Today I saw the video below for the first time “Math class needs a makeover” by Dan Meyer from his TED talk back in 2010. Dan describes how today’s math curriculum is teaching students to expect – and excel at – paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. In his talk, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.
As a former Maths teacher his message really resonated with me. Last year I had been encouraging some of my teaching peers to introduce more open inquiry SOLO Taxonomy task based questions into Mathematics. This has been brought about by my own experience of the benefits of this model of learning in the Social Sciences supported by digital technologies, an area where I have a particular passion for and which I had been teaching over the last few years. What I have found particularly troubling, but understandable up to now, is that many Mathematics Teachers argue that their subject is different and must be treated as such: “Students need ongoing repetition of skills practice in maths to enable them to learn properly” and there is the often argued point in New Zealand, and likely in other countries “we don’t have the luxury of time to do investigate stuff, we have so much content to get through and so little time”. But, the counter to that I would argue, and that Dan alludes to is: that we constantly have to review content that the students forget anyway.
Why not do it differently and turn it on its head. Let us throw away those hapless mind-numbing textbooks, the ones that scaffold the questions down and make the maths so mind-numbing as so simply demonstrated by Dan. Why not ask simple interesting questions and get the students to unpack the problem and develop the solution in their own ways. We can be their to assist when they need it. This has been my model of student inquiry in the Social Sciences and the students really do switch on – why not in Maths. A number of Maths teachers will no doubt roll their eyes and say “we need to get real, we have assessments to worry about”. However, the failure rate and disinterest in Maths as a subject is too large to ignore, along with the ongoing demand for extra Maths tuition which has become a burgeoning industry.
Taking it Further with Inquiry & Investigation
Removing the scaffolding as described by Dan is a great step to allowing students to think. I suggest going further and and bringing more open-ended research and inquiry into Mathematics. Motivated and engaged students seeking answers to real questions, who will go online and investigate, and will come up with all sorts of amazing alternative answers and theories. Students who will operate in collaborative groups to tackle problems and identify for themselves what parts of a particular problem are the most significant. Where learners are given multiple opportunities to operate at the SOLO Taxonomy Extended Abstract Level: Planning and Prioritising, Arguing, Predicting and Reflecting – then Evaluating and Justifying their results and the approach they took. Let us turn our schools into centres of rich authentic learning, inquiry and research. Let the Mathematics have real meaning and application where the student seek out, identify and learn the skills, with the support of their teacher, when they are needed. Don’t let our schools be places that kill the creative and inquiring mind.
Here are just a few investigate Mathematics Questions for Secondary School that I came up with after watching the video:
“What is New Zealand’s most successful Sports Team?” – topical as New Zealand are about to play in the World Cup Cricket Final, and play in the World Cup Rugby Final Tournament later this year – this question opens up interpretations of “success”, measurements of wins, losses, percentages. Nr of teams performing. Good debate. Research. Statistics. Class project. Historical Research
“Are there enough fresh water resources to provide for the needs of the world population?” – this problem would allow for debate as New Zealand faces a polluted rivers crisis. How much fresh water is needed for the world population. What is population growth rate? What is water pollution rate? Where are fresh water sources? This could be broken down to research local (New Zealand), to global
“Is it really worth buying a house in Auckland?” – Currently New Zealand’s largest city has a housing crisis with prices rising fast along with the population but houses in short supply. These factors would be good to look at along with investment returns on houses. There are a range of good maths issues here. Also opportunity to include spreadsheets, graphing.
“Minimum wage or living way? Which is fairest?” – Political arguments in New Zealand could be used to introduced this one as some have put forward the idea of a “living minimum wage”. Students could explore the background and then determine what it is, what is the cost of living, and what is inflation.
“What is Uber and why are taxi drivers complaining?” – Uber is threatening the taxi industry and police have recently cracked down on Uber causing possible law changes. Students could explore what Uber is. What do Taxis charge and what does it cost to run a Taxi/Car (very relevant). How does Uber work and how do they charge. Will it put Taxis out of business?
