Culturally Responsive Mathematics Teaching (CRMT) 文化回應數學教學

Adapted from CRMT Unit Planning OR Lesson Observation & Analysis TOOL (Aguirre & del Rosario Zavala, 2013), the framework can be used to plan and analyse mathematics lessons in multiple ways to support the mathematical learning of culturally and linguistically diverse (CLD) students. It facilitates the analysis of the strengths, weaknesses or limitations of the mathematical activities or tasks; evidence of student learning; instructional strategies that elicit and support students’ thinking and dialogue, as well as students’ level of participation in mathematics lessons.

此框架改編自文化回應數學教學(CRMT)中的單元計劃(單元教學活動設計)或課堂觀察及分析工具(Aguirre & del Rosario Zavala, 2013),讓老師以多角度設計和分析數學課堂,支援具多元語言及文化背景的學生的數學學習。此框架有助分析數學學習活動或任務的優、劣、局限性;學生學習顯證;引出和輔助學生思考和對話的教學策略,以及學生在數學課上的參與度。

Cognitive Demand認知需求
The lesson includes tasks or activities with high level cognitive demand (having multiple entry points and solution strategies) that require or enable students to explore and analyse mathematical concepts and procedures, and develop thinking or reasoning strategies.

The lesson involves mathematical thinking that utilises multiple representations, and demands explanation or justification.



Depth of Knowledge & Understanding知識和理解的深度
The lesson enables students to sustain a focus on a mathematical topic or unit, to understand the problematic nature of ideas by arriving at a reasoned or supported conclusion, and to explain how they solved a problem.

The lesson supports students’ mathematical understanding and makes their thinking or understanding visible and deep.

Teacher uses strategic questioning and references to students’ work, talk or behaviour that enable students to examine mathematical concepts and/or procedures to support thinking and to clarify sources of potential confusion or misunderstanding.




Mathematical Discourse數學話語
The lesson creates opportunities to discuss mathematics in meaningful and rigorous ways, such as

  • debate mathematics ideas or solution strategies;
  • use mathematics terminology, develop explanations, arrive at conclusions;
  • communicate reasoning, and make generalisations.

Students communicate their understanding in multiple ways, through multiple representations and resources.


  • 辯論數學概念或解題策略;
  • 使用數學詞彙,發展論證,得出結論;
  • 交流推理過程,並嘗試歸納。


Language Support語言支援
The lesson provides academic language support for Chinese or English language learners. It focuses on the development of mathematical discourse and meaning making, not the correct “English” or “Chinese”.

Teacher uses second language strategies (e.g. revoicing, gesturing), multiple modes of discourse (e.g. informal language, academic language) and representations (e.g. pictures, objects, written and spoken words, symbols) in a variety of interactions.



Power & Participation權力與參與
Mathematical [knowledge] authority is valued or shared among students, rather than concentrated in a few, with multiple participation structures that facilitate students’ engagement and participation.

The lesson values student mathematical contributions and addresses status difference among students, all students can actively participate and involve in mathematical activity.



[Culture] Funds of Knowledge〔文化〕知識資產
The lesson connects mathematics to cultural or community knowledge. Students are asked to analyse the mathematics within their lives and community contexts, and how the mathematics helps them understand the context.