There is a huge shift in mathematics education away from memorizing procedures and toward deeper conceptual understanding. How do we achieve that? One way is by asking the right questions. When questioning becomes part of your instructional routine, you might be surprised by the responses to what you thought was an easy question. For example, I asked a group of 4th graders, “What does fifths mean?” I thought that was a pretty straightforward question, and I thought they would be able to easily tell me that it meant the whole had been divided into five equal parts. Nope. Truth be told, it’s experiences like that that shift my instructional pedagogy. I knew at that moment that I needed to focus more on the questions I ask students. Enter guiding questions.
Where do good questions come from?
If you Google “guiding questions elementary math”, you will get lots of hits. As with anything on the Internet, some will be more useful than others. But it’s not so hard to actually develop your own. A great place to start is your standards.
I am working with my 3rd graders on fractions, so I started with the TEKS related to fractions. For each standard, I thought of questions I might ask that would uncover student understanding. Here is the list of questions I generated with expected answers:
- What is a fraction? (a whole that has been divided into equal parts)
- How can we represent fractions? (number lines, strip diagrams, pictures)
- What does the denominator tell us? (the number of equal parts the whole is divided into)
- What does the numerator tell us? (the parts we are counting)
- What is a unit fraction? (a fraction with a numerator of 1)
- Why is 1/8 smaller than 1/4? (the more parts the whole is divided into, the smaller the parts)
- How could you explain equivalent fractions? (fractions that name the same amount of the whole or the same point on a number line)
- How can you compose 3/4 with unit fractions? (1/4 + 1/4 + 1/4 = 3/4)
- What does fifths mean? (a whole that has been divided into 5 equal parts)
How can we use questions?
Now that I’ve got a list of questions, how do I use them? I find the most effective use of questioning is during small group instruction or conferences because of the interactive nature. While it’s certainly fine to have students respond to the questions in writing in a Math Journal, I prefer to hear a student’s response and be able to respond immediately in the event there is a misconception or probe further if their response is unclear.
I have started actually including my guiding questions in my lesson plans. The questions I generated above cover the entire unit for fractions, so I won’t ask them all in the same lesson. As I’m teaching a lesson, the questions just naturally become part of the conversation. Having them in my lesson plans reminds me to include them. Because skills are cumulative, the guiding questions become a valuable formative assessment. I want to make sure my students thoroughly understand what a fraction is and the meaning of the denominator before I begin my instruction on equivalent fractions. My guiding questions can help me determine if my students are ready to move on. An added benefit of using guiding questions is that it ensures our mathematical conversations include the use of key vocabulary terms.
If you have thoughts or resources related to the use of guiding questions, I hope you’ll share them in the comments!