“Where is the best position on a rugby field to take a conversion after a Try is scored on the 5 metre line?” – Kickers often take a kick back a certain distance to take a conversion (try to place kick between the posts) after scoring a Try in Rugby (the equivalent of a Touchdown in American Football). Is there an optimum distance back for the kicker. This introduces the idea of angles. One could walk out to a rugby field or similar and take a look.
“What is the quickest that a large jumbo passenger aircraft can get to its optimum cruising altitude?” - I have seen some of those Aircrash movies about planes not being able to ascend to steeply, otherwise they will fall out of the sky. I am sure students will be able to gather enough information to find out about cruising altitudes, maximum angle of ascent and takeoff speeds and speed, distance and time. This question gives them plenty to work with. You could then go beyond this question to ask: How far does the plane get? At what altitude can get get to before it can start turning? (I am sure these answers are available online).
“What is the maximum number of people that can be packed into a rock concert?” – I have used this myself after telling a story. The students were fully engaged and we could fit the whole population of the world in a small geographical area of New Zealand. Great memories of some of my Year 10 classes.
There are a multitude of rich questions I am sure that other current Mathematics Teachers will have thought of. Again, fantastic video I wish I had seen earlier.
Guest Post by Chris Bester (Y9 Social Studies Teacher at Palmerston North Boys’ High School)
During the year my Year 9 Social Studies class studied Australia as a topic with special emphasis on the issues Aboriginal people faced during and after occupation of Australia in 1788 by Britain. The topic allowed us to do an assessed research inquiry to be internally peer assessed and then to use the research and develop the topic into a cross curricular exercise with their ICT teacher (Mark Callagher) to use a video presentation tool. Here is a link to the full research inquiry task.
The students had to develop three of their own focussing questions to guide their research on a chosen topic (a range of topics were allocated). In class research as partners, students were able to present their inquiry in their specific topic to the task, which was peer assessed on SOLO taxonomy. They then developed a script from their research and presented in documentary format with the guidance of their ICT teacher using the WeVideo tool. They were shown very early in the task some model research clips on YouTube how to create effective documentary productions. It was also a very solid base for the students as they prepared for examinations on this topic.
One of the most pleasing successes was that I could play the clips of the topics that were to be covered for examinations as part of revision. The students could take notes from these videos and with earlier teacher presentation in class were able to gain high marks in the examinations.
Below is a Playlist of the videos that 9GI Social Studies created in this task (who, for international audiences, are boys aged at 13 years old – some going on 14).
Note: Apologies if some videos do not play due to blocking in some countries due to copyrighted snippets of music, but others will play.
My Year 10 Social Studies class had the topic of Global Issues to tackle.
This is an interesting topic but can be really dry if the teacher retains control and tries to teach the facts. I decided to hand it over to the students and get them to create a documentary in pairs on a Global Issue. We still had the important problem to overcome that the whole class needed to cover topic content for the end of year examination, but I felt that we could deal with that later on. The topic is perfect for me as a teacher to model the statement in the New Zealand Curriculum (page 36) encouraging us to “explore not only how ICT can supplement traditional ways of teaching but also how it can open up new and different ways of learning“.
I then made available a range of Global Issues topics for the students to choose from which they would research and present in documentary format together in pairs. The issues ranged from ENVIRONMENTAL ISSUES to HUMAN ISSUES to more POLITICAL ISSUES. Students chose using Google Forms with 3 preferences and topics were then allocated.
As this was my first attempt at something new there were a few things I would do differently, however I would have to say that this was a major success for engagement and improving student learning. So much so that another teacher half way through this tasks adapted the same assessment task for his Australian Aboriginal Issues Internal Assessment Task for a Year 9 class that we co-taught (me Y9 ICT and him Y9 Social Studies) the following term.
