To understand a student’s strengths and struggles read all about ten essential questions to uncover what students know about math.
Before we get started with the nitty-gritty teacher talk, if you are wondering what questions to ask students about math, grab my free guide.
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How I Figured Out What Essential Math Questions to Ask
Many times, while teaching a math lesson, knew students weren’t making the connections to be able to understand a concept or skill. I needed one quick question to be able to “see” their thinking. If I could pinpoint exactly what they did and did not understand, I could provide very targeted support to help them get over the “hurdle”.
The types of questions I needed to ask were often questions that students would need to rely on conceptual understanding to be able to answer. For example, if we had just finished working on a lesson on equivalent fractions and I asked a student if 3/6 was larger than 8/14, I would be looking for the student to explain that 3/6 is the same, or equivalent to ½ and 8/14 is a little more than ½ because 7/14 would be half. So no, 3/6 is not larger than 8/14.
What Did Their Answers Tell Me?
Often, when I asked the right questions and really leaned in to listen to the answer, I learned just as much from what students didn’t say as what they did say. Students who are able to communicate their thinking were often further along in conceptual understanding than those students who struggled to find the right words or who had approached math as a series of memorized facts.
I learned so much by listening, and observing. If I ask a student what the sum of 300 and 675 is, I am observing their strategy of adding these two numbers together. Are they adding the hundreds first, then adding on the 75 afterwards? Are they trying to visualize the two numbers stacked vertically so they can use the traditional algorithm? Are they using their fingers to support counting? Are they able to “think out loud?”
It’s Not About the Right Answer
I can’t stress this enough – it is not about the right answer. It is the reasoning and strategy behind the problem solving that is critical to understand. Once you know the caliber of their thinking and how they attempted the problem, you have a front row seat to their thinking, their understanding, their use of strategies, and their ability to reflect and connect their thinking through communication.
Let me give you an example to illustrate this idea. If you asked a student what the difference is between 65 and 85 and the student asks for a pencil and paper so they can use a traditional algorithm to subtract, then you know the student’s number sense is not strong enough to develop strategies for working fluently with numbers. If the student begins by counting up from 65, either by 5’s or 10’s that tells you the student recognizes several things: 1) The difference between two numbers can be found with a strategy to “add on” to the smaller number, 2) adding 10 to any number will result in the same number in the one’s place.
What if you ask a more difficult question like what is the difference between 55 and 94? A student with great number sense strategies may say something like, “I added 40 on to 55 which is 95, then I took one away to get to 94, so it is 39.” For a more in-depth look at using place value to support student’s ability to subtract check out A Different Way To Teach Subtraction
Establish a Routine For Asking Questions
Have you ever had that moment as a student when you were working away and suddenly noticed the teacher looking over your shoulder as you worked on an assignment? I don’t know about you, but I absolutely froze up and my brain instantly stopped working.
This is the opposite of what we want students to feel. They need to be comfortable and relaxed if they are going to take their time to think, reason and then communicate about it. The more conversations you can have in the classroom about how people are thinking about math and the strategies they are using to figure things out, the more clues students will give you about how they are thinking.
How Do I Know What Questions To Ask?
Well, it depends on what you want to know. It is important to uncover what understandings students have about certain topics like:
- Place Value
- Adding and Subtracting
- Order of Numbers
- Properties of multiplication and division
- Fractions
- Decimals
- Powers of Ten
- Volume
- Patterns
Let’s say you are going to start teaching rounding to third graders. You want to start with rounding to the nearest ten. The first thing you may want to know is if students can count by fives from 0-100. This is a prerequisite skill that they will need to be successful in rounding numbers to the nearest ten. The second prerequisite skill they need is to be able to identify what two tens a number falls between. If students have a strong place value foundation they will be able to answer the question, “If you count by tens, what two multiples of ten is 84 between?”
There are hundreds of great questions you can ask students to uncover what prerequisite skills and understandings they have about math. Need more ideas? Check out my free guide 10 Essential Questions to Uncover What Students Know About Math. This free guide includes information on how to spot students’ strengths and struggles.
When Should I Ask These Essential Questions?
These questions are great for many different situations. I keep a few questions ready for the students who finish fast and seem to pick up concepts quickly. Once I am assured they are solid in their understanding, I can confidently send them off for a “next level” activity that will stretch their thinking a bit.
Sometimes you may have a student who you just can’t quite pinpoint why they are not thriving. A hint: many times problems can be traced back to place value, even in the upper grades! A great resource for upper elementary place value ideas is a blog post by Teach, Think, Elementary Place Value in Upper Elementary
Ask questions to understand how they are with basic number sense. Sometimes knowing what strategies they use to add and subtract simple numbers will give us a wealth of information about next steps for them.
Final Word on Using 10 Essential Questions to Uncover What Students Know About Math
Seek to understand. We are all learners of math and the classroom is really a learning lab where we are experimenting with what and how to learn. The more students participate in their own learning experience, the more engaged they will be. Using essential questions to uncover what students know is important to move them along the journey of learning math, but it also models seeking to understand each other and asking questions to learn more about what students need for the ultimate learning experience.
