## MathTreks starts with CURIOSITY, CHOICE, CHALLENGE

To select a problem that authentically answers your teenagers’ question ‘When am I going to use this math?!’, MathTreks begins by understanding what they find interesting, and their passions determine the problem’s context.  We then target a problems’ mathematical rigor to be ‘just right’ – a challenge that’s within your teenagers’ reach but requires an intellectual stretch.  Combined, the meaningful context and appropriate mathematical goals, set your teenager up to be invested in the problem.

Consider these two problems – a typical ‘word problem’ from an Algebra I textbook and a MathTreks’ problem that addresses many of the same math goals.  Which would your teenagers find more engaging?

To select a problem that authentically answers your teenagers’ question ‘When am I going to use this math?!’, MathTreks begins by understanding what they find interesting, and their passions determine the problem’s context.  We then target a problems’ mathematical rigor to be ‘just right’ – a challenge that’s within your teenagers’ reach but requires an intellectual stretch.  Combined, the meaningful context and appropriate mathematical goals, set your teenager up to be invested in the problem.

Consider these two problems – a typical ‘word problem’ from an Algebra I textbook and a MathTreks’ problem that addresses many of the same math goals.  Which would your teenagers find more engaging?

## Typical algebra problem ## MathTreks' problem

Your teenagers choose the problems’ context – and, they choose the solution.  That’s right.  MathTreks problems have multiple possible solutions.  At each juncture in the problem-solving process, students take the lead in deciding which approach they will take towards solving the problem.  In addition to opening up the possibility of comparing the benefits of different solution methods, students reflect on their experience with decision-making in a low-risk environment.

Below are two problems – a common problem with only one solution and a MathTreks’ problem with multiple possible correct answers.

Your teenagers choose the problems’ context – and, they choose the solution.  That’s right.  MathTreks problems have multiple possible solutions.  At each juncture in the problem-solving process, students take the lead in deciding which approach they will take towards solving the problem.  In addition to opening up the possibility of comparing the benefits of different solution methods, students reflect on their experience with decision-making in a low-risk environment.

Below are two problems – a common problem with only one solution and a MathTreks’ problem with multiple possible correct answers.

## Common problem ## MathTreks uses a SEMI-STRUCTURED problem-solving approach

MathTreks uses mathematician George Polya’s framework as a guide for problem-solving and then intentionally provides little direction on how students are to approach a problem.  In selecting a ‘just-right’ problem, we aim for students to be well-equipped to tackle the mathematical challenge.  Our goal is for students to be as independent as possible in solving the most complex problem.  For this reason, we provide little scaffolding upfront and add it on an as-needed basis.

### George Polya’s Problem-Solving Framework

As a famous mathematician in his own right, Professor George Polya was dedicated to developing future mathematicians.  The simple framework he outlined in his book, How to Solve It, continues to be a widely-adopted approach.  There are four main components, which students may undertake in consequently steps.  Or, more often, students will move ‘forward’ and ‘backward’ in through the four phases as they developer a deeper understanding of a problem.

### George Polya’s Problem-Solving Framework

As a famous mathematician in his own right, Professor George Polya was dedicated to developing future mathematicians.  The simple framework he outlined in his book, How to Solve It, continues to be a widely-adopted approach.  There are four main components, which students may undertake in consequently steps.  Or, more often, students will move ‘forward’ and ‘backward’ in through the four phases as they developer a deeper understanding of a problem.  #### The Four Elements of Polya’s Framework

1. Understand the problem
2. Plan an approach for solving the problem
3. Execute the plan
4. Reflect

#### The Four Elements of Polya’s Framework

1. Understand the problem
2. Plan an approach for solving the problem
3. Execute the plan
4. Reflect

### What is ‘scaffolding’?

Scaffolding refers to the ways in which a teacher supports a student in solving a problem.  For example, a common approach to multi-step problems is to break it down into parts – a, b, c, d.  Each part usually provides a prompt and perhaps a graph or equation to stimulate students’ thinking.  As students encounter roadblocks, a teacher may provide a hint, underline an important word/phrase, or remind the student of a similar – but simpler, problem.   These are scaffolds that help a student solve the problem.

### What is ‘scaffolding’?

Scaffolding refers to the ways in which a teacher supports a student in solving a problem.  For example, a common approach to multi-step problems is to break it down into parts – a, b, c, d.  Each part usually provides a prompt and perhaps a graph or equation to stimulate students’ thinking.  As students encounter roadblocks, a teacher may provide a hint, underline an important word/phrase, or remind the student of a similar – but simpler, problem.   These are scaffolds that help a student solve the problem.  ### Why begin with little scaffolding?

At MathTreks, our goal is for students to assume as much of the cognitive lift of solving a task as possible.  When students struggle, teachers provide in-the-moment, tailored support.  Until students reveal that they are stuck, however, we give students the opportunity to grapple with a problem’s complexity.

### Why begin with little scaffolding?

At MathTreks, our goal is for students to assume as much of the cognitive lift of solving a task as possible.  When students struggle, teachers provide in-the-moment, tailored support.  Until students reveal that they are stuck, however, we give students the opportunity to grapple with a problem’s complexity.