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.

~~~~~~~~~~~~~~~~~~~~~~~~

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.

~~~~~~~~~~~~~~~~~~~~~~

Credits: All links go to original sources.

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

~~~~~~~~~~~~~~~

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.

~~~~~~~~~~~~~~~

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

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The WISE model - A quick and nasty guide to evaluating classroom ICT use.

I’m fortunate to be able to visit every classroom in our school. Like most schools, we have invested heavily in ICT. Are we getting value for money? Is the investment really improving educational outcomes? In some classrooms I could answer “Yes” - but in some the answer would have to be a disappointing “No”.

It is not necessary to have an in-depth formal instrument or formal testing to get a sense of how well ICT is being used in classrooms.     

The first “rule of thumb” indicator I have is a simple one - are the students CREATING product ...or CONSUMING product... or both?  If the students are simply consuming product, i.e. using “drill and practice” programs or merely absorbing content from the ‘net, then ICT use in the classroom is likely to be making only a limited contribution to student learning. However, if students are CREATING product then there is a good chance that ICT is being put to good use.

If students are creating learning artefacts then a simple acronym provides another lens through which I can quickly evaluate the significance of the classroom program. That acronym is  WISE.

WISE stands for...

W hy? (or WHAT). Why is ICT being used? Could similar artifacts be produced via traditional means? A hand drawn poster is as valid as a Publisher document for example.   What are the teacher’s  SPECIFIC objectives, what are the SPECIFIC curriculum links? What can students achieve  using computers in this context that could not be achieved otherwise?   

I mportant (or interesting) Is the project / experience both IMPORTANT and INTERESTING to the student? (Tasks need to be important or interesting to the student - not just ”fun”.)  If not, then the chances are that the task is electronic “busy work”.

S haring.   How are the students sharing both their end product and the process of creation?  How are they sharing their artifact with the educational community beyond the classroom? If they are not sharing the artifact...why are they producing it in the first place?  If it only has worth inside the context of the classroom then why would students value it? If it has wider significance why is it not being shared?

E valuation.  How do the students demonstrate their learning? Is the artifact itself significant outside of the classroom environment?  What skills need students display / include? Do they know this? How can a development of skills be demonstrated?

