In her book Mathematical Mindsets: Unleashing Students' Potential Through Creative math, Inspiring Messages, and Innovative Teaching, Jo Boaler lists six ways to change a ordinary activity into a rich mathematical task. The use of any or all of the six ways described below will increase a tasks "richness" and will help students to think like true mathematicians.
1. Open up the task so there are multiple methods, pathways, and representations.
2. Ask the problem before teaching the method
3. Ask the problem before teaching the method
4. Add a visual component and ask students how they see the mathematics
5. Extend the task to make it 'low floor' and 'high ceiling'
6. Ask students to convince and reason; be skeptical
Incorporating one or all of these six changes does not need to be difficult. I saw a great example while visiting the classroom of a science teacher earlier this week. He was teaching a chemistry class where he was asking students to find the density of irregular shaped objects. The students were given an overflow cup and a very short list of instructions.
| DIRECTIONS |
First, watch the following video of Archimedes
Then, design an experiment to measure the density of 4 irregularly shaped objects
Next, create and design a data table for data collection.
Finally, come up with a way to represent your results.
I have personally seen this same activity presented to students with a full set of step by step instructions that take away the students imagination and opportunity to struggle and learn. This way, the task is wide open for the students.
All six of Jo Boaler's ways for making a task rich can be met with this simple set of instructions and with a purposeful instructional pedagogy that allows all students to enter the activity, use their creativity, and explain their thinking Instead of telling the students what to do. This teacher let them figure out what to do and how to represent their results. He did not have to search the internet for a creative and rich tasks on density, he only needed to make simple changes to an activity in front of him.
If you have traditional STEM task that you'd like to develop into a rich one, please do not hesitate to reach out to me. I would love to help you develop your idea.
This post brought to you by Dan Devine, Secondary Implementation Associate
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