# Depth Of Knowledge For Math

Many teachers are looking for ways to make their math lessons more engaging, and asking students to apply their knowledge in new contexts is one way that can help motivate them. Depth of knowledge (DOK) is a framework for helping teachers think about how well students understand the mathematical concepts they are learning and what it means for them to be able to apply those concepts in new situations. In this article I’ll explain what DOK involves and why it’s useful for teachers and parents who want their children to learn math concepts deeply.

## Depth Of Knowledge For Math

### 1 What DOES Depth Of Knowledge Involve?

Depth of Knowledge is a way of describing what students know and can do, based on their age. It is used to help teachers plan lessons that match the needs of each group in their class.

In Depth Of Knowledge, teachers identify where students are at on a continuum from simple recall to abstract thinking. For example, at the beginning of the year, your students might be able to recognize and write numbers up through 20 but not much beyond that. As they progress through school, they would move toward higher levels of learning including calculations with larger numbers and solving multi-step problems such as long division or equations with fractions.

### 2 Higher Order Thinking Skills

Higher order thinking skills are the skills that require a student to analyze, interpret, apply, evaluate and create. These skills are important for students to be able to think critically and solve problems.

When teaching math it’s important that you teach these higher order thinking skills in all of your lessons.

### 3 Bloom’s Taxonomy

Bloom’s Taxonomy

The Bloom’s Taxonomy is a classification of cognitive learning objectives that defines six categories of learning, from the lowest level (remembering) to the highest level (creating).

Each category has three sub-categories:

- Remembering – what you have learned
- Understanding – how things work and relate to each other. It requires students to demonstrate their knowledge by explaining its relation to other topics in class, or showing their understanding of its significance. This requires them to think critically about a problem or question posed by an instructor.
- Applying – using information in new situations, such as explaining how this applies in your own life or how it works with other ideas being studied. For example, if you were studying relationships between countries and then had an assignment on which country would win an Olympic event based on population size vs GDP per capita vs number of gold medals awarded so far historically (they actually did this!). Your answers would be applying what you’ve learned about relationships between countries and sports teams/athletes because they’re both teams!

### 4 Webb’s Depth of Knowledge Framework

When you think about the level of knowledge a student has, there are many ways to describe it.

For example, one way is by using Webb’s Depth of Knowledge Framework. In this framework, students are shown a learning objective and then given opportunities to demonstrate their understanding in different ways. The idea is that students will learn more deeply when they have multiple opportunities to show what they know.

There are five levels of knowledge:

- Level 1 – Reciting information (telling)

This is where most students are on the first day of school! They repeat back what they’ve been told without really understanding it on deeper levels. An example would be when a teacher asks you if your desk needs paper or pencils—you answer right away even though you don’t know why those things would be needed at this time or place during class time! This type isn’t really thinking critically about what they’re saying either; instead they simply give an answer based off how others may react if said differently than expected (eagerness).

### 5 Dr. Norman Webb – http://www.crcpd.org/

Dr. Norman Webb is a professor of education at the University of Florida and a leading expert on DOK. His research focuses on the role of knowledge acquisition in learning, particularly as it relates to mathematics instruction. Dr. Webb has developed the Depth of Knowledge Framework (DOK), which describes levels of knowledge required for various tasks within higher order thinking skills that are used across all subject areas and grade levels.

Dr. Webb’s DOK model consists of six levels:

- KNOWLEDGE: Basic facts and concepts necessary to perform a task;
- UNDERSTANDING: A more sophisticated understanding that takes into account specific details;
- APPLICATION: An understanding of how information can be used in new ways or applied to new situations;
- ANALYSIS: The process by which information is broken down into individual parts or components so we can examine them more closely;
- SYNTHESIS: The ability to put pieces together into an overall picture or concept; AND COGNITION/REFLECTION (COGNITIVE PSYCHOLOGY): This level includes both thinking skills such as problem solving and decision making, as well as self-awareness and interpretation skills

### 6 Depth Of Knowledge For Math

Depth of Knowledge for Math is a framework that can be used to assess student learning. It breaks down the curriculum into different levels, each with its own set of expected student abilities and understanding. The first two levels are foundational, while the next two are more advanced and involve higher-order thinking skills.

The first level involves basic operations, such as adding and subtracting numbers up to 10 or 20. This level also includes constructing written numbers using ones, tens and hundreds place value; identifying some number sentences (addition or subtraction) that have been written backwards; and recognizing numerals 0 – 5 when they appear in oral language contexts.

The second level involves mental computation strategies for addition and subtraction involving small numbers (up to ten); understanding number properties including comparing two digit numbers using greater than/less than signs; counting objects from least-to most-or vice versa; understanding how many objects there are if they’re grouped together in twos/fours/sixes etc.; recognizing patterns such as “even paired with even” or “odd paired with odd.” At this stage students should also be able to recognize all ten digits 0 through 9 when these numerals appear in oral language contexts like sentence structure or conversation between people talking about math problems etc..

### Closing

Depth of knowledge is an important concept for teachers to understand in order to create learning experiences that are effective for all students. It is vital that teachers have a deep understanding of what depth of knowledge looks like and how this can be assessed through assessments such as Bloom’s Taxonomy or Webb’s Depth of Knowledge framework. The implications for school reform are vast when we look at adopting new methods of assessment with an eye towards understanding student thinking skills, rather than just rote memorization.