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#1 2020-11-29 08:11:43

MrsGC-UK
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Translating quadratic equation language for a mathphobe

Hi  smile

This is a difficult situation: I am 55, English (as opposed to any other country's educational system), and achieved low-level maths scores in my secondary school education (CSE grade 3, I think - I haven't looked at my exam certificates in 32 years; I remember doing fractions, but I don't think I got further than the most basic algebra lesson, which says you use letters not numbers).

I have been asked to help a teenager who is in her final year of secondary education, and who has learned that she is unable to learn things in the school system - especially maths things.  I have a small ability to help people find a love of learning, and to be able to help translate concepts that I understand into something someone else can understand.  I asked the young lady to give me an example of what she struggled with, and she picked quadratic equations.  I'm looking at the "mathisfun" website, and I'm looking at several others, such as https://plus.maths.org/content/os/issue29/features/quadratic/index , because part of the problem for both myself and the young lady is that we just do not relate quadratic equations to real life.  That is: what cash-in-hand good are they?

I'm beginning to get some idea of what their purpose is, very dimly.  CORRECT ME IF I'M WRONG ON ANY OF THIS, PLEASE  big_smile

Quadratic equations show, in either a graph or a formula, a mathematical prediction of what something is when it has at least one fact that can be changed.  The aspect that changes (variable?) is the thing that makes it a prediction, not a fact.

What I'm struggling with right at the moment, is that I don't "speak" maths.  I don't understand it's language, grammar, or accepted rules.  I never have.  But I love knowledge for the sake of knowledge, and I don't mind a challenge.  I will learn something, and that's good enough for me.

Is there someone who can please help me to start so far below an acceptable level of maths that I can bridge the gap between what I can do to translate this information, and what that information is?

I can't use the LaTeX typing I saw discussed on a sticky post, and it's probably <cough, cough> years since I last coded html for either websites or forum posts so I'll just use URLs and specify what I'm looking at.

To answer the question of "what cash-in-hand good is a quadratic equation", I see images such as the football player at the head of the page https://www.mathsisfun.com/algebra/quadratic-equation.html  and I understand that:
- the (professional) footballer (read soccer player if you're not English) is kicking the ball, aiming for a particular point in the football ground in front of him;
- he is predicting where it will go, based on a variety of factors;
- his brain is doing a quadratic equation taking in variables like weight of the ball, its relative motion, and his personal skillset, plus the amount of muscle use needed to produce the required velocity, and the exact spot his foot needs to connect in order to produce the required arc for getting the ball to the desired point, and any others that apply;
- his brain does all of that without doing a single conscious maths function - it just _does_ it (one of my points to her is that she can _do_ seriously complex maths, she just doesn't know how she does it, everytime she so much as reaches for her mobile phone).

Based on the picture and the explanation with it, I see that the quadratic equation will predict or explain what the footballer has to do to get the ball to the right place.

What I need to do is to find a way of explaining to her how that gets written down.  I started looking at the pages https://www.mathsisfun.com/algebra/introduction.html  and https://www.mathsisfun.com/algebra/definitions.html  but I would like to be in conversation with someone to check what I am understanding correctly before I attempt to translate it.  No good trying to translate bad grammar, after all  wink

I hope there is someone out there who can think down to my level, and has wonderful patience with my kind of crazy  smile

Thank you very much for reading this far.  God bless you.

smile  Glenys

#2 2020-11-29 08:20:46

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

Hi all, part 2 ...

I am in fact so out of date of using forums and other discussion groups, that I registered, and then posted under the guest listing.  I'm sorry.  But this post is in my registered entity, where the original is in my unregistered one.

smile Glenys

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#3 2020-11-29 20:55:41

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Translating quadratic equation language for a mathphobe

hi Glenys,

Welcome to the forum.

Yes, you've come to the right place.  I have taught maths in Uk secondary schools for 37 years so I ought to be able to help.

Here's a start.

Maths is full of equations for all sorts of things.  For example the formula for converting degrees fahrenheit into celsius is this

I've used Latex to make that appear 'nicely'.  I typed C = (F-32) \times \frac{5}{9} and then boxed it in with square brackets math and square brackets /math

If you click on any piece of Latex you'll see the underlying 'code' that made the piece.

