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Zero: Much Ado About Nothing?

Zero represents nothing and as such is very important in our Hindu-Arabic base ten number system. Its job is as a placeholder in our base ten place value system. I think place value is the most important part of the primary Maths curriculum. But, many children find ‘place value’ to be a very sophisticated idea and difficult to understand, which has serious implications for their arithmetic calculations[1]. This difficulty is because the idea of place value is abstract and young children learn in a concrete way. They often see numbers as meaningless abstract symbols, so need lots of work with concrete materials such as Cuisenaire rods and/or paddle-pop sticks, before they can connect with and find meaning in such abstract concepts as numbers. Common difficulties are, for example:

Many children write five cents as .5 and fifty cents as .05. They also have difficulty when using the subtraction algorithm to find:

103-

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These difficulties reflect the fact that arithmetic is not a natural development of the brain[2]. Rather, it is a cognitively complicated process, which does not have a biological origin. It has to be carefully learnt by children and carefully taught by teachers.

This complexity can be viewed by taking a historical perspective.  The symbol and meaning of zero was not invented until quite late in historical terms. The Hindu-Arabic symbols that are so familiar to us, 123456789, were invented in India about the year 700 AD. Through trade and commerce these numerals gradually came into use in the Arab world. However, in Europe the system that was generally used was Roman numerals.

In the eighth century in Europe the Hindu-Arabic symbols were known mainly by academics and clerics. At the time, there was lobbying against the universal adoption of these new and revolutionary symbols by the Roman Catholic Church and vested interests.

At that time, the Roman Catholic Church regarded anybody who was not a Catholic as heretical. Furthermore, any people from the Arab world were thought to be infidels and anything they produced – the work of the devil. And so by association the numerals 123456789 were thought to be the work of the devil.

So, in Europe Roman numerals were generally in use and continue to be used today in some clocks and special circumstances. Roman numerals are not easy to use, and so before the introduction of Hindu-Arabic symbols some clerics and monks devoted their lives to Roman numeral calculations. These clerics had a vested interest in prolonging the status quo and the continued use of Roman numerals and so strongly lobbied against the use of the new, devilish Hindu-Arabic symbols.

Of course with Roman numerals there is no need for a zero, because zero is not needed as a placeholder. For example, in the Roman system, X= 10 and C=100.

Gradually people recognized that this new Hindu-Arabic number system was far simpler and easier to use when undertaking any arithmetical task. However, to indicate an empty place they used a space. This presented some difficulties because for example 1 3 could represent 13 or 103 or 1030 or 1003, depending on how big the space was. It was particularly important in financial transactions to be clear about what these new symbols represented. And so a refinement was made. Instead of leaving the space between numerals a circle was used around the space to indicate that there was a ‘missing’ entry [3]. For example, 1 o 3. Gradually the zero, with which we are so familiar was invented and the arithmetical rules of its use developed by Brahmagupta in the year 665.

Writing in the 13th century, John of Halifax explained that there is something that ”signifies nothing” but instead ” holds a place in signifies for others”. His manuscript proved popular in the universities. But it would take the invention of Gutenburg’s printing press to bring these ideas to a much wider audience. P49[4]

Tammet also comments that Shakespeare’s generation were likely to be the first generation of schoolboys to learn Arithmetic using Hindu-Arabic symbols in school (which was the King’s New School in Stratford).

This general use of the Hindu-Arabic symbols in arithmetic is very late compared with the development of reading and writing. Reading and writing were first developed in Mesopotamia, which is now Iraq. This is thought to be around the 3000 BC. In evolutionary terms this is also very recent, which again reflects the fact that reading and writing are not natural developments in the brain.

We all take for granted the three “R’s: Reading Writing and Arithmetic. We forget that they are NOT natural and easy things for children to learn, in fact teaching the three “R’s” REALLY IS rocket science.[5] It is amazing that so many of us can read, write and calculate so fluently.

 

[1] http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/lvl2place.aspx

[2] Dehaene, S. (1997). The Number Sense. Cambridge UK: Oxford University Press.

[3] Devlin, K. 2011, The Man of Numbers: Fibonacci’s Arithmetic Revolution, Bloomsbury.

[4] Tammet, D. 2012, Thinking in Numbers, Hodder & Stoughton

[5] Moats, L. C. (1999). Teaching reading is rocket science. Retrieved from https://www.scribd.com/doc/27456514/Teaching-Reading-is-Rocket-Science

 


 

Note – we’re actively encouraging comments on these posts! If you’ve got a response or opinion you’d like to share, let us know! You can either post this as a comment below, or contact Ann directly at awillia732@gmail.com.

