From my personal experience, the two topics that get ignored the most is probability and statistics. I know I end up skipping over it in high school because I often need to finish the main mathematical concepts and I run out of town. I know many teachers who do the same simply because the probability and statistics sections are incorporated into most math classes and don't seem to fit.
There is this perception that statistics should only be taught as a separate class in high school and in some, it's an AP class for those who have finished all their required math classes. Unfortunately, many do not think schools should be teaching statistics before then.
It has been pointed out that people are currently exposed to so much data via the internet and people need to be able to interpret it. Consequently, studying statistics, even from kindergarten, is an important skill in today's society. Unfortunately, most people are not very good at statistics unless it is in a context they love, such as in sports or fantasy leagues. If you speak to someone who is into basketball, they can give you all the stats for their favorite team or player or if they are involved in a fantasy league, they know the stats of every player so they can create their team.
So why start have students learn about probability and statistics so early? It takes a while for students to develop sound statistical thinking and reasoning and for that it has to start in kindergarten. Right now, the common core standards introduces formal stats in the 6th grade and middle school but elementary grades can focus on collecting, organizing, and describing data in a variety of ways. It is also important for all students to make sense of graphs and data in subjects other than math, in subjects such as science and social studies.
Furthermore, all statistical lessons should be sprinkled throughout the different units rather than treating the topic with one chapter out of the book. It has been suggested that we begin introducing probability and statistics to kindergarteners, we ask students about their personal preferences such as type of music, television show, or ice cream flavor, or look at measurements like number of books, heights of students, or shoe size for measurements. Even in kindergarten, students can create their own surveys and begin to analyze the data they collected.
When statistics is taught throughout the school year in math and other topics, it helps students develop critical thinking skills and to think more critically about the topic in general. In addition, statistics does not always work the same way as most math. For instance, math is usually taught so students follow a series of steps to come up with the answer but in statistics is about context and the answer making sense.
Furthermore, it is important to take most elementary school activities a bit further. For instance, if you have students who count and chart shoe sizes for everyone in the class and then graph all the results, most times, the lesson stops there but it is important to have students analyze the data they collected. Analyzing the data helps students learn more about grouping and scales which help in Algebra and Geometry. tHis helps build mathematical reasoning.
When we start teaching statistics in elementary and we have students analyze the data, they develop a sense of data and statistics so by the time they reach middle school, they are ready for a proper introduction of the topic and have a solid foundation for the topic. Let me know what you think, I'd love to hear. Have a great day.
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