Depth and Complexity: Ethics… In Math!?
Of all the prompts of Depth and Complexity, ⚖️ Ethics is my favorite. It instantly highlights controversy, grey areas, and takes students deeper into any content area.
Ethics (and depth and complexity in general) can seem least applicable in math. But here’s the problem: we’re often stuck thinking about math as practicing problems over and over. To add depth and complexity, we have to raise our sights above just practicing algorithms. We have to move students towards higher-order thinking and ethics is perfect for this.
Here’s how you can use the ethics thinking tool to add depth to math.
What Are Our Common Issues?
Rather than just trying to think about ethics in a single practice problem (say, 202 ÷ 7), consider posing this question to students:
What common problems (or ethical issues) do we run into when doing long division?
Let them think a while and then do a brainstorm. You’ll get a bunch of ideas from your students. Don’t be afraid to sit in silence as they think some more.
Ideas might include:
- I forget to line up the decimal places
- I mix up the order of the steps
- If I multiply wrong, the whole problem gets messed up
Keep going until you have 5 or 7 or so.
Now that you’ve brainstormed common problems (or ethical issues), you can move up Bloom’s Taxonomy. Raise the thinking towards analysis, evaluation, and synthesis. Perhaps we will:
- Group these issues based on their similarities.
- Rank the issues using some criteria (most common, most damaging, etc)
- Create long division problems that would lead to each ethical issue.
- Develop a children’s story explaining how to avoid these most common of problems.
This is one way to push past the “ok do more practice problems but this time they’re harder” differentiation anti-pattern. We’re getting kids thinking about their own thinking (aka meta-cognition).
Evaluate Multiple Methods
Whenever students have multiple ways to solve a math problem, we have an opportunity to discuss ethics. We can ponder:
- What are the pros and cons of each method?
- What are the ethical issues inherent in each method?
- When is each method most appropriate and most inappropriate?
Then, as always, move beyond mere identification and climb up Bloom’s:
- Is there a time that Method A is better than Method B? What about the reverse?
- Which method has the most serious downsides? The most limited upsides? The most specific uses? Etc.
- Can we create sample problems that are best solved with Method A? Method B?
- Develop a Mathemagician’s Handbook that instructs new students in how they can know when to use each method.
Rather than just practicing each method over and over, get kids using those higher-order thinking skills by focusing on the ethics of a method.
Reflection
The ethics prompt is fantastic for looking back on completed work. After homework, a quiz, or a test, take time for students to think back on the ethical issues they faced. Ethics is perfect for reflection.
I especially like combining ethics with patterns!
Looking back on my past three tests, I notice I have a repeating problem… To beat this pattern, I’m going to…
This, again, is moving students beyond just practice, practice, practice. We’re getting them thinking, not just memorizing.
Depth and Complexity should always move beyond just making a list. Get kids up to those higher-order thinking skills: analyzing, evaluating, and then synthesizing.