Three Underutilized Mathematical Language Routines
Newer curriculums are beginning to embed Mathematical Language Routines in their daily lesson plans. It may surprise educators that despite being shared in 2017 by the Stanford Graduate School of Education, they may already have experience and understanding of the application of these routines. Most have connected popular structures such as Number Talks, Three Reads, or Which One Doesn't Belong. However, the eight categories of Mathematical Language Routines (MLRs) include some of the most widely used yet little recognized avenues for meaningful mathematical classroom discourse.
Same/Different Many are familiar with which one doesn't belong, however under MLR7: Connect and Compare, resides a simple yet underutilized structure called Same/Different. The idea is basic yet flexible. Display two mathematical figures side-by-side and prompt students on how the two are the same and different. Same/Different is accessible because it limits the number of stimuli down to two, without overwhelming cognitive demand on learners. The figures are generally visual in nature, but can also represent expressions or procedures.
Co-Crafting Co-crafting is a diverse routine that has taken on many forms, however the core idea is to allow students to explore the context of a problem before applying values or procedures to solve. Generally, this appears in lesson plans as numberless tasks and word problems, however co-crafting has three broad categories. Co-crafting questions provides students with a context without a problem to solve, allowing students to create their own questions using the information given. Co-crafting problems gives students information without a context allowing students to create their own familiar setting for the math that they will utilize. Co-crafting scenarios allow students to analyze visuals to ascertain what is happening in what they see, and can take the form of a variety of graphs with key information removed before being revealed bit-by-bit.
Information Gap tasks are usually written off due to the fact that very few resources exist to support its implementation. Despite the perceived effort needed to plan and prepare, many info Gap activities require minimal set-up. Information Gap refers to a collaborative problem where all of the information resides within a group, however no one person has everything they need to find a solution. This may be a group task where everyone has one piece of the puzzle, or a partner activity where one person has the context in question while the other has the data needed. Additionally, Information Gap activities can take the form of announcing or presenting a value or expression that may appear in some fashion or representation somewhere in the room, allowing students to apply their own meaning and potentially uncovering misconceptions.