The difference of the 9th graders’ math problem solving ability in New Taipei city.

本研究在探討新北市九年級的學生在七、八年級的數學課程內容上，有哪些解題上的差異(參考本文第一章第三節名詞解釋)。依據民國97年教育部修訂之九年一貫課程綱要數學能力指標，設計15題計算題，並隨機抽樣新北市五所學校九年級學生進行施測，經統計答題結果並輸入統計軟體TESTER for Windows 2.0版與SPSS 15.0中文版，得出結論歸納如以下五點： 一、不同的性別，在解題能力上，男生的答題表現明顯優於女生的只有在以下三個部份：關於價格打折的折數比例概念、複雜的乘法公式計算，以及空間圖形概念，其餘的部分沒有顯著差異。整體而言，男生的解題能力只比女生略好一點點，但並未發現有顯著的差異。 二、看起來計算複雜的題目，若需要善用解題技巧(特別是乘法公式)才容易解的出來，學生的答題表現會相當的不好。 三、解方程式的題目，學生的答題表現較佳，特別是二元一次聯立方程式的題目，會比一元一次方程式和一元二次方程式來的更好。 四、在國中七、八年級的數學課程內容，學生的答題表現最差的在於以下兩點： (一)將等差數列、等差級數的公式活用，解決生活上相關的問題。 (二)利用特殊三角形的性質，找出三角形全等的條件，證明出題目所要求的邊或角。 五、同樣都是幾何的題目，學生們對勾股定理的答題表現，會比利用特殊三角形的性質求角度，以及利用三角形全等求邊或角這兩種題目，表現得更好。The purpose of this study is to discuss what different ways the 9th graders use on solving the seventh and eighth's math questions in New Taipei City. According to Competence Indicators or Benchmarks of math in "Grade 1-9 Curriculum", the researcher designed 15 questions and random sampled 9th graders from five schools in New Taipei City. By analyzing these data through statistic software, TESTER for Windows 2.0 and SPSS 15.0, the researcher drew conclusions from evidence as follows: 1. About the ability to solve problems, boys just did a little better than the girls but the statistic result didn’t achieve significant difference. However, the result showed that boys actually did better than girls on three parts of the math problems – discount ratio concept, complex multiplication formula, and spatial concept. 2. Students couldn’t do very well on those problems along with complicated calculation, especially when they need to use the multiplication formula. 3. Questions about equation, students could have better performance. Besides, they could do better on linear equation in two variables than first degree polynomial in one variables and quadratic equation. 4. In math curriculums of the 7th and 8th grade, students did the worst on the following two points: (1) Solve the associated problems in their life by making good use of the formula of arithmetic progression and arithmetic series. (2) Find out conditions of congruent triangles by using the character of special triangle and prove the triangle side or angle what the question asks for. 5. When it comes to geometric questions, compared with these two kinds of questions - getting the angle by using the character of special triangles and getting a triangle side or the angle by congruent triangles, students can do better on answering Pythagorean theorem