Higher Level Questions for Math

Instructor: Sharon Linde
An important part of teaching includes asking questions. Teachers need to push students to think deeply by asking high-level questions. Read on to learn what high-level questions are and how to apply them to teaching math.

What Are Higher-Level Questions?

The focus on education today has shifted from students being able to recall information to a deeper, more reflective type of thinking. Have you noticed how curriculum now asks questions on a higher level? High-level questions ask students to be metacognitive, or think about their thinking.

Compare high-level questions to low-level questions, such as those that simply require students to recall information. When memorizing math facts, students don't need to use much processing information. High-level questions require students to take what they know and apply it in different ways, such as analyzing, creating and evaluating. Not familiar with these terms? Here's a brush up.

Analyze, Create, Evaluate

Planning for high-level thinking means developing lessons that push students to use taught information in new ways. Students must apply learned knowledge, which means you can tell whether or not they truly grasp a concept. Three high-level skills are top of the heap.


To analyze a math concept, students need to be able to understand the base concept and think about it differently. For example, a student may be given two sets of data and asked to compare and contrast, as in the example below.

Example of Analysis for Two Sets of Data

A teacher can use the data above to ask questions like 'What soda characteristics seem to be important to students?'


Another high-level skill asks students to create. This broad term is used to describe any creation made to represent understanding of mathematical concepts, ranging from a diagram to a more expressive type of art project. In some classrooms students draw pictures to show their understanding of a problem. Students might also create math games.


Finally, students applying high-level skills are often asked to evaluate. This doesn't mean they're given a test. In fact, the opposite is true. When using evaluative skills in math, students are showing their understanding by determining if a problem or answer makes sense.

Evaluative questions include:

  • What would happen if...?

  • What would changing X do to Y?

  • Which part is the most important and why?

Do you see how analyzing, creating and evaluating are more complex math skills than lower-level skills, such as recall? Great! Now let's take a look at some qualities of higher-level questions in math.

Characteristics of High-Quality Questions

High-level math questions involve analyzing, creating and evaluating, but also have a few more qualities in common.

  • A high-level math question often has more than one answer, such as 'Which question is the most challenging to you?'

  • Students using high-level math thinking usually are asked to synthesize, or pull together several operations. For example, 'How does X affect Y if you add Z?'

  • High-level math thinking presents problems that can be solved in different ways, like 'How is this question similar to X?'

  • Often a higher-level question creates a spark of interest from students, making them want to explore further. 'How would you have taught this skill using a video game?' is a sample question along this scope.

  • High-level math questions are challenging yet engaging, such as 'What is the point of completing Step 1?'

Open Versus Closed Questions

Questions teachers ask can either be considered open or closed. However, higher-level questions in math are open. Open questions spur deeper thought with an answer that goes beyond surface thinking, while closed questions simply require memorization to solve a problem. Let's look at a closed and open question.

Closed question: How many gumballs are in the bowl?

Do you see how this is a closed question? There is just one right answer, and to get the correct answer the student merely needs to count the objects. Here it is as an open question:

Open question: How can you organize the gumballs to make them easy to count?

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