I recently wrote and reflected on my visit to Eastern Carver County school district. This school of personalized learning was interesting, to say the least, and potentially the future of public education.
[Side note: I am still unsure of the logistics that are placed within a personalized learning school, but Dan Meyer would agree that they are not necessarily better than traditional schooling. Following Dan Meyer’s blog post, I should actually be calling it individualized learning. Individualized learning looked fantastic when I saw it in play, but what if we place it in the center of inner-city public schools? I would like to see the demographics in which individualized learning is being placed. I am not placing stereotypes, but if you give this system of individualized learning to a group of students, not every student will take advantage of the freedom in an appropriate manner.]
I am curious how many students would be more challenged by a traditional school setting, than individualized learning, or vice versa. Within comments on Dan Meyer’s blog post, someone responded in regards to technology not being able to challenge students. If this were true, are we challenging students enough in the public-school system? I am curious where the line is drawn for how much we can do for the students in the high school system, especially if we want them to be prepared to take on the real world. The real world is not going to consistently remind them to turn assignments in (advisories/study hall), the real world is not going to give students the perfect problem they have been trained for. The real world is not going to have well thought out answers, so should we challenge students more often by simply giving them performance tasks that require them to think deeper? Should we provide more problems that do not yield “friendly” answers? I understand teachers incorporate such tasks, but I am not sure how often.
Unlike many millennials, I am not one to inform the world of social media on my life achievements. I have accepted a job at Parnassus Preparatory School in Maple Grove, MN. My school revolves around a classical education, the very system that created such distinguished individuals as Plato, Aristotle, etc. This system seems new but has been present for thousands of years with the exception of the recent century. These students that are challenged from a young age in a traditional classroom setting may not respond in the same manner to the challenges I have witnessed in an average public school. I am not sure what is making our students feel challenged, other than not being exposed to such problems for a majority of their lives. I have a handful of first-hand experiences I will share.
Problem number five (above) was on a recent quiz of ours that I created. I found the problem online and felt I must provide an image for the small chance students do not know what a parking garage is. I understand this is not the clearest problem, but I required the students to think slightly more than the usual problem given to them asking for a value ‘x’. If I gave students this exact problem with a labeled triangle, 90% of them would solve the problem correctly. Instead, this problem was given and the number probably drops closer to 65-75% of students answering correctly. I wish I had concrete evidence but the quizzes are already handed back. Regardless, many students had questions during the quiz of where the 130 feet goes, and what angle we are trying to find. Why did this problem give students so much trouble? As my teacher and I say, we are not “spoon-feeding” the students with this problem. This requires them to think a little further than the stereotypical math problem and problem solve.
This problem above was given on a quiz retake. I am unsure why I provided triangles with these problems, but felt it was a small factor in challenging students thinking by assuming it is a right triangle. The original quiz I created had one triangle of each: acute, obtuse, and right. The three problems above are two obtuse, and one right triangle. Out of the handful of students that tried a retake, two of them directly asked me why there was not acute triangle, and assumed they were wrong. I love when I have students second guess themselves. I often remind them to be confident in their work. This is another problem I feel is present within current education, as previously discussed. Students are given this perception that in situations like this, the answers obviously have to be one of each type of triangle. Even though two of the handful of students that retook the quiz asked me about this, I feel most of them were questioning if their answers were correct due to this fact.
Lastly, I mentioned not so “friendly” answers as another problem I have witnessed in the school system. More so, the lack of unfriendly answers within problems. It makes all of us mathematicians happy when we solve a problem that results in a whole number. The problem above was on a regular quiz, this is the key that I created. I am unsure if it was me being mean, stupid, creative, or all of the above. Unfortunately, if students do not solve for the missing sides in the order I did, then simplified radical form is not entirely possible. Thus, I created a mess for myself grading. Setting aside the poor creation of the problem, focus more on how this threw so many of my students out of wack. Most of my strong students had no problem with this, at least in answering correctly. I am sure I made almost every student second guess themselves with these answers. I felt bad initially until I realized there is always a quiz retake for up to 90%! What is wrong with these answers? They are not friendly whole numbers we were hoping for, so it must be wrong right?
I love challenging my students in any way possible, especially if it means the stakes are low. Exposing students to such problems in the classroom will prepare them for a real world of problems they will be able to confidently solve, and understand it is not a problem out of the textbook waiting to yield a “friendly” answer. I look forward to beginning the next chapter of my life in classical education, and being exposed to techniques to challenge my students. As I was reading in my classical education handbook, this educational system provides students with the “tools of learning” to apply towards any challenge they are faced at in life, rather than the focused subject matter.