Depth and Complexity in Math? Yes, Math!

kids and depth and complexity

It is widely understood that the Depth and Complexity Framework is the differentiation solution that provides instructional tools to empower your students and inspire them to become independent thinkers and creative problem-solvers. The pedagogical approach of Depth and Complexity is unique because it is applicable across all subject areas and grade levels. It simply adds a deeper level of complexity and rigor to any content – especially math!

Deep and Complex teachers start with a plan! Ask yourself three easy questions…

Which icons fit?

Math units and concepts are centered around your state or district standards. So, ask yourself, “Which icon or icons fit naturally with my standard?”

Example: A 5th-grade Geometry standard states, “The student applies mathematical process standards to classify two-dimensional figures by attributes and properties. The student is expected to  (A) classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.”

It is easy to see that the iconic prompt of Patterns would be useful here to focus students on classifying the attributes and properties of 2D figures. Another iconic prompt that fits well is Rules. Once students classify the patterns, they will need to focus on the hierarchy of the 2D shapes to show their understanding. 

How will students demonstrate their understanding?

Gone are the days when students are sent home to practice dozens of math problems on their own. An effective teacher thinks through the steps necessary for students to learn a new concept and show their understanding. Then they create meaningful ways for students to discover mathematical processes and internalize concepts. 

Using the 5th-grade Geometry example standard, the teacher should first invite students to observe a variety of model 2D shapes and document the patterns they notice. The class would then share and discuss their observations. Next, small groups would work together to classify the observed patterns and arrange them into a hierarchy. Small groups would then present their findings to the class, and the whole group would work together to determine and justify the best hierarchical presentation. By allowing students to observe and discover the Patterns and Rules on their own, the deep and complex teacher allows them to lead their own learning and solidify their understanding. 

How can I differentiate this concept?

We all know that the one-size-fits-all approach to teaching is antiquated and does not meet students’ needs. Providing differentiated learning experiences when you are tasked with teaching a single concept can be tough. Never fear – the Depth and Complexity Framework makes differentiation easy! The iconic prompts are naturally differentiated. Every student approaches new learning with their own schema. Pairing their background understanding with the icons as a verb to cue thinking, each child is free to develop their own interpretation of the concept. For example, one student may observe the models of 2D shapes and notice the patterns of sides and corners. Another student may look at the same models but have more experience with vocabulary and notice the patterns of vertices, parallel lines, and congruent angles. 

Another approach to differentiating a concept is to allow students to choose their own icons to focus their thinking. This method puts the impetus of learning on the student’s shoulders and motivates them to take charge of their thinking to show mastery of a concept. Using the 5th-grade Geometry example, a teacher would introduce the concept using Patterns and Rules and invite students to choose another icon to focus their thinking during independent practice. One student may choose to stick with the modeled iconic prompts and add Details to concentrate on specific facts and attributes of 2D shapes. Another student may choose to add Multiple Perspectives and dig into the different ways in which 2D shapes can be classified based on various views. 

To see some math planning in action, check out the following clip from this fall’s online summit with one of our master trainers, Daniel Brillhart. Daniel teaches advanced mathematics to gifted elementary students and shows how easy it is to integrate Depth and Complexity into math.

Like what you see? The Depth and Complexity Library contains a new subscription called The DC Buffet! This subscription consists of over 40 short clips that are searchable by subject area and grade level – and it is growing every day. Plus, if you want to dig deeper into a concept, there are 1-hour courses available with videos and assignments for PD credit. Sign up now!

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