These might be two of the most essential questions for learning going back to the time of Socrates (http://bit.ly/14YbHhQ) who continuously asked his students, "What are you thinking and how do you know what you're thinking is true?" Not only is it necessary for us to know what our student know, it also vital for us, as teachers, to think about what we know and how do we know it.

I'm taking a very good course on teaching through Coursera and the Common Wealth Education Trust, and the course instructor, Professor John MacBeath has asked us to think about our own thinking as well as our students. As teachers, he has asked us to do the following exercise, which really opened my eyes to my own thinking and assumptions about teaching and learning:

- What do I know about learning?
- What do I know about teaching?
- What do I know about the context for learning?
- What do I not know about learning?
- What do I not know about teaching?
- What do I not know about the context for learning?
- What would I like to know about learning?
- What would I like to know about teaching?
- What would I like to know about the context for learning?

One of the things that I found out about what I didn't know about teaching for learning was how to make my students' thinking visible. When I was considering this lack of knowledge about my own teaching, it became a top priority for me. Fortunately, there are a lot of resources about making your students' thinking visible. One given to us in the course is the website "Visible Thinking" (http://bit.ly/1PHbunj). Although the idea of visible thinking seems like an obvious one to tackle, it might prove useful to "have a think" ourselves, as John MacBeath puts it, to consider the problem of making our students' thinking visible. MacBeath asks us while showing the graphic of the different cats, "How do you know what your students are thinking?" And the answer is, we don't know...unless we ask them.

Imagine that we have asked students what we think will be a simple problem, but suddenly we find ourselves with a perplexing one like the teaching in this video (http://sms.cam.ac.uk/media/1165318).

I found the teacher doing an excellent job at asking her students to evaluate the problem of dividing 1 by 2, and she seems to be aware of her students grappling with a concept that may change the course of their learning. While watching this video, I thought, "Wow, what an amazing learning moment!" The teacher almost has her students to the answer, and they are responding to her question and displaying some thinking, but then she allows the students to change the problem, thereby retreating back to firmer ground. If only she had broken the stick in two and asked them to think, is this one stick, two sticks, or two halves of a whole stick? Or even better, had one of the students break the stick and then ask the class how many sticks they had.

We should top and take a moment to think about the questions the teacher is asking. How many of the questions asked by the teacher are what appear to be display questions. In other words, questions that the teacher already knows the answer to, such as "Is this number right?" Then think about how many reference questions the teacher is asking, in other words, questions that ask the students may respond openingly to about their thinking.

Watch how the teacher gives the students choices, which leads them to the amazing moment of learning when the student chooses to divide 1 by 2. As I watched, I thought, "Oh, no. How will they get this difficult concept?" I was even more amazed when the student gave 1 as the answer to the question. She writes one on the board and ask the students, "Is this correct?" The students intuitively say "No." The teacher replies, "Why, what's wrong?" This question elicits multiple answers. Later she asks, "Look at this sign, in between here, is this correct?" At this point, we can supposition that the teacher wants to change the numerator. But she also asks, "[students' name] thinks the answer is 2. How many think this is correct." And by polling the students, she begins to understand what her students are thinking and then asks the students who think 2 is not correct to explain to the other students why. Some students say the answer is 1 and other say the answer is 2. Unfortunately, we can't hear the reasons the students give, and the teacher returns to asking if the numbers in the boxes are correct. Then she shows the student the stick and asks them, "How can I divide this stick by 2?" and the students answer, "I can't." Then the teacher goes on to change the numerator. Do we have the right reasoning here? Yes, if you want to stick and the lesson to deal with whole numbers. But what an amazing feat if the teacher would have introduced to the students the idea of halves of wholes or fractions.

Today, teachers are asking students "What is the evidence?" or "Why do you think that?" While, I think these two questions are linked, they are not necessarily the same thing. Think of what the evidence would have been from the lesson from above. We have a stick and the stick can't be divided in two. Really? That only gives us evidence of limited reasoning (not incorrect). Could we have extended the reasoning for this lesson and said, "Ok, here is something new to think about. We can divide this stick by two and get two halves. The are not two sticks, but two halves of one stick. Think about that for a moment." Then we would have an opening for new ways of thinking and stronger evidence for our reasoning.

I'm not a math teacher, and I don't expect to be able to teach a lesson better than the teacher in the video, nor should I second guess the lesson that she taught and the reasons for teaching the way she did. But as an English teacher to speakers of other languages, the lesson of making thinking visible is a powerful lesson. Often we ask students, to communicate and by communicating students must make choices in meaning. If I ask a student, "How are you today?" and the student responds, "not good," should we correct the student and say, "No, you mean 'not well.'" Then how are we misdirecting their thinking and meaning making choice? Don't people say "not good" all the time? Wouldn't it be better if we recast and said, "Oh, not good or not well. I'm sorry to hear that." This way, we don't make assumptions about what the students wants to say, rather we present another meaning making choice.

In addition, what if we insist on our students saying whole sentences, such as "I am not well." But in reality, we co-construct language and almost never hear the subject and verb repeated in conversation openings because such information has already been given. Do our students realize the difference between given and new information and how that is structured in sentences? How then do we make our knowledge of the language system visible to our students?

I believe the answer is making sure as teachers that we are thinking about language and showing how we think think about language. Instead of asking for specific language forms, we showing how to use language to communicate and providing moments where we think about the "form, meaning, and use" of the language. For example, if we ask ask our students, "What did you do today?" and our student replies, "I woke up. Then I ran about two miles. Then I went to school." Could we then the student, "Why didn't you say, "I wake up?" or "I run about two miles?" and "What's the difference?" Then we can see if the students can explain the difference in using the simple past events that occur in the near past versus using the present simple to describe actions that are habitual. By asking students about the language they use for reasons they use it, we are opening opportunities for students to think about their awareness of language and to demonstrate their knowledge of collocations and patterns in addition to how language is constructed through meaning making choices. This approach, it seems, would work well with the action based language lessons in which students use language to do something, thereby providing an opportunity for us to ask students "what did you say and why?"

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