Mathematics from the masses #4

Each month I collect some of the gems from the web that relate to mathematics.  This month there are fewer links than previously - maybe I’m just becoming more selective...


So you think you know how to teach mathematics?

• Mathematics curricula all over the world require teachers to teach with rigor.  But what does it mean?  This brief and insightful piece by NCTM President Linda M. Gojak sheds some light on what it should mean.
• Every successful teacher knows that motivated students learn more and more easily than less engaged students. But how do you motivate students in the mathematics classroom? This info from nctm has some useful tips, more correctly they are   philosophical positions that generate teacher behaviour that all teachers could benefit from adopting - and not just in mathematics classes.
• This post at mashable features 8 videos with a mathematical theme showing how much fun can be had with mathematics.
• Another piece from nctm, this time showing how conservation of materials at school can save money.  Most of the ideas are not fully fleshed out - but a bit of creative thought could spark a series of “How much money could we save by...” questions.

Resources

• ICT Magic is a site dedicated to the use of technology to enhance education. This link goes to a section devoted to some worthwhile maths games etc.

Hmm....

• I’m really not sure which side of the fence I’m on with this issue - mobile phones in classrooms. Education Week reports on a study that finds up to 39% of middle school students in the USA use their smart phones for help with homework - yet only 6% are allowed to access their devices during class time.  I’ve taught high school classes so I understand the reasons behind the ban during lessons - but I also understand that smart phones are very powerful devices, most have more computing power than the combined computing power in the control room at NASA during the moon landing.  Surely we can use these resources in some way?
• This piece at Slate tells us that there is now a “new” largest known prime. Discovered by Curtis Cooper of the University of Central Missouri it is  257,885,161-1 - a number so large that it apparently takes 17 425 170 digits to write it.  If you want to get a sense of that click here.  Some interesting discussion and background in this piece - well worth a browse.

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Mathematics from the masses #3

The web is full of great material dealing with mathematics.  Below is a selection of sites, reports and ideas dealing with mathematics in general and the teaching of mathematics more specifically.   The criteria for inclusion is completely idiosyncratic - if it appeals or interests me, or if I think if might be useful to maths educators it gets included.  Enjoy... but be warned - there are some sites listed this month that are seriously distracting and damaging to productivity.

So you think you know how to teach mathematics?

• You have to be smart to do well at school maths right? Wrong. This report  of a German study finds that motivation and work habits are more important than IQ.  Educators should not be surprised by this finding as IQ as a predictor of success (even if it could be measured properly) has long been deemed of questionable worth as a predictor of anything much.   Attitude is everything –  a “growth mindset” is frequently (always?) found to be more important than innate ability.
• Maybe the best teachers are students? This study found a program that used older students to tutor younger ones was very effective. Given so many other initiatives fail this might be worth trying in other places...
• Maybe we simply need to get students to spend more time at school? NPR reports that a number of states in the USA are trialing just that in an effort to curb holiday brain fade and forgetfulness of material “taught” last year. (Maybe making the material worth remembering might be a better approach...)
• Maybe we should all just up and move to smaller towns and leafy suburbs.  This  study reported in Education Week has found that rural and inner city tend to underperform in mathematics relative to their peers from other areas.  (Again, I’m not sure this is really news to experienced teachers.)
• I’m not sure if this is new or simply supporting an understanding of teachers all over the globe. A study has found that students who struggle with mathematics use a different part of the brain to those students who are competent at mathematics.  Those that cope well appear to be using a part of the brain that accesses memory for facts - lending support to the old fashioned notion of automatic recall of basic number facts as being important in mathematical performance.   It has to be said that the study involved only a relatively small number of participants (N=43), but given the hi-tech nature of the study this might not be a major indicator.

Resources:

• Wolframalpha is a great site for online calculations.  This blog from the creators shows some really useful automatic displays related to simple calculations - most if not all teachers of mathematics would be able to find a use for this site - so easy to use but with so much potential to explain answers...   I really like the fact that a completed numberline of the calculation is provided almost instantly - which makes it a really handy way of explaining order of operations to primary age children.
• The PBS Learning media site has lots of useful video / teaching material on a range of subjects -  including mathematics. The parent site can be searched for via subject and grade level. Well worth investigating for some teaching media.
• In a similar vein, everybody’s favourite site “lluminations” continues to be an almost unbeatable source of sound resources based around active learning principles.
• On a related theme comes this blog item revealing that use of Interactive White Boards in maths lessons not only improves student attention and participation but leads to improvement in  maths scores.
• Looking for a really simple site that makes use of your IWB?  This site from harcourtschool allows simple arrow clicking to create visual matchings of equivalent fractions.

• In the same vein, the old fashioned geoboard gets a virtual makeover at the mathlearningcentre.  It may not be as organic as the “hands on” variety but it is still lots of fun … and has the distinct advantage that the “rubber bands” can’t be flicked all over the classroom.

• Mathrecap is a site edited by Dan Meyer - presumably the same maths teacher who made a name for himself with his TED talk on teaching mathematics.  The site recaps (which no doubt explains the name) a variety of presentations made at maths conferences around the USA.   A source of some very worthy techniques and good ideas for maths instruction.
• Normally I’d avoid any article  using the word “cool” in the header - but this time it leads to a collection of maths games suited to primary students.  It’s, … well, ... cool - especially the game called B-Cubed.
• This NPR piece gives some nice examples of how New Zealand teachers are teaching probability - applying Murphy’s Law (“Anything that can go wrong will go wrong”) to stats. Does butter really always fall butter side down?  Some cartoon graphics provide a good starting point for other like minded engaging explorations.
• Math Munch is a blog after my own heart - a site dedicated to cherry picking the best of the web’s maths related site and sharing them with people with a similar mind set.  It is updated on a regular basis (usually weekly) and has a host of really useful educational mathematics related sites as well as material that is simply of a mathematical nature.  Highly recommended - you will almost certainly want to put this one in your favourites.

Hmm....

• Does mathematics make research sounder? Yes - well, apparently we all think so. A recent piece reported on at Freakonomics cites a study where academics were asked to evaluate the strength of research papers - some of which were doctored with meaningless maths out of context.  The maths "enhanced" studies were considered to be the stronger.  The really scary thing here is that the participants all held post graduate degrees.   So what chance does the general public have?
• A rather depressing report in the Mailonline cites UK authorities requiring teachers to return to “traditional” methods of teaching long multiplication and division and away from more progressive processes based on mental maths and number sense.  Looks like the pendulum of reform didn’t even get to complete a full swing ...  teaching procedural competence replaces conceptual understanding yet again...
• Is there a relatively simple formula that governs how long we (and just about everything else) will live? This NPR piece tells more … it appears so (well... maybe). Perhaps. Possibly.

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If you found this post useful you might enjoy my maths page.
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Credits:

All links to original sources.

Image details here.