Maths materials – tools or manipulatives? A walkthrough query.

Posted on September 4, 2008 by mwalker

Readers of my blog will know that we have Michaal Ymer, an educator with a focus on maths, coaching teachers in classrooms. Michael early on in his work with us presented three main messages:

  • students need maths materials to manipulate so that they get a better understanding of concepts – less abstract.
  • maths materials need to be organised in learning spaces so that students are responsible for getting the material they need and being responsible for packing it up.
  • teachers need to present clear instructions or pictures [birds eye drawings – photo 1] of what students need to set up for the lesson. The picture drawn by a year 1 teacher shows a table with two students and the following materials set up: tub of counters, a pencil, some paper and a dice. When students have this set up they join the class for the group instruction period. This means when the teacher instruction is over students can go straight on with the task rather than forgetting the instructions as they spend time setting up – simple but effective as I have watched younger boys sometimes spend 10 or more minutes locating the equipment before they start – and thus forget the purpose or strategy just demonstrated by the teacher.

When we were walking through the junior classes during maths lessons this week I noted lots concrete material being used in activities – however was the material really supporting them construct a mental picture of the operation they were performing?   Well it seemed lots of materials were being used for the activity – roll dice place counter over number on sheet – but not lots of material that students used to create the mental pictures of the operation, with some exceptions – the last picture has the student with some counters for the activity and different counters for manipulating the mental equation.

As we reflected after the walkthrough we began to pose some questions:

  • in a sequence of lessons students might first learn the activity before learning the skill or strategy to be practiced in the activity: e.g they might learn the roll and cover up game first before learning the strategy to count on from the first number instead of starting from 0 every time. How would we know the lesson sequence we were viewing unless we consulted the planner on the teacher table, desk or interactive whiteboard  – next walk through ask for planners to be on the table or board  so that we can get a quick picture, if needed – making feedback more specific. 
  • opportunities for assessment – the middle picture of a prep class showed students measuring a track using counters – some were counting to 60 or more, others counting on from numbers and some even writing the total – we need to devise simple strategies to record the observations and not detract from our incidental teaching as we move around the group. What a great task – all can start and many have different exit points of learning – caters and engages all – fantastic!
  • concrete materials that help students think or picture maths concepts might better be labelled manipulatives [I think this is an American term?] while others might be classified tools for the activity – students might need both?  

I wonder if other teachers and principals doing walkthroughs question similar instructional strategies? If so please comment as I’d appreciate the feedback.    

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Is personalised learning the holy grail?

Posted on September 2, 2008 by mwalker

I was watching the Da Vinci Code movie the other night and got to pondering was the holy grail that so many knights had fought to find and in some cases protect, in fact Mary Magdalene’s sepulchre as the Dan Brown’s book suggested.

In the movie it’s the paintings of Leonardo Da Vinci that provide clues as to what the grail may be and why. While many Catholics denouce the bookand its reported to be full of inaccuracies its an amazing story and it got me to ponder is personalised teaching a similar story of failed quests.

In the quest for personalised learning we must examine our practices and tools we use for the task just like Robert Langdon, the main character, who was a Professor of Religious Symbology at Harvard University did when he examined paintings for clues to find the grail. One such practice is the tool of planning.

When I first started teaching in the late 70’s, yes that long ago, we were expected to prepare the yearly course by the end of February which was taken up by the principal and commented upon. Then the weekly planner was prepared, complete with colourful clouds to depict headings, based on the yearly planner and this was inspected by the principal or year level coordinator and signed off on a regular basis. The course was based, at first on the 1954 guidelines which were replaced by other central documents. The philosophy might have been we have a set body of knowledge and testable skills to get through in a year for each grade level with set texts and it was the teachers job to mark the roll, plan the units in a year long syballis and then teach and test with marks being recorded in a test booklet. The test booklets were also collected and examined by the principal on a regular basis.

Where was the student’s prior knowledge and skills taken into account? Where were there tasks that had multiple exits points to cater for the range of leaners in our classrooms. 

I recently heard another model of 6 week units of work as this allowed units to roll over the mid term holidays rather than start and stop again. This planning model is being used in a family of schools in Toronto with some success. The teachers collect initial data on students understandings and skills, plan units of work in English and Maths, agree on an assessment task and rubrics to be used in 6 weeks and cross mark each others student work samples. During the six weeks the teachers meet on a weekly basis to look at some student work that will provide some clues as what and how they are learning and then modify the planner. 

