Mathematics from the masses #2

The web is awash with wonderful resources for teaching mathematics - plus some sites pedalling pedagogy best avoided.  What follows is a purely personal selection of some of the more interesting and worthwhile sites that beamed out from my screen this month. (Follow the underlined blue links to be taken to the sites mentioned.)

So you think you know how to teach mathematics?

• The 2011 TIMSS study was out this month - and produced much hand wringing all over the globe.  This link takes you to a site where you can access the report - and commissioners comments etc.  It seems that maths education is in trouble just about everywhere.
• This is probably not news to most mathematics teachers - an article from the broader press that highlights the changes away from textbook focussed instruction and the improvements that can come with it.  US site dailybreeze.com reports on the success of teaching for meaning rather than memory in a local high school.
• A collection of maths instructional videos at Mathcasts. Suitable for  high school students.
• From the Detroit News comes an article of schools installing analog clocks in order to help children tell the time.  It goes on to mention their experiences that children can use digital clocks more easily - but that this doesn’t necessarily translate into genuine understanding of the concepts involved. A welcome example of ensuring conceptual understanding over procedural competence.
• From England’s Guardian newspaper a sensible discussion about reform of the mathematics curriculum in England - with the observation that you can’t necessarily “cherry pick” techniques from one country and transport them to another, but recognising that the approach of some countries does seem to produce better results than others.
• Also from England is this piece on the BBC site discussing the fact that rushing through the curriculum does not allow for the development of deep understanding. It is an issue for teachers all around the globe.   This is an issue more worthy of discussion than the hand wringing that has been seen around the world as the latest round of international testing results have come out.  Surely getting the curriculum right, and creating space for genuine understanding of the key developmental concepts is more important than the current league table results? Fixing the former will address the second.
• Vedic mathematics is a fascinating - and neglected area. This post / video at Firstpost provides an introduction to those who are not familiar with it - and might prompt further exploration. A personal blog about the fascinating story behind the “rediscovery” of Vedic mathematics might also interest.
• Why is the sky blue? This simple question takes some serious explanation - and is not without mathematics to make sense of the science.  Would suit upper high school students.
• The “12 days of Christmas” gets a fair run in many mathematics classrooms at this time of year.  This self produced video on youtube uses it to explore triangular numbers and goes on to the classic “handshake at a (New Years Eve) party for good measure. Fun and has potential if pitched at the right grade level.  (Apologies to the anonymous creator - can’t attribute due to lack of details in the clip.)

Just for fun

• This prediction trick has been around in more traditional forms for a while - but it has been given a retweet for the youtube generation by Richard Wiseman. Lots of fun.  
• This video is great - The Amazing Anamorphic Illusions. If you like the illusions there are links to the images so you can “perform” the same trick yourself.

Hmmm....
A collection of TED talks about mathematics.

• 8 math talks to blow your mind -  hard to elaborate on the title really. My favourite was / is Benoit Mandelbrot’s talk on fractals - but that’s just a personal preference. They are all worth watching over a cup of coffee.
• “Is Zero an even number” asks the BBC. Brief piece re the public perception of zero.

More from before

• In Maths from the Masses #1 I linked to some research suggesting that some people literally feel pain at the thought of “having” to “do” mathematics.  This is piece from the Newstatesman follows a similar vein  - but interestingly, people’s fear of mathematics seems to disappear when they actually start “doing” it (as opposed to merely completing endless calculations).   This is a widespread issue and impacts on  parents. How do parents who suffer from maths anxiety support their children at home?  This piece from the Irishtimes.com addresses this issue via the lens of confidence rather than calculations and contains some sensible advice.

Math page
If you enjoyed this post you might enjoy exploring my maths page which features other posts of a similar nature - some with video worth using with students, and some recreational maths developed to share a love of mathematics.

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Credits: All links go to original sources.

Image from Google images:  http://web1.northmead-h.schools.nsw.edu.au/moodle/pluginfile.php/2/course/section/1/maths21-15bpx4o.gif

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How to be a great maths teacher #2 - what the research continues to say

There is no shortage of people telling teachers how to improve education.  Sometimes it seems that all the educational experts are either cutting hair or driving taxis - or perhaps in public office.  So it is useful to find clearly written advice based upon educational research and free from economic motivations. The International Academy of Education (IAE) publishes a series of pamphlets that distills educational research into useful summaries of current teaching techniques that have been found to promote student learning.  ”Improving student achievement in mathematics” by Douglas Grouws and Kristin Cebulla provides a succinct  summary of how effective educators  can approach their teaching.

