# 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?

## Math and Puzzles

Good resource/idea for math teachers!

I’ve experimented with using more math puzzles in the classroom this school year.  I continue to find that games and puzzles have the potential to engage students in meaningful ways. Similar to games, puzzles can encourage collaboration and perseverance skills that will help students long-term.

About a month ago I came across a free puzzle maker called Tarsia.  Tarsia is a program for PC users that allows the creation of different types of digital puzzles that you can print out. There’s a large database of math puzzles that are compatible with Tarsia here. A colleague and I have used them during our math station activities.  Students work in collaborative groups of 2-3 to complete the puzzles.  Last week I heard students having math conversations about whether a specific piece fits or not.  Hearing students confirm their reasoning for putting a piece in a particular place can be useful…

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