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In order to be convinced of student understanding, I need them to show me in a variety of different ways. Make connections, relationships between ideas

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I think it depends on what I am assessing and what is appropriate for that standard.  For example explaining what you remember about the pythagorean theorem or quadratic formula is perfect for both of these topics. You can have someone explain the process of factoring, where it is you, what it finds on the graph but I still like to see a student factor a problem and then explain what type of problem factoring is used in and why.

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I think it goes beyond just explaining their process. If a student truly understands something then they should be able to make connections between related concepts and use those connections to solve a problem or create something.

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Read, write, speak, compute, graph, apply and connect

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I think all problems show some form of understanding.  Obviously more open ended questions, real world examples show a higher level of understanding

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“Create your own” type questions. For example, you might ask students to create a polynomial function that would require the  quadratic formula to find solutions.

Also, you could ask students to justify each step of their solving process.

You could ask students to create an oblique triangle with measurements that would yield an ambiguous case when solving using the Law of Sines.

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Relationships between ideas… connections

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Access multiple methods

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Questions that are more open ended (share what you know about ...., what is the relationship between ....)

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Read, write, analyze, use, solve

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You are able to perform and explain the task at had. You are also able to take the topic and apply it to additional problems or topics

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To understand means to be able to explain and do a task, problem, etc

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Understanding is not only know how to do something but also why you do it that way. 

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Understanding is not only know how to do something but also why you do it that way. 

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Explain the difference between…