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A Very APP-y Christmas

The following is part of an article in the November 2017 edition of the magazine Melbourne’s CHILD. The article is called “Early bird: An early education update” by Natalie Ritchie.

Lisa Kervin, Associate Professor in Language and Literacy and Head of Education Research with Early Start, University of Wollongong. She’s nearing the end of the three year study with educational psychologist Irina Verenikina, and doctoral student, Clara Rivera, into how young children use technology not just as consumers but as creators, as they conceptualise the phenomenon of “digital play”.

Many parents worry that screens are “bad”. What is the current consensus (or disagreement) on the role of digital devices in early childhood?

As parents, we tend to view technology in young children’s lives in fairly distinct binaries – it’s either a “good” or a “bad” thing. However, a lot of our evidence is drawn from TV watching behaviour. Often, parents’ concern about screens derives from a fear of sedentary behaviour. Our research team’s work is pushing back on that. Screen time is a reality in children’s lives. Our team is arguing that not all screens are equal. The quality of the content, and what kids do with it is what’s important.

Children’s apps make the biggest share of the market on iTunes. Many of them are labelled “educational”, but there maybe no real basis for that label. People ask us for a list of recommended apps, but with the market changing so quickly any list is outdated the minute you create it. So instead, our team has created guidelines to help parents and educators identify useful apps. We know that imaginative day is of fundamental importance for three to five year-olds. At that age children are engaged at their highest cognitive levels in imaginative play.

To choose a good app, look for these criteria;

 

  • What situation does it present to the child? Is it spontaneous, self motivating, requiring self initiated actions and imagination? Does it allow the children to experience something they wouldn’t otherwise experience, like being a train driver?
  • Is it open-ended? Does it make children make their own decisions? Our team is a little worried by levelled games, when goals are predefined and the motivator to play is the sticker or the points.
  • Does it give children opportunities to produce, to bring their own photos in, to invent their own experiences and create? Children like attractive graphics that they can easily manipulate. An uncluttered screen design that doesn’t have children tapping and swiping just to get to the action is the thing to look for.
  • Our team argues very strongly that digital play that is solitary and quiet is not a good thing for young children. If it’s play that allows them to invite others in, such as a simulation where kids can talk and find one another, that can be exciting. Talk with other children and adults Is fundamental to a child’s development.

 

We used our criteria to analyse the top grossing apps on iTunes. Not all of them matched the criteria, but we were left with some that we were able to trial with children as we closely observed their play.

We’ve captured some neat examples where on screen-play has been the motivator for off-screen play. For example, kids might extend an eco-system from a digital game into the real life home, and on-screen language has infiltrated other off-screen play scenarios. That’s exciting for us.

If you could improve early child-care tomorrow, what would you do?

The more time children have to play, the better.

The current generation is the first to grow up with technology. It’s not in every child’s hand, but it’s in many children’s hands. Just as we make good choices about physical play equipment and furniture, we need to support children by careful and judicious choices for digital play. We need to activate those higher cognitive levels that come with imaginative play.

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Top Ten Tips to Find a Tutor

One of the most frequent questions I am asked is ‘How do I find a good tutor?’  Parents want to do the best for their children particularly if the children have a Specific learning Disorder (SLD) such as dyslexia, dyscalculia, dyspraxia or dysgraphia, or a combination of all of them.

Finding a good tutor for your child is not going to be easy:  Some parents have unrealistic expectations, are looking for a ‘silver bullet’ or a ‘cure’.  There is no cure, just a lot of hard work.

The hard work is going to be done by your child, you only have to provide your hard earned dollars.  The money invested in a tutor can be a major investment, but your child is going to invest far more in terms of blood, sweat, tears and self-esteem.

When any large investment like a house or a car people usually need to do some research, so how much more important is your child?  You need to do some research.

For instance, when buying a car, would you say to your friend?  ‘Can you recommend a car for me to buy?’  Your friend might say ‘I think my Honda Jazz is great, you should get one.’  But you have a dog so need a wagon.  All kids are different but kids with SLDs are very different.  You need to do some research.

