## Promoting productive math discussions is an essential part of helping students think, question, and problem solve-effectively. Here are a few tips for how to use these in your remote learning classrooms.

In this week's Big Ideas Learning and National Geographic Learning Blog, I would like to present some approaches to classroom questioning and discourse. These ideas can be used by teachers to scaffold the expectations of mathematical thinking by utilizing a hierarchy of questions and promote productive math discussions. At a time where learning is still taking place remotely, it is essential to consider what is useful at this time and what we can take back into the classroom relating to quality questioning and effective discussions in math.

Using effective questioning techniques have long been regarded as a fundamental tool for creating productive math discussions (Nystrand et. al, 2003). The differences in students' thinking and discussions can often be attributed to the type of questions that teachers ask. However, research continues to highlight that 90% of teachers’ questions are surface-level, knowledge-based questions focusing on recall of facts (Nystrand et.al, 2003). Developing surface-level knowledge is essential. However, it is just as crucial to moving into the deeper levels of understanding to stimulate mathematical thinking that can arise from making connections, engagement in problem-solving and investigations. We need to consider the right time to move from surface to deep, without going too deep too quickly. Educational research continues to show that teachers ask few questions that encourage students to use higher-order thinking skills in mathematics (Nystrand, et, al 2003). So how can we use questioning to create productive discussions in math?

Within the context of developing a mathematical depth of knowledge and the ability for all students to transfer their knowledge from one context to another, it is useful to ask different types of questions at the various stages of the learning to promote classroom discussion. This may include planning questions for discourse and questioning or tuning in to a new concept by teaching surface-level concepts before moving into deeper-level knowledge that requires connections and conceptual understanding. These questions can be used by the teacher to guide students through investigations and to stimulate their mathematical thinking. Another function of these questions is to gather information about the students' knowledge and strategies. In previous blogs, I have discussed the use of the SOLO Taxonomy to develop and differentiate what surface and deep levels look like and how the verbs that are associated with each of those levels can assist in developing the appropriate questions for the different levels within the learning sequence.

### 1. Tuning into math -- clarifying and prompting questions

These questions are used to inform teachers of what the students know and consider their prior knowledge. These questions take the form of open-ended questions that focus the students’ thinking in a general direction and give them a starting point. They can be questions such as:

- What does this remind you of?
- What are some examples of ... ?
- How could you sort these?
- How many different ... can be found?
- Tell me more about …

### 2. Questions that affirm surface-level understandings

These are factual questions that ensure that students understand the basic concept of what is being taught. The questions that are considered either right or wrong and often rely on working memory. They do not require making connections, rather knowing the answers.

- What happens when we ...?
- How many ways can you find to ...?
- What can be made from ...?
- How can you order these?
- What are the specific characteristics of …?

### 3. Questions to stimulate and engage students in mathematical thinking by making connections and going deeper

These questions assist students to focus on strategies, connect to previous experiences, and help them to see patterns and relationships. This aids the formation of a robust conceptual network. The questions can serve as a prompt when students become 'stuck.' Teachers are often tempted to turn these questions into instructions, which is far less likely to stimulate thinking and removes responsibility for the investigation from the child. It is essential that students have the surface-level knowledge and understandings about the specific content before going deep or asking these questions.

- What is the same? What is different?
- How can we apply this to another situation (a real-life situation)?
- How can you justify your answer?
- Why did you use that strategy?
- How can you group these in some way?
- What are some things you could try?
- Can you find more examples?
- Can you see a pattern? Can you explain it?
- How can this pattern help you find an answer?
- What do you think comes next? Why?
- Is there a way to record what you've found that might help us see more patterns?
- What would happen if ...?

When considering the way to use questioning in our current state of remote learning, there is a temptation to ask the whole class the following questions:

- Are there any questions?
- Does that make sense?
- Does that help?

There is rarely a response when teachers ask a more generalized question as students don't want to ask what they see as something they should know or are often embarrassed to ask. Suggested online questioning tools include Google Forms, Kahoot, and Quizlet. Additionally, students can submit video recordings of themselves using applications like Flipgrid. Teachers should provide timely, specific, and instructional focused feedback on questions answered via these applications and bring it back into the next class to then use to promote classroom discussions. Here are a few more useful digital applications.

When using questions to promote discussions, apps such as Socrative, Microsoft Teams, Padlet, and Google Classroom are great options to consider. Like in the classroom, it is useful for students to have the chance to answer and develop their questions as well as have the opportunity to respond to questions in a discussion board format to encourage collaboration and idea sharing leading up to the discussion. Teachers can set up shareable documents so that students can collaborate in small groups. They can read and comment on one another's work.

Whichever app is used, as teachers, we must consider the pedagogical benefits and purpose of using digital technology for communication and collaboration with others. At the end of the lesson, try and evaluate your practice by considering if your questions were posed at the right time. What discussions took place with these questions as prompts throughout the lesson (either surface or deeper stages of their understanding)? Were there times that questions could have been asked throughout the lesson? How did this impact the discourse and discussions? Did everyone participate?

Effective discussions in math help students think, question, and problem solve effectively. Many students are technologically savvy, critical, and divergent thinkers who are becoming active and informed citizens. They want to know not just what they are learning, but why they are learning it. Giving voice to students allows them to raise their understandings, ideas as well as share their thoughts collaboratively with their peers.

Reference:

Nystrand, M., Wu, L. L., Gamoran, A., Zeiser, S., & Long, D. A. (2003). Questions in time: Investigating the structure and dynamics of unfolding classroom discourse. Discourse Processes