From falling snowflakes to our entire galaxy, we count fifteen incredible examples of mathematics in nature! Snowflakes exhibit six-fold radial symmetry, with elaborate, identical patterns on each arm.
Ask almost any scientist about their work, and the conversation will involve the data they collect and analyze. The use of data in science is often captured in science classrooms as an ill-defined link between math and science that may not reflect authentic data practices Tanis Ozcelik and McDonald Students often find themselves collecting data to confirm obvious conclusions within highly structured labs, and data become a way for students to demonstrate the precision of their methods rather than a tool for explaining a phenomenon.
For scientists, data are much more: Data are used for the inductive process of theory building Windschitl et al. In other words, data can be used to tell rich narratives about relationships, phenomena, places, and other facets of the natural world through both inductive and deductive processes.
Learning how to read the stories within data is a learned skill that must be intentionally taught, not only to K—12 students, but also to teachers. Through the Numbers in Nature, Math on the Mountain NiNMoM project, teachers and scientists were brought together to collaboratively explore data that tell the stories of two locations in Central Oregon: The project partners included: Bachelor; five master classroom teachers experienced in teacher—scientist partnerships; and 24 other classroom teachers.
The 29 teachers including master teachers on the project included elementary teachers fourth through sixth grades and middle and high school science and math teachers.
Because the curriculum frameworks were designed for each grade level and then developed by teachers for their own classrooms, the project was able to accommodate this wide breadth of content and developmental levels.
Teachers represented all six school districts in the Central Oregon region: They were recruited through e-mail and district administrators, and received a modest stipend, substitute teacher coverage, and graduate professional development PD credits.
Participants, including teachers, scientists, and project coordinators, spent time unpacking the nature of data literacy, examining myriad data collected at HJA or Mt. Please see Appendix A in Resources for examples of these threads.
Data literacy The NGSS and its foundation document, A Framework for K—12 Science Education, describe eight practices that are central to science and engineering and that must be taught in schools. Although these might bring to mind skills related to designing and conducting experiments, just one of the practices addresses experimentation.
Rather, half of the NGSS practices are explicitly focused on the use of data: Two of the eight CCSS mathematics practices include facility with using data: However, teachers often struggle with incorporating the use of data into the science classroom Mayes et al.
Throughout this project, participants spent considerable time on first defining data literacy see Appendix B in Resources and then on working through teaching practices that can foster data literacy. In the data literacy conversations Figure 1participants wrestled with what it means to be data literate and what data skills an average student needs to be successful upon high school graduation.
Although the process generated an extensive list of components, the conversations facilitated a common language for the group to discuss data. As described in the next section, teachers received instruction on data literacy pedagogy, as well as considerable practice in using data to discern explanatory stories of places and phenomena.
Our intention with the project was to focus as much time and effort as possible on collaboratively looking at and preparing authentic data sets for student-friendly analysis so that both teachers and students could appreciate data literacy as a tool that gives them access to the richness of the natural world, rather than as a technical skill that is inaccessible to all but the most mathematically talented.And even though these problems may appear to be recreational or magical in nature but they are actually based on sound mathematical concepts..
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The second question, hard to answer from the standpoint of mathematics-as-art or human invention, could be posed by Morris Kline: the study of mathematics and its contributions to the sciences. "Math is our one and only strategy for understanding the complexity of nature," says Ralph Abraham, a mathematician at the University of California Santa Cruz, in NOVA's Hunting the Hidden. Mathematics, physics and chemistry can explain patterns in nature at different levels. Patterns in living things are explained by the biological processes of natural selection and sexual selection.
Most of my physics colleagues take them to mean that nature is for some reason described by mathematics, at least approximately, and leave it at that. Let’s take a look at how these numbers appear in nature.
Fibonacci In Nature. One of the easiest ways to explore Fibonacci numbers is to count the petals on a flower. Very often there will be 5, 8, 13, 21 or 34 petals–or a number very close to that. I love, love, love finding fractals in nature.
I’m a bit of a math geek and hippy nature lover, and several times a week I go on what I like to call Math Walks, where .