## CORE Experiences in Math: Problem Solving

Over the past 40 years or so, a lot of research has been conducted relative to problem solving; real-life, meaningful problems have become the central component of effective mathematics instruction. Generally speaking, the teacher presents an interesting, real-life problem for the students to solve—something that students will likely want to solve. Then, using an inductive process, the teacher leads the students to possible solutions and to the development of problem solving skills and dispositions. Detailed discussions of this approach can be found here, here, and here.

Now, let's step back and consider this CORE learning experience from a macro-level. Students tend to find the experiences engaging because they provide an interesting task to complete. Problem solving, in fact, is an integral part of human life. Consider typical television shows: at their most basic level they involve unique characters trying to solve a mysterious or funny problem, one that often can be wrapped up within 30 minutes or an hour. Sometimes problems continue throughout a series and are integral in long-term story and character development. But the point is that problems are something we find interesting in a variety of domains, from drama to science, from literature to math. As teachers and parents we can tap into this CORE learning experience with inductive reasoning to make math learning much more interesting than the typical "I do, we do, you do" didactic approach.

So, how does this relate to the arts. Well, to begin with, stories are integral to problems and to the arts. Stories, as representations/presentations of problems can be experienced through song, dance, drama, and visual art. Here are some more specific ideas:

Furthermore, the arts present a variety of problems that call for quantitative and spatial reasoning in order to find a solution. Here are some examples:

Now, let's step back and consider this CORE learning experience from a macro-level. Students tend to find the experiences engaging because they provide an interesting task to complete. Problem solving, in fact, is an integral part of human life. Consider typical television shows: at their most basic level they involve unique characters trying to solve a mysterious or funny problem, one that often can be wrapped up within 30 minutes or an hour. Sometimes problems continue throughout a series and are integral in long-term story and character development. But the point is that problems are something we find interesting in a variety of domains, from drama to science, from literature to math. As teachers and parents we can tap into this CORE learning experience with inductive reasoning to make math learning much more interesting than the typical "I do, we do, you do" didactic approach.

So, how does this relate to the arts. Well, to begin with, stories are integral to problems and to the arts. Stories, as representations/presentations of problems can be experienced through song, dance, drama, and visual art. Here are some more specific ideas:

- Dramatize a story problem with dialogue, vocal expression, and body language.
- Dramatize a story problem with pantomime.
- Use multiple bodies to model a problem.
- Represent a problem through a visual illustration.
- Music, the Fibonacci Sequence, and Phi

Furthermore, the arts present a variety of problems that call for quantitative and spatial reasoning in order to find a solution. Here are some examples:

- How to transfer a small picture to a larger space.
- If a painting costs x amount, how much is that per square inch? How much would it cost for a bigger painting? What other factors, in addition to size, should factor into determining the price of a painting or other work of art? How much time does it take an artist to create a work of art? How much longer would it take for larger or smaller works?
- How are works of art organized spatially? Consider balance, complexity, variety, unity, etc. Measure and find ratios.