It’s possible that you may recall, while in grade school, learning and memorize many facts, procedures, and calculation steps for solving mathematics problems. Indeed many of us seasoned adults can recall spending time during our early elementary school years memorizing multiplication tables. It wasn’t until the 1990s when educators began to question the usefulness of teaching students to memorize such math facts prior to learning more complex math concepts. But more recently, there have been educators who have begun to re-emphsize the importance of teaching students to memorize multiplication tables and other basic math facts as a precursor to learning other math concepts.
Mathematical Thinking
However, using the memorization of math facts and procedures is not the same thing as using mathematical thinking for problem solving from the perspective of those who are trained users of mathematics. And, there are mathematically trained people who have spent time writing about the distinctions of this thinking approach.
Some early writing on the use of mathematical thinking was done in 1996 by math research and educators, Cuoco, Goldberg, and Mark. They introduced a collection of thinking and reasoning concepts that they referred to as Mathematical Habits of the Mind. These concepts were introduced as a series of thinking strategies that are acquired and regularly used by trained mathematicians. The idea was to introduce a collection of thinking strategies, to the math educator community, for use as curriculum components to enhance the training of students in the art of mathematical problem solving. The Cuoco, Goldberg, and Mark article is an interesting read and if you have the time, I recommend reviewing it.
Why Seasoned Adults Need Mathematical Thinking
Having spent many years training in and also teaching mathematics principles, I strongly believe that mathematical thinking strategies are useful to seasoned adults well beyond the walls of a mathematics classroom. For one, it’s no secret that aging can lead to cognitive declines suggesting that engaging in activities that help nurture our mental agility are quite welcoming for us. That is, given the opportunity to train beyond just practicing routine mathematical procedures and performing calculations–to learning mathematical thinking strategies can likely be quite beneficial. Examples of some widely beneficial mathematical thinking strategies that come to mind include the ability to:
- Visually recognize different types of patterns
- Be attentive to language choice and apply precision to the communication of ideas
- Detect and uncover hidden assumptions made in arguments or claims
- Identify commonalities, connections, and relationships between seemingly different things
Developing and practicing mathematical thinking habits, such as these, helps us to apply proven reasoning strategies to all aspects of our world from a quantitatively analytical perspective. This skill is particularly useful for us, in todays world, where ever changing advances in technologies seem to continually rewrite how we need to engage with our environment, meet our goals, or make life transitions. Mathematical thinking usefully underlies the ability to comprehend the origin of many of these advances.
The above mathematics thinking list is not a complete listing by any means. And, Cuoco, Goldberg, and Mark are not the only experts who have written on the topic of mathematical thinking and have shared interesting approaches and techniques that we could all benefit from learning. Stay connected to learn when my mathematical thinking sessions are offered.
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