In math, the usual curricular pathway – or sequence of courses – starts with algebra in eighth or ninth grade. This is followed by geometry, second-year algebra and trigonometry, all the way up to calculus and differential equations in college.

This pathway still serves science, technology, engineering and mathematics (STEM) majors reasonably well. However, some educators are now concerned about students who may have other career goals or interests. These students are stuck on largely the same path, but many end up terminating their mathematics studies at an earlier point along the way.

In fact, students who struggle early with the traditional singular STEM pathway are more likely to fall out of the higher education pipeline entirely. Many institutions have identified college algebra courses as a key roadblock leading to students dropping out of college altogether.

Another issue is that there is a growing need for new quantitative skills and reasoning in a wide variety of careers – not just STEM careers. In the 21st century, workers across many fields need to know how to deal effectively with data (statistical reasoning), detect trends and patterns in huge amounts of information (“big data”), use computers to solve problems (computational thinking) and make predictions about the relationships between different components of a system (mathematical modeling).

What’s more, sophisticated computational tools provide us with mathematical capabilities far beyond arithmetic calculations. For example, large numerical data sets can be visually examined for patterns using computer graphing software. Other tools can derive predictive equations that would be impractical for anyone to compute with paper and pencil. What’s really needed are people who can make use of those tools productively, by posing the right questions and then interpreting the results sensibly.

These alternative pathways involve activities that go beyond students writing examples down in their notebooks. Students might use software, build mathematical models or exercise other skills – all of which require flexible instruction.

Both new and old pathways can benefit from new and more flexible methods. In a traditional classroom, students act as passive observers, watching an expert correctly work out problems. This approach doesn’t foster an environment where mistakes can be made and answers can be questioned. Without mistakes, students lack the opportunity to more deeply explore how and why things don’t work. They then tend to view mathematics as a series of isolated problems for which the solution is merely a prescribed formula.

Conversely, classrooms that incorporate active learning allow students to ask questions and explore. Active learning is not a specifically defined teaching technique. Rather, it’s a spectrum of instructional approaches, all of which involve students actively participating in lessons. For example, teachers could pose questions during class time for students to answer with an electronic clicker. Or, the class could skip the lecture entirely, leaving students to work on problems in groups.

Regardless of pathway, all students can benefit from active engagement in the classroom.

(Story via The Edvocate)