Research is also necessary because a Parliamentary inquiry said  ‘There were also concerns raised that tutors operate in an unregulated environment’, page XIV (http://www.parliament.vic.gov.au/file_uploads/ETC_Homework_Inq uiry_final_report_PWkrPPVH.pdf)

1 Money

You must choose how much you are prepared to spend: A Rolls Royce or a Honda Jazz?  Tutors typically cost somewhere between $80-$150 per hour.  Just because they charge more does not mean that they are better tutors, just more expensive.  Some tutors call themselves ‘consultants’ or ‘therapists’.  However they are all basically just teachers who want to work with kids who have SLDs.  You need to do some more research.

2 Location

Where you live matters unless you can also invest your time into ferrying your child to and from the tutor’s place.

Learning Difficulties Australia (LDA) https://www.ldaustralia.org/  is a professional association of teachers, speech pathologists and other professionals, highly regarded in the community, which has a list of tutors/consultants sorted by their location, so this is a good start. LDA also requires teachers to have extra specialized qualifications in order to be on their LDA Online Tutor search. Additionally, LDA Consultant Members are expected to continue their professional development in the learning difficulty field and must submit yearly evidence showing ongoing learning that conforms to strict standards for continued renewal of their LDA Consultant registration (https://www.ldaustralia.org/consultants.html)

3 Qualifications

The minimum qualifications any tutor should have is a registration with the Victorian Institute of teachers’ (VIT).  The VIT is the regulatory body which ensures that teachers have done an approved University teacher training course.  In order to maintain their registration teachers are also required by the VIT to keep up to date by undertaking Professional Development (PD). It is important that tutors have teaching qualifications and are registered with their teacher registration board that ensures they meet professional standards for teaching

VIT registration of a person can easily be checked by using the VIT website here: (http://www.vit.vic.edu.au/search-theregister/_nocache) You can search by their name and/or registration number.  This search also tells you when registration was first granted, which will give you an idea of how experienced the tutor is.  If they are not registered –Don’t go there!

4 More qualifications

Most teachers who are interested in working with kids who have SLDs undertake further specialised training.  Unfortunately this is where it gets a bit murky.  There is no regulatory body in Australia whose job it is to monitor the quality of such Professional Development providers.  Anybody can put up their shingle and charge whatever the market will bear.

Fortunately Alison Clarke (http://www.spelfabet.com.au), has done much of the research into appropriate programs as she was on the Professional Development committee for Learning Difficulties Australia.  The list of training providers can be found on her blog here: (http://www.spelfabet.com.au/2016/03/upcoming-training-insynthetic-phonics/).  If your tutor has done one of these you know its good.

If the qualification is not on the list: Look at their specialised qualifications and ask them what they mean and if you can view their certificates.  If they get angry or have ‘lost’ them.  Don’t go there.  (I am very proud of my qualifications because it took me a lot of blood sweat and tears to get them – I would never ‘lose’ them.)

Seeing the bits of paper is important especially if the qualifications are from overseas.  In the UK or the US there are many excellent specialized courses.  Just make sure your tutor has done one of them and exactly what it is and what it involved.

5 Evidence-based Professional Development courses.

Another help through the murky waters of PDs is AUSPELD.  AUSPELD is the Australian Federation of Speld Associations and is also highly regarded in the community. (http://auspeld.org.au/)

The peak body for anybody with SLDs to go to in this state is Speld Vic.  Each state has its own Speld organisation, all coming under the umbrella of AUSPELD.

AUSPELD has a free, online version of ‘Understanding learning Difficulties for parents’.  This has a list of evidence based interventions here: (http://uldforparents.com/contents/selecting-asuccessful-intervention-program/what-does-the-research-tell-usabout-different-interventions/). This also lists the degree of evidence and rough costs. (Again remember the Rolls Royce factor –high cost is no guarantee of a quality course).

This information does not recommend the ‘best’ course for a tutor to do or the ‘gold standard’ course because there is no ‘best’ course.  If you tutor says there is a ‘best’ course and she has done it, ask for the article that proves it, written in a peer-reviewed journal.  (There aren’t any!)

This research will give you a guide through the murky waters of PDs.

6 The choice

After having found a tutor you like the look of, you must put her to the vital test.  Your child!  The choice is not just yours but also your child’s.  There must be a good relationship.  If not- Don’t go there!

A good relationship is important as the tutor must exploit a child’s strengths and ensure he succeeds.  Success is the key to motivation.  Children need the motivation if they are going to carry on and undertake all the hard work they will need to do.

