Task link: Number Transformer Challenge. Linear relations, rate of change.
I used this task with my Grade 9 students to introduce the linear relations (rate of change) unit. Colleagues seem to ask for direct instructions about how to build tasks into the classroom so this post gives an example of how I used this particular task.
- My students enter the classroom and I visibly randomize them into groups of three. Through experience I have found groups of three to be the ideal. To randomize the students I use a deck of cards or the iPad app Be Seated.
- The groups find a vertical surface to write upon (white boards, chalk boards, windows, glass on the doors. Anything that dry erase markers will erase from). Each group will have one white board marker.
- In this task I provided each group with one handout. (often I read the task aloud only once). The groups will work on the task. I will have the groups switch the job of the “recorder” once in a while by calling out, “switch the pen.”
- This task I witnessed most groups inductively reason the linear equation from a table of values (students seem to naturally construct a table of values). Some members of the groups took over the task but that was ok. At the end of the task the examples on the board were produced by the students.
Day 2/3 Tutorial with graphs, table of values and equations.
I carried these student produced examples over the next two classes to build connections between data points, rates of change, constants and graphs.
- I used DESMOS graphing calculator for students to plot the points from the table of values produced on day one (this was accomplished in randomized groups, usually each group had one person with a device to use with DESMOS).
- I was apparent that the side lesson I needed to provide was guidance related to the algebra required for building a table of values from a linear equation.
Great task. Thanks youcubed.org (youcubed.org provides a fantastic assortment of tasks)
Communities of Character.
If you ask adults about their experiences with mathematics most will have a traumatic story that dates back to elementary school. They can recall who was good at math and who was bad at math. The idea that everyone has skill at math is not even considered.
As a mathematics educator I am deeply situated within an education “community” (ironic how we use that term) which almost single handedly is responsible for the work that reinforces the individual. Test based assessments that focus on algorithms rather that concepts. Ranking students as “regular” and “modified”. Mathematics as the “gatekeeper” for university entrance. Entrance to university perceived as being based on marks alone. Teachers feeling judged based on the accomplishments of their students on standardized tests.
“But we live in an era and under a testing regime that emphasizes individual accomplishments, not community cohesion. Even when schools talk about values, they tend to talk about individualistic values, like grit, resilience and executive function, not the empathy, compassion and solidarity that are good for community and the heart.” (David Brooks, Communities of Character. New York Times, Retrieved November 27, 2015, http://mobile.nytimes.com/2015/11/27/opinion/communities-of-character.html?_r=0&referer)
The mathematics classroom seems to be a microcosm of the “haves” and the “have-nots”. “P or not P”. There is no space in between. Brooks’s article (along with some study of Socratic education) led me to reconsider what the space in between consists of; this space contains the interactions between the pupils. Within these student interactions teacher look to find the learning, the questioning, the socratic dialogue critical to move students beyond their current knowledge. This is the construction of new knowledge to help narrow the gap between the “P and not P”.
Communities of empathy are a powerful place to look for what educationally is required in a classroom setting to help students develop valuable skills that will move them all forward and keep them learning. Everyone has a place of value in a classroom community.