Abstract mathematics has value on its own. But math is also a tool: for science, for practical everyday use, and for satisfying curiosity about how the world works.
Success in math is also essential to keep student's options open to a wide variety of interesting, and well paying, careers. The math skills needed in those careers have been changing. The math standards have changed along with them. While students are still responsible for learning to add, subtract, multiply, and divide, there is now a greater focus on working with fractions and statistics, and using all of a student's skills in problem solving.
This is not an easy change because
1. Problem solving can be hard.
2. It is difficult to classify specific problem solving skills.
3. Progress in problem solving is difficult to measure.
This can make teachers, students, and the adults in their life, gravitate to a math curriculum centered on basic operations where clear right or wrong answers make it is easy to measure growth and to feel successful. However, this kind of math instruction does not prepare students to use math as a tool in science, in a career, or to solve problems.
While students do need to learn what operations mean and when to use them, we need to remember that calculation is just a means to an end. We should not sentimentally withhold the use of technology like calculators and computers, so that we can take advantage of the opportunities they give us to save time and take on yet more challenging and relevant work.
Which brings us to how to teach such a broad, challenging subject.
The most common barriers to success in problem solving tend to be reading skills, a lack of basic conceptual understanding of operations, and endurance. To work through these barriers, we introduce problem solving with visual and video based problems (There are examples of these in the green links sidebar and on the problem solving pages).
This allows students to have a successful initial experience with challenging tasks by presenting the problem without text. It also allows for authentic tasks, such as verifying facts that students are told on T.V, working through the cost of construction for real buildings, measuring the force of gravity, and learning how a car's computer calculates fuel efficiency.
Next, we focus on organizing one's work. As math becomes more complex, with lots of steps and data, students need find ways to organize information. We compare each other's work, look through work from previous years' students, and look at the work of professional scientists and mathematicians in search of ideas and best practices. This gives students experience with separating a task into steps, using diagrams and labels, and making tables.
Finally, we work through actual problem solving tasks, focusing on judging how reliable our solutions are.
At this point, the stage is set to tackle more traditional 'word problems,' of the type encountered rarely in the real world, but often in text books and tests. Students often note that in such word problems the hardest part, finding the data to solve the problem, is done for them.
Equally important in this approach to math is that students, having worked through very tough problems in the past, know how to jump in and start organizing their work, even when faced with a difficult or stressful task. This is what really sets students up for success both inside and outside of school.
teachers doing silly things
2. Math in the Real World
3. Critical Thinking
4. 3 Act Math Videos
5. Visuals to Plan Investigations
6. Sites I Use to Plan