Posing purposeful questions reminds me of the third CCSSM Standard which is Construct viable arguments and critique the reasoning of others because teachers should pose purposeful questions to gauge student understanding and students communicate their understanding back to the teacher through their arguments of why they got the solution they did. There are five types of purposeful questions teachers ask students which are all used for different purposes. The first type of purposeful question is gathering information, which teachers use when want students to recall basic facts or definitions (mostly things that are memorization). This is a question used to assess students because it usually has a right and wrong answer and can help the teacher gauge whether or not the student understands. The second type of purposeful question is probing thinking, which is used when teachers want students to explain, elaborate, or clarify their thinking and reasoning and why they came up with that answer. This is also an assessing question because the students are just explaining how they got the answer and not farthing their knowledge. The third type of purposeful question is making mathematics visible which teachers use when they want students to make connections between mathematical concepts or ideas. This is an advancing question because it connects the topic to other topics they have already learned which expands their knowledge and helps make connections. The fourth type of purposeful questioning is encouraging reflection and justification which is used when teachers want to get a deeper insight into students thinking and reasoning. This is also an advancing question because teachers often use this question for students to argue the validity of their work making them think about why the answer they got is correct. The fifth and last type of purposeful question is engaging with the reasoning of others, which teachers use when they want students to learn from the reasoning of their peers. This is definitely in the category of advancing questions because it makes students think about things in the way their peers did which may be different than their own reasoning, In my placement last year, I remember my CT using questions that are in the category of encouraging reflection and justification because it was a first grade ESL class and ESL students develop speaking skills much faster than writing skills so they were able to verbally explain their thinking better than they could write it down. My CT also asked a lot of gathering information questions because they were learning basic addition and subtraction and he wanted them to memorize the math facts. When I am in my placement or in my own classroom in the future, I think the hardest type of question for me to ask my students will be making the mathematics visible because it will take more preparation on my part to think of ways the current lesson connects to previous lessons.
My high-level learning task is still a work in progress but I have written it below with an example of each of the teacher question types:
Emma and Jack both have some books. When they combine the books together, they have 10 books.
Your classmate says that Emma has 4 books and Jack has 6 books. Is your classmate correct?
What other quantities (numbers) of books could Emma and Jack have?
Ask your neighbor what numbers they used and see if they are correct
Gathering Information: Your classmate says that Emma has 4 books and Jack has 6 books. Is your classmate correct?
Probing thinking: How did you know that your classmate was correct or not?
Making Mathematics Visible: What other quantities (numbers) of books could Emma and Jack have?
Encouraging Reflection and Justification: Why can Emma and Jack have different quantities of books that each add up to 10 in total?
Engaging with the reasoning of others: Ask your neighbor what quantities of books they think Emma and Jack both have and have them explain why they think that. Why do you think your neighbor is correct or not?
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