Their research suggests that teachers can improve mathematical learning via;
1.Opportunity to learn
The extent of the students’ opportunity to learn mathematics content bears directly and decisively on student mathematics achievement.  “As might be expected, there is also a positive relationship between total time allocated to mathematics and general mathematics achievement.”  No surprise there I suspect - but this aspect is worth contemplating; “Short class periods in mathematics, instituted for whatever practical or philosophical reason, should be seriously questioned. Of special concern are the 30-35 minute class periods for mathematics being implemented in some middle schools.”
2. Focus on meaning
Focusing instruction on the meaningful development of important mathematical ideas increases the level of student learning.  Teachers should stress “...the mathematical meanings of ideas, including how the idea, concept or skill is connected in multiple ways to other mathematical ideas in a logically consistent and sensible manner.”
3. Learning new concepts and skills while solving problems
Students can learn both concepts and skills by solving problems.  This clearly addresses the “chicken and egg” issue of some teachers - it is NOT necessary to teach specific computation techniques BEFORE addressing real life applications. “There is evidence that students can learn new skills and concepts while they are working out solutions to problems.”  
4. Opportunities for both invention and practice
Giving students both an opportunity to discover and invent new knowledge and an opportunity to practise what they have learned improves student achievement. The research finds that in the USA over 90% of class time is spent on practicing routine procedures.  In Japan about 45% of instructional time is spent practising routine procedures, 15% applying procedures in new situations and 45% inventing new procedures or analysing new situations. Like to predict which system is ranked higher in international comparisons?
5. Openness to student solution methods and student interaction.
Teaching that incorporates students’ intuitive solution methods can increase student learning, especially when combined with opportunities for student interaction and discussion.  Student interaction - sharing their solutions and the how they approached maths tasks - makes for enhanced student learning.  The notion of a good classroom is a quiet classroom with children working in isolation is simply not supported by the research. Students learn better when they interact - which, if the social-constructionist theory of learning is applied,  is what we would expect.
6. Small group learning
Using small groups of students to work on activities, problems and assignments can increase student mathematics achievement.  Again, co-operative methods of teaching featuring both group goals and individual accountability are associated with enhanced student learning. Teachers would be advised to select mathematical tasks that lend themselves to group exploration rather than simply getting students to “work together” on standard tasks.
7. Whole class discussion
Whole class discussion following individual and group work improves student achievement.  The adult in the room need not be the only teacher in the class.
8. Number sense
Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important.  Number sense - that feeling accomplished people get when they get an answer that “doesn’t look right” - is an important part of developing mathematical skills...and it requires that students are actually thinking about what they are doing, why they are doing it,  and estimating / predicting internally what sort of result would be reasonable.
9. Concrete materials
Long-term use of concrete materials is positively related to increases in student  mathematics achievement and improved attitudes towards mathematics.  So, a warning sign of a less than effective teacher may be the pile of worksheets students are expected to complete. Combine this with a lack of manipulatives or concrete support materials and students have a problem - and it isn’t the mathematics.
10. Students’ use of calculators
Using calculators in the learning of mathematics can result in increased achievement and improved student attitudes.   Study after study support this notion. The use of calculators enhance mathematics learning.  Why? It lets the students think about the mathematics, not the calculation.

Grouws and Cebulla add a caveat to their list of behaviours - the quality of the implementation of the teaching practices listed above greatly impact upon student learning; for example, it is not only whether manipulatives are used but how they are used that determines effectiveness.  

Much of this list will not be new to those with an interest in mathematics education. However, it seems to my casual eye that mathematics classrooms are often still the domain of worksheets with a focus on procedural competence rather than conceptual understanding, places of compliance rather than engagement.  Reading and discussing research findings such as this may help us improve the quality of our mathematics teaching. Reading the original pamphlet would be worthwhile for all teachers with an interest in the area.

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An earlier post - “How to be a great mathematics teacher - what the research says” was mined from another pamphlet in the IAE’s “Educational Practice Series”.  The post summarises the content of that pamphlet and provides links to the original source material - which is well worth reading.

Those with an interest in improving mathematical pedagogy might like to read a related post dealing with the work of Alistair McIntosh - Improving numeracy with the 7Cs.

Those with a general interest in mathematics might enjoy the maths page on this site which collects a range of posts dealing with mathematics.

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Credits: All links go to original sources.

