數學素養導向—應用真實評量於國小學生數感概念

The Orientation of Mathematics Literacy: Utilizing Authentic Assessment on the Concept of Number Sense for Elementary Students

服膺108課綱數學素養國家政策，本研究目的為依數學素養導向，即以真實評量探究國小學生在數感概念的表現。真實評量的優勢在於與生活結合的真實性。參與者為桃園縣某國小四至六年級學生，四年級有93位，五年級有95位，六年級有95位，共283位學生參與。統計方法採用獨立樣本t考驗與順序性邏輯迴歸進行分析；質化方法依評分標準的四等分制進行學生解題策略分析。依t考驗檢視四至六年級學生，三題的題目難度均有顯著差異。依順序性邏輯迴歸分析結果，四至六年級學生於題1並未出現差異，但於題2與題3，四至六年級學生則出現不同的答對機率，即學生的表現依年級愈高而有較好的表現。於質化分析結果，學生的解題策略於題3出現較大的變化，四至六年級學生均出現較多猜測性的解題策略，其原因可能為學生對於生活情境的概念不理解所致。本研究建議有三︰首先，教師應將真實的生活情境帶入數學課程，以落實數學素養的學習趨勢；其次，應考量資料特性採用適當的統計模式，如順序性邏輯迴歸分析，能推算出四至六年級學生於題目分數的比率；最後，從多重計分的標準可釐清學生的認知學習概念。

To meet the trend of 108 mathematics curriculum standards, the aim of the study is to fulfill the authentic assessment to explore primary students’ performance on the concept of number sense. The advantage of authentic assessment is to connect with life context beyond school. Total 283 participants were from 93 fourth graders, 95 fifth graders, and 95 sixth graders. Students were sampled from one elementary school in Taoyuan city. For the quantitative methodology, the t-test for independent sample methods was taken to explore whether students have different performances. Additionally, the ordinal logistic regression was applied to analyze the response rate among the three questions for different grade levels. The qualitative methodology was adopted to analyze solving strategies of students in different questions by the four levels of coding criteria. The results of the ordinal logistic regression reveal that fourth to sixth grade levels are indifferent in item 1, but response rates are diverse in item 2 and item 3. The results indicate that students’ performances are better while their grade levels are higher. In qualitative analysis, the results expose the variant guessing-problem solving strategies among different graders in item 3. The possible reason can be ascribed to their incomprehension. Three suggestions are recommended in education fields. Firstly, to meet the trend of mathematics literacy, primary teachers should design the real-life situation into mathematics lessons. As a second, based upon the nature of data, it is crucial to take advantage of the proper statistical model. Finally, the problem-solving strategies of students can be corresponded to their cognitive learning levels via the authentic assessment.