Math Education Concepts

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Thinking Mathematically

When you are passionate about something, you tend to relate almost everything else to that “thing.”  For me, that “thing” is math.  I relate almost everything in my life to math.  Whether it’s my hair (curl pattern, texture, etc.), my dishes (the way they are stacked in my cabinets), the highway (the number of car spaces between my car and the car in front of me), or even the shadow on my dining room wall (it’s a reflection of my light fixture and it’s shaped like a sine curve reflected across the x-axis).

I think mathematically… I count the number of steps it takes to get to the bottom of the stairs, I count the number of tile squares it takes to create the pattern on my bathroom floor, I count the nails in the walls, and I count the number of holes there are in the design of my laundry basket.

So, do I think mathematically because I happen to enjoy math or do I enjoy math because I think mathematically?  Either way, I am passionate about mathematics and mathematical concepts and ideas.  And as much as I try to hide behind my desk (and avoid teaching), I still get excited when having conversations about all things math!  Thanks for the brief conversation S. from NC!


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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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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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Professor: Simpsons “the most mathematical TV show ever”

REBLOG: Professor: Simpsons “the most mathematical TV show ever”.