Ο ε ᜪ Ǻ ಔ ࠠ ǵ ޔ ᑈ ࠠ ᆶ К ၨ ࠠ Ο ᜪ ޑ ४ ݤ ୢ ᚒ Ƕ ᜢ ܭ Ԝ Ο ᜪ ޑ ᚒ Ҟ ၁ ಒ ᖐ ٯ ӵ Π Ǻ ! ಔࠠ ೭ ᜪ ୢ ᚒ ֖ Ԗ ԋ К ٯ ޑ ٿ ᅿ ໆ ኧ Ǵ ٯ ӵ Ǻ ! Ȩ 2 ݄ 6 ϡ Ǵ ວ 4 ݄ ा б ӭ Ͽ ϡ ǻ ȩǶ ! Ȩ 2 ಔ Ԗ 6 Γ Ǵ Ѡ ً ё ֤ 4 ಔ Ǵ ፎ ୢ Ѡ ً ё ֤ ൳ Γ ǻ ȩǶ ! Ȩ ྭ ྭ و 2 Ϧ ٚ 6 ϩ ដ Ǵ و 4 Ϧ ٚ ा ൳ ϩ ដ ǻ ȩǶ ! Ȩ 2 చ 6 Ϧ ϩ Ǵ ! 4 చ ௗ ଆ ٰ Ӆ ൳ Ϧ ϩ ǻ ȩǶ ! ޔᑈࠠ Ԝ ᜪ ᚒ Ҟ ӧ В த ғ ࢲ ύ த ـ ޑ ٯ η ࣁ ी ᆉ य़ ᑈ ܈ ᡏ ᑈ ޑ ୢ ᚒ Ǵ Ԝ Ѧ ᗋ Ԗ ಔ ӝ ޑ ୢ ᚒ Ǵ ᖐ ٯ ӵ Π Ǻ ! Ȩ ݿ ݿ Ԗ 6 ҹ ऽ Ǵ 4 చ ᑿ η Ǵ གྷ གྷ ࣮ Ԗ ൳ ᅿ ऀ ݤ ǻ ȩǶ ! Кၨࠠ Ԝ ᅿ ᚒ Ҟ ֖ Ԗ ٿ ᅿ ໆ ኧ ᆶ ಃ Ο ᅿ ໆ ኧ ԋ К ٯ Ǵ ೭ ᜪ ޑ ٯ η ೯ த ௶ ॊ ၨ ߏ Ǵ Ꮲ ғ Ψ ၨ ל ܔ ೭ ᜪ ޑ ୢ ᚒ Ǵ ᖐ ٯ ӵ Π Ǻ ! Ȩ 2 ᓐ Ф Ϻ ё ᔒ р 31 Ϧ ϲ ޑ ᗲ Ѫ Ǵ ߓ ᔅ դ դ ޑ ၭ Ԗ 6 ᓐ Ф Ǵ 4 Ϻ Ӆ ё а ள ډ ൳ Ϧ ϲ ޑ ᗲ Ѫ ǻ ȩǶ !
6.
