The more I’ve learned in this class, the more I’ve come to appreciate the Standards for Mathematical Practice. To explain what I mean, I’ve created the following to summarize what the current mathematical practice standards are.
This is part of the Common Core. When the common core first came out, there were clearly changes in the depth and breadth what we taught. For Utah, the order changed because they adopted the integrated model (meaning instead of Algebra, Geometry, and Algebra 2, it’s Secondary Math 1, 2, & 3). The main concepts and skills are still there, just approached with these practice standards in mind. Curricula and teachers, in attempting to follow these standards, have approached math in a completely different way than how earlier generations were taught. It hasn’t been an easy task before me, but it’s been worth it. I’ve recently gained a new point of view of it through the MAET coursework.
To show how I now see the Standards for Mathematical Practice (and why it works so well with the masters level classes I’m taking), I’m going to address each of the standards.
Make sense of problem and persevere in solving them. The book A More Beautiful Question by Warren Berger describes a system of learning and improvement. He describes successful problem solving of many different people and companies (Berger, 2014). In order to make sense of a problem, more questions must be asked. Persevering to solve the problem is where a great deal innovation and reform have come from. What would the world be like, for example, without the perseverance of Thomas Edison?
Reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, look for and make use of structure, look for and express regularity in repeated reasoning. These could all fit in the definition and how-to of teaching complex thinking. In the link in the previous sentence, reasoning abstractly, constructing viable arguments, critiquing others, and looking for patterns all have to do with complex thinking.
Attend to precision. Probably one of the most challenging aspects for me in writing these posts has been to attend to the detail of writing and citing in APA format. Precision to these details have made the difference between getting a perfect score or a lesser score.
Use appropriate tools strategically. This is basically what TPACK is. Basically, TPACK is a way to describe what should be happening in every modern classroom. There are three main parts to TPACK: technological, pedagogical, and content knowledge. They all overlap and come together to form this framework we teach in. These are standards for mathematical practice and describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. This applies to how teachers teach with technology within the mathematical framework. For students, this means knowing when to use a calculator, online resource, book, etc. effectively.
Modeling with mathematics. Describing the things we’ve learned in this class in blog form is a way that we have modeled what we’ve learned in these classes. In math, it’s important to also model situations with mathematical equations, graphs, sentences, tables, and so on.
What I see now, through the lens of this class, is these standards are basically a Wicked Problem and that each standard lines up with something in this class. For me, a wicked problem is a problem worth doing, though it can be frustrating. From experience, I can say that trying to teaching those standards at the same time is overwhelming. Tempting as it is to have the attitude “if these are all so hard to do, why try?” Knowing now that it’s a Wicked problem makes the attempts at teaching them better framed. The ramifications for attempting to solve/implement (and persevere) may not make a huge difference on a macro level (changing the world) but it will improve the lives of those who try. Trying to teach those standards will make the math world, at least, a better place one class at a time.
Mathis, W. J. (2010). The “Common Core” Standards Initiative: An Effective Reform Tool? Boulder and Tempe: Education and the Public Interest Center & Education Policy Research Unit. Retrieved from http://epicpolicy.org/publication/common-core-standards
Standards for Mathematical Practice (2016). In The Common Core State Standards Initiative. Retrieved from http://www.corestandards.org/Math/Practice/