國小四年級學生對數學文字題的閱讀理解研究─以「整數加減法運算」為例

Abstract

數學閱讀指導是基於學科閱讀指導的必要性而產生，數學教科書是學生學習數學的重要資源和工具。國內的數學課本是以問題為核心概念，其編寫方式的基本假設是透過問題情境的鋪陳及解題策略的分析，來達成概念傳遞的目的，因此文字題是數學課本內概念的主軸。 可是學生在解數學文字題時，不僅要能熟悉計算的過程，同時也要能閱讀文字題的語意部分，理解問題的要求及其所提供的條件來解決問題，也因此造成數學文字題往往是大多數學生害怕的課題，其可能原因是解決一個文字題涉及「計算能力」與「語文理解和數學概念聯合運作的歷程」（秦麗花，1996）。因為從語文式的數學變成形式數學的過程中涉及許多的轉換，導致學生閱讀理解的困難。 本研究欲透過SFL的理論來分析數學文字題，檢視數學文字題中有哪些語言特徵？學生對不同題形的語言特徵的理解情形為何？ 所以首先以文獻中對數學文字題的分類標準進行題目的分類，以SFL的理論來分析數學文字題，再請學生閱讀不同類型的數學文字題後進行解題，將學生的分數分成高中低三組，從三組中各挑選兩位學生進行不同語言特徵的訪談。 研究中發現學生易受到題目中體現時態及情態的人際成分的影響，將其理解為「加」或「減」的意思，而忽略過程詞的意義。學生對於合併型題目的連接詞「和」之理解情形，大都表示是加起來的意思。然而學生在比較型題目的環境成份「比」的理解情形分成兩種類型。另外，學生透過算式表達對句子間的理解，大部分學生在改變型、合併型及等化型的題目都能寫出符合題目文字語意順序的算式。Mathematics reading instruction is a produce derived from the necessity of reading instruction. Mathematics textbooks are essential for students to study mathematics. The mathematics textbooks published by local publishers take the question-oriented approach, which is to help students construct concepts through laying out situations and problem- solving strategies. Therefore, the writing topics are like the main shaft in mathematics textbooks.

In order to solve a problem in their textbooks, students do not only have to be able to calculate but also be able to read the questions correctly, because the writings provide necessary clues to form equations. For this reason, a lot of students are frightened by mathematical word problems. A possible explanation is solving a writing topic involves “the computing power” and “the procedure to combine language understanding and mathematics concept”. The transformation from language coded mathematics to number coded mathematics causes difficulties in understanding mathematical word problems.

This research uses the SFL theory to analyze mathematical word problems, examining language characteristics in mathematical word problems, exploring student understanding to different forms of topics.

Therefore, the first part of the research consists a literature review which aims to classify mathematical word problems by the SFL theory. Then students are asked to solve different types of mathematical word problems. Students are then divided into three groups according to their scores, and two members of each group are selected for an interview to further analyze their understandings to the problems they have tried to solve previously.

The researcher found that students are easily influenced by the interpersonal components in the problems and misunderstand them as “to add” or “to subtract” instead of understanding them as a process phrase. For example, students misunderstand the conjunction word, and, as to add. Nevertheless, most students are able to transform word topics into mathematical expression in the changing, merging and molding topics.