Month: September 2014

Primary school teaching ‘based on pseudoscience’

mathmoconsulting Primary

Hard-hitting words from Professor Stephen Dinham, Chair of Teacher Education and Director of Learning and Teaching at the University of Melbourne, Australia. From the abstract of his Keynote Address to the Australian College of Educators National Conference last week:

“Australian primary students are out-performed by their secondary peers in relative terms on international measures of student achievement. This paper explores some explanations for this discrepancy including the role of content knowledge in primary curricula, a general lack of an evidence base for teaching and learning in primary education with a propensity to adopt fads and fashions and the increasingly unrealistic and untenable expectations placed on primary teachers and schools.

A solid research evidence base for teacher pre-service and in-service teacher education is essential and there is a need to question from this basis of evidence current practices and untested assumptions underpinning primary teaching and schooling.

If such transformation can’t be achieved, coupled with a rethinking of the expectations held for primary schools and primary teachers, then further decline in relative and absolute terms seems inevitable.”



Primary school teaching ‘based on pseudoscience’
Pupils being experimented on with methods rooted in folklore, dogma, ritual and untested assumptions, Australian College of Educators president to say
theguardian.com | by Bridie Jabour

Science, Data and Decisions in New Zealand’s Education System

mathmoconsulting Primary

Benjamin Riley, Director of Policy and Advocacy at the NewSchools Venture Fund, USA, has just completed a seven month fellowship in New Zealand, visiting schools all over the country. His report is incredibly timely for us, just as we call upon everyone in the education community – teachers, parents and students – to demand better standards and appeal to scientific evidence for improved teaching practices worldwide.

In his report, he describes the Numeracy Project as one of two “vexing” issues. From the section “Suspicions around the Numeracy Project”:

‘At one urban decile 10 school,…the lead teacher responsible for mathematics suspected that the Numeracy Project had “swung the pendulum too far” in teaching strategies to solve maths problems rather than developing mathematical content knowledge and fluency in algorithms. A secondary school mathematics teacher…was even more critical: ‘They can say what they want, but repetition is key [to learning basic maths facts]. We almost need to start from scratch with students, and undo bad practices…Their basic number skills are bad. They come in and cannot divide at all. They do not see multiplication as multiple addition. Kids [are being given] too many strategies, they can’t decide which is better. In maths, there should be freedom…but there is also order.’

There is also a footnote with an enigmatic statement from the Ministry of Education:

‘After reviewing a draft of this report, the Ministry offered the following comment: “There are a number of studies locally which reach similar conclusions to those in the report, and which are consistent with international studies. These conclude that there is a need for more developed and fluent number knowledge in the early years and more systematic teaching in specific areas such as place value and early algebraic knowledge”. Whether this confirms the Numeracy Project is being phased out or not I’m not entirely sure.’

What do you think?

Too much math education is based on pet theories

mathmoconsulting Primary

This excellent article points out the faulty logic of certain educationists.

“Proponents of inquiry-based instruction often claim that many adults struggle with math, citing this as proof that their unsubstantiated techniques should be adopted in math classrooms. While it is true that some adults struggle with math, this is not an argument for adopting inquiry-based learning any more than it’s an argument for using jumping jacks to teach kids math since inquiry-based learning has not been shown effective…. It is incorrect and insulting to great teachers of past years to argue that instructional techniques used with previous generations did not produce creative problem solvers.” – Assoc. Prof. Anna Stokke

Show your working – it really helps

mathmoconsulting Secondary

“Show your working” is a common request in high school maths exams.  Yet, in the modern learning environment, where worksheets and workbooks are common place, students don’t get a lot of practice at this important communication skill.  With so much content to deliver, there is little time left for teachers to teach students how to craft a good solution.  Furthermore, textbooks with answers at the back generally do not show any working.  It’s no wonder so many students find writing out mathematics both difficult and puzzling.

So, why should you bother to show your working?  Here are some points worth considering.

