# Lesson Objectives and Overview

The goal of this lesson is to look at strategies to: handle student misconceptions, work with students with disabilities in math, address math anxiety, increase student understanding of the language of mathematics, and helping students learn appropriate study skills. This focuses more on strategies that the teachers can be helping their students to learn and be aware of in order to be more effective in the classroom, whereas the next lesson will focus more on strategies the teacher may employ to make the learning more interesting and of value to the students.

# Learning from Misconceptions

## Pre-Activity

Start by thinking of common misconceptions you've encountered either in your own learning of math or misconceptions held by your students.

## Using the misconception as a launching pad

Misconceptions can be used to build connections and strengthen student understanding. View the following slideshow and look at the examples of misconceptions and how they are dealt with here: Misconceptions in Mathematics

## Key Points

• Students develop misconceptions from constructing their own understanding of new ideas based on previous ideas or false extrapolation.
• Misconceptions need to be addressed and challenged.
• Students learn via cognitive conflict and the resolution thereof.
• Mistakes and misconceptions are different things. Mistakes are the result of being careless whereas misconceptions are from applying concepts incorrectly.
• Misconceptions are often shared by many students.
• Students need to communicate their understanding in order for teachers to diagnose the source of the misconception.
• Problems and activities that challenge the students' understanding are helpful in resolving misconceptions, and should be looked at as part of a group discussion.

## Post-Activity

After viewing the slideshow, consider how the ideas here could be applied in your classroom. Come up with a specific example of a common misconception your students have and give your plan for how to correct that using the ideas discussed in the slideshow.

# Assisting Students with Disabilities

## Activity

• Based on your reading, what are the most effective strategies for teaching students who struggle with math?
• Have you used any of the methods suggested here in your own practice? What was the outcome?

# Managing Math Anxiety

Many people have fear and stress reactions when it comes to doing math, this is referred to as math anxiety. Prior to going to the reading below think of how you would expect someone to act when experiencing such anxiety. Then come up with possible suggestions for overcoming this anxiety. Compare your thoughts on this after the fact.

Follow the links are to handouts on math anxiety, what it is, and how to manage it:

## Application

Knowing strategies for dealing with math anxiety is only useful if the students are aware of them. How can you as a teacher help your students to be aware of and deal with math anxiety? Think of ways that you could present strategies for dealing with math anxiety in your classroom.

# The Language of Mathematics

Mathematics is effectively a language in its own right, with its own definitions, and its own collection of symbols with their own meanings and conventions. In order to properly understand mathematics a person must be fluent in the language, truly understanding its alphabet and its vocabulary, and be familiar with the syntax. A common problem for students is recognizing within a sentence what the pieces mean and how to write it in the language of math. Terminology and symbols from mathematics may be either unfamiliar or have a meaning that differs from the meaning previously known by the student. Below is a collection of examples from http://www.ascd.org/publications/books/105137/chapters/Mathematics-as-Language.aspx:

Students in learning the language of mathematics need

• To have opportunities to communicate their understanding of mathematical ideas using appropriate terminology.
• To work with mathematics from several angles including; seeing the terms and symbols visually, drawing and writing these themselves, hearing the terms in proper context, and to use the terms themselves in proper context.
• To come up with their own way of explaining what terminology means, in a way that they understand.

## Activity

Read the articles linked here: [The Digest: Language in the Mathematics Classroom] and [Learning Mathematics Vocabulary].

# Study Skills for Mathematics

Often times students are at a loss for how to best study for math. As a teacher you can point students in the right direction and give them the tools to study effectively.

## Tips for Studying Mathematics

• Practice, practice, and practice some more. Mathematics is learned by doing and is not absorbed by osmosis. Practice problems from the text or come up with your own problems that are similar to those covered in class and in the text.
• Show up to class every day, physically and mentally. That means participating actively in the discussions and the working out of problems.
• Learn to take good notes.
• When you don't understand something in class, ask for help in understanding.
• Prepare for class by reading ahead in the text and looking over notes prior to class.
• Use outside of class resources like office hours, help labs, study groups, etc...

Look below to the additional resources for more detail on how to study mathematics.

## Activity

Do your own research on ideas for how to study mathematics, then create a one page handout for your students outlining best practices in how to study for mathematics. Then come up with an engaging method to share these ideas with the class along with the handout.

# Problem Solving Strategies

Students are often at a loss as far as how to go about solving a problem in mathematics. Giving strategies to students for how to solve problems can be very helpful in them gaining independence in solving real life mathematics problems. We consider the four step process suggested by Polya:

1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Look back