After a conversation with Kathryn Freed today, the topic of questioning students came up. Thoughts started flying through my head so I decided to try and blog them before they flew south for the summer.
A student sits down in Math class. Their teacher, Mr. Anderson, greets the class and relates how excited he is for this year. Then he explains class expectations to the students. One of his expectations is that students Think about their work and to make sure they have attempted the problem before calling on him for help. “Do not be surprised to have your question answered by a question.”
This IS one of the first things I do in class. I tell the students that my class will be different that others they have had. We will have fun, we will do projects, we will talk about Math. I expect them to challenge me when they do not believe I am right, I expect them to defend their answers. I expect them to think about Mathematics, not just come to class, practice a set of problems and leave.
One thing I do expect students to do is answer questions when they ask for help. I need to know where they are coming from in order to get them where they need to be. This is my most powerful assessment that is also the easiest to implement in the classroom without disruption, or even student knowledge of it being administered. These are questions I typically use:
1. What do you think you should do? OK, let’s try it.
I have to admit, this IS my go-to question. After I go through a couple of initial questions (#2), I hit em with this. This is the question that typically gives me all of the information I need to get students through a problem. They will tell me what they feel they should do, and why. After they give me their game plan, we set it into motion. Am I worried that students will do the wrong thing? NO. To me, you can never truly do the wrong thing unless you are using some rule you remember from Mr. Johnson’s class but you have no clue why you would use it. One of the beautiful things about math is that there a many different ways to work through a problem, and when students tell me what they intend to do, I know how to help.
2. What can I help you with? What don’t you understand about the problem? What did the problem tell you to do?
Is is a group of initial questions I go through when a student first calls me over. I have students verbally tell me what they need help with. Typical responses are “Everything.” I remind students that they can’t possibly need help with everything, and ask them to narrow the issue down so we can work on one part at a time. They then hit me with “I don’t understand the problem.” This means that they did not read the problem, normally students will give the assignment a browse-over and automatically decide which problems are “hard.” So I hit them with the third question. If students can’t summarize the problem to me, I ask if they read the problem. I would say 95% of my students say no. I then ask them to read the problem softly to me. I take this extra time to ensure that they did indeed read the problem. Earlier in my teaching I would tell students to reread the problem and I would get back to them only to find that they still did not read it. Having student read the problem softly to me also gives me an insight to their reading skills and comprehension- things that I will need to collaborate with my Language Arts teacher in order to successfully help the student.
3. I like how you have shown your work, why did you do these steps?
I have found that the best way to get students to give me their honest thoughts on a problem, I need to give them a “feel good” before I expect them to explain. I encourage students to show their work, and although I never tell them “I will have all steps written out!”, when I start asking them to explain how they are working on the problem they realize that they need to have “notes” to help them explain their reasoning to me. I use this question when I notice that the student has taken a lot of effort to attempt the problem, but it is essentially question 1 in disguise. This gives me insight to how they are thinking about the problem and sets me up for success in asking the right questions to get them to work through the problem and find an answer.
4. You have done great work up to this point, why do you feel stuck?
I am sure every teacher has the student who knows their stuff, but lacks the confidence to feel they are arriving at the right solution. I have found by giving them this small acknowledgement but still ask them a question about what they are doing, they feel that they have started on the right path and they analyze why they may have thought they needed help. Typically I have to only ask this question a hand full of times to these students before they start making great things happen, all on their own.
5. Now where do you think you should go?
This is my go-to question #2. Students dazzle me with outstanding work and explanations, and instead of telling them “that’s it!”, I ask them to decide on the next phase of their master plan. I will ask students this at any stage of their problem, and especially when students think they have the answer. This makes them think back on what mathematics they did, and determine whether they need any additional steps. It is great to see their face when they realize they finished their problem, and they know they got it right. Best moment ever.
6. When you see a problem like this, what does it make you think of? So how do you think we should solve this?
Sometimes students need a push to get them thinking. They try to be too mechanical and decode the problem without thinking of it’s context or what it is trying to say. Once again, this is a revised version of question 1, but students tell me prior knowledge of the problem type which helps me to determine if they are missing skills, need scaffolding or just did not think critically about the problem.
7. What kinds of patterns do you see?
I believe that my students can be successful in Algebra if they really know 2 things: Patterns and Linear. I ask this question all the time about random things. What patterns do you see in my posters? What patterns do you see in the hall? What patterns do you see in the class hour? etc. Getting students to compare and analyze things for patterns in 8th grade Algebra will allow students to find success on problems.
8. Have we solved a problem similar to this one? What did we do to solve it? What do you think we need to now do to solve this problem?
There are many times that we work on an example, and I send my students off on practice problems and suddenly find 10 hands in the air. I ask these questions to get students thinking about the processes we did, what they know. I encourage them to try known methods on new problems. Take tools that you know and apply them to problems you haven’t seen. Students have a huge arsenal of mathematics when they come to me in 8th grade, but a very small amount of confidence on how they can apply that knowledge. Make a point of showing students what may seem impossible is indeed, possible.
9. Does that make sense?
Speed = Mathematics has really done a number on our students. Many of my students rush through practice problems just to turn it in and get a grade. They do no critical thinking about their work or even it’s accuracy. I ask students to predict and estimate, before we start a group problem. That way when we arrive at a solution we can compare it and see if it’s what we should expect.
10. Why do you think your answer/method is right?
When students answer a problem confidently, I ask them this. I then see a flash of panic across their face as they realize I am not going to say “You’re right!” Answers are important, but also share with the class how you did it and why you think you are correct. Students learn the best from their peers, they are a valuable tool that is often underutilized.
11. Why do you think your answer/method is wrong?
I have students who have an answer, but are certain it is wrong. The thing I can never figure out is why they are OK with having that wrong answer- they don’t feel a need to fix it. The answer to this question tells me if the students are just guessing, don’t totally understand the material, have the answer right and just have a confidence issue, or are just too lazy to put effort into the work. Asking why they think they are wrong to me is more important than asking why they think they are right.
12. Why do you think that the problem is hard?
Many students skim. They don’t read the problem or even create a context for what the problem is defining. This question will allow you to give some starting hints on how students should start the problem before you launch full scale into solving it. Students will say a problem is hard so you work it out with them or the class just to avoid the problem.
13. Will that always work? How do you know?
Challenge their claims. Make them call upon their knowledge to defend their answers, theories and beliefs. Students will learn more from this type of questioning versus 10,000 practice worksheets.
14. What do you predict will happen next? Why do you think that?
Predictions are very important in mathematics. It allows an informal evaluation of what is going on, without pressure of being wrong. It also creates a starting point from where students can tackle a problem. When they get done, they compare their answer to their prediction and reflect on their work. If you never call on students to predict the outcome or answer then you are not totally engaging their mathematical thinking.
15. Is there somewhere else in this room you could find the information you need? Why didn’t you check that resource first?
I use this to try and create independence. Students have textbooks, notes, posters, examples and even peers as sources of information. Many 8th graders feel that only their teacher can truly help them, and by the time they leave me at the end of they year they realize that they have many different resources to help them solve problems. Creating independent students is very important to their success in High School, College and life. Students will not like you not answering all their questions right away, but will appreciate later the lesson in self-reliance that you build by doing it.