by Dina O’Brien, Math Specialist and Instructional Coach, NJ:
Questioning is an important instructional strategy. Asking the right kind of question will increase student curiosity, help students make connections to the Math they are learning, and elicit critical-thinking skills. Teachers can learn so much about students from their responses to the questions and decide what further strategies are necessary. The need for students to justify their answers and reasoning should be expected. Recently, I shared a newsletter with teachers in my building focusing on The Big 8 (Mathematical Practices). In the newsletter, I included sample questions for each Standards for Mathematical Practices (SMP).
Do You Have the HOTS for Math?
This is one of my favorite topics: Higher Order Thinking Stems for Math (HOTS for Math). Teachers want to engage students with questions that challenge them to dig deeper. When students are problem solving, there is more to it than just asking them what you, as a teacher, need to find out. Talking with students about the strategies they will use to solve the problem and asking them "What do you think the answer or result will be?" can lead to further questions. When students get stuck, it is important to ask them "How did you tackle a similar problem in the past?" Students may need to be reminded of problem-solving strategies. Asking students questions such as "Would it help to create a diagram?" "Make a table?" or "Draw a picture?" may spark different ways to solve the same problem. Standards for Mathematical Practices #3 has students critiquing the reasoning of others. It is okay for students to see how other classmates solved the problem, but then follow up and ask the student if they can solve it another way and compare the work they have done so far. Analyzing mistakes helps students become better mathematicians. Making connections between ideas and applications is also important. Asking students "What ideas have you learned before that would be useful in solving this problem?" allows students to make connections between skills and apply them in different situations. Once the problem is solved, it is important for the students to reflect on their work. Reflecting and asking reflective questions to the students can help them connect the process to future problems. In my opinion, it goes deeper than "How did you get your answer?" Asking students to explain why their answer is reasonable or not links back to the beginning of the lesson when you asked, "What do you think the answer or result will be?" Students should be able to describe their method to the class and explain why it works. These are just some of the ways you can dig deeper with your Math questions.
What Uses of Mathematics Did You Find in the Newspaper Last Night?
This year, I put a newspaper on the door of my room titled “Math in the News.” I asked students to clip articles or headlines and explain the math connection. They would then post it on the door. This upcoming year, I would like to extend that and include questioning. I would like them to create questions based on the clippings they find. This flips the questioning to the students to create, however. So, modeling of higher-level thinking questions should be taught previously. Look at the weather for a week where you live compared to another country. Have students find the mean, median, and mode of the data. The classified section of the paper is also a great place to connect math. Have students figure out the cost of running a 30-word ad for one week or estimate the number of ads on the page based on columns per page.
TenMarks Math Teaches Questioning
TenMarks Math lessons provide ideas and resources to teach different math standards. There are guided questions to use as you work your way through a lesson. You can print it out and project the problem portion of the lesson on the screen so the students can't see the guided questioning part. I have used these (as well as additional questions I wrote) in a small group to reinforce a specific standard.
Questioning should begin with pre-assessing and continue through to post-assessments. The questioning in TenMarks Math lessons gets deeper and deeper as the lessons go on, leading to the opportunity for students to extend and apply their understanding of the concept. To assess students' readiness for a standard, there are some guiding questions. Teachers use these questions, as well as other forms of pre-assessing, to decide if the standard should be taught to the whole group or to a small group of students. Two of my favorite questions to ask students are: "What are you trying to figure out?" and "What strategies are you going to use to solve it?" TenMarks Math lessons include these questions often. This allows students to have math talks and reason with each other about different ways to solve a problem. I believe that the more demanding the task is, the higher level the questions will be.
I am currently reading Principles to Actions Ensuring Mathematical Success for All put out by the National Council of Teachers of Mathematics (NCTM). It discusses four types of questions: gathering, problem thinking, making math visible, and encouraging reflection and justification. All types of questions are necessary, but each is used for different purposes. Gathering questions may be used to find out what students know, while other questions justify their reasoning. Teachers may have a set path they want their questions to take or may be more open to more of an investigation. Either way, the questions you ask should help students clearly identify their thinking about the problem and help students connect ideas as they make sense of mathematical concepts. Once you judge their response, they stop any further thinking about the question. Dig deeper with your questions and watch their mathematical thinking grow.
Dina is currently a Math Specialist and Instructional Coach in Edison, NJ. Before that, she was a teacher in grades 1, 2, 3, and 5 over a 15-year span. She is passionate about creating lifelong learners and meeting the needs of all students. She loves to attend EdCamps and learn about the newest resources available and tools to improve student learning. She is a NJ Ambassador for The Education Calendar, which lists and promotes upcoming events across the nation. Get in touch with Dina on Twitter, her Reflections blog, or the James Madison Math Resource website.