This acronym is hardly cutting edge. (I could dignify it beyond it’s worth and call it “The WISE model”.) However, it does provide me with a lens through which to quickly get a sense of how well ICT is being used in a classroom.   As with all technology, classroom ICT is neutral - it is how well it is being used that is important. And to assist with that we all need to be a little WISE when it comes to classroom use of ICT.

~~~~~~~~~~~~~~~~~~~~~~

Credits:
Image = Google images
http://blog.lib.umn.edu/tel/blog/Computers-TwoKdgStudents.jpg

The Poor Scholar's Soliloquy

I came across this piece only recently - despite it first appearing in 1944. Despite its age it seems as modern as tomorrow.  I don’t think any commentary that I could add would improve it. The author, Stephen M. Corey, was Dean of Teachers College, Columbia University.

THE POOR SCHOLAR'S SOLILOQUY

Stephen M. Corey "Childhood Education" - January 1944

No, I'm not very good in school. This is my second year in the seventh grade, and I'm bigger and taller than the other kids. They like me all right, though, even if I don't say much in the classroom, because outside I can tell them how to do a lot of things. They tag me around and that sort of makes up for what goes on in school.

I don't know why the teachers don't like me. They never have very much. Seems like they don't think you know anything unless you can name the books it comes out of. I've got a lot of books in my room at home-books like Popular Science Mechanical Encyclopedia, and the Sears & Wards catalogues--but I don't sit down and read them like they make us do in school. I use my books when I want to find something out, like whenever mom buys anything second-hand I look it up in Sears or Wards first and tell her if she's getting stung or not. I can use the index in a hurry.

In school, though, we've got to learn whatever is in the book and I just can't memorize the stuff. Last year I stayed after school every night for two weeks trying to learn the names of the presidents. Of course, I knew some of them--like Washington and Jefferson and Lincoln, but there must have been thirty altogether, and I never did get them straight. I'm not too sorry though, because the kids who learned the presidents had to turn right around and learn all the vice-presidents. I am taking the seventh grade over, but our teacher this year isn't so interested in the names of the presidents. She has us trying to learn the names of all the great American inventors.

I guess I just can't remember the names in history. Anyway, this year I've been trying to learn about trucks because my uncle owns three, and he says I can drive one when I'm sixteen. I already know the horsepower and number of forward and backward speeds of twenty-six American trucks, some of them Diesels, and I can spot each make a long way off. It's funny how that Diesel works. I started to tell my teacher about it last Wednesday in science class when the pump we were using to make a vacuum in a bell jar got hot, but she, didn't see what a Diesel engine had to do with our experiment on air pressure, so I just kept still. The kids seemed interested though. I took four of them around to my uncle's garage after school, and we saw the mechanic, Gus, tear a big truck Diesel down. Boy does he know his stuff!

I'm not very good in geography either. They call it economic geography this year. We've been studying the imports and exports of Chile all week, but I couldn't tell what they are. Maybe the reason is I had to miss school yesterday because my uncle took me and his big truck down and we brought almost 10 tons of livestock to the Chicago market.

He had told me where we were going, and I had to figure out the highways to take and also the mileage. He didn't do anything but drive and turn where I told him to, Was that fun. I sat with a map in my lap, and told him to turn south, or southeast, or some other direction. We made seven stops, and drove over 500 miles round trip. I'm figuring now what his oil cost, and also the wear and tear on the truck--he calls it depreciation--so we'll know how much we made.

I even write out all the bills and send letters to the farmers about what their pigs and beef cattle brought at the stockyards. I only made three mistakes in 17 letters last time, my aunt said, all commas. She's been through high school and reads them over. I wish I could write school themes that way. The last one I had to write was on, "What a Daffodil Thinks of Spring," and I just couldn't get going.

I don't do very well in school in arithmetic either. Seems I just can't keep my mind on the problems. We had one the other day like this:

If a 57 foot telephone pole falls across a cement highway so that 17 3/6 feet extended from one side and 14 9/17 feet from the other how wide is the highway?

That seemed to me like an awfully silly way to get the width of a highway. I didn't even try to answer it because it didn't say whether the pole had fallen straight across or not.

Even in shop I don't get very good grades. All of us kids made a broom holder and bookend this term, and mine were sloppy. I just couldn't get interested. Mom doesn't use a broom anymore with her vacuum cleaner, and all our books are in a bookcase with glass doors in the living room. Anyway, I wanted to make an end gate for my uncle's trailer, but the shop teacher said that meant using metal and wood both, and I'd have to learn how to work with wood first. I didn't see why, but I kept still and made a tie rack at school and the tail gate after school at my uncle's garage. He said I saved him ten dollars.

Civics is hard for me, too. I've been staying after school trying to learn the "Articles of Confederation" for almost a week, because the teacher said we couldn't be a good citizen unless we did. I really tried, though, because I want to be a good citizen. I did hate to stay after school because a bunch of boys from the south end of town have been cleaning up the old lot across from Taylor's Machine Shop to make a playground out of it for the little kids from the Methodist home. I made the jungle gym from old pipe. We raised enough money collecting scrap this month to build a wire fence clear around the lot.

Dad says I can quit school when I am sixteen, and I am sort of anxious because there are a lot of things I want to learn--and as my uncle says, I'm not getting any younger.

