Math Education Concepts

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Concept-Based Learning and Math

Concept-based learning is not a new idea, but one that should get far more attention than what I’ve seen.  I recently found the following definition on “What Is IB?”

“Concept based learning is about big transferable ideas that transcend time, place, situation. Content just focuses on facts while concept focuses on making sense of those facts and the world around us. Content based teaching may not get beyond information transmission/superficial learning. Concepts are a way to organize and make sense of learning.”

When thinking about teaching and learning mathematics, concept-based learning makes the most sense.  Why? Situations change, contexts change, numerical values change, students change, etc.  If a concept is taught and learned, then changing the context or situation will not affect how to apply a concept.

I recently helped a student prepare for the math section of the upcoming SAT.  One question in the practice book showed the graph of a line with no numbers.  The question asked the student to select the equation of the line.  If the student knew the concept of graphs of lines (slopes, y-intercepts, etc.) then they would have been able to solve the problem easily.  They could determine whether the slope was positive or negative and whether the y-intercept was positive or negative.  Without the understanding of these concepts, the student was not able to answer the question.  Once I explained the concepts and details, then the student understood.

Concept-based learning should be a central focus when teaching mathematics.  Otherwise, students will continue to stumble over content when situations and contexts change.

What are your thoughts on concept based learning?


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Tangible Parting Gifts

I can’t believe the year has gone by so quickly!  It’s already the end of May and there’s only one week left for final exams.  While my time at Salesianum School was short, it will be remembered.  I have memories that will last me a lifetime.

My memories are those that made me laugh, yell, admire, love, and befriend!  Any high school math teacher can relate to the mixed emotions that are experienced in (and out) of the classroom!  It’s not new.  Maybe some day I will share some specifics about those emotions and experiences.

Today, I want to share two tangible gifts I received this year.

1. A t-shirt with my name on the back.  The significance of the t-shirt is that the students labeled me as a teacher who “Keeps it real.”  I gave it to my students straight, no chaser, and they appreciated that.  If they asked questions, I did not sugar coat the answers (whether the questions were about math, friendship, dating, or life).  One of the parents purchased the t-shirts for the entire class (Thank you Mrs. R.).

T-shirt designed by 414-2.

Keepin’ it Real T-shirt designed by 414-2

2. A”K” shaped crepe.  One of my students hosted a French exchange student this year.  Toward the end of the 4th quarter my student earned a 92.2.  He needed a 92.5 to get an “A.”  The exchange student asked me to boost the student’s grade.  I told him I would if he would make me some food using an authentic french recipe.  So they made crepes (the french exchange student used his mother’s recipe – or so he said he did).  It was delicious, so I will deliver on my word.  He was a good student so I would have bumped him .3 points anyway (especially since he missed a few days of school while he was away at France as an American exchange student).

K-shaped crepe made by French Exchange student and his host

K-shaped crepe made by French Exchange student and his host

These are two of the tangible gifts I received this year.  The intangible gifts are too many to name here.  But to name a few I gained friendships, respect, knowledge, love, life-lessons, memories, and so much more.  I will miss my students, but they will always be close in my memories.


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Seven Secrets of How to Study Math and Science | Citywide Math and Science Institute

Seven Secrets of How to Study

Seven Secrets of How to Study Dr. Stephen Jones

 

As the school year comes to a close, remember to review your study strategies, skills, and habits in preparation of your final exams.  Read this blog about studying for math and science subjects and learn new ways to improve your grades.

Seven Secrets of How to Study Math and Science | Citywide Math and Science Institute.


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Bridging the Gap Between Arithmetic and Algebra

Copied from DragoArt.com

Copied from DragoArt.com

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?.