This is a different model to our current 10 week planner which has a stop start feel to it. When I posed a planning cycle question to teachers at a recent team meeting I attended there was some enthusiasm to look at the newer model as 10 weeks was considered too long a period to plan ahead. 

This is a different model of curriculum planning for it considers the students learning [through looking at student work] and adjusts instruction on a regular basis. This might be moving closer to this holy grail of personalised learning. I await further feedback from the team leaders meeting later this week. 

Update 3/9/08

Team leaders approved the change of planning format to shorter more frequent sessions so that instruction can be adjusted based on the frequent analysis of student learning [looking at certain pieces of student work]. For 2008 teachers will have a 1/2 day planning session next week and another 1/2 day in the 5th week of term. We will see how the planning develops.

For those wanting to see the end of the movie again – here it is – and those who have another curriculum planning model that moves closer personalisation of learning closer to the grail please contact me.

 

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500 Years of Women in Art

Posted on September 1, 2008 by mwalker


 

Thanks to John Connells work I have found a great blog for the art lovers by Phillip Scott Johnson. Women in art featues 500 famous paintings which have all been listed.

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Challenges of learning to change and changing to learn

Posted on August 28, 2008 by mwalker

This 5 minute clip is useful for educators either as individuals or in teams in schools to talk through and using technology to so new things in new ways. It challenged me – do we have classrooms or learning communities [go outside the 4 walls]? These are not mutually exclusive I don’t think but it makes a point that if we don’t use technology to go beyond the 4 walls then we limit the learning opportunities of our youth. Technolgy is about social networking and building relationships way outside your normal boundries. I like the images in the clip.  

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tests and the Rudd education revolution

Posted on August 28, 2008 by mwalker

Today the Prime Minister of Austalia, Hon Kevin Rudd delivered a speech at the National Press Club on the education revolution. I received a transcript of the speech which for me had several highlights:

While Australian schools stand up reasonably well in international comparisons, our competitors are quickly catching up. A 2006 OECD study shows Australia’s average performance in reading literacy worsened between 2003 and 2006, primarily because of a decline in the percentage of high-performing students.It shows that in scientific literacy, 40 percent of Australia’s Indigenous students, 27 percent of students in remote schools and 23 percent of students from the lowest socioeconomic quartile performed below the OECD baseline.Australia also has relatively low levels of Year 12 completion by OECD standards.

Conversely, the evidence shows that each additional year of schooling increases individual earnings by around 10 per cent. Another recent study found that increasing a country’s literacy scores by 1 per cent against the international average is associated with an increase in living standards of 1.5 per cent of GDP per capita.

Research shows that nothing at school influences student outcomes more than excellent teaching. It has measurable impacts on cognitive, affective and behavioural development. Studies suggest that the quality of teaching accounts for something between 30 and 60 per cent of the outcome across these areas. A McKinsey report on the world’s best performing school systems last year highlighted the importance of recruiting the top university students into teacher training.

In Korea, those recruited into teaching are in the top 5 per cent of students; in Finland, they are recruited from the top 10 per cent and in Singapore and Hong Kong, the top 30 per cent.I believe our teachers are our greatest economic asset.We need to re-establish in Australia that teaching is a great profession and a great calling for the best and brightest of our university graduates.

We must insist on teaching excellence in every school.

And insist that school leadership is strengthened, particularly in schools where the learning needs of students are most acute. To establish new national standards to reward both principals and the best performing teachers. To provide additional funding to encourage school systems to invest in teacher recruitment, development and excellence.

I want school principals to have the autonomy to make more staffing and salary decisions at the local level, to tackle local problems like poor literacy and numeracy. And I want teachers spending their time doing what they do best – and that’s teaching – not losing their valuable hours in paperwork or on tasks better handled by support staff.

But it is not unreasonable to expect that schools with a similar mix of students and similar starting points should do equally well. What parents most want to know is what difference a school is going to make – in other words, the extent to which it is adding value to the results of their students.

We should not tolerateunder performance. It damages the students irreversibly. It fails their families. And therefore it must change. Where it is clear that individual schools are not up to the mark, we need to be prepared to invest money and effort to lift their performance. And where despite best efforts, these schools are not lifting their performance, the Commonwealth expects education authorities to take serious action – such as replacing the school principal, replacing senior staff, reorganising the school or even merging that school with other more effective schools. Tough action is necessary if we are to achieve real change. And it’s tough action that our reform payments will reward.

