Welcome families! As the winter gets near, let's explore a powerful way to spark joy in math at home through Reasoning and Proving. What exactly is "Reasoning and Proving" in math? It's about explaining why something is true, or how you know. It's moving beyond just giving an answer to explaining the thinking process behind it. Whether a child is explaining why one season is better than another, or how they figured out how many cookies are left, they are engaging in reasoning and proving – a critical life skill!
Connecting it Back to the Classroom
Reasoning and proving is a fundamental "Mathematical Process" that students are developing from Kindergarten onwards. When a students learn to reason and prove, they build a much deeper understanding of the mathematics than if they simply memorize a series of steps or procedures. For example, knowing why 2+3=5 (e.g., "because if I have 2 and add 3 more, I get 5") is more powerful than just recalling the sum. This ability to explain their thinking is essential for problem-solving across all areas of mathematics and helps students make sense of the world around them.
Engaging in Reasoning and Proving at Home
Here are some ways to engage students in some reasoning and proving though everyday math conversations at home:
- Ask "Why" and "How": After an answer is given; or a choice is made, simply ask, "Why do you think that?" or "How did you figure that out?"
- Encourage Different Approaches: "Is there another way you could solve this?", “Does this strategy always work?” Why or why not ?” This shows there's often more than one path to a solution.
- Actively Listen: Give students time to articulate their thoughts, even if it's messy at first. Model curiosity, not judgment.
- Value the Process: Praise students thinking and effort, not just getting the "right" answer. "I love how you explained that!" , “I can really picture your thinking in my head!”
- Use Everyday Situations: "Why do you think this line for the cashier is shorter?" or "How do you know we have enough wrapping paper for all these gifts?"
A Fantastic Resource for Families: WHICH ONE DOESN’T BELONG?
A wonderful tool for sparking these conversations is "Which One Doesn't Belong?"
Visit Talking math with kids' website.
Present a set of four numbers, shapes, images, or objects. The challenge is that any of the four can be the one that "doesn't belong," depending on the rule or attribute you identify. For example, show four shapes: a red square, a blue circle, a red triangle, and a blue square. Some responses may be:
- "The circle doesn't belong because it's the only one without straight sides." (Reasoning about shape attributes)
- "The red square doesn't belong because it's the only red shape that is also a square." (Reasoning about color and shape)
- "The blue square doesn't belong because it's the only shape that's both blue and a square." (Reasoning about unique combinations)
The beauty of "Which One Doesn't Belong?" is that there's no single "right" answer. Instead, it requires students to observe, analyze, categorize, and most importantly, justify their reasoning. This naturally leads to rich discussions where they're compelled to reason and prove their thinking.
By making reasoning and proving a natural part of your family conversations, you'll be fostering confident, articulate mathematical thinkers.
Happy math talking!