With working two jobs to pay child support, while trying to also get through college, my stress level has been on overload the past several weeks. I am happy to have found the emotional energy needed to prepare and write this blog entry. Month after month of sleep deprivation, from trying to do too much, eventually triggers the law of diminishing returns. Ambition is a good thing when tempered by wisdom.
Technology is ever changing. Graphing calculators and programs have been around for a while but they are getting better and more powerful to use. From a recent journal article (http://www.nctm.org/Publications/mathematics-teacher/2014/Vol108/Issue5/Graphing-Projects-with-Desmos/), I learned about a free graphing calculator program available at https://www.desmos.com/calculator. This program does more than graph equations, it also allows you to import images (such as water from a fountain) which can be used to plot the graph of parabolas or other equations corresponding with the image. Art and beauty in the world around us contain shapes and patterns related to math. Modern entertainment, such as movies and computer games, runs on and is driven by math. Today’s world runs on ones and zeros. There is so much more to math than the often tedious, ordinary, and even boring regular math traditionally taught in school. Incorporating and making connections with things that kids love will help them see math as part of a much larger world. Without those connections, they are like Neo before waking up from the Matrix – unaware of the vastly larger and more useful world of math.
Another way students can make learning connections is through classroom discussion. Jeff Foxworthy famously said, “women don’t want to hear a man's opinion, they want to hear their own opinion in a deeper voice.” (https://youtu.be/-4EDhdAHrOg) Similarly, teachers sometimes seem as if they don’t really want to hear a student’s opinion (when asking questions for which the teacher already knows the expected answer). Higher level thinking is not promoted when the goal of questions is to provide validation, in the form of recitation, of the teacher’s already known answers relating to what is in the text.
An older article (Research Matters: Classroom Discussions of Literature by Rick VanDeWeghe http://www.ncte.org/journals/ej/issues/v93-1), outlines the findings of a study that was done which shows the positive impact on student achievement when there is less monologue on the part of the teacher and more genuine questions and dialogue from students. An “authentic question” is one that does not already have a predetermined answer. Students become more engaged in learning when they are the ones asking the questions since, “unlike teachers, students don’t (typically) ask questions when they already know the answer.” Student questions are the most important driver of dialogue style classroom discussions. Teachers can promote the chance for this type of discussion by validating what students say and incorporating student contribution (“uptake”) in comments designed to “initiate, nurture, guide, and sustain (discussion) momentum.” In other words, thought-provoking discussion is more likely to occur when teachers encourage independent thinking through student generated questions.
By relating things which matter to students (through the use of technology) and by encouraging original thought (through student generated discussion) teachers can engage students in collaborative learning. Students become active partners with the teacher rather than recitation repeaters of what the teacher already knows. The teacher becomes more a discussion leader than (“traditional”) teacher with the students as fellow teachers. In becoming teachers of themselves and each other, students while teaching learn.