Descartes invented the x-y graphing idea so you could make a graph of that formula by using y and x instead:

If you go to this page

https://www.mathsisfun.com/data/function-grapher.php

and change the equation to (x-32)*5/9 you'll get the graph for changing F into C.  [note that the grapher 'understands' * for multiply and / for divide]

Don't panic when no graph appears.  It doesn't show with the basic default scale. You'll have to adjust the scale using the zoom (drag right) and you can click and drag to see other bits of the graph.

Equations where x occurs like that give rise to straight line graphs.

If an x squared term occurs (usually written as x^2 on this forum) then the equation is called a quadratic, and the graph is always a curve.

While you're looking at the grapher page try this equation:

and you will see a typical quadratic graph.

There's several examples of quadratics here:

https://www.mathsisfun.com/algebra/quad … world.html

Hopefully that will give you a starting point.  Post back when you want more smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#4 2020-11-29 22:41:14

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

Thank you, Bob  smile

I will go and do that and post back in a day or two.

Glenys

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#5 2020-12-04 09:56:22

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

Hi Bob  smile

I have had a go through the first few pages of the Algebra index, thank you.  In trying to translate these concepts for the young lady, I found that the balancing analogy (with judicial scales) made me remember that there are alternative types of scales.  The outline of antique balance scales bears a passing resemblance to a wink emoji.

Translating this balance analogy means that as you work through the various simple examples given on the site, you can check that you have completed the balance by putting a ring around both sides, and a link curve underneath (giving a smiley emoji).  This is followed by cancelling out, leaving the answer of 'x' on one side, the equals sign in the middle and the answer on the other side, again putting a ring around them, and a linking curve underneath: a second smiley emoji.

This technique will enable her to remember to balance each side.  If I can work out how, I’ll put up a photo of the page of samples I did.

I tried the sample page of questions, and found that several of them were actually more technically advanced than the level of the page they linked from ( https://www.mathsisfun.com/algebra/introduction.html ).

On that note, if you have any contact with the designer of the Algebra Index, they would do well to move the Algebra Definitions to the top of the Index.  I was working through in the order the pages were presented, and found a good deal wasn’t explained to my satisfaction, which the Definitions helped somewhat with.

But not to worry, I’ve figured out a bit more, and would like to check each aspect as I devise a translation for it, if that’s ok  smile

Glenys

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#6 2020-12-04 10:01:48

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

Sorry - I can't figure out how to post an image that's on my computer without uploading it for a web address  sad

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#7 2020-12-04 21:07:37

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Translating quadratic equation language for a mathphobe

hi Glenys,

I like your idea for helping the young lady how to remember a set of instructions using emojis.  smile

Years ago it was possible to upload images to the forum server but it became necessary to switch to a new server and that facility was not included in the new deal.

Another member recommended that I join imgur.com and upload my images there.  It's what I have used ever since.  imgur has changed its front page a little since I wrote the following instructions but you should be able to follow what to do.  What is needed is the bcc command which can be copied directly into a post.

http://www.mathisfunforum.com/viewtopic … 06#p352606

post 1686

I think the algebra page you are referring to was written after the other pages so it's not really meant to be page 1 of an algebra course.  One of the strengths* of the MIF material is the cross referencing between pages.  So click around the site and find the pages you need.  If you encounter a question with which you need help, I'm happy if you post it here and I'll try to post what you need.

Bob

* I also think the explanations are very clear, with easy to understand language, good diagrams, good use of font changes and colour and some excellent interactive pieces.  I haven't found a better site on the internet.  All the work of the MIF founder MathsIsFun himself.  He is working on a science site so leaves the day to day stuff to the other admin and moderators.


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#8 2020-12-04 22:25:42

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

Hi Bob  smile

Thank you for both the encouragement and the background information on MIF.  It's good to know who is behind a given site, and a little of what its history is.

Let's see if this will work, then smile

I've created a Google photo album called "Algebra Smile Emoji (MathsisFun)": https://photos.app.goo.gl/cJfK24PsUJgqDfZC7

Here you should see a representative image borrowed from MathsIsFun, to explain the progression, an antique balance scale (borrowed via Google search), and 3 images showing how the suggestion illustrates, using the sample questions from the quiz at https://www.mathsisfun.com/algebra/introduction.html

My note for the young lady states that the smiley emoji illustrates the principle of "What is done to one side must also be done to the other side", but it also illustrates this basic level of algebra, which is that "algebra is a maths statement that: The maths on one side is equal to the maths on the other side" (in other words, both sides are equal, both sides balance).

