CRMT Framework

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.

課堂包含高層次認知需求（具有多個切入點和解決方案或策略）的任務或活動，協助學生自行探索和分析數學概念和程序，發展學生的思維或推理策略。

課堂上，老師使用不同的呈現方式，要求學生解釋或證明，以培養學生的數學思維。

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.

課堂讓學生持續關注某數學主題或單元；通過合理論證，理解問題的複雜性；並解釋他們是如何解題。

課堂協助學生理解數學，將他們的想法形象化，達致更深入的理解。

老師透過具策略性的提問和引用學生習作、談話或互動行為，協助學生自行檢視數學概念和／或程序，以輔助他們思考及澄清潛在的混淆或誤解之處。

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.

課堂上，老師創造機會讓學生有意義和嚴謹地討論數學。方式如下：

• 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。

學生透過多種呈現方法及資源，以不同方式交流他們的理解。

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.

課堂為中文或英文語言學習者提供學術語言支援。其側重點在於數學話語的發展和意思的形成，並不在於正確的「英文」或「中文」。

師生互動過程中，老師使用第二語言教學策略（例如：重新表達、手勢）、多種話語模式（例如：日常語言、學術語言）和多種呈現方式（例如：圖片、實物、文字和說話、符號）。

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.

所有學生均重視或共享數學〔知識〕權威，而非只集中在少數學生之中。爲此，老師提供多種參與方式，提升學生的投入感和參與度。

課堂重視學生的數學貢獻，致力解決學生間的地位差異，令所有學生都能夠積極參與和投入數學活動。

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.

課堂連結數學知識和文化或社區知識。學生要分析他們日常生活和社區中出現的數學，並觀察數學如何幫助他們理解社會環境。