7 In school

In Victoria, provided a tutor has VIT registration, and with the approval of the school, a tutor is allowed to take a child out of school during the day, in order to tutor her.  This has a couple of advantages.  Tutors are usually busy before and after school and the child does not have to face more work at the end of the school day when they are exhausted.  (Some schools also allow suitably qualified teachers, who work as tutors, to provide specialised learning support at schools)

8 Qualifications caveat

Qualifications are important because they get tutors over that first hurdle and enable a tutor to get the vital VIT registration.  However, I know of many, older teachers who do not have lots of letters after their names.  They are excellent, dedicated teachers.  This is basically what you are looking for:  A tutor who can relate to your children and who knows their stuff and how to teach.

9 More about courses

As you have seen, AUSPELD has a number of recommended courses.  They all have one thing in common.  They all  teach Structured Synthetic Phonics (SSP).

This is important as all the evidence from reading researchers tells us that this is how all children learn to read.

Structured           This means, for example you teach the sounds in in a structured way.  From simpler sound/letter correspondence to those that are more complex.

Synthetic              This means that the sounds are built up (synthesised) by blending them together.

Phonics                 Simply is the link between the sound, the printed word and its meaning.

10 Efficacy

The tutoring given should work.  Your child should improve.  If not, find another one.  If you have any complaints tell the tutor.  If they are from LDA, tell LDA.

However, remember that by nature specific learning difficulties are ‘persistent’ and do continue throughout an individual’s life time to some extent. The degree of progress is also dependent on how severe the learning difficulty is. The earlier learning difficulties are identified, and effective intervention implemented, the better the long term prognosis. Internal factors such as resilience and persistence also play a role.

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NAPLAN: How to Cook the Books

The Myschool website is a huge database. It was originally set up by the federal government as a snapshot of how schools were performing in Australia to help parents choose a school for their child. However, like any database it is subject to “garbage in, garbage out”.

When you type in the name of the school where the website says “Find a school”, there is lots of information about the school. When you click on ‘NAPLAN’ there is also lots of information about the NAPLAN results. At a recent ResearchEd conference, Prof. John Hattie stated that the important information was ‘student gain’. This represents how the school has contributed to children’s learning.

Looking at these graphs, which have a nice steep straight line, might initially give an impression that the school is doing a great job.

(N.b. – click on images to view in full size)

But ticking the box ‘Schools with similar students’ might give a more nuanced picture, as this compares the school with schools which have a similar Socio Economic Status (SES). (There are many studies, which show that there is a close relationship between high SES and academic achievement.)

Ticking the other boxes, ‘Students with the same starting score’ and ‘All schools’ gives the full picture. This particular school is doing well compared to all schools because it has a high Socio Economic Status (SES) and is in an affluent area. However, it is not doing quite so well compared with other schools with a similar SES.

There is another statistic which is important and that is the ‘Percentage of students in this year level for whom previous NAPLAN results (2 years prior) are available’.

On this page, NAPLAN results for the selected school relate only to matched students. Matched students are those who sat two consecutive NAPLAN tests at the same school and have results at two year levels. Results are shown only for schools with five or more matched students.

This school appears to be doing incredibly well compared to other schools of a similar SES, until you look at the ‘Percentage of students in this year level for whom previous NAPLAN results (2 years prior) are available: 60%’.

This means that only 60% of students sat NAPLAN in both years. However, clicking on attendance gives a rate of for the school of 98%. So where were the other 40%?

There is anecdotal evidence that some schools pressure the parents of children who have dyslexia, dyscalculia or other issues which may lead to under achievement, to absent their kids on NAPLAN testing days. This boosts the schools averages, as above and skews the data. Garbage in, garbage out!

Some anecdotal reports:

https://theconversation.com/declining-NAPLAN-participation-rates-are-likely-skewing-the-data-42821

http://www.couriermail.com.au/news/queensland/NAPLAN-bias-schools-exclude-children-with-communication-impairments/news-story/b13c34fcba09bfe6a05d1590878de609

https://www.amazeeducation.com.au/media/special-needs-kids-excluded-from-NAPLAN/

According to The 2015 NAPLAN report:

‘Since 2010, when withdrawals were first reported, there has been a general increase in the withdrawn rate. Despite this trend, the large percentage of students participating each year ensures that results are reliable and valid at the state, territory and national level.’ (P.325).

Are they equally valid at the school level?