Image: via google images: http://www.kingslangley.ps.education.nsw.gov.au/images/Math-Symbols.jpg

Mathematics from the masses

The web is awash with wonderful resources for teaching mathematics - plus some sites pedalling pedagogy best avoided.  What follows is a purely personal selection of some of the more interesting and worthwhile sites that beamed out from my screen this month. (Follow the blue links to be taken to the sites mentioned.)

So you think you know how to teach mathematics?

• “Stop teaching Calculating, Start Learning Maths” - Conrad Wolfram

Conrad Wolfram is renown as a “boat rocking” thinker and innovator.  This presentation challenges current educational methods for teaching mathematics.  In an entertaining speech Wolfram asks what is mathematics and then describes it as a four stage process consisting of:

1. Posing the right question
2. Putting the question into a mathematical framework or context
3. Calculating
4. Converting the answer back into a real world context.

Wolfram states that students spent 80% of their time at stage three - performing calculations, often manually.  He states that this is odd given that computers / calculators can do this much better than any human brain and that we should be concentrating our efforts on the other three stages.  A thought provoking video lasting 26 minutes - watch it over a coffee and think about it long after.

• Open ended questions.

The maths world is awash with the power of open ended questions rather than a steady diet of closed questions.  But how do we formulate good open ended questions?  This powerpoint, based upon the work of Peter Sullivan, shows how it can be done.

• Early Counting . Research cited at edweek.org says that teaching pre-schoolers to count (as opposed to just recite numbers) to 20 is an advantage later in life

Resources that you might find useful.

• A pinterest site shared by classroom teacher Laura Chandler with lots of resources used by mid-primary teachers.  Not all of it pushes the boundaries of mathematics teaching but much of it would be useful to classroom based teachers at this level.

• Mathplayground - a good site for classroom teachers with lots of areas to explore - allows effective teaching not just drill and practice.

• NCES Kid’s Zone.  A collection of web based tools for graphing and probability for primary students.  The applications are accessed via buttons on the top of the screen.
• A+ click A wide ranging free site from grad 1 to 12 covering wide range of mathematics. Problem and logical thinking questions to suit the needs of most teachers.
• How many texts are sent every day in your town?  The New York Times provided this bit of maths based on a perhaps surprising statistic - that the number of texts sent last month fell for the first time in history.  However, the linked article provides all the information students would need to extrapolate to your home area. If we assume that the number of texts sent per person is constant across all areas (but we may choose not to accept this assumption - coming up with another figure might be useful in itself) and the population of our area is (???) then how many texts might be sent from our home?  In fact, challenging the statistics provided might be even more fun. What is the average number of text sent each day by members of your class? Would this hold true across all grade levels and classes? How might we find out? Once done, what is our estimate?

Hmmm...

• Not everyone enjoys mathematics.  New research has found that just thinking about doing mathematics can cause headaches in some people.  
• Still on the brain, Scientific American reports research that suggests that the brain can do mathematics unconsciously. (This might explain the phenomena of students who appear asleep in class but still manage to get some work done.)

Math page
If you enjoyed this post you might enjoy exploring my maths page which features other posts of a similar nature - some with video worth using with students, and some recreational maths developed to share a love of mathematics.

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Credits: All links go to original sources.
Image from Google images: 
Image from Google images:http://www.ihub.co.ke/blog/wp-content/uploads/2012/10/social-media-banners.jpg                                                    ~~~~~~~~~~~~~~~~~~~~~~~~~  

How to be a great mathematics teacher - what the research says

Being a teacher is hard work. Being an effective teacher is even harder. It is surprisingly difficult to find clear advice on how to improve classroom performance - or rather, it is surprisingly difficult to find advice that is pedagogically sound or not advocating some form of educational bandwagon. To the rescue comes a series of pamphlets produced by the International Academy of Education - an organisation with the aim of producing “a syntheses of research on educational topics of international importance”.  Despite the somewhat weighty title of “Effective pedagogy in mathematics” they have produced a highly readable, highly relevant booklet containing some principles of effective mathematics instruction.

