Author Archive | Larissa Fradkin

Is the term “function” well defined?

I have discovered that even experienced teachers do not notice that the word “function” means two different things in different contexts, sometimes it means the “dependent variable f(x)” (like when we say “increasing function”) and sometimes it means “an operation f(  )” (like when  we say “define the function as f(x)=x+2”). Some students, particularly, those sensitive to […]

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Algebra Xplained!

Many feel that algebra has more to do with abracadabra than with logic!  In many instructions the emphasis is on the fun tricks.  This is a classical misdirection!   In the booklets offered here we start from the beginning and have algebra Xplained  – that is, made plane, X and all!   Love is understanding… […]

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Why lecture and how?

Why lecture and how?  When you start  teaching maths to STEM students it is important to establish first what the students  know and what they don’t.  The school curriculum changes all the time and you might attract different cohorts in different years, whatever the reason, no two intakes are exactly the same.  You can then […]

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What are qualities of a good math teacher?

Let us leave aside the personal qualities, such as love and passion for the profession, and concentrate on professional qualities of a good math teacher for modern times.  In the past learning was more often than not equated with memorizing and an effective teacher was the one who could come up with most memory devices […]

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Division by zero is undefined!

A rather confused discussion of this statement appeared recently on Here is my take on things: Division by zero is undefined whether you work with real numbers or complex numbers. Khan’s video on the subject is a bit confusing. The consistent exposition of algebra is given in Euler’s “Elements of algebra”.  There division is defined by saying that a/b=x, a unique […]

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Will MOOCs replace Universities?

Here are a few things that in my view, will prevent MOOCS from replacing Universities altogether: 1. STEM students with weak backgrounds do not understand mathematical symbols. Therefore, they cannot read the simplest mathematical texts or follow the simplest mathematical explanations. To get real education they need a teacher who will patiently teach them the […]

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To MOOC or not to MOOC?

There is a lot of buzz around the MOOC initiative (Massive Open Online Courses).  Internet is a marvellous invention and of course, should be used in education.  However, creating a really useful resource is a huge undertaking, just filming lectures is not enough.  It is a good start, but is not enough.  At Sound Mathematics […]

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Order of Operations in Elementary Algebra

I find rules such as GEMDAS or PEMDAS or BODMAS somewhat misleading. There is no reason to perform addition before subtraction or multiplication before division. I would use PEMA instead (operations in parentheses first, then Exponentiation and the associated inverse operation of extracting roots and taking logs, then somewhat easier operation of Multiplication and the […]

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I  am listening to a programme on the radio by Alex Bellos extolling the virtues of teaching arithmetics as music.  I always feel sad when teachers put competency over comprehension.  Of course, at work, competency is king, what matters is only whether you accomplish your tasks and how quickly.  But when learning, comprehension should be paramount, eventually it […]

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Timely Feedback

Many worry these days about providing students with a meaningful and timely feedback.  Many try using modern technology – audio feedback and such.    While very useful sometimes  such approaches can be very time-consuming and not necessarily better than a time-honoured and low tech solution – the Socratic dialogue.   Most teachers I know think […]

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How to teach Elementary Algebra to college students in 3 weeks

Sound Mathematics is pleased to offer training materials suggesting how to teach elementary algebra to college students. We offer an article and a power point presentation with suggestions on how to teach elementary algebra to college students.  These training materials discuss difficulties experienced by STEM students when studying algebra as well as common mistakes and […]

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A free digital book on Elementary Algebra for college students

We are pleased to offer a free digital book on Elementary Algebra for college students and teachers STEM students often struggle with elementary algebra.  As an introductory offer, Sound Mathematics offers complementary maths/math digital books , including the digital book on Elementary Algebra for college students and teachers, explaining most of  its mysteries.  You are […]

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