One of the most pleasing successes was that I did not teach the topic content to the students prior to the exam. Instead I played 3 of the student created videos to the students on 1. Poverty & Global Inequality, 2. The Greenhouse Effect & Global Warming and 3. Deforestation just prior to the recent end year examinations. The students took notes from these videos and over half of them chose this essay for the examination with many of them writing excellence essays and two gaining full marks.
Students creating top quality content good enough to help other students learn is the ultimate testament to the success of any task.
The main things that students have learned from this task are:
how to collaborate effectively on a large scale research and presentation task
how to write good focus questions (and the need to revisit and re-write them when needed)
how to research and gather information in a way that avoids plagiarism
how to write a script – put research information into another form (other than an essay to answer the focus questions)
how to present information as a documentary considering factors which influence audience emotion such as:
use of titles
use of colour
powerful images and appropriate images to back up points
modulation of voice, use of emphasis
influence of music
balance of audio, silence, voice, type, etc…
The Video Creation Tool we used was WeVideo
WeVideo is fully cloud-based and allows for collaboration between the students who worked on Chromebooks and from home. The education version comes at a cost to the school for signing up but having tried it, I would thoroughly recommend it. We are now looking at signing up the entire school for 2015. Note: Our Media Studies department also trialed WeVideo and are also planning to roll out for all Senior Media Studies for next year.
There were a range of things that the students, and I, learned from our first foray into producing documentaries. One of the things that we will certainly do differently next time is refrain early on from using snippets of popular music as students run into problems once it is published on YouTube. Although copyrighted and allowed to play – it leads to pop-up adds and warnings and blocks in some countries. There are a range of free background music styles freely available in YouTube editor providing good backing music for video creation.
Below is a 10BA Social Studies Global Issues Playlist which you can watch at your leisure
All produced by 10BA Social Studies (who, for international audiences, are boys aged at 14 years old – some going on 15). Note: Apologies if some videos do not play due to blocking in some countries due to copyrighted snippets of music, but others will play.
The satisfying outcome from this task was that, when each group explained to the class why they had added the content and linked ideas as they had, they were all completely different.
What is Australia? by Rishabh, Kaleb, Omar and Antoine(below) shows a wide range of content, well explained and easy for someone who knows little about Australia to absorb.
(Zoom in or Expand for easier viewing)
What is Australia? by Aidan, Kevin and Doug is another that shows a wider range of content, however their diagram demonstrates that you can give a lot more information in a simple and clearer way and colour, when used sparingly, can be highly effective.
What is Australia? by Finn D, Finn M, Jeffrey and Ronan has the group taking a very different approach. The diagram at first appears less visually appealing showing a narrower range of topics covered. However, a closer look at what they are saying demonstrates a deeper and higher level of understanding through their connections (by linking) within the diagram. They even make observations of irony when it comes to core values and rights of groups within Australia.
This task goes to show teaching can often be about giving students authentic and challenging tasks to extend their thinking. This, supported by great digital applications and good exemplars, means that the teacher’s role is to make them self available to guide and challenge the students as they work on the tasks. My students loved working on this task, both in class and at home, which makes Lucidchart a great collaborative and accessible tool to enhance teaching and learning. Remember, it’s the learning, stupid!
I did some analysis of how my Year 10 (New Zealand 14/15 year old) Social Studies class in Term 1 (February-April) understood SOLO Taxonomy and surveyed them as to how they understood it to help improve their learning. The results were quite impressive.
Among other class references and tasks, I introduced SOLO into three specific larger tasks across the same Causes of WWII topic, two of which have already posted about:
The THIRD was an End of Topic Moodle Forum Debate using students rating each others entries as described below:
Moodle LMS Forum Topic Debate using Student Ratings
First of all I prefer using Moodle Forum discussions as opposed to Facebook, Twitter or other formats of student topic discussion & debate. The reason for this is that, in my experience, students feel safe in this environment and it is clearly under the management of the school where we can set our own guidelines. That is, the Facebook “standards”, or in many cases lack of, can be left at the door and the students clearly understand this. Secondly, Moodle has many inbuilt tools which can be used in the forums which I will now explain.