Much of what the prime minister said rang true. However my hope is that national tests will not form all of the data sets used to measure school performance otherwise what is happening in the States might happen here – teachers and students valuing the test rather than authentic learning. Teachers at Elsternwick this week debated notions of pressure and stress as we tried to raise the achievement bar  and close the education gap.

The video stresses the importance of getting validated rich assessment tasks rather than pencil and paper tests. Take heed Prime Minister or we might end up dumbing down real learning in favour of what can be easily tested.    

 

 

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Sage words for bloggers

Posted on August 27, 2008 by mwalker

I have just stumbled upon Chris Lott’s blog which has provided some sage like words to explain why I share my thoughts on a blog and …. the words were written 500 years ago by Michel Montaigne.  

[An account of a trivial event] would be rather pointless were it not for the instruction that I derived from it for myself […] Now as Pliny says, each man is a good education to himself, provided he has the capacity to spy on himself from close up. What I write here is not my teaching, but my study; it is not a lesson for others, but for me.


And yet it should not be held against me if I publish what I write. What is useful to me may also by accident be useful to another. Moreover, I am not spoiling anything, I am using only what is mine. If I play the fool, it is at my expense and without harm to anyone.

If I had written to seek the world’s favor, I should have bedecked myself better, and should present myself in a studied posture. I want to be seen here in my simple, natural, ordinary fashion, without straining or artifice; for it is myself I portray. My defects will here be read to the life, and also my natural form, as far as respect for the public has allowed. Had I been placed among those nations which are said to live still in the sweet freedom of nature’s first laws, I assure you I should very gladly have portrayed myself here entire and wholly naked.


Thus, reader, I am myself the matter of my book; you would be unreasonable to spend your leisure on so frivolous and vain a subject.

 My blog provides me with an opportunity to make sense of what I do for myself as well as sharing my work and thoughts so that others by chance or accident might profit or provide me with perspective.   

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Virtual Worlds Tour

Posted on August 26, 2008 by mwalker

I came across the short 6 minute clip which shows about 50 online virtual world games. It has some excellent quotes and I am sure teenagers will recognise many of these worlds. I am just sharing at this stage.

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Phone a friend in exams?

Posted on August 26, 2008 by mwalker

I have just finished reading Chris Betcher’s post on PLC in Sydney where year 9 girls sitting an English test were able to use a phone to search the Internet for an answer as long as they quoted the source. The papers were busy calling this cheating rather than asking the question what’s behind this practice and is it for all tests or just certain types of tests. Chris’s comment is well worth a read.

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“Lessons from the Supreme Tester” by Julia Gillard

Posted on August 25, 2008 by mwalker

 

Julia Gillard is reported to have said this month that she was blown away by the works and ideas of Joel Klein, the former Assistant Attorney General of the United States – anti trust division. Mr Klein has been the Chancellor of the New York City Department of Education for the past few years and is committed to improving student learning. An article in the Australian reported: His “key words were accountability and transparency, and the linchpin was a schedule of standardised tests in maths, science and English that would determine whether students won promotion to the next year of school. The practice of social promotion was to be weeded out. The test results were to be made public along with a host of other school information, including qualitative assessments of schools, parent and teacher surveys, and the grading awarded to each school at year’s end.

Schools that failed to show improvement in students each year or scored a consistently low-letter grade faced being restructured or shut down. The teachers who worked there were to have no guarantee of another job.

The tough love was to come with better pay for teachers and principals, more school autonomy and academic support for struggling students, including an intensive summer academy, parent co-ordinators in every school and better translation and interpretation services. After six years, statistics show high school pass rates are up, parents are more engaged with their kids and schools are safer.”

Julia can I make a suggestion or two. Firstly testing is not teaching – building the instructional skills and content knowledge of teachers and a curriculum that has challenging tasks whilst not as sexy as no social promotion of students headlines does it in the higher performing systems around the world. So on the PISA results for OECD countries , which I commented on in a previous post, we are about 5th in the world and you go to one of the poorer performing systems, New York in a country that rates 16th or worse on the same tests and try and copy their solutions. Please Julia why not read the work of academics like Richard Elmore or Michael Fullan who all advocate building teacher capacity in the classroom, controlling entry level qualifications for teachers and working on a rich curriculum first – before being impressed. Feel free to comment!  

