Author: natbanting

proofs

Exploring Negative Bases

I love it when math works as it should. Such was the case last night when I was looking for a problem to explore. I began by checking my favourite blogs for a quick puzzle before bed. Nothing really stuck, so I tried some searches on twitter. (#math #mathchat #puzzle usually get the job done). I found a puzzle that intrigued me and began to work.

Before I mention the puzzle, I want to say a quick word about school maths. I have a great personal interest in mathematics, and am able to move on past problems that don’t pique my curiosity; we do not afford students the same opportunity. I wonder, if students were given more freedom, if they too would find puzzles and topics that interest them. This is a not the topic for this post, but is an interesting debate in mathematics education. I digress…

First Day Tasks

You don’t get a second chance to make a first impression.

This is naturally true, and although I don’t believe that you can build or destroy a successful semester in one class, it is definitely important to put your money where your mouth is on the first day. I have spent the past few days digging around my materials for the best possible starter activities.

I had some very helpful responses from the twitter-verse, and it prompted me to somehow sort out the information being provided to me. In the past, I have had very productive lessons on the first day. Not productive in the “coverage”sense, but rather in the “intriguing” sense. My goal was to define a set of characteristics that, in my opinion, create a suitable opening day problem.

games pattern probability

A Declaration of Independence

Post author By natbanting
Post date August 16, 2011
No Comments on A Declaration of Independence

I used to be roommates with a magician. He kept all of his materials locked up in a trunk in our hall closet. Although he had devoted himself to the study of human psychology, I still convinced him to crack open the trunk and show me a trick from time to time. This experience was one of the most frustrating yet intellectually stimulating experiences of my life. I was a mathematics undergrad immersed in a stressful environment of number theory, numerical analysis, and abstract algebra. I was being trained to reason effectively, and his antics refreshed my perspective on reality. Life often muddies mathematics; such is the unfortunate reality.

reflection statistics

The Blue Jays Defense

Baseball is mathematically based. It is the best link between the generally nerdy domain of mathematics and generally manly domain of professional sports. The one downside to this statistically driven machine is that the stats can be selected and used to benefit almost any argument proposed. Major League Baseball keeps such extensive records of stats, that there is always an obscure one in support of your argument. Right now the league is in an uproar over the Toronto Blue Jays sign stealing controversy. Some anonymous players claimed that the Jays were stealing signs with a 3rd party and that effected the amount of home runs they hit at home. In an article by ESPN, they use the personal witnesses’ accounts to bring up the topic, but claim that:

group theory pattern tasks

Un-Locking Prior Knowledge

Post author By natbanting
Post date August 8, 2011
2 Comments on Un-Locking Prior Knowledge

I enjoy mathematics in the morning. It wakes my brain up, and makes my coffee that much more comforting. Much of the deliberate mathematics learning that I do takes place in the morning. I say deliberate, because mathematics always finds ways to sneak itself into all parts of my day. Morning is just when I open the door and embrace the learning with open arms.

Today’s dose came courtesy of @republicofmath via @jamesgrime. The problem took longer than I expected, but the result was quite eloquent. I ended up using a method that I had no intention of ever using again. It was the use of this prior knowledge that made the experience valuable.

estimation numeracy tasks

Large Number Numeracy

Gigantic numbers are all around us. This has never been more apparent since the US Debt ceiling became a major issue. The facts and figures are thrown around by the news, and joked about on Late Night television to the point where their potency is diluted. Not many Americans seriously understand what a trillion dollars is. That statement can be broadened to include all earthlings. The comprehension of large numbers is a very interesting task, especially given the role that the media plays in our students’ lives.

reflection

Messy Mathematics

This post is really a vehicle to get a comment that I received on my blog more face time. I thought the potency of the words could not be ignored. It was in response to my post entitled Measuring Roots.

To get the full story, first read that particular entry. Basically, I was reliving my encounter with a small boy where he challenged me to answer a square root problem. He let the answer slip prematurely, and quickly rephrased his question. It was very obvious that he had the answer in mind before the question had begun.

Using this idea, I wrote:

“For students, no matter how young, math begins with an answer. You then form a question, jeopardy style, to help disguise the number. In this case, the child’s thinking shone through because he leaked his answer prematurely.”

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?”

golden ratio reflection

Jets Logo Not So Golden

The experienced hockey fan will recognize the title of this post as a reference to Bobby Hull, who was a legend with the Chicago Blackhawks before coming to the Winnipeg Jets in 1972. He became one of the biggest draws in the fledgling WHA; his blinding speed and rocket shot gained him the nickname “The Golden Jet” league-wide. The Winnipeg Jets folded in 1995, and only returned weeks ago. Today was the unveiling of the new Jets logo; an event that I refreshed the same page for hours to witness. There had been numerous leaks over the past few weeks, but nothing had been confirmed. When the page loaded at exactly 5:00 PM EST I saw this image:

numeracy probability statistics

The “Nearly” in Mathematics

Post author By natbanting
Post date July 20, 2011
No Comments on The “Nearly” in Mathematics

Mathematics is the purest form of science, or at least that is what they tell us in university. This ideology carries over into the school staff; it wasn’t long until another member of the staff referred to me as a “math guy”. As much as this label is also self-imposed, I still struggle to understand what it means. The labels “english guy”, “phys-ed guy”, and “science guy” all persist within the building as well, but there is something that about the title of “math guy” that gets me.