Help Your Kids Think Like Mathematicians
When your students tackle a math problem, do they rush through to get to the “right” answer as quickly as possible? If so, they may be missing an opportunity to reflect and deepen their understanding, to practice thinking like a mathematician.
So how can parents encourage their students to pause and reflect productively on those challenging math problems?
Let’s start with …
Why Self-Reflection Matters in Learning
Education research shows that students who reflect on their learning have better academic outcomes than those who don’t. Multiple studies show self-reflection can help students:
• Become more confident learners
• Develop a growth mind-set that enables them to persevere through challenges
• Set goals and develop strategies to meet those goals
• Deepen the connections between new knowledge and prior learning
• Communicate their understanding to others
In fact, this is why self-reflection exercises have been incorporated into Connections Academy’s math curriculum. In these exercises, students are asked to reflect on how they feel about math, what their preferred problem-solving strategies are, and how they evaluate their own math skills, strengths, and weaknesses over time. In essence, students become aware of how they think, what they already know, and what they still need to learn about math, so they can take charge of their learning.
Applying Self-Reflection to Math Problems
The math Time to Talk sessions offered by many Connections Academy®–supported schools are one way we help students put these self-reflective skills to work. In this supplement to their usual math coursework, some students in grades 3–6 may be invited to attend half-hour LiveLesson® sessions to collaborate on a math problem developed by math specialists.
As Nicole Pulkkinen, a member of the team behind the program, explains, “Each problem is designed to start with a task that has many entry points to build students’ confidence and to provide multiple pathways for getting to a solution.” Teachers or math specialists facilitate Time to Talk sessions, asking open-ended questions that help students model solid mathematical reasoning.
With no single “right” route to the answer, students come up with different ways to solve the problems, defending and critiquing one another’s problem-solving strategies during their discussions. As they look for the most efficient solutions, students strengthen their understanding of mathematical concepts and practice their reasoning and communications skills.
Perhaps most importantly, the sessions provide a safe and inviting place to make mistakes and learn from them. In fact, the sessions are so inviting that Pulikken says most students who attend one of the sessions will return for more.
5 Questions to Support Mathematical Thinking
So how can parents and Learning Coaches help students become more reflective mathematical thinkers?
Whether helping your students with homework or calculating how long they will have to save in order to buy a new game, you can start by asking the same kinds of open-ended questions our math specialists use in our Time to Talk sessions:
1. What are you trying to determine or solve? Before your students dive right in, encourage them to take some time to see the problem in its entirety, to get an overall sense of it.
2. Can you describe the problem in your own words? Some students struggle with translating mathematical symbols. However, when you ask them to describe a problem verbally, they’re able to slow down and “see” the problem more clearly. For more visual learners, you can also ask, “Can you describe this problem with a diagram, chart, or picture?”
3. What do you think you should do first or next? Note the emphasis on “you,” meaning the student. As a parent and/or Learning Coach, you want to encourage your students to take ownership of their learning. So you want to avoid explaining how to solve the problem or, worse still, solving it for them. Instead, allow them to struggle a little so they learn to persevere.
4. What do you already know about the problem? Encourage your students to look at smaller parts of the problem or see similarities with other types of problems they’ve solved before. By connecting today’s problem to yesterday’s lesson, they solidify their understanding of the underlying concepts and make critical connections to prior learning.
5. Does your answer make sense? This particular question pushes students to evaluate their solutions. Is the number smaller or larger than they expected? Like using GPS when traveling, knowing the general destination can prevent your students veering dangerously off course when technology or user input fails.
For Further Reflection…
How do you encourage your kids to reflect on their learning? Do you have any surefire questions to inspire mathematical thinking?