Is My Math Instruction Effective?

In elementary and middle school, teacher-directed instruction never seemed to work for me.  I grew bored quickly and then promptly zoned out.  I’d either doodle on paper or mentally plan out my afternoon.  That kind of focused instruction didn’t work for me; however, when I was in school, direct-instruction led by the teacher was all I ever received.  To this day, there are holes in my knowledge base because of it.  My math skills are limited and my understanding of scientific concepts is fuzzy at best.  Yes, I know that 99% of the responsibility was with me, I do wish I had had more chances to really play with the math skills as I learned them in school.  While each new day brings with it opportunities to fill in those cracks and holes with knowledge caulk, I do wish I could spend more time building upon my foundation rather than solidifying what is already there.

Due to this limited knowledge base, I find myself struggling at times to effectively introduce and discuss new math concepts in my STEM class.  Because I don’t fully understand the inner workings of integers, I find it challenging to explain the hows and whys of them to my students.  Why does subtracting a positive number from a negative number result in a smaller negative number?  I know that it does but I don’t understand it on a high enough level to be able to effectively explain it to students in a meaningful manner.  Why does subtracting a negative number from a positive number elicit a larger positive number?  I use a number line to demonstrate this to the students but I feel as though I could use more specific words or examples to clarify it for them even better.

Since I don’t fully grasp the concepts as a learner, I find it challenging to delve into them as a teacher.  Sure, I use fun activities at the start of my lessons to get the boys excited about the concepts, but is that enough?  Is excitement enough to motivate them to want to learn so that they ask the right question to allow them to fully understand the skills covered?  Of course I model the skill on the board and get the students engaged and involved in the various mathematical processes.  I do still wonder, though, is my method of instruction the most effective?  Is there a better, more meaningful way for me to instruct my students on the skills covered?  While I use the proper vocabulary terms, am I also properly labeling and describing the steps involved?  Last week, I introduced the concept of multiplying and dividing fractions.  After covering multiplication, I asked for volunteers to explain how to divide rational numbers.  One student raised his hand and said, “Butterfly wings.”  What is he talking about?  What do butterfly wings have to do with dividing fractions.  I had him come to the board and explain what he meant.  He circled the diagonal numbers and the intersecting circles sort of resembled butterfly wings.  So cool, I thought.  Yes, cross multiplication is one way to do it.  So, I clarified butterfly wings and gave him the term cross multiplication.  I’m trying to teach each process appropriately, but I still worry that I am not providing them the best, most effective instruction.  I feel as though there is more I could do to help them fully grasp and understand the concepts.

I know you’re probably thinking, “Are they meeting the objectives on assessments and homework?”  The short answer is, “Yes, for the most part.”  I work individually with those struggling students during class the following day.  I want to be sure they have a strong understanding of the skills before moving into seventh grade math.  Two students need much support, while the others are quite self sufficient and are able to think logically very easily.  I provide the struggling students with extra practice and modelling.  This seems to help with most of the skills practiced thus far.  I’m not worried about them being able to apply the skills on a basic level.  I am worried, however, about them being able to apply the skills to more abstract, higher-level math problems they will face next year.  Am I explaining each skill or objective in a way that will allow them to fully comprehend every aspect of the skill?  If not, what else should I be doing?

As this issue causes me to worry about how prepared my students will be next year, mathematically speaking, I want to devote some time over the upcoming March Break and summer vacation to really dig into the math concepts covered in the sixth grade.  How can I be sure I am effectively teaching the adding and subtracting of rational numbers?  I want to go online and find some reputable and helpful resources and also choose some quality professional texts to read to boost my confidence and foundational math knowledge.  I want to be sure I am the best teacher possible for my students so that I can support and challenge them appropriately.


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