Teaching with and through Maps

Background and Content Rationale

In the unit, The Touchstone Atlas, students will construct an atlas of self-created maps that reflect their experience in navigating the world and transfer the skills they used in the creation of their maps to navigate unfamiliar concepts encountered in later units.  The composition of an atlas is similar to the way a voyage is planned, argues Jacob, further asserting that “the didactic clarity moves through an order of exposition that is also an order of viewing.”⁶  The order through which concepts will be highlighted and uncovered in creating a didactic artifact intends to foster students’ ability to both internalize and explain their learning to one another.  Students will journey from creating a map of their personality on a Waterman Butterfly Map Projection template (where they will make intuitive decisions about scale as they assign personality traits to differently sized land masses on the map); to determining scale factor on scale drawings and maps; to understanding scale factor as k, the constant of proportionality; to recognizing that a globe necessitates a new way of measuring and intuiting that pi is the constant of proportionality between the diameter of a circle and its circumference. This progression follows the scope and sequence of 7^th grade content as outlined by DCPS with use of the Illustrative Mathematics curriculum, ensuring that students will remain on pace in completing Required Curricular Tasks (RCTs) allowing for their data to be analyzed with the data of their peers across the district. While construction of this unit employs backward planning given the standards assessed on the RCT, the assessment is viewed as one opportunity to demonstrate learning transfer, rather than as the apex of the learning. The touchstone atlas students construct will promote sense-making, a skill that prioritizes critical thinking and application over memorization of procedures to address particular test question types.

The usefulness of a map is determined by both the maker and the user. Maps are interdisciplinary, lying at the intersection of art, science, history, and math. While the creator has motivations for the emphasis or diminishment of certain information on their map, the motivations may not be clear to the user. The user may interpret things that were not intended. The obvious implication is that students will need to be discriminate about what they include in their maps—considering what they wish to communicate to observers. The larger goal, however, is for students to become, and recognize the ways in which they become a different audience for their own work as they learn new math concepts and language through mapping.  Students will discover that an artifact they created for one purpose can be used to communicate things of which they had no previous awareness.

When tasked with mapping at the outset of the unit, students will likely create maps with inconsistent scale. Reflecting on these novice maps in class discussion will serve to provide context for deriving the meaning of and necessity for scale in their drawings as the unit progresses. Further, as the year advances, students will find themselves drawing conclusions that will not only help them understand new information but also compel them to critique and revise their previous work when presented with new information. Students may notice patterns for solving more advanced problems outside of the prescribed order of the scope and sequence. This occurs because in promoting sense making, idea expression is encouraged. In these instances, “it is our responsibility as educators to structure, highlight, and bolster these opportunities, making explicit the many different ways that mathematical ideas are communicated, rather than acting as “the keepers’” or “the givers” of language.”⁷ 

Maps created in the Touchstone Atlas unit will be used to create a touchstone for connections in future 7th grade units to shift from focusing on culminating the unit with a single capstone. The term capstone implies that the job has been completed and marks a crowning achievement. Meanwhile, a touchstone provides a reference opportunity by which to test or investigate something new. Rather than placing a capstone on a unit and moving on to the next seemingly unconnected unit, students will build a touchstone by creating a portfolio of maps, or a touchstone atlas which encourages its own revisiting and unpacking when students are presented with new types of problems to solve. Students will be encouraged to consider how their previous experience can help them make sense of patterns in new problem types, demonstrating learning transfer by applying acquired skills appropriately while also remaining open to considering new ways of navigating unfamiliar terrain.

The goal of the Touchstone Atlas to preview and ground the major work of the 7^th grade curriculum is lofty but necessary. Students need opportunities to connect with material in various ways in order to experience the level of transfer required to perform on assessment items requiring them to apply multiple skills and concepts at once. In the 2024-2025 school year, 85% of students enrolled in my 7^th grade math class scored in the two or more grade levels below band, with 72% of students placing in three or more grade levels below band on the beginning-of-the-year diagnostic. Many of them enter the class having never been told that they have demonstrated mastery on an exam, so aiming for conquest in math is not a natural inclination—people tend to conquer things when power is within reasonable reach. Building a touchstone atlas is an aim to put a means of connection and learning transfer in reach for all students despite their incoming placement level. Learning transfer requires students to remain engaged and connected with content instead of separating content into ‘can master’ and ‘cannot master’ categories. When the goal shifts from conquering step-by-step procedures to connecting with and remaining curious about content, students develop critical thinking skills that transfer.