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## Class Opener – Day 60 – Herding the Cats

After a wonderful Thanksgiving break (made more wonderful by the Eagles win over the Cowboys!), it’s the 3-week sprint to the holidays, followed by 2 full weeks before final exams.  There’s a lot of stopping and starting going on, which doesn’t help continuity when thinking about class content.  In my AP Stats class, we are deep into our unit on experimental design, which is filled with ideas, terms and arguments must different than a traditional math class. Groups are working through their “Old Wives’ Tales” project, and after grading some student responses this weekend I need an opener which brings the whole class back into the Stats circle. My friend Glenn Waddell has some awesome resources for statistics on his website, which provided inspiration for today’s opener – a short video from ABC News featuring the placebo effect.

For today’s opener, I asked students to design an experiment which could prove (or disprove) the efficacy of the WYFFT “energy drink”.  This gave groups much to talk about, and a thorough discussion of elements of experimental design, including:

• Treatments: WYFFT is not a “real” drink, it’s just soda. Students conjectured that the labeling and associated signage were the actual treatment. We can compare this vs a plain bottle, or against no drink at all.
• Matched-Pairs: could subjects plausibly participate in both treatments? Is this reasionable?
• Blocking: could the implied reaction be different in men than in women? Perhaps we should have two different experiments?
• Response: what exactly are we measuring? What would be a suitable activity to measure a change in energy?
• Randomization: how will subects be selected for the treatments?

And we are off and running after a long turkey-induced rest!

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## Reflections from TMC14, Part 1 – Steve Leinwand and NRICH

This past weekend, I had the pleasure of participating in Twitter Math Camp 2014, held in Jenks (Tulsa) Oklahoma. 150 math teachers from around the USA, Canada and England, many who had only previously shared ideas and personalities via twitter and blogs, met to share their ideas, successes, best practices, and favorite activities. Morning sessions focused on course and task-specific study groups (I participated in the Statistics group). Afternoons started off with teachers sharing “My Favorites”, followed by a keynote (Steve Leinwand, Dan Meyer, and Eli Luberoff) and a menu of teacher-led sessions. Today is the first of a few recaps I’ll share of this jam-packed learning event.

There’s a crappy 80’s movie “Over the Top” which starred Sylvester Stallone as a professional arm-wrestler who eventually battles for custody of his son (yes…this was a pretty craptastic movie). In the movie, Sly motivates himself by turning his baseball cap to the side. This action triggers some arm-wrestling adreniline receptors, a competitive “on” switch, and Sly is then prepared to kick butt (or…arm).

This is my best description of Steve Leinwand.  A self-described “math education change agent”, Steve is a mild-mannered math expert…until you place him in front of an audience, at which point the Mathmazian Devil emerges! I have seen Steve talk in person twice now (do yourself a favor and check out his Ignite talk on Youtube) and his inspirational message leaves me in a constant reflective state over my classroom practices.

In this time of debates over Common Core, “fuzzy math”, dots and standard algorithms, it’s refreshing to hear a speaker attempt to tackle the question “what is math?”.  In his presentation, Steve offers up two options for defining mathematics:

A set of rules to be learned and memorized to find answers to exercises that have limited real world value.

OR

A set of competencies and understandings driven by sense-making and used to get solutions to problems that have real world value.

Clearly, the first definition is not correct, though I fear there are many who would find aspects of the definition acceptable.  I, and the room, gravitated towards the second definition, but is this a complete picture of mathematics?  I have 2 quarrels…

First, the phrase “problems that have real world value” bugged me quickly, conjuring images of contrived real world problems where kids factor expressions which never really occur naturally so they can find where a fake baseball which ignores some pretty important laws of physics might land.

Does “real world value” necessarily imply context? If a math problem provides insight into an abstract pattern, and the process provides some structure later to tackle real world scenarios, then by transference, the problem had real world value. so I have become ok with this aspect of Steve’s definition.  But I’d like to move beyond the perception that mathematics only adds value if it can be attached to the real world.

Working backwards in Steve’s definition, we reach the phrase  “used to get solutions”? Do all math problems have solutions? Is the primary goal of math to find a solution? Have we failed if we don’t find a solution? Some of the strongest formative mathematical experiences I have had centered around problems for which I never found a solution, or perhaps did not have a unique solution.  I prefer “used to analyze scenarios, either abstract or real-world.”

I appreciate Steve in that he challenges teachers to think about the many ways their students may approach similar problems, sieze opportunities to discuss methods, and let students determine their optimal strategy. Many of the common core math debates focus on method: there is a strange “my way or the highway” attitudes towards standard algorithms. Its refreshing to have Steve champion alternate methods so passionately, and he offers his admiration for the 3rd Standard for Mathematical Practice:

Construct viable arguments and critique the reasoning of others.

The ability to analyze, critique, and assess method is equally as important as the math being done. All of us who talk to parents, colleagues and stakeholders need to remember this and do a better job at effectively communicating the message of what math is really all about.

The Enriching Mathematics site, NRICH, presented by Megan Schmidt in an afternoon session, provides problems with multiple entry-points which lead to argument sharing.  In the session, participants were presented with a Stage 3 and 4 problem from the site, where finding the value of the number marked with the question mark is the goal:

I chose to look at pairs of repeating symbols to craft my solution, while my tablemate dove into developing equations and forming systems. The most frustrating (but coolest AHA) moment for me when Megan offered adding sums of rows and columns as an alternate, quite obvious, possibility.  I am definiely looking foraard to exploring these problems and sharing them with my classes.

Thanks to Steve for giving us all the inspiration to think differently about classroom practices, and to Megan for the perplexing hour of sharing!