Research used for the Common Core includes the NCTM process standards and the strands of mathematical proficiencies as specified in Adding It Up.
Principles and Standards for School Mathematics describes a future in which all students have access to rigorous, high-quality mathematics instruction: ...knowledgeable teachers have adequate support and ongoing access to professional development. The curriculum is mathematically rich, providing students with opportunities to learn important mathematical concepts and procedures with understanding...
One strong component necessary to make this vision become a reality is through the use of increasing communication in the classroom. One of the five process standards expresses what this communication should look like in PreK-12 classrooms. As we explore the "processes and proficiencies" outlined by the Common Core Standards, one must recognize that the skill of communication is the common denominator.
Instructional programs from prekindergarten through grade 12 should enable all students to--
- Organize and consolidate their mathematical thinking through communication;
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
- Analyze and evaluate the mathematical thinking and strategies of others;
- Use the language of mathematics to express mathematical ideas precisely.
So what would this communication look like in the mathematics classroom? Students would be asked to justify their reasoning, to formulate questions about something they find challenging or puzzling, to communicate their understanding and/or confusion to others, to organize their thinking, and to reflect on their own learning.
Getting students to express themselves clearly and coherently is not an easy task. This article is an attempt to give a practical idea of how we can increase communication in the classroom through the sound practices of asking open higher-level questions. If communication is the goal, the questions become, "How do we get them there?" and "How do we make this goal a reality?"
Have you noticed students, as well as adults, don't like to share how they solve problems? They will just say, "I did it in my head." Then we must follow up with, "What did you do in your head?" But even this does not retrieve the necessary information from the student. If we want to increase communication and dialogue, including justification in the classroom we are going to need to become much better questioners. I believe questioning is the key to make this goal a reality in the classroom.
I remember taking a questioning class in college, or maybe it was embedded into one of my methods courses, but it was only taught/learned at the knowledge level. I could name Bloom's Taxonomy hierarchy of questions but I did not internalize or practice these types of questions when placed in my own classroom setting. I had the knowledge but I didn't know how to apply this information to my classroom. Does this sound familiar? This failure to apply is the same thing we often notice about students. If we only teach knowledge-type of content, they don't necessarily know how to apply that information in real-world settings or to other content areas.
This article describes a process I use with teachers to help them identify and develop different types of questions and successfully implement them into their classrooms to increase the communication and dialogue of their students.
The Process to Move From Knowledge to Classroom Application
I was working with a group of fourth grade teachers who wanted to increase the level of questioning in their classrooms. I knew they were already doing a great job at questioning, but they wanted to continue to grow and become even better. As we began the process below, we realized not only did they need to become better questioners but the goal was also for theirstudents to become better questioners. I believe the following steps could also be used with students.
Step #1: Open Sort
Give teachers/students (in groups of two or three) a large sheet of paper and a stack of small cards containing different types of questions. I usually have the questions printed or written on card stock. It is important that you have a large piece of paper under the cards, because later in the process the group will be taping their question cards to the paper.
Sample questions:
- Can you describe your method to us all?
- Does this make sense?
- Why is that true?
- How does this picture model the problem?
- Can you explain your work?
- How did you tackle similar problems?
- Would it be helpful to draw a picture, or make a table?
- How did this tool help you to solve the problem?
- How would you describe the problem in your own words?
- Can you think of a counterexample?
For a complete list of all the question cards used in this process, contact me at michelleflaming143@gmail.com
The teachers/students are given time to sort the cards into categories of their choice. This is called an open sort. After sorting, groups quickly share how they chose to sort, and identify similarities and differences in the groupings. Either verbal sharing or a visual sharing is appropriate.
