TeachNow, Teaching and Learning With Processes in Math

In looking at the California Common Core Standards for Algebra 1 I realized that the standards are written in a way that is not that compatible with performance-based assessments. The standards are broken down in a compartmentalized fashion inconsistent with how one might use the skills described in real-world situations. When designing or analyzing things, one checks the work by switching between the text representation (specification), the mathematical model, the computer simulation, and graphical output to ensure things are consistent. In the event a mistake/error is suspected, one must troubleshoot, which could involve checking the Algebra by hand. One works between disciplines and between representations of the Mathematics based on judgement and experience. Good Performance-based assessment should mirror that process or aspects of it. The standards at this level are more basic because you need the student to build a certain level of fluency and automaticity in their work. You have...

Engineers are trained to use a specification to guide their work. Specifications are like standards in that they are statements with some detail that define the space an engineer can move in to create a very detailed and technical design. Standards define the themes and ideas a teacher has to turn into detailed development of student abilities. The term backwards design explicitly connects to engineering as design is basically looking at the need to develop the tool that fills that need. “Understanding by Design” is basically presenting the Engineering design approach in terms that are accessible to those in education. So from my training, backwards design and unpacking standards are the natural way of working. When I first worked in a school that allowed me to choose material, I used the NCTM standards for teaching Algebra 1, Algebra 2, and Geometry. The NCTM standards are similar to the Common Core High School standards and overlap significantly. Consequently, I haven’t found unpac...

This post is an example of how I use backwards design for the creation of a set of lessons for Algebra 1 which is taught in Eighth grade in my school. We are located in Beijing, China and we are teaching California Common Core Math Standards for the traditional High School track (the 2013 Electronic Edition). There are no standards from the Chinese government that address the teaching of Mathematics in Private schools, although there is talk of requiring the material be taught in Mandarin till Grade 9. That is a battle being fought at a much higher level than mine, so I am not dealing with that wrinkle here. Next year, our students will be studying the Cambridge International Examinations IGCSE Mathematics Syllabus 0580, so we do adjust the standards in G8 to align with the requirements of IGCSE. Specifically, the students take written exams in two papers at the end of tenth grade for a total of four hours . In addition, some of the terminology is different and Cambridge forbids...