~~~~~~~~~~~~~~~~~~~~~~~

The piece speaks for itself and needs no augmentation from me.  However, I find it saddening that this piece could have been written today.  Has education changed so little over the years?

~~~~~~~~~~~~~~~~~~~~~

Credits:
Text = Stephen M. Corey, "Childhood Education" - January 1944

Image =  http://www.maebs.com/articles/Liz_Davies/TreeAcrossTheRoad.jpg

Educational reform; like building a plane - in flight!

I love this clip. To me it is a wonderful metaphor for educational reform.

One of the major issues with educational reform is that schools have to be operational while education is transformed. We can’t simply shut down the schools and learn new and more effective educational techniques. We need to test and trial our learning when and where it matters - in the classroom with our students. We need to learn new skills while we teach via established methods. There are those who suggest that teachers can learn new approaches when students are on vacation - and to some extent this is true. However, the important aspects of classroom teaching can only be learnt through implementation in the real world - and that means while the students are present. There is a time when a trainee pilot needs to land a plane in real life and not in a simulator.

There are obvious issues with this. Our students are not guinea pigs or lab rats. We should not experiment with them. On the other hand, we need to continually improve our practice - and that means we need to be constantly trialling new approaches or trying to refine and enhance established ones. This balance can be difficult to achieve - perhaps this explains the almost glacial pace of school reform.

Clearly there are risks involved in any educational reform - if any innovation is ineffective then students suffer in comparison to what they may have achieved with another approach. However, there are more risks involved in educational stagnation and ignoring new possibilities and potentials.

So how do we build an educational plane in flight? We start by being clear about what we want to do and why. We acknowledge that established techniques may not be appropriate in this operational environment. We try to anticipate any likely issues and develop responses in advance - or at least be observant and flexible to respond to issues as they arise. We clarify our roles - who does what, when and to what standard? Who checks and assists? How do we know when we have succeeded? We accept that the task may be difficult - but, if we are clear about our objectives, it should be worthwhile.


And then we take a deep breath and build our plane.

~~~~~~~~~~~~~~~~~~~~~~~~

Credits: EDS commercial via youtube @ http://www.youtube.com/watch?v=L2zqTYgcpfg

Original idea to link to education: Thanks to a long forgotten presenter at a SPERA conference in Darwin who used this clip in his session.

A track less travelled

Like most people I am a creature of habit.  I am also a keen bush walker - partly for exercise, partly for photography, partly for personal therapy.  My most favourite site just happens to be a World Heritage area less than two hours from my home - Cradle Mountain.

I tend to stick to well  trodden paths when I visit. With scenery like this waiting why not?

When you know you will be seeing this why would you go elsewhere?

Yet that is just what I did recently - due, in part, to weather conditions.  Seeing as though my favourite tracks were shrouded in morning mist I went on some of the less well known tracks... and “discovered” this...

and this...

I even met some of the locals...

Not only did I add some gems to my walking catalogue but I also discovered tracks to two other destinations that I had been wanting to visit.  In short, by breaking my habits I discovered some “unknown” locations - but also found some exciting places to explore in the future.

So how does this relate to education?  It struck me that my habits prevented me from exploring other options and opportunities.  This happens in classrooms too.  How many teachers cover the same material every year?  How many people use the same task design year after year? No doubt these are successful teachers - if it didn’t work they wouldn’t do the same things repeatedly.  Yet this approach reduces innovation and exploration of alternate methods - especially in the nature of what the students do.  The curriculum may dictate what students are to be taught - but usually teachers have freedom to select how they  present and get students to explore material.  This is easy to say but possibly a little harder to do - but there are some simple ways for teachers to expand their instructional horizons.  

One might be to use this resource - the Kelly Tenkely's blooming peacock.  This resource identifies areas of Blooms taxonomy and then identifies software that addresses that mode of thinking.  Another llist, by Kathy Schrock ,does the same thing but limits the software to that produced by Google - meaning free and web based. Andrew Churches' Blooms Digital Taxonomy  worksheets also provide advice on how to address Bloom via technology. One way for teachers wishing to expand their skills and move beyond their current habits into 21st Century skills might be to choose one new piece of software per unit and become an accomplished user of that site or program. Once done, select another site that suits your purpose from the next level up in Bloom’s taxonomy. Over a relatively short period of time teachers will have learnt not only a range of useful skills and programs  but shifted their teaching towards the higher end of Bloom’s spectrum.

Taking a fresh look at how we teach and trying something different is likely to be very rewarding - for the teacher as well as the students.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If you like the images displayed in this post you may like to view this video I made of walks completed last year. 

Schools - Formula 1s or 4X4s?