I'll go to the next translation section in a separate message, and using separate albums for each.  Then there's no difficulty following them, and that should assist any other readers of the thread.

Thank you again  smile
Glenys

Last edited by MrsGC (2020-12-04 22:31:00)

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#9 2020-12-04 22:51:04

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

ALGEBRA USES TEXT-TALK

This analogy was prompted by a comment from an elderly guide when we visited a museum some years ago.  He pointed out that the Romans had invented text-talk, because on any given Roman inscription there is a significant amount of abbreviation.

Looking at the grammar of a basic algebraic equation, I see the same principles:

In text-talk you either:
1 – miss letter out = brb (be right back)
2 – spell things wrongly = ur (your)
3 – mix letters and numbers to create word meaning phonetically = gr8 (great)

Following this out:

Any letter used in algebra means some sort of meaning, some sort of number, which stands in place of a word/name/value/concept.  Thus, ‘x’ stands for ‘unknown’ in common usage.  This is the same principle as item 3, using a number to denote a phonetic meaning.

+

When showing multiplication of a letter by a number, algebra misses out the space between the number and the “times”, “times by”, or multiplication symbol.  This is like text-talk missing out letters.

+

When balancing an equation, you have to do two things:
   - work out what to remove to get “x = ...”
   - Remove it by doing the opposite in that part of the equation.

Doing the opposite is like misspelling words.  When you’ve decided what the misspelling should be, then the misspelling has to happen on both sides of the equation, both sides of the equals sign.  This is like using the same misspelling in a text message for the same word.  Your word, in this case, is the value you are finding.  You have to use it on both sides for your message to make sense.

+++

As with any analogy, there are limits to the illustration by text-talk, and it will probably break down further into complex algebra.  However, it may be enough to give the young lady confidence in just looking at how equations are constructed.  Right now, not unlike myself, I daresay she looks at an equation as being not much different to a randomly generated password, with the same kind of sense and logic to it ... and the same kind of bar or access to the knowledge it guards wink

smile  Glenys

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#10 2020-12-06 22:37:26

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

Hi Bob  smile

Moving on, as I don’t want to lose momentum with the young lady, I looked at what the equivalent was of “parts of grammar” for algebra.  I saw that it was “parts of an equation” on the introduction page https://www.mathsisfun.com/algebra/definitions.html

Algebra is like a pop group, I thought.

VAR – Variable, the mystery member of the group.  Doesn’t say much, but what is said is important.  Var hides inside a cloak for most of the performance, only showing the costume in the solution.

CON – Constant, the dependable one that doesn’t change.  Can be either a number or a letter, but whichever outfit is picked, it stays for the whole performance.

OPE – Operator, the bossy one, telling everyone how to perform.  Ope sets the tone of the performance, the layout of the set, and the result in the solution.

COE – Coefficient, the talkative one that parrots Var’s words.  A coefficient always multiplies a variable.  Whatever shyness or little glimpses there may be of Var, Coe will make Var look much bigger during the performance.  But Var remains the most important part of the solution in the finale.

And, of course, there is not only the performance itself, but as part of it, the build-up to the finale, in which the skin-tingling, blood-pumping, show-stopping solution is the best part of the performance.  An act can perform all sorts of hits in the run-up to the finale.  Some of them will be a favourite song, some will be less favourite, but all combine to create a great show.  There should even be an encore - where the solution gets checked - and which runs through 'favourite pieces' again.

smile  Glenys

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#11 2020-12-23 00:19:03

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

I had an email notification that @stivemorris had replied to my enquiry, but I'm unable to view the link the email provides.  Please feel free to post again or to message me.

smile  Glenys

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#12 2020-12-23 21:27:36

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

Re: Translating quadratic equation language for a mathphobe

hi Glenys

stivemorris  joined yesterday and made a post on this thread.  He then deleted it.  Many new members don't join because they want to talk maths but rather just to advertise some product.  Let's wait and see what is posted next.

Best wishes for Christmas and the New Year.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#13 2020-12-27 05:11:03

MrsGC
Member
Registered: 2020-11-29
Posts: 10

Re: Translating quadratic equation language for a mathphobe

Thank you very much Bob  smile  God bless 2021 to you and your family too.

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