# Math Education Concepts

## Bridging the Gap Between Arithmetic and Algebra

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I have been teaching college level precalculus for several years.  A running theme of concern has been the lack of preparedness of my students for the course.  The struggling students somehow place into the course, but clearly are not prepared.  My assessment is that the students’ basic algebra skills are weak.  But what happens when a student takes algebra for the first time, but are not prepared?  Why are some students ready for algebra and some students struggle with the basic algebraic concepts covered in Pre-algebra or Algebra 1 courses?  What do you do as a teacher when you are faced with the challenge of bridging the gap between arithmetic and algebra?  How do you incorporate these concepts into your lessons without losing algebra “teaching time?”

This is an issue many Algebra 1 teachers face.  The common concern is that students taking Algebra 1 lack basic arithmetic skills.  But these skills are necessary for success in Algebra 1.  For example, many students struggle with adding fractions.  What happens when those same students have to solve equations with rational expressions?  If they have not mastered adding fractions, they will not be able to solve equations with rational expressions or they will experience difficulty when faced with these problems.

To me the answer is clear… Teach students so that they master basic arithmetic skills before they enter Algebra 1.  This charge is for elementary school teachers.  Here is the reality…  This is not always accomplished.  Elementary school teachers probably have their reasons for why this is not happening, across the board.  In the meantime, students are required to take Algebra 1 with whatever skills they have acquired.  This presents a problem to secondary teachers who have students entering Algebra 1 lacking the basic skills needed to learn and master basic algebra concepts.

How do you bridge that gap as an Algebra 1 teacher?  What does that bridge look like?  How do you help these students without hindering the advancement of the students who were fortunate to have mastered these skills?

These are very valid questions with many valid answers.  What are your thoughts?  What have you done in this situation?

## The Most Important Math Process

AKA: Order of Operations / Operator Precedence / PEMDAS / BEMDAS

Although there is so much you can do with math, without structure there is no point. If there were no rules to follow, it would be chaos – which is a fascinating math-logical reasoning in and of it-self. The process of the Order of Operations is to define the rules in solving equations. Used in basic arithmetic to calculus, this process is of the utmost importance in methods utilized in Mathematics because it sets the foundation for solving anything.

History

No one seems to be sure exactly when the Order of Operations took precedence in figuring out the… order of operations. The presence of this procedure can be considered to be influenced by the grammar and language when describing an equation (Peterson, 2000). On the website Dr. Math, it is mentioned that “multiplication has precedence over addition.” I take…

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## Percentages

Percentage is the ratio of a part to a whole.  More specifically, one part of one hundred.  For example 50% is one 50 parts of one hundred.  Percentages can be written as fractions, decimals, or percentages.  They all translate to the same idea or concept.  Percentages can be presented as a pattern of behavior of numbers (parts of a whole).

We should teach our students all parts of percentages, some with more emphasis than others.  Students should have an understanding of the several ways percentages can be represented.  Students are usually apprehensive about learning about percentages.  They know that percentages have something to do with decimals and fractions and they are uncomfortable with either topic.  In order to teach percentages effectively, teachers must understand the terms and concepts associated with them (fraction, ratio, decimals, etc.).

One way to relay percentages to students is to present a whole item.  Take a part of the whole and discuss the remaining part or the part taken.  Both can be represented as a fraction, decimal, and then a percentage of the whole.  I repeatedly use this type of example to help my students understand the concept of percentages and their usefulness.

How do you teach percentages to your students?  Is your method different for each grade level you teach?