Why Use a Variety of Math Tools?

I just finished a professional learning opportunity entitled Using Tools to Enhance Mathematical Understanding.  A large part of our discussion was based around the purpose of why students, K-12, should use various tools (concrete or representational) to solve math problems. 

This blog is designed to give four reasons why using math tools can be beneficial to any K-12 classroom.

1. CCSS for mathematics describes 8 Mathematical Practices for all students.  Mathematical Practice #5. Use appropriate tools strategically.

"Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations...  Mathematically proficient students at various grade levels are able to use technological tools to explore and deepen their understanding of concepts.      

 

2. Math tools encourage students to be active rather than passive learners of mathematics.  When students are engaged using math tools (concrete or representational), teachers are encouraging understanding of mathematical concepts not just memorization of routines or procedures.

3.  Using math tools correctly bridges the gap between the informal mathematics and the formal mathematics and helps us diagnose students understanding of concepts and the misconceptions they hold.  In other words, math tools allows us to see inside the minds of our students and what they may be thinking about different concepts.

4. Math tools allow us to appreciate the variety of ways students use to solve problems.  "Generating multiple solutions to problems in an essential strategy in mathematics."  - Seefeldt and Wasik, 2006

A few conclusions from the mounds of research available on using math tools.  Teachers who use math tools effectively can have a positive affect on the learning of mathematics for their students.  Students at all levels and all ability levels can benefit from expressing their ideas using concrete tools, pictorial tools, and mental mathematics.  Incorporating math tools effectively into math lessons in meaningful ways helps students to grasp math concepts with greater ease, making teaching most effective.

So how do we go about applying this information into a classroom setting?  Check out 5 Steps to Use Math Tools Strategically In the Classroom.  In this article I share practical ideas of how to create a math toolbox that requires students thoughts and inputs to the purpose of each tool.