# Using Guiding Questions to Probe Student Understanding

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 youย *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,ย 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 experiencesย 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?ย
*(a whole that has been divided into equal parts)* - How can we represent fractions?ย
*(number lines, strip diagrams, pictures)* - What does the denominator tell us?ย
*(the number of equal parts the whole is divided into)* - What does the numerator tell us?ย
*(the parts we are counting)* - What is a unit fraction?ย
*(a fraction with a numerator of 1)* - Why is 1/8 smaller than 1/4?ย
*(the more parts the whole is divided into, the smaller the parts)* - How could you explain equivalent fractions?ย
*(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?ย
*(1/4 + 1/4 + 1/4 = 3/4)* - What doesย
*fifths*mean?ย*(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, soย 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!

I found this book to be a great resource…Good Questions for Math Teaching: Why Ask Them and What to Ask, K-6

Yes! I have that one on my bookshelf!

Thanks for sharingโฆI love this concept. Hope you can please share some k-2 example questions for more inspiration.

Thinking Theough Quality Questions is also another great read for how to form great questions.

Does anyone know of a good book for middle school questioning?

This was such a great read, and extremely helpful in getting out of the comfort zone in how math is being taught to our children!

Hi,

I am very interested in your online class and ordered the Guided math workshop book. My question is, our school uses Math in Focus text books and children’s math workbook, how do use my math curriculum with guided math. This is the piece of the puzzle that I can’s quite find.

We will discuss how to incorporate your current resources during the course of the book study. ๐

how well does this method work for a child going into 5th grade that has always had spiral method I really want to change her except I am unsure as what the difficulty in changing would do. any advice?

I’m not sure exactly what you mean by the “spiral method”, but good questioning will benefit any student!

I have been working on my questioning, particularly in the maths block. An idea that I got from my colleague was to create question prompt cards and wear them on a lanyard to remind me to refer to my questions! You can continue to change the cards to suit the current concept and store for reuse and/or have some general question prompts that live on your lanyard ๐

Hi, Donna! I’ve followed you for years! Do you have an email where I can ask you a math coaching question privately? Thank you!

I have a hard time creating advancing and assessing questions. Any help would be greatly appreciated.

Two great books that will help get you going are Good Questions for Math Teaching and Good Questions: Great Ways to Differentiate Mathematics Instruction in the Standards-Based Classroom.