Mathematics for Teaching

Making Sense of Equivalent Equations and Expressions

Erlina Ronda — Fri, 14 Jun 2013 14:28:21 +0000

Making Sense of Equivalent Equations and Expressions

Here are some questions your students have been wanting to ask you in your algebra class. Daniel Chazan and Michal Yerushalmy in their article On Appreciating the Cognitive Complexity of School Algebra posed these questions about equivalence of equations , solving equations, and equivalence of expressions for us teachers to ponder upon. How often do we [...]

Original by Erlina Ronda

Why PEMDAS is ‘morally’ wrong

Erlina Ronda — Tue, 28 May 2013 18:19:38 +0000

Why PEMDAS is ‘morally’ wrong

Here’s a video that explains why you need to memorise PEMDAS order of operation and why you don’t need to. Minute Physics who made this video made a mistake in assuming that PEMDAS is taught in schools without emphasising that multiplication and division should be done whichever comes first from left to right. But he [...]

Original by Erlina Ronda

What is an algebraic function?

Erlina Ronda — Mon, 27 May 2013 15:01:49 +0000

What is an algebraic function?

An algebraic function is a function created by applying the operation of addition, subtraction, multiplication, division, and extracting the nth root. Let me give an example. Suppose you have the function f and g where f is a linear function and g is a constant function. Let f(x)=x and g(x) = -3. We can create [...]

Original by Erlina Ronda

What is algebra?

Erlina Ronda — Tue, 21 May 2013 17:03:36 +0000

What is algebra?

Didn’t we say in our algebra class that in the grades they study about numbers and so now they will be studying letters instead? Didn’t we say that in algebra we now use x instead of box (in 3 + ___ = 15, we now write 3 + x = 15)? And isn’t it that [...]

Original by Erlina Ronda

Unpacking mathematics – a geometry example

Erlina Ronda — Fri, 10 May 2013 13:38:16 +0000

Unpacking mathematics – a geometry example

Engineers, mathematicians, and mathematics teachers all deal with mathematics but it is only the math teacher who talks about math to non-mathspeakers and initiate them to ‘mathspeak’. To do this, the math teachers should be able to ‘unpack’ for the students the mathematics that mathematicians for years have been so busy ‘packing’ (generalising and abstracting) [...]

Original by Erlina Ronda

A Geometric Model for the Lunch Date Problem

Erlina Ronda — Sat, 23 Mar 2013 02:02:53 +0000

A Geometric Model for the Lunch Date Problem

A mathematical model is an abstract model that uses mathematical language to describe and understand a situation. Here’s a nice video that presents a model for the Lunch Date Problem. The video below shows a step-by-step tutorial using SketchPad to build a geometric model of the problem. What is nice about this video is that it [...]

Original by Erlina Ronda

Why do we ‘invert’ the divisor in division of fractions

Erlina Ronda — Sun, 17 Mar 2013 07:56:34 +0000

Why do we ‘invert’ the divisor in division of fractions

The easiest (and the most common) way to teach division of fractions is to just give the rule: To divide 5/8 by 2/3, just multiply 5/8 by the reciprocal of the divisor, 2/3. That is, 5/8 ÷ 2/3 = 5/8 × 3/2 = 5×3/8×2 = 15/16. If this is all we want our students to learn why [...]

Original by Erlina Ronda

Pentagon to Quadrilateral Puzzle

Erlina Ronda — Mon, 11 Mar 2013 14:14:31 +0000

Pentagon to Quadrilateral Puzzle

Puzzles involving cutting shapes and forming them into different shapes helps reinforce the idea that area do not necessarily change with change in shape. It is also a good activity for developing visualisation skill and spatial ability. The puzzle below is from one of the leaflets at the booth of Japan Society of Mathematical Education last ICME [...]

Original by Erlina Ronda

911 math assistance service

Erlina Ronda — Wed, 06 Mar 2013 23:23:11 +0000

911 math assistance service

A four-year old calling 911 for math assistance. History tells us that zero was invented much later than most of the numbers. It was not even accepted as a number right away. Why should we expect a four-year old to think of it then? And take-aways without context for them? Anyway, this video is cute. [...]

Original by Erlina Ronda

A 21st century skill: reading and writing codes

Erlina Ronda — Wed, 27 Feb 2013 00:35:03 +0000

A 21st century skill: reading and writing codes

In Should We Do Away with Calculation, Conrad Wolfram says that if you want to know if students understands a computational procedure, ask them to do a program, let them code it.Here is another video which calls students to learn coding. The video titled What Schools Don’t Teach featuring Bill Gates, Mark Zuckerburg, and other software [...]

Original by Erlina Ronda