flipped classroom Khan Academy technology trigonometry vine

Ambiguous Case Vines

We all live in a consumer’s world, and we do an amazing job at acting entitled. These two factors have culminated in the invention of Vine–an app used to create six second, looping video clips.

Yet another way in which students can create, share, and network around media. Unfortunately, I feel like my students don’t often have an attention span longer than a Vine video.

graphing numeracy PBL projects relations technology

YouTube Relations

My goal this semester was to continue to improve my use of formative assessment (largely through the use of whiteboarding) and expand the role of Project-Based Learning in my classroom. Up to this point, I have developed a wide-scale PBL framework for an applied stream of math we have in the province called Workplace and Apprenticeship Math. Those specific topics lend themselves very well to the methodology; they are a natural fit for PBL. I am still looking for ways to branch the intangibles from PBL into a more abstract strand of mathematics–one that includes relations, exponents, functions, trig, etc. 

classroom structure PBL projects technology

Project-Based Pitfalls

Those of you who follow me on twitter or read this blog regularly know I have been struggling to implement wide scale Project-based Learning (PBL) into my Workplace and Apprenticeship mathematics courses. This strand of classes is probably unfamiliar to those outside of Western Canada. I have included a link to our provincial curriculum below. You can skip to the outcomes and indicators to view which topics need to be addressed. (Page 33)
classroom structure technology

Polling in Math Class

This past Monday I attended a professional development focused around technological infusion into our teaching. I will be the first to admit that this topic is not often tailored toward the math teachers in the building. In the morning, virtual classrooms and movie making dominated the discussions. I didn’t see the implications for my mathematics classroom, until the afternoon. A facilitator introduced me to the SMS text messaging technology of polling.

functions linear functions tasks technology

Linear Functions With a Bang

Many teachers tell me that it is their creativity that limits their ability to be adaptive in the classroom. Somehow the “reform” movement (or should I say re-movement) has pigeon-holed itself into a connotation where high-energy teachers give vague tasks to groups of interested students. Out of all this, curricular outcomes explode in no particular order. This can’t be further from the truth. In my view, the biggest steps toward changing student learning is changing teacher perception.

Khan Academy reflection technology

Khan’s Place in Math Education

It seems that every educational blogger has voiced an opinion on the growing popularity of the Khan Academy. I am actually quite surprised that Musing Mathematically has largely avoided the topic during its meager 5 month existence. The movement of online lecture snippets has polarized those in the educational community; some teachers detest that Khan claims that sitting in front of his computer can even be close to “education” while others realize the efficiency of his method and subscribe wholeheartedly. I have been sitting passively over the last few months reading developments and arguments, and yesterday evening found an article that solidified my opinion of Khan. As an educator, I applaud his vision and initiative, but I feel like he is overestimating his project’s niche of influence. 

functions pattern technology vertical line test

Destroying Functions

I have spent the better part of 2 weeks going over various mathematical relationships in my Grade 10 class. They have been represented as tables of values, arrow diagrams, and sets of ordered pairs. Relationships, both qualitative and quantitative, have been defined, analyzed, and graphed. My focus on graphical literacy has been previously detailed on the blog. See this link for details.

Numerous relationships were handled. Students we required to create a family tree and then represent its branches as a table of values and set of ordered pairs. Throughout the various exercises, the words “input”, “output”, “domain”, and “range” were consistently used. My family tree mapped the connection between a Domain of “Names” to a Range of “Familial Relationship”. Some of my ordered pairs then became:
right triangles roots tasks technology

Measuring Roots

I stumbled upon the “root” of this activity late in the school year after I had already taught the unit on radicals and their approximate values to my Grade 9s. I modified its purpose, but the original framework is credited to John Scammell. (@scamdog) I found the concept to be a fairly easy one for the students to grasp once the identity of a root was explored. Students know what a square root is. In fact, I was challenged by a 7 year old boy who I was babysitting just the other day. His older sister–an 8 year old genius–was obviously giving him a crash course in radical mathematics. She had explained to him that square roots can be presented as a problem. He challenged me with this:
“What is the Square Root of 3? I mean, what is the square root of 9?”
factors polynomial technology

Manipulative Revelation

I completed school before manipulatives were in vogue. I am still not sure that they are today (where I teach). I know that my department’s manipulatives are locked up in a cupboard. In this Potter-like clandestine state, I didn’t even learn of their existence until the end of the year. I was moving classrooms, and found a pile of algebra tiles that the previous teacher had left behind. I didn’t discover that I had manipulatives available to me until, ironically, I inquired where I could dispose of this rather large supply of algebra tiles. When I opened the doors of the cupboard, my eyes were bombarded with a vibrant display of primary colours; it is the bright reds, blues, and yellows that initially deter high school students from using these instruments. It creates an aura of immaturity and frivolity. They are coloured in such a way that one may expect students to pack their algebra tiles up neatly and proceed to recess or nap time. Kindergarten students play with blocks; algebra deals with “big-kid’ stuff–no use for toys.