According to the authors of the booklet,  Glenda Anthony and Margaret Walshaw, both associate professors at Massey University and also directors of the Centre of Excellence for Research in Mathematics Education, the traits of effective mathematics pedagogy can distilled to;

1. An ethic of care
Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies. “Teachers who truly care about their students work hard at developing trusting classroom communities.”
2. Arranging for learning
Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas.
3. Building on students' thinking
Effective teachers plan mathematics learning experiences that enable students to build on their existing proficiencies, interests and experiences.
4. Worthwhile mathematical tasks
Effective teachers understand that the tasks and examples they select influence how students come to view, develop, use and make sense of mathematics.
5. Making connections
Effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences.
6. Assessment for learning
Effective teachers use a range of assessment practices to make students’ thinking visible and to support students’ learning.
7. Mathematical communication
Effective teachers are able to facilitate classroom dialogue that is focused on mathematical argumentation.
8. Mathematical language
Effective teachers shape mathematical language by modelling appropriate terms and communicating their meaning in ways that students understand.
9. Tools and representations
Effective teachers carefully select tools and representations to provide support for students’ thinking.
10. Teacher knowledge
Effective teachers develop and use sound knowledge as a basis for initiating learning and responding to the mathematical needs of all their students.

The booklet is well worth reading and expands upon the extracts presented above.

There is little contained in the publication that will shock educators with an interest in mathematics teaching who have ventured beyond the use of standardised worksheets or textbooks.  However, there are some really reassuring aspects to this booklet. What pleases me most is that an ethic of care is mentioned first - caring for both the student as a learner of mathematics but also as a person.  This reflects the adage I first heard decades ago when I was training; “Students  don’t care how much you know until they know how much you care.”  Mathematics tends to have a dry and dusty “skills based” reputation so it is reassuring to see such a significant body placing emphasis on the teacher-student relationship as being of fundamental importance to effective teaching.

When we care about our students as much as the subject good things tend to result.

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Those with an interest in improving mathematical pedagogy might like to read a related post dealing with the work of Alistair McIntosh - Improving numeracy with the 7Cs.

Those with a general interest in mathematics might enjoy the maths page on this site which collects a range of posts dealing with mathematics.

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Credits:
All source material is hyperlinked within the post.
Image via google images: http://montymaths.files.wordpress.com/2012/09/20120930-1150041.jpg?w=490

What you see is what you get - literally

This is a very well known optical illusion - it seems that everyone has seen it.  Everyone knows that it is either two faces or a vase.  Wrong.  It is both. It is two faces and it is a vase - but you can’t see them at the same time.  It is a classic demonstration of attention equals perception - we see what we are looking for.

Over time, we tend to wear lens’ that frame our vision, that shape our perceptions. We  learn from experience and form our world view according to those experiences.  However, once our world view is established the reverse seems to happen - our expectations and beliefs  actually shape our perceptions;  in other words, we see what we expect to see. Literally.  No less a figure then Einstein wrote about this - and he believed that we not only tend to see what we expect to see but that we ignore what doesn’t fit our expectations.   This holds true, not only for psychological perceptions - but also for our physical bodies. What we think determines what we feel.

For educators this is significant. We’ve all heard studies of self-fulfilling prophecies where teacher expectations predict student achievements.  (Strangely enough we tend to recognise this as a theoretical consideration but rarely seem to acknowledge it in our own practice.)  In short - we tend to see a child as a slow-learner, smart, a behaviour problem...and ‘lo and behold the child performs to our expectations.  The child who is perceived to be a behaviour problem tends to become a behaviour problem,  or at least is perceived to be one.  Perception does indeed become reality.

This means that children may become locked into our version of  reality … which in turn becomes their own. Our view of students may become their version of themselves.

Perhaps an answer is in training ourselves to look for the things that surprise us, for the things that don’t follow a pattern or meet our expectations.  We need to train ourselves to see what is really happening rather than think in mental cliches.  In practice this is not as easy as it seems.  The notion of  observing students, really observing, is important.  Perhaps the increasingly popular notion of the “focus child” offers some help.  During this time, as well as learning the strengths and areas for further development, perhaps teachers should try to discover something that surprises them about the student, to find out something that they did not know about the child, to take the chance to remind themselves that this student is also a person.

When we approach our students with a deficit model we limit our perceptions to what they can’t do.  Shifting our focus to what they can do, perhaps adopting a strength based approach, and helping them to build on that might just provide  the shift in emphasis that is needed to re-engage those students who can’t see any relevance or purpose in schooling.

It’s an idea worth looking at.

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Related posts dealing with “The more I practice the luckier I get - Mindset and Carol Dweck”  and another dealing with the importance of attitude - “The second most important word in education” may also be of interest.

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Credits:
Links are active and go to the appropriate sites.
Image via Google images: http://s2.hubimg.com/u/2012669_f260.jpg

The second most important word in education?

It has been said that the most important word in the language is a person’s name.  And it is probably true - we all respond well to the use of our name, we feel that the speaker knows us, which makes us feel valued.

But, at  professional development session recently with Dylan Wiliam, author of “Embedded formative assessment”,  he mentioned a word he ranks as the most important word in education.  “Yet.”
It is a simple word that carries a powerful message.
Consider the child who says “I can’t do this.”  The educator’s response is “Yet."


The message is clear - this simple word sends powerful messages;

• You may not be able to do this task now, but with effort and practice you will be able to.  

• You have the capacity to do this.
• You can improve.
• You can get better.
• You can and will learn.
• Making an excuse is not an escape -you can and will learn this thing.

What a simple way to deliver a powerful message - possibly the most effective way of sending this message I’ve come across - yet.

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Readers might like to read a longer and more detailed post on a similar theme - “The more I practice the luckier I get - mindset”  here.

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If schools are gardens of children - I want to plant seeds

Schools have been likened to gardens. It’s well known that the German educator Friedrich Frobel coined the term “kindergarten” - which means “children’s garden”.  If that’s the case, then teachers can be likened to gardeners.  The metaphor has much to recommend it - but recently I’ve been asking myself do I do anything but weed the garden? Do I actually plant any seeds?

For classroom teachers the answer to this is easy - of course teachers plant seeds. They do it every day, in every lesson.  But the answer is not so obvious for educational administrators. Sure, we work hard to ensure that the garden has everything it needs, and we support our “gardeners” to the best of our ability.  But it is the “gardeners” who actually plant the seeds.

So today I left the paperwork for 15 minutes  and sat on the floor while a grade one child read me a story.   I did a lot of other work today - including some significant weeding and supporting of the “gardeners”. I dealt with a lot of students - but mostly “weeding” or perhaps “pruning” might be more apt. I did a lot of good things.  But as I walk towards the car park thinking of the highlight of my day it was the 15 minutes I spent on the floor hearing a child read.

I had planted a seed.

The curse of Max Headroom in the classroom...and everywhere?

Many years ago there was a short lived T.V. program called “Max Headroom”. It was a spoof on egotistical T.V presenters and supposedly hosted by the worlds first “computer generated host”. It wasn’t -  it was a heavily “made up” actor.  Part of the scenario was that the world had evolved into a place where there was a TV everywhere - in every private room, in every public place - everywhere. Everywhere you went in this future world Max was there with you, babbling away in the annoying smarmy language that is the domain of television hosts. There was no way to escape this for the TVs came with no “off” switch. The television could never be turned off, never be silenced - it was a constant aspect of people’s lives.

What was once a parody is now almost reality. Screens are with us now far more than even in the Max Headroom scenario - screens are not only everywhere but they are mobile; computers, tablets and smart phones mean that we now have screens with us everywhere all the time.  Children in cars now don’t have to ask “Are we there yet?” They may have DVDs to watch or PSPs (or equivalents) to keep them occupied.The social impact of this is debated frequently in social media and serious literature.   

I’m far from a luddite. In fact, I am a huge fan of technology. I enjoy being online and consider the web as much a part of my recreation as of my employment.  

But it occurs to me that, in an age of “screenagers”, we are actually missing something. Our students are conditioned to rapidly respond and react to stimuli via the screens. They can find out what other people think in an instant.  But what do they think? When do we teach them how to reflect?

I’m not simply speaking here of using the powerful  “wait time” approach when asking questions in the classroom. When do we teach students that there are some things that Google can’t answer, that merely “liking” something on Facebook is not really making a social contribution or a sign of involvement?

I’m talking about giving students time in which to think about matters of substance to them.  But what are these significant questions? What is important to our students?

Perhaps we should ask them.  
In person.
Face to face. 

As Miles Kington said, "Knowledge is knowing the tomato is a fruit, wisdom is not putting it in your fruit salad."  

Since knowledge is now effectively available at the press of a button we need to develop wisdom and understanding - and that means giving students time to think for themselves.

Unless of course there’s an app for that.

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Credits:
Active links go to original sources.
Image via Google images:

How an apple changed my world...

I’m a little uneasy writing this post.  It takes me so far outside my professional comfort zone that actually committing my thoughts to screen is challenging.  But, if there is even a grain of truth in what follows, the implications are significant...