  1. In a written exam, there is no kudos in working everything out in your head or getting the wrong answer quickly.  It gets you no extra marks.  In fact, if working is required, writing down only the final answer will cost you marks.
  2. Getting the right answer is not as important as understanding the steps you took to get there.  That’s not to say that getting the right answer isn’t important.  Quite the opposite.  It’s so important that you want to be confident you’ll be able to get the right answer every time you encounter the same type of question.
  3. Showing your working is not supposed to be a nuisance.  It is meant to explain, with justification, how you arrived at your final answer.  Rather than being a nuisance, it should actually help both you and your teacher/marker to understand your work better.  Whoever is marking your work is not a mind reader.  Even you might have trouble understanding what you did when you look back at your work, sometime later, if you haven’t provided enough detail!  But if you have made a mistake and the steps are written out clearly, it will be much easier to identify where the misunderstanding occurred and correct the mistake.
  4. Use your brain power wisely.  Most students are faster and more accurate when they write things down because they can focus on the accuracy of each step rather than holding everything in their heads.  If you think that not showing your working will save you time, think again!  What if you make a mistake?  You won’t save any time if you get a wrong answer quickly and then have to re-do the calculation.  And that’s only if you notice.  If you’ve written down your steps, you are more likely to spot any mistakes and only have to re-do part of the calculation.
  5. If, in an exam, you’ve written down nothing but an incorrect answer, you’ll get no marks.  However, if you’ve written down an incorrect answer but have shown your working, there is a chance that your marker will be able to find something in there to justify giving you a partial credit.  In fact, if you made only a tiny numerical slip, it might be overlooked and you might still be awarded full marks.

Hopefully, you are now convinced that showing your working is a good idea.  Here are some tips on how to get started:

  1. Read quality worked solutions, and then practise writing out solutions in a similar manner.
  2. Articulating your ideas in writing helps you to understand better what you are doing.  You need to start practising this skill with the easy questions, when you know what all the steps are.  If you can’t do it for the easy questions, you won’t be able to do it for the harder questions either!  In actual fact, the harder questions might not be as hard as you think, if you are well practised at breaking down a problem into smaller steps.
  3. Knowing how much working to show requires a bit of judgement.  Again, refer to quality worked solutions for guidance.  Here is a good rule of thumb: when you are writing out a solution, imagine that the person reading your solution is someone in your class who doesn’t know how to solve the problem.  Would that person be able to follow your solution and then understand how to solve the problem?  Try it yourself: swap solutions with a friend and see if you can understand each other’s solutions.  It might give you a better appreciation of what it takes to write a clear and coherent solution if you try reading someone else’s work.
  4. Solving word problems is generally a test of whether you can extract information from the question and apply it correctly. So, identify when you are making explicit use of information or numbers supplied in the question and make this clear in your solution. For example, if you are calculating the area of a circle with diameter 6cm, a good written solution might be:
    Radius r = × 6cm = 3cm
    Area of the circle = πr2 = π × 32 = 28.27cm2
  5. Understand the precise meaning of the equals sign (=) and use it correctly. The equals sign does not mean “Here is the answer:” or “Here is my next line of working:”. The equals sign means “is equal to” or “has the same value as”. Naturally, as the words suggest, it only makes sense to use the equals sign to indicate that two expressions (not equations) are equivalent or have the same value. For example, if I wanted to multiply 3 by 4 and then add 17, I would write:

    3 × 4 + 17 = 12 + 17 = 29

    and not: 3 × 4 = 12 + 17 = 29. The latter is what I call a running calculation.  It might be how we think through the calculation in our heads, but, as written, it is nonsense because it says that 3 × 4 is the same as 12 + 17.

The benefits of writing out your mathematics solutions in full cannot be understated. With continued practice, you will understand things better and have more certainty of your answers, particularly when attempting harder questions. Ultimately, you will feel better prepared and more confident when you go into your exams.

Dr Audrey Tan, Mathmo Consulting

Why Education Experts Resist Effective Practices

mathmoconsulting Primary ,

Here is a powerful and compelling paper written by educational psychologist Prof. Douglas Carnine, entitled “Why Education Experts Resist Effective Practices (And What It Would Take to Make Education More Like Medicine)”. It exposes deep-seated flaws in what passes for educational “research” and how damaging it is to the teaching profession.

“Just think how often ‘research shows’ is used to introduce a statement that winds up being chiefly about ideology, hunch or preference. …The education field tends to rely heavily on qualitative studies, sometimes proclaiming open hostility towards modern statistical research methods. Even when the research is clear on a subject – such as how to teach first-graders to read – educators often willfully ignore the results when they don’t fit their ideological preferences.

“[Project Follow Through] compared constructivist education models with those based on direct instruction. One might have expected that, when the results showed that direct instruction models produced better outcomes, these models would have been embraced by the profession. Instead, many education experts discouraged their use.

“In this insightful paper, Doug examines several instances where educators either have introduced reforms without testing them first, or ignored (or deprecated) research when it did not yield the results they wanted.”

Without testing them first? Ah yes, we know something about that, don’t we? It’s time for everyone in the education community – teachers, parents and students – to demand better standards so that these sorts of mistakes never happen again.