Mathematical Habits of Mind: Justify Why

Justifying Why is a Mathematical Habit of Mind that helps us understand and explain why a math rule or statement is true. By using things like patterns, structure, and other math knowledge, we can understand if an idea or solution is always true, sometimes true, or never true. This skill helps us understand math better and have deeper discussions, which can empower us to tackle more complex problems. To practice this skill, we can explain our answers and do tasks that ask us to justify why a rule works. We should also practice justifying both informal strategies and commonly used procedures, and think about if a generalization will work for all cases or just some cases when we explain why it's true.

Deciding on a family pet is an example of Justifying Why. Suppose a family is contemplating between adopting a dog or a cat. They justify their decision to adopt a dog based on their active lifestyle, the companionship they seek, and the time they have to devote to pet care. These considerations are drawn from their understanding of pet behavior and their assessment of their own daily routines. After living with the dog for a few months, they reflect on their decision. They find joy in active play and companionship with the dog but realize the time commitment was underestimated. This reflection helps them to acknowledge the validity of their initial justification and to learn from the aspects they underestimated, enhancing their decision-making process for future scenarios. This simple process of decision making, justification, and reflection mirrors the Mathematical Habit of Mind Justify Why. It encourages the practice of logical thinking, reasoning based on evidence, and learning from reflection, which are skills valuable not just in math but in various aspects of life.