Research by RobertJ. Marazano says, "Ask students to identify similarities and differences on their own." While teacher-directed activities focus on identifying specific items, student-directed activities encourage variation and broaden understanding, research shows. Research also notes that graphic forms are a good way to represent similarities and differences.* Engage students in comparing, classifying, and creating metaphors and analogies. (1)
Step #2: Closed Sort
Give groups the category titles from the 8 Mathematical Practices from Common Core State Standards in math that you would like for them to sort. This is referred to as a closed sort. These cards are also on card stock but in a different color than the question cards. The categories, I ask them to sort by are:
- Make Sense of Problems and Preserve in Solving Them
- Reason Abstractly and Quantitatively
- Construct Viable Arguments and Critique the Reasoning of Others
- Model with Mathematics
- Use Appropriate Tools Strategically
- Attend to Precision
- Look For and Make Use of Structure
- Look For and Express Regularity in Repeated Reasoning
Sometimes the questions may fit into more than one category. If this is the case, the placement is irrelevant. The process of the group discussing where they go and why is much more important than where it truly fits. The power is in the discussion and the thinking.
At the end of step 2, groups can quickly share their results and ask questions of other groups.
Step #3: Understanding Open vs. Closed Questions
In this step, teachers/students will discuss the differences between open and closed questions and understand the potential value of using open questions with students.
In some research these differences in question types are referred to as fat/skinny questions or divergent/convergent questions. Whichever terminology you are familiar with and would like to use is up to you. The concept, not the terminology is what is important.
Closed questions can be answered with a simple one-word answer. For example, the question "Could you try using a number line?" could be answered with a simple "No".
Research shows that most questions we ask our students are closed. Closed questions have their place, but in most classrooms they are vastly overused. The type of question needs to be determined by the purpose. Closed questions are great for quick and easy ways to check comprehension and retention of important information.
Open questions, on the other hand, should be used when wanting to encourage discussion and active learning in the classroom. Open questions tend to be warm and inviting. Open questions are great if the goal is to clarify a vague comment, to prompt students to see a concept from another perspective, to support their conjectures, to respond to one another, to investigate an alternative strategy, to make predictions, to organize information and make connections, or to reflect on their own learning.
Sanders (1966) stated, "Good questions recognize the wide possibilities of thought and are built around varying forms of thinking. Good questions are directed toward learning and evaluative thinking rather than determining what has been learned in a narrow sense."
With this in mind, teachers need to be very intentional about the purpose of their questioning and design a process in which they can be cognitive of their own questioning skills and purpose. I also believe that to truly create a climate of discussion in the classroom, this should also be a goal for our students.
Step #4: Identifying Open and Closed Questions
Ask groups to go through the questions and if it can be answered with a one-word answer, turn over the card. For example, a card that says, "Can you guess and check?" (Yes) would be turned over. If the question can only be answered with more than one word ("Why is that true?"), it should remain face-up.
Groups now look for similarities among the open and closed questions. It is extremely important that the groups identify the similarities through their discussions. They should notice that closed questions seem to start with Can, Could, Would, and Does. Open questions typically start with What, How, and Why. Once this pattern is noticed move onto the next step.
Step #5: Changing Closed Questions into Open Questions
In this step, groups will rewrite the closed questions and make them open questions. This asks them to apply the new knowledge that open questions typically begin with what, how, and why. They may choose to keep the question closed, but add a follow-up question that is open. For example: "Do you agree with_______?" (Closed) "Why or why not?" (Open).
Once all questions have been re-written to become open questions, groups tape the cards onto the white paper. At this point, the teacher collects the posters chooses a sampling of questions to include on a poster which will be hung in the classroom. Until we (teachers and students) become better at asking open questions, we need a visual aide to help us.
The poster shows students that questioning and communication are important and essential tools in our classrooms. It also provides prompts that allow teachers (and students) to practice these questioning skills until they become more proficient.
Conclusion:
Effective questions can almost instantly change the level of communication and the climate in the classroom. Using open questions and closed questions at just the right time and based upon the purpose of the questioning will usually provide the response that you are looking for from your students. Closed questions can be used to simply attain one or more pieces of information. Open questions will be needed to reach the goals of the Common Core Standards and the Principles and Standards for Mathematics (NCTM):
- Organize and consolidate their mathematical thinking through communication;
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
- Analyze and evaluate the mathematical thinking and strategies of others;
- Use the language of mathematics to express mathematical ideas precisely.
To make this vision a reality, open questions must become the norm for both teachers and students. It's time to take our knowledge and apply it each and every day in our classrooms.
Research:
1) McRel - Classroom Instruction That Works
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