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國中教甄|數學數學109 年第 84 題單選題

The following is a statement of “algorithm for square-root multiplication" in a secondary school textbook, “The product of the positive square roots of two positive numbers is equal to the positive square root of the product of the two positive numbers." After teaching, Ms. Guo found that most students learned the expressional representation of this statement, but did not understand the above statement. Please choose the most effective teaching activity from the following to help students understand the statement.

AThoroughly re-teach the concept of the algorithm
BGive students corresponding numerical expressions of the statement, such as ${ \sqrt { 2 } } \times { \sqrt { 3 } } = { \sqrt { 6 } }$ , and ask students to describe it with words
CAsk students to start with a part of the statement and gradually expand it and then judge the relations among all mathematical objects in the statement正確答案
DAsk students to do more exercises pertinent to the algorithm
答案與詳解
C
正確答案
學生已具備符號表徵能力但缺乏文字敘述的理解,透過拆解長句並逐步建立數學物件關係的鷹架策略,最能有效提升數學閱讀理解。

逐選項解析

AThoroughly re-teach the concept of the algorithm✕ 錯誤
學生已經學會符號表徵,問題出在文字閱讀理解而非概念本身,單純重新講述概念無法解決長句理解的困難。
BGive students corresponding numerical expressions of the statement, such as ${ \sqrt { 2 } } \times { \sqrt { 3 } } = { \sqrt { 6 } }$ , and ask students to describe it with words✕ 易錯陷阱
學生已經對長句文字感到困惑,直接要求他們用文字描述數值式,難度過高且缺乏鷹架,容易產生挫折感。
CAsk students to start with a part of the statement and gradually expand it and then judge the relations among all mathematical objects in the statement✓ 正確
DAsk students to do more exercises pertinent to the algorithm✕ 錯誤

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