It is an old adage that the more you know, the more there is to learn. Improving as teacher is a lifelong process, and whether you’re just starting in the classroom or have taught calculus for years, it should be your goal to consistently invigorate your methods and to think critically about the way you interact with students. As technology continues to evolve and infiltrate the classroom, math teachers have an especially unique opportunity to leverage computers and other electronics in a way that makes numbers approachable, visual, and most of all — fun.  Math is an important part of life, and though it’s an historically dry subject, with a little applied passion it can change the way your students think about the world.

Below is a compilation of resources for math professionals and teachers, including various teaching styles, links to mathematics journals for inspiration, and an abundance of sites dedicated to making math instruction accessible, fun, and worthwhile.

Academic mathematics journals are a great way to see what is current in the field, especially if you have an interest in theory.  Whether you see yourself teaching elementary children, high school students, or at the collegiate level, academic journals are often a source of intrigue and inspiration.

Math Teaching Strategies and Methodologies

There is a wide spectrum of methods and strategies – and opinions on these strategies — when it comes to teaching students mathematics. But despite this variability, there are a few core ideas around which most methods and curricula are shaped:  the appropriateness of the material for the student demographic, available resources, grade level expectations, and even personal preference.  Choosing the right method is often an iterative process that becomes perfected only after years of adjustments, and student success and retention often hinge on a teacher’s awareness of this fact.  Instructors tend to adopt methods with which they feel most comfortable, but stepping outside of that zone is the flexibility that will help you excel and optimize your process to meet your students’ diverse needs.

• Lecture Method: One of the most widely used teaching strategies, the lecture method is adaptable, versatile, and allows a teacher to vary the organization and content of a presentation. Conversely, this method tends to place students in a passive role and will sometimes require extra work outside of the classroom to ensure long-term retention of subject matter.
• Inductive/Deductive Method: With inductive teaching students are presented with a concept and work through a variety of examples to learn how that concept functions; in deductive teaching, students are presented with a concept and are also given examples which illustrate the idea. These methodologies have distinct advantages and disadvantages and should be considered carefully.
• Heuristic Method: Also called the Discovery/Inquiry method, this approach allows students to take a leading role in their learning and promotes self-discovery.
• Project Method: The Project Method is considered more of a hands-off approach to teaching.  Students are given the opportunity to work in a team environment, which promotes cooperative social interaction while also creating peer feedback loops.  It is also known as Cooperative Learning.
• Assessment:  ”the process of observing and measuring learning.”
• Inventing and Testing Models
• Using Socratic Questioning
• Teaching With Visualizations
• Teaching and Learning Methods and Strategies includes information on how to develop better study strategies and habits.
• 150 Teaching Methods
• Foreign Language Teaching Methods, from the University of Texas.
• National Center for Case Study Teaching in Science includes universal techniques of interest to all teachers.

        Making math relatable

Because mathematics forces students to think about processes in a unique way, it can at first be a tedious subject to learn.  While other subjects in school give students a degree of subjective freedom when it comes to determining the “right answer,” math is different.  There is often only one answer to a math problem, and this adds a certain strictness and pressure to the discipline.  In turn, this discourages students and causes them to question their ability and the logic behind mathematics.

An interesting way to sidestep this discouragement is to link math to the real, applicable world when addressing new concepts.  By promoting a link between theory and application, students can better connect mathematical concepts to understand their relevancy and their importance in daily life.  For example, money is something that everyone in any society can relate to.  By integrating money into teaching a topic (whether it be as simple as determining hourly wages using division, or as difficult as finding the compounded interest rate on a mortgage), students will find the material more meaningful and appreciate how math will profit them in their future.

Today, rather than students only being able to hear and read about math’s real-world application, they can experience it as well.  Many great math sites exist that allow students to actively learn about math in daily life:

• Lemonade Stand: This classic computer game helps students learn the basics of running a business.
• Calculating a Car Payment: Students use formulas to calculate how they would pay for their dream car.
• Online Math Applications’ Trips: This site offers students lessons on the costs of owning a car as well as a number of other automobile-based activities.
• The Mint: The Mint provides students with information and tools on financial topics such as “Saving & Investing” and “Making a Budget”
• Ciese Classroom Projects: This site offers students a variety of real-world math problems and application.

Sites like Project SkyMath and Math in Daily Life offer unique perspectives on teaching math with real-world application.

        Guidelines for New Math Teachers

Becoming a great math teacher is an arduous process that takes a steady mixture of hard work, perseverance, and experience. Even the most highly-decorated and respected teachers started somewhere, and more than likely they experienced some bumps along the way. Here are some key tips and tricks for new math teachers to have a successful first year:

• The importance of making connections: Connecting with students and earning their trust is essential to the success of a teacher. There are many different things a teacher can do to create rapport:  consistency is important to a structured class setting; make sure to have a fair system of discipline, a fair system of grading, and a clear communication of expectations; be careful of your tone when talking with individual students and try not to come off as condescending; don’t just ignore quiet students, but rather try to make them feel comfortable and promote participation (sometimes it’s a good idea to change the seating chart and move them closer to the teacher). Connecting with students will create an atmosphere of camaraderie and promote individual participation.
• Classroom Management:  Sometimes this depends on the caliber of the students being taught, but there are different ideas teachers can utilize in order to maintain classroom equilibrium.
• Teachers should try to take a step back and look at their teaching experience as objectively as possible. Is the material being presented too difficultly? Is enough time being allotted to thorough explanation of new material?  These may be problems that the teacher can easily rectify.
• It may be a good idea for a new teacher to talk with a mentor or someone they trust, and have them visit the class. This can be helpful in determining objective ways to improve classroom management.
• Communicate high behavioral expectations, but also make sure it is clear to the students that they know the consequences of misbehavior.
• The First Day of Class is one of the most important days. This resource from Carleton College includes different strategies and videos to see what different faculty in various disciplines do on the first day of class.

       Making math fun

While more appropriate for a younger demographic (or an older math teacher that feels like being silly), there are many ways that teachers can make learning math a fun experience while at the same time increasing student retention.

• Creative Teaching Ideas: Learn about creative ways to make math fun for the class
• Super Teacher Ideas: Visit this site to learn about different games and ideas involving food, fractions, and fun
• Teacher Files: Math Lessons: Discover fun ideas and projects that dabble in a wide array of topics.
• Riddles: Riddles and brain teasers can be a great way for older students to think outside the box.
• Math Can Be Fun: Learn how this approach can help children have a solid start and learn to love math.
• Game-Based Learning
• Illuminations has hundreds of online activities and ready-made math lesson plans.
• Figure This!, mathematics activities aimed towards middle-school students.
• Reflections, from the National Council of Teachers of Mathematics, allows you to watch videos of other teachers to more critically think about your own methods.