### Welcome to Tutor Portland’s Math Tutoring page.

It’s here we will discuss everything related to 1) our strategy for math tutoring and 2) broader tips for math education more generally. With the advent of technology, math education has been shifting towards lecture-based teaching. Small group work is being replaced with time in front of an automated math computer platform. But **research shows that’s not the optimal way to learn math. **The best way to learn mathematics is through experience-based learning courses which are grounded in group work & group discussion. People learn math when they hear themselves explain their mathematical reasoning. **That’s why math tutoring is so effective. **If it’s done right, the pupil will be asked to explain her mathematical thinking. This creates an open dialogue between the tutor and pupil. **This dialogue is the key to learning math. **The following are some expert tips on math education.

**Create An Engaging Environment**

“All men by nature desire to know.”

— Aristotle

Classrooms, tutoring sessions, or any math learning environment these days needs to create a safe engaging zone. Having an engaging learning environment has been shown to help students **learn more &** **boost their confidence levels** (Ontario Ministry of Education, 2005). This zone of engagement must be an investigative space—where they can dive in discuss ideas. Math students do best when they feel safe. When they feel safe they are more likely to engage with the concepts and verbalizing their thinking. In one-on-one settings, this can be done most effectively and efficiently when a strong relationship or rapport has been created.

**Encourage & “Model” Positive Attitude**

“When you think positive, good things happen.”

— Matt Kemp

It is especially important that students develop a positive attitude around math. Attitudes like these are very contagious with students sometimes adopting the attitude of a favorite teacher or tutor. That’s why it’s so important that the math tutor models positive attitude in their own character and behavior. It’s important to understand growth and fixed mindset. Math students who develop a growth mindset will be more resilient in the face of failure and will even learn to take this as feedback for moving forward. For a growth-oriented learned, missed questions are catalysts that push them to tweak & hone their learning strategy. And it’s important the tutor demonstrate all of these qualities as well.

**Teach Math Concepts**

“The essence of mathematics is not to make simple things complicated but to make complicated things simple.”

— S. Gudder

It is so, so vital to teach the concepts of math. But this is rarely done in schools. A student is expected to spend over a dozen years learning formulas and rules without ever learning the underlying concepts. **Those concepts are the most valuable part. **Concepts are the part of math that we use over the course of our entire life. We won’t always have to calculate challenging math problems in our heads, but it will be helpful to know some important ideas like **rates of change and accumulation. **Learning concepts is also important because it helps the learner develop a framework for housing bits & pieces of math knowledge and lessons. Mathematical concepts will help you in nearly any field. An understanding of rate of change is an especially important concept to know for pre-medical programs and courses. Learning concepts, such as these, will help in all the sciences.

**Use Role Reversals**

“When the student is ready the teacher will appear. When the student is truly ready… The teacher will Disappear.”

Use a role reversal and tell your pupil **it’s time for him to teach you** the most concept you learned recently. Let them run with it. They will probably do pretty well with some prompting and help. This causes even the most uninterested student to wake up a little bit. The spotlight is on them—they have to engage with their environment—to explain the concept. If the student really isn’t getting it, you can show some examples of similar problems and concepts. This allows the student to re-group for a moment and catch up. Hopefully, he is now more motivated to learn the subject quickly so that he can explain.

**Make It A Game**

“That’s what games are, in the end. Teachers. Fun is just another word for learning.”

— Raph Koster

Some students like to play games. They are bored with traditional mathematics. You can invite them to play a game with you. When solving hard problems you can alternate moves with your student. You take one action and progress the problem forward one step. Then your partner does. You can think of point systems and get more detailed with it if you’d like. The bottom line is that you are getting the method across in a more engaging and inviting way. It’s fun. People engage with fun—even if it’s math. This allows students to “test” their ideas out and practice speaking about them and trying to formulate them in a more straight-forward and coherent way.

**Hand Out Study Materials**

“What experience cannot teach you now, mentors and books can foretell! To take the lead in whatever you do, be willing to learn and educate yourself regularly!”

―

Passing out study materials is a great idea because it will encourage students to study harder. Being given something physical makes us take ownership of it. When we hold a math worksheet in our hands, we feel as if it’s ours and thus we are more likely to study it and work on it. This also gives the tutor or educator an easy way to follow up and see how the worksheet went. Questions can then be asked based upon student’s understanding.

**Give Positive Encouragement**

“Praise the slightest improvement and praise every improvement.”

— Dale Carnegie

Math can be disheartening. It’s easy to get stuck on a problem and have no idea what to do next. This is when grit and positive mindset come in. But often a student simply needs some encouragement. When students get something right they should be praised for their hard work. Research has shown that praise can foster resilience and improve learning & retention. However, the studies point out that it is important **not to praise people for their intelligence. **Praising intelligence supports a fixed mindset. **Praising effort and improvement** supports the hard work and determination necessary to succeed and excel at math.