Table 2.

Scale to assess the level of mathematical communication skills regarding ellipse topics.

Component Skills	Skills and criteria for each skill	The expression levels of each criterion
		Level 1	Level 2	Level 3	Level 4	Level 5
Ability to understand and identify mathematical problems through communication	Understand, identify, and solve mathematical problems in written form.	Unable to understand or identify math problems.	Understand and identify the part of math problems.	Understand and identify mathematical problems and summarize a part of basic, central mathematical information.	Understand, identify, and summarize key mathematical information in a text.	Understand, identify and correctly use mathematical language in summarizing mathematical problems.
	Understand and identify mathematical problems in the form of mathematical language (digits, symbols, graphs).	Cannot understand, cannot identify mathematical information.	Identify some core mathematical information.	Know how to analyze, select and extract some necessary mathematical information.	Know how to connect, link and synthesize mathematical information.	Know how to connect, link, synthesize and select mathematical information using mathematical language.
Ability to use mathematical language in presenting, expressing mathematical contents and ideas	The ability to effectively use mathematical and mathematical language to present, explain, reason, and prove mathematics accurately, logically, and clarify mathematical ideas in a specific context.	Lack of basis when speaking and writing math. Students are not yet able to express their understanding of mathematical language.	The first step is to present and explain mathematical contents in familiar situations with single and discrete sentences. When speaking or writing a math problem, it is not logical, strict, and concise.	Understand and use mathematical language in familiar symbols and symbols to summarize and present mathematical ideas and solutions in a relatively accurate and appropriate manner.	Ability to write about mathematical ideas and solutions concisely and clearly; Analyze, evaluate, and respond to math problems logically and accurately.	Coherent presentation, close argument, proper use of mathematical language convincingly and effectively. Make connections or convert natural language to mathematical language and vice versa to accurately represent mathematical objects, relationships or solutions to mathematical problems in specific contexts.