I’ve been thinking / reading about educational reform lately. What struck me was how little things have really changed over the course of my career.   With the exception of a few islands of excellence, many of the classrooms that I encounter on school visits are predictably generic – and demonstrate pedagogy enshrined in practice now for generations.  In fact, many of the people who helped train me would be able to dust themselves off (literally in some cases) and step into the role of a current teacher easily – despite being out of the classroom for decades.

How can this be? How is it possible that the technological advances in recent years have not transformed education?  Surely, when one considers the explosion of digital technology, the growth of the Internet and the transformation of society in general, schools surely must have changed?  Yet it is still possible to visit schools that almost seem to pride themselves on resisting genuine educational innovation.  Some schools use a shield of “educational rigor” to disguise the rigor mortis that defines their programs.

It occurs to me that schools are more like Formula 1 teams than Four Wheel Drivers. By this I mean that school teachers and administrators are hard working and dedicated people working towards a common goal – they pour their energy into their jobs and do so with great skill and commitment.  The same could be said for the Formula 1 teams.  Their goal is set – and it has been for years; to make their car go faster, to go from start to finish in the shortest amount of time possible.  They do this by making minute adjustments to their car – retuning the engine, changing tyre composition, modifying the aerodynamics  and generally tweaking the car to maximise performance.  The teams have been going to essentially the same tracks for years and years; season after season, lap after lap,  with one aim – to help get the driver from point A to point B faster than anyone else.

Contrast this approach with that of the four wheel drive enthusiast. The 4x4 car is well maintained and in good order.  Great care and concern is taken to ensure mechanical reliability. The difference is not in attention to detail – the difference is the destination.  The 4x4 driver is likely to try to go to new places by new routes – even if there is only a track rather than a road – and sometimes not even a track.  The fact that the journey may be over new or rarely explored territory adds to the allure of the trip. Being “better” simply has no relevance in this context.

In short, the 4x4 driver thinks about the destination while the Formula 1 team thinks about the process.
Our schools are now the equivalent of Formula 1 pit-crews  – hard working,  skilled, focused and putting large amounts of effort into making minor revisions that produce very small advances – if in fact they prove to be effective at all. The other parallel that strikes me is that Formula 1 cars are irrelevant in any other situation. You cannot take them on “the open road”, you couldn’t use them to get the shopping, or transport the family or do any of the other required functions of cars in the “real world”.  How many of our educational practices are limited in relevance to only the school environment?  If we are to break from the unproductive “reform” practices maybe we need to be more like the 4x4 drivers – work out where we really want to go and then do what it takes to make that happen.  

We need to have a serious look at the curriculum – not just in the sense that we re-badge or reorganise it. What do our students really need?  What is the best way we can provide it for them? What activities and projects will enable them to acquire the skills necessary for modern life and keep them engaged in the process?  How can we change education from something we do to students to something we do with them? What needs to change at the class, school and system level to enable this to happen?
There are many educational issues  that would benefit from genuine consideration and action including;

• ·         What do our students want from their schools?
• ·         What are we trying to achieve – in specific terms – with our students?
• ·         What content should we have in the school curriculum?
• ·         How do engage students in the educational process?
• ·         How do we use ICT effectively in the classroom?
• ·         How relevant is what we teach to our students?
• ·         Is the curriculum ever-expanding like the universe –  or can we acknowledge that students can learn some things elsewhere and hence omit some aspects. If so, what can we cease to teach?
• ·         What is the purpose and impact of formalised testing?
• ·         How can we embed a growth mindset into students,  staff...and “the system?”

Of course, governments and education departments all over the globe have been “reforming” education for decades.  But, to return to my earlier metaphor, the mind set in use has been that of the Formula 1 team – “We already know the objective, let’s improve the process”.    However, there are other groups that have taken the 4x4 approach – and their alternatives to vanilla flavoured education are freely available on the labyrinth of the Internet.

To continue the motoring metaphor, before commencing any journey it helps to have a map so you can choose the terrain over which you want to travel.   The equivalent to that might be this site -   the Apple Classrooms of Tomorrow Today  and the associated PDFs.  The document isn’t exactly a road map – but it might help you work out where you might like to go – and provide some of the insights that might help you get there.