໒วኧՏᏢಞኳಔ
ฝ ೬ ᡏ ޑ ጓ ᒠ ݤ ߾ ε ӭ ࡌ ٬ Ҕ ޣ ஒ ঁ ނ ҹ ᔈ ϩ ೀ ܭ ό ӕ ޑ კ ቫ Ǵ ӵ Ԝ ω ૈ ۓ ނ ҹ ޑ ౽ ܈ ᡂ Ǵ Զ Ъ ೭ ኬ ޑ Ӽ ௨ ૈ ٬ ஒ ٰ ၨ ܰ ᡂ ׳ ी ܈ ක Ε բ Ƕ ! ᗦ ֖ ௲ ػ ཀ က ޑ ฝ ᔈ җ 㦲 Զ ు Ǵ ൻ ׇ ᅌ ޑ Ї Ꮴ Ꮲ ู ޑ ࡘ ၡ Ǵ Զ Ъ ᄽ ᛢ ၸ ำ ೲ ࡋ ό ा ϼ ז Ƕ ฝ ύ ਔ р Ў ӷ қ Ψ ё ᔅ շ Ꮲ ู ݙ ཀ ډ ख़ ा ૻ ৲ Ǵ ڐ շ Ꮲ ู ϭ ୌ р ᜢ ᗖ ௶ ॊ Ƕ ന ࡕ ा ள ۓ ख़ ኞ ࡪ ່ Ǵ Б ߡ Ꮲ ғ ό ᘐ Ꮲ ಞ Ƕ ! ٩ ൻ ڰ ۓ ޑ ำ ׇ ૈ ٬ ٣ ᡂ ள ᙁ ൂ Ъ ૈ ז ೲ ֹ ԋ Ƕ а Π ஒ ၁ ಒ ᇥ ܴ ໒ ว ኧ Տ Ꮲ ಞ ϣ ޑ ࢬ ำ ᆶ ጓ ᇙ ᆛ ၡ ኧ Տ Ꮲ ಞ ન ޑ ၸ ำ Ƕ ! 6.1 ໒วኧՏᏢಞϣ၁ಒᡯ ໒วᒧϡҹ ঁ Ꮲ ಞ λ ൂ ϡ ٬ Ҕ ډ ޑ ϡ ҹ Ӄ ी ӳ ӵ კ Ѥ Ǵ а ࡕ ѝ ा Ҕ ඹ ඤ Ў ӷ ջ ё Ƕ ! კѤ ᒧӅҔኳಔ ीӅҔހय़ კ ϖ ޑ Ѱ ࢂ Ў ӷ թ ᚒ Ǵ ѓ ࢂ ҁ ᚒ ޑ ૈ Κ ࡰ Ǵ ѓ Π ܫ ᒧ ࡪ ່ Ǵ Ѱ Π ࢂ ฝ ᄽ ᛢ Ƕ ! კϖ ހय़ӅҔኳಔ A ᒡΕЎӷǵૈΚࡰϷᒧϡҹ ֹ ԋ კ Ѥ Ϸ კ ϖ ޑ ۓ ϐ ࡕ ջ ё ໒ ۈ ܫ ό ӕ ޑ Ꮲ ಞ ϣ Ǵ ӵ კ Ϥ ܌ Ң Ƕ ! კϤ ހय़ӅҔኳಔ B ीᄽᛢ၂ᚒޑฝϣ ໒ ۈ ۓ კ ቫ Ϸ ቹ ޑ ނ ҹ Ǵ ִ ๓ Ӽ ௨ Ӛ ঁ ف Յ ޑ р ׇ Ǵ ӵ Π კ ܌ Ң Ƕ ! კΎ ฝጓᒠၸำ൩ ௲ ໒ ว ޑ ೲ ࡋ Զ ق Ǵ ೯ த ӧ ೕ ጄ ཥ ᜪ ࠠ ޑ ᚒ Ҟ ਔ ၨ ӭ ޑ ਔ ໔ Ǵ ՠ ໒ ว ֹ ԋ Ǵ ᜪ ՟ ޑ ၂ ᚒ ѝ ा Ҕ ς ۓ ӳ ޑ ำ ׇ Ϸ ඤ Ў ӷ ܈ ނ ҹ ջ ё Ǵ ܌ ޑ ਔ ໔ ࣬ ჹ ෧ Ͽ ࡐ ӭ Ƕ ! 