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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?


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Reducing Math Anxiety: What Can Teachers Do?

Reblogged: Reducing Math Anxiety: What Can Teachers Do?.


When Teaching Hurts

Standing in front of the class declaring all the interesting facts about mathematical concepts feels wonderful.  I enjoy math, I enjoy explaining mathematical concepts, and I enjoy watching students as they learn math.

The “hurt” is felt when it’s time to grade exams.  Some students are able to explain mathematical concepts, but have a hard time writing their explanations mathematically.  Some students can solve problems intuitively but cannot write the procedures the way they are taught.  Some students have anxiety attacks at the mere thought of taking a math exam, even when they know the material.

I understand the importance of tests, but I am a fan of assessments (not standardized, but individualized).  Most of my students understand the basic concepts that I teach and can explain them to me during class.  However, during quizzes and exams, those same students perform poorly.  This is when it hurts!  My heart just sinks when I know a student understands a concept, but cannot recall it during an exam.

The ultimate “hurt” happens when it’s time to submit final grades and students just don’t make the grade, so to speak.  My students are really “good” people who are trying to get through college so they can pursue their dreams.  Should one class get in the way?

Of course, the answer is obvious, but there are systems in place.  They are there for a reason, even when we disagree.


Teacher or Mathematician First?

Earlier this week a close friend, Lawrence, asked me a question.  And for the first time (in a long time) I had to think about the answer.

He asked me if I were a teacher or mathematician first, when I am in the classroom.  I paused for a moment to consider the question.  My first comment was that, since I have yet to earn my PhD, I am not necessarily considered a mathematician.  But I understood his question.  He wanted to know what drives me when in the classroom.  The example he used was that he is an architect first, then an engineer.  His education path is engineering, but his career path is architectural design (or something like that – sorry Lawrence).  But his real joy is designing blue prints for office buildings.  In fact, he is going to design my future institute (a post for another day).

After thinking about the question, I explained to Lawrence that it depended upon the class I taught.  This semester I am teaching a math course for students pursuing degrees in STEM related fields and a math education course for students pursuing education degrees in non-STEM related fields.  My initial answer was “both:  I am a mathematician first in the math class and a teacher first in the education class.”

This was my explanation:

In the math class the students really need to know and understand the concepts in order to proceed to the next math course.  I have to get the math concepts across to the students.  In the education class, the students need to pass a pre-service exam and satisfy this course requirement.  But they are future educators and I want to exemplify what that means to my students.  The goal for each course is different, so I teach each class differently.

My final answer, however, was that I am a mathematician first.  If you put me in a classroom and take away the math I would be less fulfilled.  I decided to teach to share my joy of math and to help others learn and appreciate math the way I do.  I know this will not happen for all of my students, but I want to reach as many as possible.  The classroom is the best place to do this!

So there you have it Lawrence:  I am a mathematician first, teaching is the vehicle I use to express and share my passion for mathematics!

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