Photo credits:
4x4 on beach
http://www.environment.nsw.gov.au/images/parks/touroperators/profiles/versions/BigRiverEnvironmntlSvcesLg.jpg

Mathematical engagement - images to delight, ignite and excite

Let’s be honest about this - in some classrooms the teaching of mathematics is as dry the Sahara Desert - and perceived to be as endless by many students. As a result engagement is lower than we would like. This is significant since student engagement is correlated to student success.

Whilst this statement is almost self evident we should be wary of accepting such comments unreservedly - evidence based practice requires that we support our beliefs.  Fortunately this is easy to do.  Any number of studies have endorsed this notion that engagement enhances achievement.   

With this strongly established the next issue is how to generate engagement? Jill Fielding-Wells and Kellie Makar of the University of Queensland found that “Research indicates  that student motivation and engagement are increased if instruction is authentic and relevant...”  Authentic here was defined as that which was cognitively challenging and connected to the world beyond the classroom.  The study found that student engagement could be improved by up to 22% by shifting to inquiry based problem solving as the method of instruction.

For those comfortable with a less  academic but equally authentic anecdotal style there is this piece showing how a high school in the USA significantly improved results in mathematics by introducing a curriculum based around problem solving with an emphasis on generating student engagement - the percentage of students “passing” mathematics skyrocketed from an admittedly low 20% to 60%.   There is thus both academic and “real world” evidence  that engagement is linked to achievement and that engagement can be increased by including certain features into  learning experiences.     In terms of student engagement generally,  it has been found that student engagement is enhanced when students are interested, challenged and feel that the work / task is important.

Several educational reformers,   such as the teams at the Apple Classroom of Tomorrow Today and the Partnership for 21st Century Skills, also advocate the increased and improved use of technology and multimedia in our classrooms to enhance both engagement and learning.

Fortunately the Internet is a rich source of motivational material.  Presenting clips such as the following could be one way of increasing interest and engagement in mathematics lessons.

The following are samples of video that could both ignite interest and engagement.

Ma and Pa Kettle Math.

While it is not the intent of this post to provide lesson plans I would suggest that this video cries out for “unpacking”.  Why do the flawed approaches used here produce the correct answer? Does this approach always “work? Are there other numbers that could be substituted for the numbers in the clip? How might Ma and Pa Kettle be convinced that their techniques are, in fact, wrong?

Pattern blocks


Even very young children could benefit from video enhanced lessons. After watching this clip an obvious question might be “Who would like to create their own version of this?”  Given that this is created via the  “stop motion” technique a simple digital camera and one of the many free video creation programs is all that would be created to really involve the students.  


LEAF TESSELATION

As well as being fascinating viewing this clip dealing with leaf tessellation lends itself to further investigation of the topic. ( Instructions for making non-regular tessellating shapes abound on the Internet - here’s one - and every free drawing package on the Internet or buried within operating systems has the capability of creating them.)
NATURE BY NUMBERS

Older students could unpack just some of the elements of this wonderful video.  I’d suggest that if students were able to identify and explain all the concepts embedded in this engrossing video then their mathematical knowledge would be well beyond the norm - and the beauty of it is, in order to do so, some reasonably advanced teaching and learning would be required.  


The Internet is a rich source of such videos.  There is clearly scope for including web based video into our mathematics classrooms - especially as motivators at the early stage of projects. The use of such images is one way that we can delight,  ignite and excite our students - or at least increase engagement.




Those who found these videos interesting and can see a place for them in their practice might also enjoy an earlier post with a similar collection of clips here.

Those who are interested in using such images but would like some guidance on how they might be included meaningfully into a classroom project might find this post on Project Based Learning useful.



Acknowledgements:
All links go to original sources of documents.
Image: http://www.dailygalaxy.com/photos/uncategorized/2008/04/27/stella_2.gif

Tesselating shapes PPt;

www.curriculumpress.edu.au/sample/pages/tessellated_shapes.ppt