Common Core Math (CCM) Practice Standard 4

Opinion – Learning to Learn and the “Growth Mindset”

Before we leave the idea of “not good at math” too far behind, it might help to examine how we envision education and learning in general. Education is much more than just school; it is a lifelong process. You are proving this by taking on CCM as an adult. School has the potential to accelerate this process when it helps students learn to learn. It is no surprise that our children’s attitudes enable lifelong learning. In her paper, Brainology, Transforming Students’ Motivation to Learn (NAIS, School Matters, Winter 2008), Stanford Psychology Professor Carol Dweck makes several points that can help us help ourselves and our children become life-long learners.

“Many students believe that intelligence is fixed, that each person has a certain amount and that's that. We call this a fixed mindset, and, as you will see, students with this mindset worry about how much of this fixed intelligence they possess. A fixed mindset makes challenges threatening for students (because they believe that their fixed ability may not be up to the task) and it makes mistakes and failures demoralizing (because they believe that such setbacks reflect badly on their level of fixed intelligence).

“Other students believe that intelligence is something that can be cultivated through effort and education. They do not necessarily believe that everyone has the same abilities or that anyone can be as smart as Einstein, but they do believe that everyone can improve their abilities. And they understand that even Einstein was not Einstein until he put in years of focused hard work. In short, students with this growth mindset believe that intelligence is a potential that can be realized through learning. As a result, confronting challenges, profiting from mistakes, and persevering in the face of setbacks become ways of getting smarter.”

Professor Dweck has backed up her thesis with extensive experimentation among students from pre-school through middle school. Her results show that attributing student achievement to focus and hard work generally results in a growth mindset, attributing that success to intelligence generally does not. Since setbacks and successes in my own career tend to confirm Professor Dweck’s findings, I will integrate the concept of the growth mindset into future essays.

CCM Lesson of the day: CCM Practice Standard 4

Model with mathematics.

“Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.”

Comment:

To be clear, this step means that, as appropriate, use your knowledge of math to solve problems. However, taking this a step further, using math in areas of interest to us, such as sports statistics, shopping, finance, cooking using recipes, carpentry, etc., is an excellent way to reinforce multiple concepts.

Process implications:

Use math in routine activities to reinforce concepts and operations.

Definitions

Proportional: Two amounts are proportional it they change at the same rate so that the relationship between them does not change.

Applications and Examples

In baseball, a player’s batting average is computed by dividing the total number of hits by the number of times the player batted less the number of times he drew a walk was hit by a pitch, or hit a sacrifice bunt or fly.