
Last Updated October 2009  
The Child DreamerAs a child in elementary school, I sensed that I was not learning science and math at the rate that I desired. I dreamed that as an adult I would have a job in the sciences, and that I would help a group of interested kids get a jump start on the sciences. All this was not to follow the lines that I had anticipated, and I would eventually develop a belief that all students could have greater access to the sciences. The Youth Challenger of IdeasWhile still in high school I got into a habit of anticipating ideas in math and science that we would eventually learn, and challenging the ideas the we were learning. For example, before graduating from High school I had tried to trisect angles, and expand Pascal's triangle to a plane. Upon starting calculus in college I anticipated that there would be a function that had itself as a derivative, and that that function might have interesting qualities. The Young Citizen I frequently found myself involved in discussions with people about numerical ideas in the news. I was consistently shocked by how highly educated people, who were good at calculations, showed no understanding of the concepts they were talking about. People commonly made major errors interpreting graphs. They made seriously erroneous conclusions about what the numbers meant, and how the numbers were related. I was concerned that their math education had been wasted. They knew how to calculate, but not how to understand what they were calculating or why. 


The Young EngineerAs an engineer, I started to realize my education did not fully focus on my real success. For example, I was assigned to write subroutines in assembly language for control devices. For one problem, I took only about one hour to develop a solution that would work. However, it took me about three days to develop a way to explain to the method to other engineers. We all know that engineering is about problem solving, but it is also about communication. Over time, I learned to communicate technical ideas. I have since reached the point where various people have credited my ability to make complex ideas easier to understand. The EducatorBefore I learned about the NCTM Standards, I was already working with students. For a college class I researched what things limited my students' learning of mathematics. I came to the shocking conclusions that we test and teach in a ways that actually discourages reasoning. The next semester, I learned about the NCTM and their Standards; mathematics is problem solving, reasoning, and communication, all motivated through application. The experts at NCTM had come to the same conclusions I had! I now had a clear goal as a soontobe math teacher. As a new teacher in the Philadelphia, ready to jump right into the dream of meaningful mathematics, I quickly found out that promoting high standards would be a greater challenge that I had anticipated. Many things would stand in the way. The barriers would include the following:
I realized that reaching the high standards would be a much greater challenge than I had anticipated. Reform would not be instant; I would spend my whole career seeking better ways, and helping others recognize why change would be beneficial. 

The Dream ReinforcedWhen I met Ms. Barone, we talked about the successes she was having in her classroom. Her firstgraders were already working with Roman Numerals. I reasoned that if they could do Roman Numerals they could do Binary (Computer Mathematics.) I created an outline of patterns that occur in Binary and gave it to Ms. Barone. I fully expected her to say, "Karl, don't you think this is a bit hard for firstgraders?" Instead, she tried it with her class, and had very good results. We continued with other experimental math lessons having very good results. What I believed to be true was proven: children will achieve at levels higher than we imagine, if only given a chance. A few years later I started teaching at an expeditionary school. We were having phenomenal results. Students were designing houses and playgrounds, and giving their advice to city planners. I teamed up with the science teacher and together our students did advanced research on climate change. Our students were accomplishing amazing things. Setbacks Again With NCLB and state laws bearing down on our school we needed to work out some of our curriculum details and improve our test scores overall. To accomplish this, the school hired curriculum coordinator, and extra testing was implemented. As before, expert advise from teachers was now rejected. Teachers were even reprimanded for discussing high standards, or using projects instead of testprep in their classrooms. Curriculum kinks were ironed out, even as real student successes decreased. Students became less selfmotivated and no longer produced as amazing projects. Closing CommentsPerhaps even those of us who believe in high standards have a lot to learn about the potential of young learners. Students can accomplish amazing things when we make their interests part of their learning, when we help them understand their weaknesses as opposed to drill them on "the basics," and when we encourage them to support each other. Teachers can accomplish amazing things when we acknowledge their strengths and interests, when they support each other. Students and teachers both tend to accomplish the least, when arbitrary rules and methods come down from above that don't acknowledge their input and when they are reduced to scores from arbitrary testing methods. Do we have the courage to run schools with these perceptions in mind? 