I set up a some earlier forum discussions, leading up to the final forum, getting students to discuss/debate questions such as:
1. Who was to blame for World War One? (This was a good question because the students had already researched and built a diagram with lucidchart) 2. Was the Treaty of Versailles Fair or Unfair on Germany?
By the time of the 3rd Question, upon which the students had gained a better understanding of SOLO Taxonomy in the class/school, I added the TEACHER RATING ONLY function into the forum using SOLO Grading and enabled it so that all students could view what I graded each of them. I challenged the students to improve the quality of their arguments. Here is the question that I rated their arguments on:
3. Should/Could Hitler have been stopped at the Rhineland?
Students who received Multistructural were motivated to improve to a Relational argument. Those that received Relational were motivated to write an Extended Abstract argument. Everyone in the class were out to avoid a Unistructural argument. What I clearly observed, as compared to previous discussion entries, was a clear motivation by the students to research and write a better argument when debating online with each other. They were also looking at the merits of each others arguments more closely and better challenging each other
The next stage was to raise the stakes in the the final debate – Student Ratings:
I added the functionality for the students to be able to rate each others. I explained that it was a real privilege and took them through their understanding of what the SOLO ratings meant. To help, I placed the scale below in the debate instructions alongside the forum debate question (q.4 below). They were instructed to rate at least 5 other entries before they made their 2nd entry and they had to rate an entry before they replied to it. They were clearly instructed to rate the quality of the argument, whether or not they agreed or disagreed with it:
4. A simple question: “What caused World War Two?”
The students really responded and took the debate seriously. I have never seen such a high quality of analysis, debate and level of understanding from a Year 10 class of what essentially is or has been a Year 11 topic. Using SOLO Taxonomy, from my point of view, really did raise the level of motivation and understanding to new levels. BUT, enough of what I think, let us hear from the students…
Results of class student survey at the end of the topic using Google Forms
The students were asked to complete an extensive (up to 20 minute) survey on there understanding of SOLO Taxonomy.
One of a range of questions asked them to rate how useful SOLO Taxonomy as a tool had been for each of the three tasks mentioned at the beginning of this post. ie the group charting task, individual research task and the forum rating task. Here is a summary of their answers:
The most telling result here is that the majority of the students overwhelming rated SOLO Taxonomy as very useful in assisting them in the forum discussion debate. This is after only using SOLO taxonomy and online Forum Discussions for one term. That SOLO can be extended across to in class debates, and other in class or online activities is very powerful not to mention that it is a cross-curricular tool for teaching and learning.
A collaborative tool like Lucidchart enables students to easily research and share their creative ideas together, either at school, or online while at home. There are a number of charting and mindmapping tools out there, but Lucidchart impresses me as the easiest to use and collaborate with. Even better, as a Google Apps school, our students have Single-Sign-On and its integration with Google Docs/Drive is such that students can add and sync updated lucidchart diagrams straight into their Google Documents. Fantastic stuff…it just keeps getting better.
At the start of this year, for their 20th Century History topic, my class of Year 10 Social Studies students were given the task to: Create and present to your class a diagram answering the question: “What Caused World War One?”
Groups were given resources such as a video to watch but from there it was left entirely up to them. Given a simple, accessible and reliable tool in Lucidchart, students were able to develop their inquiry, research and collaborative skills and even show some artistic flair. Often as teachers we feed the students too much information and do not trust them enough to find the information out themselves. Given a well constructed task these students really enjoyed the task of co-creating the knowledge. At the end of the task the students presented their diagrams to the class and explained WHY they had constructed their diagram and made the connections and emphasised the particular information they had.
Student groups were named after World War II leaders for the duration of the topic.
