One of the common concerns I hear from parents of students in K-12 schools is that math has changed and that they didn't do this kind of math when they were in school. When addressing their concerns, I let them know that Math hasn't really changed, however, the process of teaching and learning math is much better understood now. Today, there is definitely less of a focus on the rote learning (drill and kill) of years gone by.
This article focuses on the processes involved in learning and teaching math in the K-12 classroom today.
Today, math standards or curricula include both content and processes. The Common Core Standards list the following mathematical practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
K-12 curriculum/standards have these practices/processes in common. Here is a simplified list:
1. Problem solving
5. Proving and Justifying
6. Making connections
What does this look like in a math classroom?
Students should be:
demonstrating that they understand the problem, asking questions, trying different strategies, determining the best strategy, looking for patterns, determining whether a formula is needed, work backwards, analyze and evaluate thinking, exploring possibilities, making inferences, justifying their answers, explaining their thinking, providing evidence, using appropriate representations to show their answers, and use correct mathematical language and appropriate vocabulary to name a few.
How do students demonstrate all of this?
Although they will still learn many of the basic math skills, they will learn the processes above by problem solving. The basic skills give them some of the necessary tools needed but the rich problems in math will allow them to apply deep thinking skills which will assist them throughout the lives.
Rich math problems are usually problems that can be solved by using more than one method, they are problems that will require learners to think critically rather than apply a simple computation.