6.2 ಔᙃኧՏᏢಞϣ၁ಒᡯ ൩ ҁ ࣴ ز а ४ ݤ ௲ Ꮲ ࣁ ٯ Զ ق Ǻ ε ӭ ኧ ޑ Ꮲ ู ӧ ၮ ᆉ ҅ ኧ ४ ݤ ୢ ᚒ ਔ ܰ ኧ ӷ و Ǵ Զ ޔ ௗ Ҕ ന চ ۈ ޑ Б ݤ ஒ ܌ Ԗ ኧ ӷ у ଆ ٰǴֹ ӄ ؒ Ԗ ७ ኧ ཷ ۺ \4^Ƕਥ Ᏽ Ј Ꮲ ৎ ᆢ ݀ ථ ୷ )Wzhputlz*ޑ ޗ ว ᇡ ޕ ፕ ࣁ ୷ ᘵ Ǵ ࡰ р Ȩ Ꮲ ғ ᐱ ҥ ֹ ԋ ޑ բ ȩ ᆶ Ȩ Ꮲ ғ ӧ ԋ Γ ڐ շ ϐ Π ֹ ԋ ޑ բ ȩ ϐ ໔ ޑ ຯ ᚆ ࢂ Ꮲ ғ ޑ ё ૈ ว Ƕ ܌ а Ǵ Ꮲ ู ӧ ४ ݤ ၮ ࡘ ߄ ۘ ೀ ܭ ӝ ԋ ၮ ࡘ ය ਔ Ǵ ځ ჴ д ॺ ϝ ค ݤ ೀ ൂ Տ ໆ ޑ ᙯ ඤ ୢ ᚒ Ǵ Ԝ ਔ ӭ ൞ ᡏ ฝ ௲ ё ਔ ڗ ж ԋ Γ ᇶ Ꮴ ޑ ف Յ Ǵ ڐ շ Ꮲ ู լ ܺ ֚ ᜤ Ǵ ٬ ᆫ ൂ Տ ໔ ޑ ᜢ ߯ ࡌ ҥ ଆ ٰ Ǵ ճ ᙯ ᡂ ډ ಕ ܄ ӝ ԋ ၮ ࡘ ය Ƕ ! ᔈ Ҕ ፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ ಔ ᙃ ኧ Տ Ꮲ ಞ ޑ ၸ ำ ၁ ॊ ӵ Π Ǻ ! २ Ӄ р ޑ ࣁ ᓉ ᄊ ޑ ฝ य़ Ǵ ϣ ࣁ પ Ў ӷ թ ᚒ ᆶ ܴ Ꮲ ಞ ᔈ ၲ ډ ޑ ૈ Κ ࡰ Ǵ ӵ კ Ζ ܌ Ң Ƕ ! კΖ ᓉᄊკЎ၂ᚒ ځ ᆶ ર ෳ ᡍ ό ӕ ޑ Ӧ Б ࢂ ٬ Ҕ ႝ တ թ ᚒ Ǵ ᆶ ޑ ጕ ෳ ᡍ ό ӕ ޑ Ӧ Б ࢂ ߚ а ຑ ۓ ૈ Κ ࣁ Ҟ ޑ Ǵ ځ ࡪ ່ ύ ќ Ԗ Ҏ ᐒ Ǵ ӵ Π ܌ ॊ Ƕ ! ค ፕ ᓉ ᄊ კ Ў ၂ ᚒ ǵ ϕ ӭ ൞ ᡏ ၂ ᚒ ܈ ኧ Տ ௲ ϣ ࣣ ࣁ ൂ ᒧ ᚒ ޑ Ԅ և Ǵ เ ᚒ ޣ ऩ Ԗ ҅ ዴ ϸ ᔈ ਔ Ǵ Π ঁ Ꮲ ಞ Һ ୍ ߡ ׯ ᡂ Ƕ ! ჹ ܭ ҂ ૈ բ р ҅ ዴ ϸ ᔈ ਔ Ǵ ௲ Ծ ኘ ܫ ฝ а ᄽ ᛢ ᚒ ཀ Ǵ ӵ კ ΐ ǵ Μ ǵ Μ ǵ Μ Β ܌ Ң Ƕ ! კΐ ϕӭ൞ᡏ၂ᚒᄽᛢฝय़ 1 კΜ ϕӭ൞ᡏ၂ᚒᄽᛢฝय़ 2 კΜ ϕӭ൞ᡏ၂ᚒᄽᛢฝय़ 3 კΜΒ ϕӭ൞ᡏ၂ᚒᄽᛢฝय़ 4 เ ᚒ ޣ ӧ ϕ ӭ ൞ ᡏ ၂ ᚒ ฝ य़ ύ Ǵ ё ӧ డ ค ਔ ໔ ज़ ڋ ޑ ݩ Π Ǵ ᙖ җ ख़ ኞ ᗖ ό ᘐ ख़ ፄ ᢀ ࣮ ᄽ ᛢ ၂ ᚒ ϣ ޑ ฝ Ƕ ! Ԝ ਔ เ ᚒ ޣ ऩ Ԗ ҅ ዴ ϸ ᔈ ਔ Ǵ ߡ ၢ Կ Π ঁ Ꮲ ಞ Һ ୍ Ƕ ӵ ݀ เ ᚒ ޣ ؒ Ԗ р ҅ ዴ ϸ ᔈ Ǵ ߡ ೱ ่ ډ ڀ Ԗ ᆶ Ԝ ϕ ӭ ൞ ᡏ ၂ ᚒ ࣬ ӕ ૈ Κ ࡰ ޑ ϕ ӭ ൞ ᡏ ၂ ᚒ ϐ
ᜪ ՟ ᚒ Ƕ җ ܭ Ԗ ख़ ኞ ф ૈ Ǵ Ӣ Ԝ Ꮲ ู ӧ ၸ ӭ ԛ ޑ ڐ շ ϐ ࡕ ಖ ૈ ࡌ ᄬ р ޕ Ǵ ၲ ډ ᆒ ዕ Ꮲ ಞ ޑ Ҟ Ƕ ! ঁ Ꮲ ಞ ࢬ ำ ޑ ڋ ӵ კ Μ Ο ܌ Ң Ƕ ! ! კΜΟ Ꮲಞࢬำڋკ 7
.
่ፕ
ޑ ᇡ ޕ ڗ ӛ ፕ ӧ Չ ၗ ૻ ᑼ Ε ௲ Ꮲ ਔ Ǵ લ Ю ቸ ܄ Զ ค ݤ ᆶ ᆛ ၡ ᄊ Ꮲ ಞ ࣬ Ǵ ჹ ܭ ό ӕ ᆛ ၡ ௲ Ꮲ ी Ϸ ό ӕ ឦ ܄ ޑ ፐ ำ ࢂ ց ૈ ࣬ ܭ ӕ ѳ Ѡ ύ ϝ ฅ Ԗ ࡑ ࣴ ز Ƕ Ӣ Ԝ ᙖ җ ϩ ٦ ᆛ ၡ ௲ Ꮲ ी Ϸ ᆛ ၡ Ꮲ ಞ ᡍ ϐ ࣴ ز ൩ ᡉ ள ख़ ा Ƕ ! ҁ Ў ග р Α ঁ ᔈ Ҕ ፄ ӝ Ԅ ຑ ໆ ࢎ ᄬ ܭ λ Ꮲ ४ ݤ ኧ Տ ௲ ϐ ᇙ բ ޑ ཷ ۺ ᆶ ࢬ ำ Ǵ ځ Ҟ ޑ ࣁ ٬ Ꮲ ู ኧ Ꮲ ४ ݤ ी ᆉ ወ ૈ к ϩ ว ච Ǵ ό Ӣ ࣁ ୯ ᇟ Ў ޑ ᎙ ᠐ ૈ Κ ၨ ১ Զ ቹ ៜ ᡄ ᒠ ၮ ࡘ ޑ ࡼ ! ҁ Ў ൩ Ѥ ߾ ၮ ᆉ ύ ޑ ߃ ໘ ४ ݤ ጓ ᇙ ኧ Տ ௲ Ǵ ҂ ٰ ё ว ׳ ӭ ᜪ ՟ ௲ Ǵ ֹ և Ѥ ߾ ၮ ᆉ ܌ ᔈ ڀ ഢ ޑ Ӛ ૈ Κ Ǵ а к ჴ ᆛ ၡ ኧ Տ ϯ ޑ Ꮲ ಞ ϣ Ƕ Ԝ Ѧ Ǵ ம ፓ ӧ Ծ ך ԋ ߏ ᆶ Ь Ꮲ ಞ ё ٬ ᆛ ၡ Ꮲ ಞ ុ ό ᘐ Ƕ Ӣ Ԝ Ǵ ໒ ว ׳ ӭ ᓬ ፦ Ъ ಄ ӝ Ꮲ ғ ᑫ ፪ ޑ ኧ Տ ϯ ௲ ׳ ࢂ ୍ ϐ ࡚ Ƕ ! ҁ ࣴ ز ϐ ӭ ൞ ᡏ ฝ ௲ ޑ ܄ ڀ Ԗ ᄽ ᛢ ᚒ ཀ ޑ ф ૈ Ǵ ٠ ၲ ډ ϕ ǵ ᐟ ᓰ Ꮲ ಞ ޑ Ҟ ޑ Ƕ Ԝ Ѧ Ǵ ҁ Ў Ψ а Ӄ ϩ ᜪ ௲ ޑ ᚒ ࠠ Ǵ ӆ Ҕ ς ۓ ӳ ޑ ำ ׇ Ϸ ඤ Ў ӷ ک ނ ҹ Ǵ ၲ ډ ё ז ೲ ໒ ว س ӈ ޑ ᜪ ՟ ግ ಞ ᚒ ٮ Ꮲ ู ࡌ ᄬ ޕ ޑ Ҟ ޑ Ƕ ! ! ୖԵЎ [1]ՖᄪਦǵഋӵǴȨύλᏢၗૻ௲ػᕴᙔკޑϣ ఼ᆶᆒઓȩǴၗૻᆶ௲ػǴ22-28 ।Ǵ҇୯ 90 ԃǶ [2]ֆ҅ρǵֆذەǴၗૻᑼΕ௲ᏢჴٯϷ࣬ᜢୢ ᚒ—аޗࣽࣁٯǴ҇୯ 90 ԃǶፕЎว߄ ܭȨཥШइፐำ௲Ꮲ--ΐԃೣፐำᚒ௲ػࣴ ȩǴѠৣεǴѠчѱǴ҇୯ 90 ԃ 9 Д 21 ВǶ [3]݅ηѴǺȨ୯λΟԃભኧᏢࣽ҅ኧ४ݤཷۺȩ ϐز—а၂ᚒᒧቻԔጕࣁϩ୷ᘵǴ୯ ҥѠύৣጄᏢଣ௲ػෳᡍीࣴز܌ᅺγፕ ЎǴ҇୯ 91 ԃǶ [4]୯ৱǴவᏢಞࣽמว࣮ၗૻᑼΕ௲Ꮲޑϣ ఼Ǵ҇୯ 90 ԃǶፕЎว߄ܭȨཥШइፐำ௲Ꮲ --ΐԃೣፐำᚒ௲ػࣴȩǴѠৣεǴ ѠчѱǴ҇୯ 90 ԃ 9 Д 21 ВǶ [5]ഋలႍǺӭ൞ᡏ܄ෳᡍ—аኧᏢკᆶޜ໔ ЬᚒࣁٯϐࣴزǴ୯ҥҬ೯εᏢᏢଣᆛၡᏢ ಞᅺγӧᙍᅺγፕЎǴ҇୯ 93 ԃǶ [6]ᚑ҉ǵՖᄪਦǴၗૻࣽמᑼΕᏢಞሦୱी ߃Ǵ҇୯ 90 ԃǶፕЎว߄ܭȨཥШइፐำ௲ Ꮲ--ΐԃೣፐำᚒ௲ػࣴȩǴѠৣ εǴѠчѱǴ҇୯ 90 ԃ 9 Д 21 ВǶ[7]Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Eds.), Handbook of research on mathematics teaching learning (pp.276-295). Reston, VA : NCTM; NY | Macmillan Publishing Co.
[8]Vergnaud, G. (1983). Multiplicative structure. In R. Lesh & M.Landau (Eds.). Acquisition of mathemalics concepts and process (pp.127-174). New York Academic Press.
ᓉᄊ၂ᚒ Πঁ ᓉᄊ၂ᚒ ӭ൞ᡏ၂ᚒ เᒱ เჹ เჹ ӭ൞ᡏ၂ᚒ ᜪ՟ᚒ เᒱ เჹ