I was intrigued when shown some isolated images from Masuro Emoto’s book “The Hidden Messages in Water”.    In essence the claims are simple - that our thoughts and words can impact upon water. When water exposed to various influences is frozen and photographed under certain conditions crystals are often visible - and there can be significant differences in the shape of these crystals. Emoto claims that positive thoughts, words and music result in well formed, balanced “snow flake” like crystals whereas negative thoughts and words produce malformed murky crystals that are not pleasing to the eye.  
The clip below provides a clever introduction to Emoto’s work.

Those who would like to see more might enjoy this slideshow via Youtube.

My reaction was one of scepticism; I dismissed it as new-age pseudo-science.  Even a layman such as myself could see flaws in Emoto’s work.  The information about how the images were captured is superficial - meaning it would be hard to replicate the work.  Only one image of each stimulus is provided.  Were all samples identical - or even similar? Were there “failures”? If so what did they look like?  How many “successful” images followed each stimulus?    These and a host of other questions flowed readily. Reading Emoto’s book did not answer these questions.  The fact that the answers to such obvious questions were not provided was, to my mind,  daming.  However, it haunted me.  What if there was some truth to it?

I soon discovered this clip which suggests that Emoto’s work may not be as obscure and off-beat as I had first thought. 

This would suggest that something odd is actually going on - unless this is an elaborate hoax, there is support for the notion that water is influenced by the people who come in contact with it.

While researching further I came across a balanced critique of Emoto’s work which asks many of the same questions that I had and is well worth reading. As worthy as the article is, the comments following  are also worth exploring. Hidden amongst the range of sceptical responses and uncritical acceptance was a link to a personal blog which showed both initiative and religious belief - in equal parts.  In a variation on a process mentioned in Emoto’s book an apple was substituted for water. Given that living things are mostly water, the theory goes, if you subject any living thing to the stimuli mentioned by Emoto then you might be able to produce an observable effect.  Quanita Rizy’s blog contains photos where the apple does in fact show such effects.  Rizy had replaced the generic positive messages with quotations from the Quran but the photos seemed to indicate that something odd was certainly occurring.  Two sides of the apple were clearly aging differently. Moreover, they provided an easily replicated procedure to test the hypothesis.
So I did just that.  I cut an apple in half and placed each half in a sealed “sandwich” bag. Then I spoke to each half - using the terminology used by Emoto himself. The positive message was “Love and gratitude” whilst the negative message was “You fool”.  (The irony of the situation did not escape me - here was me calling half an apple a fool yet I was the one talking to a piece of fruit.) The apple halves were then placed side by side in a disused room with conditions which, to all intents and purposes, were identical.Twice a day, in the morning and in the evening, I spoke the words to the fruit. After six days I asked an interested observer (you might not be surprised to see how much interest is generated when you start talking to fruit!) was asked to identify which half was in the better condition - the “Love and gratitude” half was correctly identified easily.  

This experiment now leaves me with a challenge. My small scale experiment tends to support Emoto.  I find this fascinating … and the implications are significant.  If a piece of fruit really does respond to language then how much more so is a human being affected by harsh words?  

We do not need to adopt “new age” philosophies to know that feedback that we give to students is significant. (If you need a refresher on why this is so click here.)

Regardless of the “truth” or otherwise of the water crystal belief perhaps it is timely to remind ourselves that the youngsters in our classes are more than students - they are people. Each person on the planet deserves to be valued and respected - not because it improves student outcomes, but simply because people are so much more significant than apples - or even a pretty water crystal.

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Challenge:  I will continue to “test” the hypothesis using the methods outlined above. I will also be trying a variation involving cooked rice mentioned in Emoto's book. There are examples of this on Youtube as well. I'd if I’d be REALLY interested in hearing from anyone else of a similar mind who also conducted their own investigations. “Failures” would be just as interesting as “success stories”.

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Credits.
All embedded links go to original sources.
Cover to Emoto’s book “The hidden messages of water” via Google images.
"Subway" clip via Youtube:
http://www.youtube.com/watch?v=nWn4QF6dCwM Slide show of images from Emoto's book via youtube:
http://www.youtube.com/watch?v=tAvzsjcBtx8 
Is emoto for real - critique:
http://is-masaru-emoto-for-real.com/
Quanita Rizy’s blog:
http://javeria.wordpress.com/2011/03/07/effects-of-quran-vs-effects-of-music-on-an-apple/
"Water has memory" clip via Youtube: http://www.youtube.com/watch?v=ILSyt_Hhbjg&feature=related