Depth of Knowledge (DOK) & Big Ideas Math

Webb’s Depth of Knowledge (DOK) provides a vocabulary and a frame of reference when thinking about our students and how they engage with the content. DOK offers a common language to understand “rigor,” and cognitive demand, in assessments, as well as curricular units, lessons, and tasks.


Level 1: Recall

Level 1 includes the recall of information such as specific facts, definitions,  and details, as well as routine procedures (perform a simple algorithm, provide/apply a formula, etc.).  The problem can be “difficult” without requiring deep content knowledge to respond to an item and (the problem) only has one right answer.

Some examples that represent but do not constitute all of Level 1 are:

  1. “Identify”
  2. “Recall”
  3. “Recognize”
  4. “Use”
  5. “Measure”
  6. “Multiply two numbers”

Big Ideas Math Level 1: Big Ideas Math High School; Algebra 1; Chapter 1, page 1.


Level 2: Skill/Concept

In Level 2, the focus is on applying skills and concepts, relationships, and main ideas and requires deeper knowledge than definition. Problems require students to explain how/why, and to make decisions on how to approach a problem or activity, whereas in Level 1, a student is asked to demonstrate, recognize, and preform an algorithm/problem.

Some examples that represent but do not constitute all of Level 2 are:

  1. “Classify”
  2. “Organize”
  3. “Estimate”
  4. “Collect and display data”
  5. “Compare data”

Big Ideas Math Level 2: Big Ideas Math High School; Algebra 2; Chapter 11.4, Exercise 12, page 624.


Level 3: Strategic Reasoning

In Level 3, the focus is on reasoning and planning in order to respond. Furthermore, problems require reasoning, planning, using evidence, and a higher level of thinking. Complex and abstract thinking is required and is often needed to provide support for reasoning or to draw conclusions drawn. In Level 3, more than one “correct’ response or approach is often possible. Certain activities and problems in Level 3 might include drawing conclusions from observations as well as requiring students to explain their thinking.

Some examples that represent but do not constitute all of Level 3 are:

  1. “Determine the equation and solve”
  2. “Interpret information”
  3. “Provide mathematical justification”

Big Ideas Math Level 3: Big Ideas Math High School; Geometry; Chapter 11.1, Exercise 39, page 600


Level 4: Extended Reasoning

In Level 4, the focus is requiring complex reasoning, planning, and thinking for the investigation. The cognitive demand of the task should be high and the work should be very complex with multiple steps. Students should be required to make several connections – relate ideas within the content area – and have to select one approach among several alternatives on how the problem should be solved. Level 4 activities include designing and conducting experiments, developing and proving, making connections, etc.

Big Ideas Math Level 4: Big Ideas Math; Blue, Chapter 8



Integrating Technology into a Math Teacher’s Classroom

The Common Core State Standards communicate many areas in which technology can be or should be used to enhance the learning environment for students. As states’ implementations of the Common Core progress, more schools are utilizing technology in their classrooms and integrating it more heavily into their curricula. Though technology plays a considerable role in most teachers’ daily lives, bringing it into classroom can be a challenge. What are ways that math teachers can implement and expand the use of technology in their classrooms?

Interactive Learning Tools
The Internet is full of interactive learning tools and activities that have been developed for specific math subjects. Big Ideas Math features a number of them in our Teacher Resources section that correlate directly to concepts in the Big Ideas Math series.

Graphical and Visual Representations
Tech-savvy teachers and novices alike can utilize programs like Microsoft Excel, PowerPoint, and Word to generate graphs and visual representations of concepts. There are free templates and instructional resources for creating these online. A quick Google search for Free Excel Templates for Teachers will provide many great options, or change the search query for subject-specific content. Presenting a graphical example of a ‘time value of money’ problem could make all the difference for a visual learner who has been struggling with the concept.

Connecting Classrooms
Teachers have the opportunity to connect their students with their peers all over the world thanks to technology. Two teachers who live across the country can arrange to have their classrooms connect via a video chat service like Skype to share a lesson. Teachers can develop word problems using relevant data such as the distance between the classrooms, population of each state/town/capital, and cost of living data. These adapted lessons will not only increase students’ engagement but also broaden their horizons as they interact with each other.

Additional Resources
In addition to the Teacher Resources provided by Big Ideas Math, the following websites also provide additional resources and suggestions for the 21st Century math classroom:
BrainPOP Math
Educational Technology and Mobile Learning
Innovate My School
Cobllaborize Classroom: Free Resources

Please share with us how you have successfully implemented technology into your math class!