Month: April 2012

NCTM – Saturday

Much quieter here today, as the math folk move out and an antiques show moves in. But still time for some sessions!

Essential Understandings in Grades 9 – 12 Statistics: Preparing for the Common Core.

Very excited for this session today, as one of the speakers is Roxy Peck, former Chief Reader of the AP Stats exam. Also, looking for some ideas for our freshman year prob/stat course.

Big ideas –

1. Data consists of structure + variability: look at math models but explore the big picture

2. Hypothesis tests answer the question, “do I think this could have occurred by chance?” – what hypothesis is more plausible?

3. To evaluate an estimator, you need to consider bias and the sampling method.

4. Describe variability – distinguish different ways distributions are used (population, sample, sampling distributions) and be able to compare them. As more teachers are compelled to teach stats in HS, we need to train for the abstraction of sampling distributions.

How much do sample distributions tend to look like population distributions, and how can samples differ based on randomization?

5. The way in which data are collected matters. The is a risk of error that needs to be acknowledged and quantified. Also, the collection method determines the type of inferential conclusions that can be made. If the sample is not representative of the population, we should be suspicious of generalization.

“as statistics people, we are OK with being wrong 5% of the time” – Roxy Peck

All HS math teachers will find themselves in the dual role of being teachers of math and teachers of statistics. This is a bit scary to me. While many resources are coming out which will assist teachers in presenting statistical ideas, I wonder how many math teachers are prepared to facilitate a discussion, perhaps over many class days, centering on one scenario and its many statistical concepts. A colleague, at the end of the session ,offered that his department is “petrified” of the prospect of being made to teach stats courses. Many great math teachers I know are like musicians playing classical music, adept and expert in the rhythm and complexity of math. How many of my colleagues are prepared to become jazz musicians, and have conversations meander in new and exciting directions?

After attending 2 conference in the last month, and moving through meeting rooms, with various degrees of “fullness”, I have begin to develop the “Large Ballroom Theory”

Large ballroom theory: given a large ballroom with many empty seats, people will

Find somebody familiar and sit with them
Sit in the back, for easy escapability from intolerable sessions
Sit in a location which will maximize the apparent fullness of the room, looking for bare spots

It is the last bullet which I believe could be the start of a full-blown thesis. In the photo above, think about where you would sit? On the end? Which row? Someplace equidistant to others? Or would you sidle up next to a stranger?

Uncategorized

NCTM – Friday

Back on the train. Jealous of the students and coaches from my school headed off to Penn Relays on the train, while I get off a few stops earlier for NCTM. Looking forward to the day…

Supporting the Mathematical Practices: What’s In Your Coaching Toolkit?

This session had an interesting opening activity. Seven statements about classroom culture were provided, and teachers were asked to assess themselves on a continuum? Some examples

From focus on correct answer towards focus on explanation and understanding.
From mathematical authority coming from the teacher or textbook to mathematical authority coming from sound student reasoning.

Already, the activity caused me to reflect upon the textbook-driven culture in schools, and how we approach classroom practice.

How can we provide optimal learning opportunities for students to become mathematically proficient? The team create a check list of “look-fors” which cover each of the 8 Common Core standards, and shifts in classroom practice which attempt to match the new standards.

This was one of the best sessions I have attended, as I have some great ideas here for guiding the teachers I work with through the increased rigor of the Common Core.

Unfortunately, I am off to a track meet tonight, so today’s post is a quickie. A late night tonight, then an early train tomorrow for more sessions.

Algebra Geometry

NCTM – Thursday

Very exciting day….quite a buzz as I arrived today. Looking forward to some interesting sessions in the next few days. The hard part is deciding which sessions to choose.

Teaching Proof: Lessons From an Action Research Study. Pete Johnson, Eastern Connecticut State University

Yesterday, I attended a research session on proof,where’s a 5-person panel each explained research they had done on encouraging justification and proof in both middle and high school math courses. From that session, there were two takeaways for me:

When we provide a proof, for whom is the justification intended? Who is the audience for the communication? Let’s focus on the end user.
An interesting activity is to provide a number of givens, then having students work to support the “strongest claim”. We often tailor arguments to fit our pre-determined conclusions. But what are the possibilities, given provided information?

My first session today continues my focus on proof.

“writing proofs” is not a topic or a bit of content, it is a a process, a way of thinking that evolves over time

Much of the discussion in this session focused on the following challenge:

Prove that if n is an odd positive integer, then n squared is an odd positive integer.

A few approaches emerged. Let n = 2k + 1, then simplify n-squared. Are we guaranteed that the result is odd?

Another attendee suggested letting n = m + 1, but then how do we know that m-squared is even? What is the assumed toolkit of knowns and agreed upon principle in this problem? What does it mean for a number to be odd?

Also, the group tended to focus on the oddness, but have we proven that the result is positive, or an integer?

Findings: Teaching proof as a “separate topic” does not work. Also, instruction in formal logic does not seem to transfer well to mathematical proof.

Engaging Activites for Your Classroom: technology in Middle School Mathematics

The main event of this session featured activities utilizing the TI Nspire CX Navigator system. A few years ago, I acquired the Navigator system for the TI84 calcs, and had used it in some of my classes. But, over time, I found the system cumbersome, and that the classroom payoff was not often worth the set up required. I was eager to try this updated system, as it is now wireless, and integrates with the new color CX calculators.

My first impression is that sending files has become more intuitive, and the entire interface is cleaner and less clunky than the 84 software. The examples demonstrated today were pulled from the TI Activity Exchange, and could easily be edited for use with TI Publish View, which mentioned in an earlier blog post.