師資是教育品質的核心，師資素質的良窳攸關教育改革成敗的關鍵。本研究旨在（1）發展符應時代脈動暨衡酌國情之數學教學專業知能指標；（2）建置專業考核用的指標難易度；（3）探討緊扣教育現場需求的數學師資篩選模式；（4）提供師培單位及教育行政部門適切可行數學教學知能指標，以為職前、入職及在職數學師資把關之研參。研究方法包括：（1）文本分析_梳理數學教師專業表現內涵及專業知能要素；（2）焦點座談_描繪數學教學專業知能可能圖像及釐清教師甄選現況與困境；（3）網路問卷_形塑數學教學專業知能圖像及建置專業考核用指標難易度。本研究以自編之「數學教學專業知能指標建置與現況問卷」作為研究工具，並以全國國高中職小4,103所學校的數學教師為調查對象，共回收5,807份有效問卷，計1,689校填答，所得資料的解釋具99%的信心水準，抽樣誤差為正負2.41個百分點。回收的問卷以SPSS22.0套裝軟體並搭配AMOS22.0執行相關統計分析，以結構方程模式、卡方百分比同質性考驗、多變量變異數分析、單（雙）因數變異數分析及事後比較等統計方法處理。研究發現：（1）本數學教學專業知能指標具周延性及解釋力；（2）師資篩選模式得以緊扣教育現場需求；（3）植基達成度可反應指標難易度。

　　對教育政策之建議：（1）活絡教檢教甄制度與運作，確保入職師資：1. 以教育專業特質測驗為教育學程門檻並先教檢後實習。2.教師檢定及教師甄選考科範疇各職其司，「教檢筆試」宜以教育專業知能為主，國小階段再加考專業學科知能，以強化國小師資數學專業之不足，「教甄筆試」則以專業學科知能為主，「教甄試教」測試專業教學知能及專業實務知能，「教甄口試」測試專業責任特質及專業實務知能。3. 教甄筆試宜聯合辦理各自活用，教甄筆試國中小數學內容知識與教材教法各半，高中職「內容知識」六成。4. 訂試教口試評分項目與評分重點及其配分比重。5. 教甄試教宜抽題涵蓋所有數學單元及試教前後增簡案設計與提問。6. 教甄初試筆試成績佔三成以下或為複試門檻。7. 教甄複試的試教比重七成，口試三成。8. 明訂以指標達成度的多寡等決定教師甄選合格者能否進入職場關卡。（2）善用指標於職前培育、入職把關、在職精進：1. 本「數學教學專業知能指標」涵蓋4個向度11個構念72項指標，構念具有聚合效度，構念間具區別效度，指標解釋力達七成以上，不但具有周延性且具高解釋力，而且呼應新時代良師應具之「教育愛心能」、「專業位能」、「執行力動能」。2. 各階段指標須達時間點，可反應指標達成的難易度，或做為不同師培階段師資養成重點，或做為教甄教檢篩選及在職專業考核內涵之依據及評量配分比重，得以重點培育及客觀篩選入職者，或用之於教師分級，藉之驅動現職數學教師與時俱進，維護教師的專業性及其持續性，落實學生高品質數學學習，確保學生受教權。

　　Teachers are the core of quality education. The quality of the teachers is the vital key of education reform. This research aims to : (1) Develop the mathematics teachers’ indicator of reflecting era pulse and suitable for our country. (2) Establish the indicator difficulty level for professional assessment; (3) Investigate teachers screening mode for mathematics education. (4) Provides the indicator for institutions of teacher education, administrative organizations, to reform assessment systems of pre-service and in-service mathematics teachers. The methods include: (1) document analysis _ to analyze connotation of mathematics teachers' professional performance and professional knowledge; (2) interview and panel discussion _ to portray mathematics teaching professional knowledge and clear up the status and dilemma of teacher recruitment; (3) web-based questionnaires_ shape the mathematics teaching professional image. This study adopts self-editing web-based questionnaire as a research tool. All the mathematics teachers of 4,103 schools are statistical respondents. Gathered 5,807 valid questionnaire from 1, 689 schools, can explain at 99% confidence level and the sampling error is ± 2.41 percentage points. By the SPSS 22.0 software package with AMOS 22.0 to implement statistical analysis. The SEM, χ2 test, MANOVA, ANOVA etc. are as the statistical method. This study found: (1) These mathematics teaching professional competency indicators possessing comprehensiveness and explanatory power; (2) The teachers filtering mode close to the requirements of education field; (3) The goal reaching degree can response the difficulty level of indicators. The suggestion for education policy: (1) Active teacher evaluation tests and system for selection and appointment of mathematics teachers to ensure the quality:  The education professional feature test as the threshold of teacher education program. The paper test for the certification of teacher qualifications focuses on the professional knowledge / ability of education; the paper test for teacher recruitment gives priority to discipline knowledge and ability; the trial teaching for teacher recruitment emphasizes the knowledge / ability of teaching and practice; the oral examination for teacher recruitment stresses on the characteristics of professional responsibility and the professional practice.  The paper test for teacher recruitment adopts joint-hosts & each-employment; the proportion of mathematics knowledge and teaching materials/ methods is fifty-fifty in elementary and junior high schools, the mathematics knowledge is sixty percent in senior high and vocational schools.  To stipulate rating items, key rating, partition, et al. for the trial teaching and oral examination for teacher recruitment.  The trial teaching for teacher recruitment covers all math unit and increases the design of lesson plans before trial teaching and ask questions after trial teaching.  The result of paper test for teacher recruitment is threshold or thirty percent (or less) of total score.  The proportions of second-round exam are trial teaching seventy percent and oral examination thirty percent.  The number of completing indicators, etc. is decided pass into the workplace or not. (2) Make good use of indicators for teacher education, selection of teachers and professional maintenance: These indicators cover four dimensions, 11 constructs, 72 indicators. Each construct has convergent validity, between constructs have diction validity, the explanatory power is over 70%. These indicators not only have high explanatory power, but also echo the new era mentor should be equipped with education love, professionalism, and execution. The timing of indicator should be reached reflects the degree of difficulty, can be as focal points of teacher training teachers; as the objective gist for certification of teacher qualifications, selection of teachers, and professional examination; as the proportion of the partition. These indicators used to foster teachers, select teachers, even to maintain the professionalism of teachers and their sustainability, for ensuring the right of students.