One of my primary teaching strategies was having my students think their own thoughts about mathematics in a way that was meaningful and valid. One of the activities I created to implement this strategy I call “Map of the Journey.” Like “Objects in a Bag”, it encourages reflective thinking about complex concepts.
The purpose of “Map” is to create a visual representation of the learning process. The activity is as follows: Students are given a topic, such as linear programming or rigid transformations; each student is also given a map with geographic features clearly marked (i.e., mountains, valleys, deserts, plains, rivers, etc.) The students have to list five or six main ideas about the topic and number them in some sort of order, such as importance, difficulty, relevance, or sequence. Then they write these numbers on the map where they think the geographic features best fit.
For each main idea, the students write a definition of the idea, a description of the geographic feature, and the reason why they think the two go together. By connecting the numbers sequentially, the students show their journey through the topic. They write a final reflection on what their personal “map of the journey” reveals about their learning process.
This activity was used to great effect and always got a positive response from the students. And their maps always gave me insight as to where they were in the learning process. It was mainly used as a formative assessment but it could also be used as a summative assessment.
As I go through my own learning process, I like to pause every so often and look at my own “Map of the Journey.” It gives me a better idea of what the universe is trying to teach me.