*Sharon Linde*Show bio

Sharon has an Masters of Science in Mathematics and a Masters in Education

Lesson Transcript

Instructor:
*Sharon Linde*
Show bio

Sharon has an Masters of Science in Mathematics and a Masters in Education

Learning math includes low-level questions of recalling information, and high-level questions using analysis, creativity, and evaluation. See these three skills in higher-level math questions to see what makes high-quality questions, whether they are open-ended or not.
Updated: 11/02/2021

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.

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 here. A teacher can use the data 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.

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?'

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?'

This higher-level math question is asking the student to count the gumballs, but it goes further by asking the student to think about arranging the gumballs into sets. The student is applying skills to solve problems by analyzing, creating, and evaluating.

An open question spurs conversations between students as they debate their thinking. What do these math talks look like?

Asking quality higher-level questions in math leads to rich conversations. These questions can be between a pair of students, a small group, or a whole class. The teacher is an important role model in promoting good dialogue. Students should be taught how to share their reasoning about their answers.

Creating opportunities for higher-level conversations often gives students tools to learn not only how to think in a deeper way but also how to talk about their thinking. Asking and answering higher-level questions in math sets the groundwork for students to be reflective and metacognitive. The hope is that students will also use these important life-long skills outside the math classroom.

Higher-level math questions require students to think more deeply about their work. Compared to low-level questions, which focus on recall and memorization, higher-level questions generally ask students to analyze, create, and evaluate. Teachers can create higher-level math questions by focusing on asking open questions - those that have more than one answer and path for a solution, that are challenging and engaging and are debatable.

In addition, teachers should often foster rich conversations about problems and solutions. These math talks help students take their thinking and learning to another level, allowing students to defend their thinking and listen to others' thoughts and processes as well. Teachers should model how to dialogue in math, with the hope of showing students that thinking about their thinking is a skill they will use for life.

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