This diagram by team Zhukov is particularly creative and impressive where the numerous linking which shows real understanding of causes relationships told in a nice simple way, by a group of 14/15 years olds doing their own research:
Well it has been a long time since I have posted on this blog, but that is not to say that I have not been busy and moving ahead with using a range of ICT’s in my role as Director of E-Learning at Palmerston North Boys’ High. Things have been moving very quickly for the school this year to the benefit of everyone and our new Moodle Page branded Stratus, though it still has a lot of development to go, has been very successful in helping to showcase to staff how web has so much potential in showcasing student work. It has also been a great site for acting as a Single-Sign-On facility for our main web learning apps which support learning. One of them which the students of my Social Studies class used this year is called Lucidpress which an online print and digital publishing software and is completely free for Education institutions.
All Year 10 Social Studies students are required to complete a research assignment for their Term One 20th Century History Topic.
The task for students in my Year 10 class was:
“You are a news reporter for a magazine of your choosing. You are to research, write and present a news magazine report on a significant battle of World War II which caused challenges to people”
Each report required:
An Article about the background and reasons for the event
An Article reporting from the location about the event
An article about the leaders involved
And an article about new innovations which impacted the event
This task was assessed using SOLO Taxonomy, which has proven very helpful for our students by challenging them to think about how they can move their thinking and learning to a higher level.
At the end of 2011 I had left my position as e-Learning Director at Wellington College and during 2012 worked as an e-Learning consultant and trainer to a number of schools and e-Learning PD clusters around New Zealand. It was a stimulating year where , having visiting a range of schools, I have been able to observe how different schools have faces similar challenges and adopted a range of approaches to enhance their e-Learning capabilities to advance teaching and learning. This has been informative for me having only taught at the one school during my teaching career until now. Another thing this year has illuminated for me is that I do miss the classroom and the community of the school environment. I now look forward to a new challenge in 2013 and am taking up the position of Director of e-Learning at Palmerston North Boys’ High School. This is a school with a proud tradition, committed and enthusiastic staff and fantastic boys. Their motto “Nihil Boni Sine Labore” which translates to “Nothing achieved without hard work” is something which I firmly aspire to and so look forward to making a positive impact on the school over the coming years.
From what I have learnt over the last 2-3 years experience and as I look ahead to 2013 I have come to the conclusion that for a school to move ahead with their e-Learning capability they need to recognise the needs of the modern connected learner. My thoughts are summed up in the 4 points below:
The internet has transformed learning
There needs to be appropriate learning tools and a support infrastructure in place
The role of the teacher needs to change
Pedagogy is at the heart of the use of technologies
1. The internet has transformed learning
The internet has transformed the ways by which learners’ access information and our schools and their teachers must respond or they will become irrelevant. Teachers with their specialist subject expertise are no longer the only sources of knowledge. Where teaching used to be about filling up our students as empty vessels with knowledge and then testing their retention, we must now explore new ways of thinking about teaching and learning. Individual students need to be given challenges and opportunities to pursue relevant answers to questions themselves and to develop life-long learning capabilities as well as subject knowledge. Schools will become more relevant by showing adaptability to this new world of the way that we access and share information. But before this can happen…
2. There needs to be appropriate learning tools and a support infrastructure in place
Teachers and Learners need to not only be well connected but also be provisioned with well-chosen tools that enable genuine collaboration, communication, creativity and innovation – ie to open up new and different ways of learning to occur (p36 NZ Curriculum). Learning tools should be cloud-based and low or zero cost to enable easy access for all students from anywhere and at any time. The ICT infrastructure must be an enabler, rather than a disabler which can frustrate and impede progress – teaching & learning, as opposed to administration, management or other, must be the priority when choosing tools. Student devices (BYOD) are now not an option but are an essential component for students to access their online tools to enable their ability to learn from anywhere and at anytime. Their devices should work seamlessly at school and from home. With appropriate learning tools and infrastructure in place…