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How to cope with the gradual release of reponsibility to you the learner.

Posted on August 25, 2008 by mwalker

 Today I have asked to speak to our senior students about how we might better use the new spaces in our building to enhance our learning, friendships and online presence, the building is rich in access to digital technologies.  

When using different spaces for learning and gradually releasing the responsibility for the effective use of time and space to students we still need to equip them with the skills and values. With some freedom to use different spaces comes the opportunity for some students to lose focus [despite their individual goals] wander, distract others or even bully them through exclusion or hurtful language. In our digital age some of this language can be direct or indirect through the internet or texting service.  

My task was to remind the students of our values and goals, affirm the sorts of langauge and empathy we expect and set some challenges for the future. The year 6 students have a challenge of preparing themselves for some of the learning and social challenges of secondary school and the year 5 students have the challenges of 15 months of leadership in the primary school.   

The clip [Talent Quest] really brought home the point on the need to replace our language away from judgements about people and more to inclusive and affirming language. All agreed with the goals and expectations and made commitments to improve their choices or seek further teacher direction.   
 

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Does consistency mean sameness or mindfulness?

Posted on August 24, 2008 by mwalker

At this weeks staff meeting Sarah, the assistant principal and I talked about the weeks walkthroughs posing some questions in particular the above question – is consistency between classrooms sameness or mindfulness?  We used a fish bowl strategy to share our thoughts where Sarah and I have a partly scripted dialogue surrounded by the staff. I used an interactive whiteboard to show some photos taken on the walkthroughs as a prompter for the dialogue. 

I had recently read Michael Fullan’s new book “What’s worth fighting for in the principaslship?” and he posed this same problem”.  We spent time over the week in 12 classrooms with a focus on students setting interpersonal goals during literacy sessions. This focus came from Kath Murdoch’s work with us on student goal setting to build collaborative classrooms.

We saw students using different cards to set goals and in some classrooms they had written goals on post it notes. Was the consistency in the cards or was it in the process teachers used with students? Michael Fullan called this consistency through mindfulness.

When the greatest difference in student outcomes exists between the classroom next door its an interesting question to pose – about 12 months ago I would have said sameness.   

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flipping maths instruction

Posted on August 23, 2008 by mwalker

During the week I was talking to Michael Ymer, our resident maths educator, who coaches teachers on maths instruction. He was describing a rich maths task he had set years 5/6 students during a model lesson and the various exit points he had set to differentiate the challenge for students. The challenging task once set and understood by students allowed him to rove around and spot students having problems and then provide individual or small group instruction.

The point he made was that as students move into the middle years of schooling we need to flip the traditional triangle of instruction [concepts – skills – applications] so that we teach through applications or rich challenging tasks. So often we see middle years teachers still engaged in teaching the skills [e.g. multiple algorithms in text books] and not through their application. 

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100 best teacher videos

Posted on August 18, 2008 by mwalker

I came across this mainly US oriented list of the best 100 youtube videos for teachers. There are some worth a look.

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takingitglobal.org

Posted on August 12, 2008 by mwalker

I have just joined Michael Furdyk’s learning community called takingitglobal. I heard Michael speak in Sydney last year about trying to connect the youth around the world so that we can truly understand whats happening and take action. When you join the community you get to set up a free blog: http://principalwalker.tigblog.org/. Its targeted for mainly high school students with lots of real issues and worth a look.

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August Walkthrough

Posted on August 10, 2008 by mwalker

Last week our walkthrough focused on students setting goals. Our walk focused mainly on the middle school students. This focus followed up the curriculum day with Kath Murdoch.

In the classes we visited we saw some evidence of both personal and group goals. One class we saw was practising working quietly during a writing session with the sign to remind students and in the few junior classes we visited the students were holding social skills cards made after a group brainstorm to remind the students and the teacher what their personal goal was:e.g. to remain focused and to join in the discussion.

The other photo on cross referencing was taken in a middle school classroom and it reminded me of the broader definition of literacy. The students were collecting data on invertabrates and had to learn this skill. I don’t remember when I learnt this skill as a student but I’m sure it wasn’t when I was 9 years old.    

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