Posted in: Aha! Blog > Eureka Math Blog > Implementation Support > Advancing Student Learning with Questions

As teachers, we ask a lot of questions. It’s part of the job. It’s how we learn about our students.

Questions serve a variety of purposes during instruction. We can use questions at the beginning of an activity to launch a task, during a lesson to informally assess, and while providing feedback to advance student thinking. Let’s look at how we can use intentional and purposeful questions to set students up for success, assess their understanding, and push their learning forward.

Questions help set up a math task and engage all students in the task.

At the beginning of a lesson or task, we ask questions to orient students and ensure they understand what they need to do. These questions also build engagement and buy-in from students. You might launch learning by asking questions like the following:

  • What do you notice about the problem?
  • What do we mean by _____?
  • What are we trying to figure out?
  • How is this task similar to one we’ve completed before? What’s new or different?

These questions open entry points into the activity for all students. They stimulate student thinking without lowering expectations by prompting or suggesting a specific solution path.

Questions allow teachers to individualize assessment and instruction.

As students work on math problems, you likely circulate throughout the room and monitor their progress. This is a great opportunity to ask questions to formatively assess and extend student thinking.

Assessing questions provide information about students’ knowledge and skills and help clarify what students understand about the work.

Advancing questions push a student to think in new ways to build their knowledge.

The following are general examples of assessing questions:

  • How did you figure this out?
  • Why did you draw this the way you did?
  • Why did you cross that out?
  • How do you know your answer is correct?

The following are general examples of advancing questions:

  • What would happen if we changed the number(s) to _____?
  • What is another method you can use to solve this problem?
  • What is a rule or formula that would work for all problems like this one?
Assessing questions can also help you find patterns in student work and inform how you conduct the Student Debrief or Lesson Closing.

Advancing questions naturally create differentiation because they allow you to meet students at their current point of success and move their thinking forward.

 

Let’s look at a specific example to clarify the roles of assessing and advancing questions. As you review the following work of three different students on a Grade 5 fraction problem, think about what each student might know and what would further extend their learning.

A newspaper’s cover page is 38 text, and photographs fill the rest. If 25 of the text is an article about endangered species, what fraction of the cover page is the article about endangered species?

 

Student A

Student A’s work is shown. Student A wrote the sentence, “The article is 6 fortieths of the cover page.” Below the sentence, Student A drew a rectangle and divided it equally into 5 columns and 8 rows. The 2 left columns are shaded. The bottom three rows of those 2 columns are cross-shaded. The rectangle is labeled 2 fifths on the bottom and 3 eighths on the left side.  To the right of the rectangle, Student A multiplied the fractions 3 eighths and 2 fifths to equal a fraction with a numerator of 3 times 2 and a denominator of 8 times 5. The result equals the fraction 6 fortieths.

Student B

Student B's work is shown. Student B drew a rectangle and divided it into 9 columns. Beside the rectangle, Student B wrote a question mark.

Student C

Student C's work is shown. Student C multiplied the fractions 3 eighths and 2 fifths to equal a fraction with a numerator of 3 times 2 and a denominator of 8 times 5. In this fraction, 2 is crossed out and renamed as 1, and 8 is crossed out and renamed as 4. That is set equal to a fraction with a numerator of 3 times 1 and a denominator of 4 times 5. The result equals the fraction 3 twentieths.    Student C wrote the statement “3 twentieths of the cover page is the article about endangered species.”

Students A and C arrived at a correct answer, but Student C identified a common factor in both the numerator and denominator, which resulted in a more simplified answer. Student A seems to have labeled the drawing incorrectly but still performed the correct multiplication. Student B is struggling to get started. Here are some questions you can ask to assess or advance each student.

Assessing Questions

Advancing Questions

Student A
  • How did you show 38 on your drawing? How did you show 25 ?
  • Did you start with the drawing or the arithmetic next to the drawing? Why?

  • What you labeled in your drawing as 38 actually shows 88. Why is that? How would you label your drawing now?
  • John solved this problem differently and said the article is 320 of the cover page. Is he correct? How do you know?
  • What if the problem started with different fractions, and 13⁄60 of the page was text and 750 of the text was an article? Would that be easy to draw? How would you solve that problem?
Student B
  • How does your drawing represent the information given in the problem?

  • How many vertical lines did you draw inside the big rectangle? What fraction of your big rectangle is each smaller rectangle?
  • How many vertical lines would you need to split the big rectangle into eighths?
  • What’s the other important fraction in the problem? How many lines would you need to split the big rectangle into fifths?
  • If you start with a new rectangle, how can you use what you learned to redraw the problem?
Student C
  • Why did you decide to multiply 38 by 2?
  • What does 38 represent in the problem? 25 ?

  • If 320 of the cover page is the article about endangered species, what fraction of the page is something other than the article? What fraction of the page is other text?
  • Carlos solved this problem differently and said the article is 640 of the cover page. Is he correct? How do you know?
  • Marie solved the problem and said the article about endangered species is 2340 of the cover page. Without doing calculations, how could you convince her she made a mistake?

 

Although each student’s response was unique, we found ways to advance each student’s thinking through questioning. Posing questions promotes reflection and thinking that will lead to deeper conceptual understanding and more meaningful connections between mathematical ideas. While every student is different, every student is capable of greatness. With well-placed, purposeful questions, we can advance each student’s learning and help them achieve their greatness.

Topics: Implementation Support