3. The role of the teacher needs to change
With the changing role of the teacher, we have never been more important with the best of us being continuous learners who operate within the strong disciplinary framework of our subject areas1. We are living in a technologically fast changing world where, as teachers, we need to be models of adaptability to our students. Good schools create the professional space for genuine teacher reflection and learning and acknowledge and support teachers who are at different stages. They also give the space and permission to teachers to take acceptable risks to explore new approaches in a supportive environment. In short, a teacher needs to become a modern connected learner himself/herself and embrace the tools and see the potential of how they can open up new and different ways of learning in their curriculum area or year level. Until they do that, little will change. With this in mind it is important to remember that…
4. Pedagogy is at the heart of the use of technologies
Learning tools should be utilised purposefully with individual teachers having clearly stated and well understood learning objectives when choosing an ICT tool2 to meet a particular learning need. In other words, teachers have a clear understanding of why they are using a tool. Students are being given authentic and challenging tasks to extend their thinking skills and ability to cope in an increasingly complex and connected world of growing information, multiple ideas and perspectives and with the increasing need to communicate and collaborate effectively. Teachers’ disciplinary thinking is enabling students to critique the information and misinformation and to develop and construct their own knowledge and ideas with opportunities to present their work to authentic audiences. We have enabled the modern connected learner who is engaged in authentic tasks. Just remember, it’s the learning, stupid!
1Though directed more toward secondary teachers (subject specialist), could apply to primary teachers
2Choosing an ICT tool could equally mean choosing an activity or other tool within an LMS such as Moodle
I just had a reflective read through my e-fellow research report written in 2008 and was struck by how, four years later, the Blended Learning Model is so much more relevant today.
In 2008, using Moodle’s forum tool, I encouraged a Year 11 History class to interact with the course content through a blend of online and class discussion and debate. A rigorous analysis of the value of this was completed followed by conclusions about the value of the model for improving student learning.
Also consider that the class had yet to encounter the Moodle LMS (VLE) prior to the study and that this was pre-Facebook which did not enter the New Zealand teenage scene until sometime during 2009.
The reason I believe that we, as teachers, should be using discussion forums with our students is that this is the environment that students now live and are at their most comfortable – ie regular online discussion and chat. Students are happy to discuss, comment and debate in this medium so why not bring it into learning?
I have observed a lot of Moodle courses in a number of school environments with a range of resource and activity tools being used. My belief however, is that the most under-utilised tool, and the one that has the most potential to help improve student learning is the Moodle Forum.
Last year my Year 9 History class was about to embark on their task of researching Old Boys from their school who fought in the First World War. The dual purpose of the topic was for these new entrants to learn about the history of their school, their country at the time and the battle fields of the War.
Having successfully challenged the class to use Google Docs to research and present the Ancient Rome topic, I decided to take it one step further and ask them if they would like to build a class website. This was a risky undertaking as it would require an already high level and difficult individual research task to be presented in a shared and co-ordinated approach. With some Web Design (Digital Technologies) teaching background I had confidence that I could assist a small team of enthusiastic students from within the class to help prepare and manage the technical aspects of the project.
The way that I have utilised Google Sites here is to get students to take their research work to another level. To set their expectations higher and to teach them about:
Research Quality and Standards
Writing Content for the Web
Web Presentation – Navigation and Consistency
Teamwork – Collaboration and Communication
What I have come to appreciate is that the higher the level of expectation that I set for my students then the more they aspired to meet it. For example, the more prepared, well designed and professional the student web development team made the website template look when presented to the rest of the class, then the more the sense of expectation of a higher quality of work that the class aspired to.
Of course this was my first attempt and there are things that I would certainly do differently given another opportunity at this sort of task, but I definite enjoyed teaching in this student centred, inquiry focused and collaborative style and I know that my students enjoyed it and undoubtedly gained from the experience.