TeachNow, Teaching and Learning With Processes in Math

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...

School is where students spend a large part of their lives. It is a place where a significant part of intellectual and emotional development occurs, whether it is from the curricula or from interactions with others. It is a place where a large amount of socialization occurs. I see schools as a mirror into a society that reflects how much the society cares for the individual. It is my belief that building a safe nurturing society requires the building of a classroom that is one of caring and concern for the students and teacher. This belief is based mainly on my last two years of High School and my time working for an oil service company. I attended a small International boarding school in Malta. The school had 165 students from K-12 th grade and had students from twenty-one nationalities. It was a place where peer pressure was drastically less than in traditional American high schools because having a peer group means having several people agreeing about something that acts as a ...

I have found the following things effective in creating high expectations in my classrooms: 1) Establishing that I am there to help them become adults in their thinking through the instruction of logical thought via Mathematics. 2) Teaching a problem solving process that is visible to the students and applicable to real-world problems. 3) Reflective journal writing about the strategies students use to prepare for and do summative assessments. 4) Constant reminding about how Mathematics is a fair subject (moments of genius are always followed by moments of stupidity) 5) Student work written work must be clear enough so that anyone in the world can understand what the problem is and what the student's approach was, and how the solution was obtained.  These factors combine to create an ecosystem that makes high expectations a natural consequence of our work in class. I present adult life as something quite complex and that dealing with life's unexpected pr...

This first post is for the completion of an assignment that is part of the work I am doing for obtaining my teaching certification. I am required to analyze given resources for the way in which teachers set high expectations for their students. The first video is  Roller Coaster Physics , and it shows how students in a STEM lesson for 5th-6th graders in New York apply an engineering process to examining the Physics behind roller coasters. Students are building model roller coasters using foam pipe insulators, marbles, adhesive strips and sandpaper. They have to design and build roller coasters for safety, fun and length of travel, similar to how Engineers design to a specification. The language used by the teacher to describe the way the problem is posed is the same as the language used by Engineers. This is a subtle way to create high expectations as students researching various aspects relating to their work will find many internet pages of engineering companies that use the same...