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Encouraging a Mathematical Mindset January 1, 2019

Posted by Media4Math in math.
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Before we can expect a student to answer a mathematical question, shouldn’t we want them to ask a mathematical question? Were you born answering questions? No, you were born to learn, to ask, and a child’s early years are a seemingly endless trail of question marks.

Moreover, isn’t our job as math educators to get students to recognize when some of their questions are, in fact, mathematical in nature? Many a child would be intimidated to solve a math problem, but wouldn’t they be delighted to know what they just asked is an interesting math question?

Math doesn’t start with algorithms, but rather ends with them. Math starts with questions, and sometimes those questions don’t even sound mathematical at all. We can use curiosity as the entry point to mathematical investigation.

Here is an interesting question that doesn’t sound mathematical at all:

Why do elephants have wrinkled skin?

This is a question you can ask a child with no fear of math anxiety. Their answers, whether mathematical or not, should be illuminating. Yet, it is completely a mathematical question.

Elephant

Media4Math Classroom has an entire module dedicated to answering this question, and although the target math concepts involve rational functions, the goal is to get students thinking about the question, rather than insist on an immediate answer. Yet the question about elephants can be asked of any child at any grade level.

Imagine, by contrast, telling students, “The ratio of surface area to volume reveals how efficiently an animal retains or releases heat energy.” This is not engaging. This is intimidating. It provokes the kind of math anxiety we want to eliminate from our classrooms. Also, this approach focuses on algorithmic solutions instead of the underlying question.

Asking Mathematical Questions

Getting a child to recognize that he or she just asked a mathematical question is a way of empowering the child’s math sensibilities, and creating a math mindset. For example, show them a picture of a group of balloons.

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Encourage them to ask questions based on the picture. While the point isn’t to specifically ask mathematical questions, the goal is to highlight when they have asked such questions. Any questions that include these interrogatives can be reframed as mathematical questions.

How many…?     This can involve counting, estimating, measuring, adding, or even multiplying.

How much?     This can involve measurements with money.

What colors…?   This can involve sorting, ratios, or even percentages.

Since our goal is to encourage a mathematical mindset, let the questions guide the math. Here’s an example. Suppose that as a class, you decide this is the most interesting mathematical question:

How can we make sure that most of the party balloons are red?

This is a mathematical question that has a variety of different solutions. The math skills used could involve sorting, counting, calculating ratios, fractions, and percentages. If you divide the class into small groups and have the groups discuss how they would solve this problem, you are encouraging a mathematical mindset where the mathematical investigation drives the mathematical solution.

Use this methodology to encourage students to develop a mathematical mindset. Engage a student’s curiosity and problem solving. This then puts students in a frame of mind to better understand the procedural and algorithmic side of math. They’ll begin to see that algorithms are tools of math, but that the real mathematics is in the mindset.