# Avoiding Modification and Deletion Methods

$\require{cancel}$

Deletion and modification seem to confuse students. Additive methods appear easier in my experience. Over the next few posts I wish to present a few tweaks I have used to get my students past sticking points whose existence I have struggled to understand since I was certain I had already broken it down to the simplest form. In my practice these tweaks have been extremely potent. I would like to hear about any other special fixes people have found for the other areas of difficulties.

I am not entirely happy about resorting to these techniques. The ability to use harder or conventional solving techniques is essential since not everything can be designed to be simpler. Alternative resources will use common methods rather that Mr. Masri’s Secret Recipe. However, we are all pressured to ensure our students pick up skills that will allow them to understand their subject, even if it means sidestepping basic cognition.

## Part 1 : Balancing Chemical Equations

The Balancing Equations game from PHET

Even the explicit instructions written in large letters do not deter the students.

• DO NOT CHANGE THE SMALL NUMBERS
• DO NOT CHANGE THE LETTERS
• DO NOT ADD A NEW MOLECULE (this is sometime treated as a subset of changing letters)

I would stand right beside them and watch their furrowed brows. They were unable to see any new possibilities. This will happen even with worked examples, physical demonstrations, and electronic aids. They will cycle through these three options before finally committing one of these mistake.

I have known this for a while. Students will make the mistake even if they know it is wrong because it makes sense to them. 1

With modification baked into the method, the student has to remember a larger myriad of rule regarding sanctioned and unsanctioned modification. Adding a whole molecule to address an imbalance of a single atom seems inefficient. While I can get the students to agree to the basic precepts that what they are doing changes the reaction fundamentally the link between the concepts and the method remains perfunctory to all except the brightest.

Is it possible to bake into the method a recognition of this fact?

This was not a method I had developed myself. In retrospec is is incredibly obvious. My students had a for a very long time performed well on the PHET balancing equations simulation but failed miserably with the paper method.

I will compare solving it with the traditional method2 and with my newer method. I am also going to ignore the algebraic method

## Comparing the methods

Consider the unbalanced equation

### Typical method to balancing equation

1. List out the the elements. Count the atoms for each element and place inside the table.

Elements Reactants Products
C 1 2
O 3 2
H 2 2

2.See which side has fewer atoms of one element than the other.
Notice that the are fewer carbons on the left hand side than the right hand side
3. Modify the equation. In this case add another CO2 by writing 2 in-front of it.

4. Modify your table to count these new atoms

Elements Reactants Products
C 1 2 2
O 3 5 2
H 2 2

5. Repeat step 2 3 and 4 until both the reactants are product have the same number of atoms for each element.

2nd time round
Repeat 2. See which side has fewer atoms of one element than the other.
Notice that the are fewer oxygen atoms on the right hand side than the left hand side
Repeat 3. Modify the equation. In this case add 2 more O2 by writing 3 in-front of it

Repeat 4. Modify your table to count these new atoms

Elements Reactants Products
C 1 2 2
O 3 5 2 6
H 2 2

Repeat 2. See which side has fewer atoms of one element than the other.
Notice that the are fewer oxygen atoms on the left hand side than the right hand side.
Repeat 3. Modify the equation. In this case there are two molecules that can provide the oxygen needed. Increasing either of them will break the current balance for C and H.
In cases it usually does not matter which you increase first because you will end up increasing both. A good rule is to do the one with an element that is not O or H.

Repeat 4. Modify your table to count these new atoms

Elements Reactants Products
C 1 2 3 2
O 3 5 7 2 6

3rd time round

Elements Reactants Products
C 1 2 3 2 4
O 3 5 7 2 6
H 2 2 4

4th time round

Elements Reactants Products
C 1 2 3 4 2 4
O 3 5 7 9 2 6
H 2 2 4

5th time round

Elements Reactants Products
C 1 2 3 4 2 4
O 3 5 7 9 10 2 6
H 2 4 2 4

6th time round

Elements Reactants Products
C 1 2 3 4 2 4
O 3 5 7 9 10 2 6 10
H 2 4 2 4

6. Write the final formula

There are 15 cancellations with this normal method. It is not a wonder someone non-confident students would question their technique. They are also required to keep swapping between the table and their formula repeatedly. There are also require to directly modify the line of the equation but only in a specified way. While this is quite simple it is part of a 6 step process.

Now lets see a different method that has fewer steps, eliminates any need for cancellation, requires no swapping and demonstrates the preservation of the reaction.

### Column Balancing Method

$CO_2$ $+$ $H_2O$ $\to$ $C_2H_2$ $+$ $O_2$

1. Look at the elements and count and see which side has less. Whichever side has less, add another of that whole molecule. In this case there are fewer carbons on the left so write the whole molecule that has carbon in it again below.

$CO_2$ $+$ $H_2O$ $\to$ $C_2H_2$ $+$ $O_2$
$CO_2$

2. Repeat step 1 until neither side has fewer atoms.
2nd time round
Repeat Step 1
In this case carbons are balanced but there are fewer oxygen on the right hand side.

$CO_2$ $+$ $H_2O$ $\to$ $C_2H_2$ $+$ $O_2$
$CO_2$ $O_2$
$O_2$

3rd time round
Repeat Step 1
In this case carbons are balance but there are fewer oxygen on the left hand side. A smarter student might be able to see adding another CO2 will keep this discrepancy of odd and even number of O but it does not matter.

$CO_2$ $+$ $H_2O$ $\to$ $C_2H_2$ $+$ $O_2$
$CO_2$ $O_2$
$CO_2$ $O_2$

4th time round

$CO_2$ $+$ $H_2O$ $\to$ $C_2H_2$ $+$ $O_2$
$CO_2$ $C_2H_2$ $O_2$
$CO_2$ $O_2$

5th time round

$CO_2$ $+$ $H_2O$ $\to$ $C_2H_2$ $+$ $O_2$
$CO_2$ $C_2H_2$ $O_2$
$CO_2$ $O_2$
$CO_2$

6th time round

$CO_2$ $+$ $H_2O$ $\to$ $C_2H_2$ $+$ $O_2$
$CO_2$ $H_2O$ $C_2H_2$ $O_2$
$CO_2$ $O_2$
$CO_2$ $O_2$
$O_2$

3. Write the final Formula

It is an advantage in almost every single way. Number of cancellations zero. Focus is always on the same construct. No modification to cascade through to a separate construct. Assuming the page is large enough, there is no running out of space because the original formula/table was written too narrowly spaced.

I am not satisfied with the fact that what I consider a reasonable method is a constant source of confusion for many students. Even when breaking it down and demonstrating the relative complexity between these two methods it should be within the capacity of any student to NOT change the molecules. The skill to follow instructions is entirely side stepped so cognitive development is ignored. However, now the student is able to progress in chemistry with a method that structurally reflects what we are solving.

1. I read this in Science Learning, Science Teaching By Jerry Wellington, Gren Ireson but they reference Osbourne and Freyburg. I no longer have my copy the book so I cannot track down the primary reference without spending too much money.
2. The traditional and Algebraic Method. http://www.wikihow.com/Balance-Chemical-Equations

# Stop thinking – A peculiarity of teaching

I teach students between the ages of 16 and 19, specialising on mathematical components of a more generalised course .

I am uncertain as to the location of the inflection point between pushing critical understanding and just mechanically working through procedures to arrive at an answer in learning maths. However, it still continues to surprises me the frequency at which the admirable pride and inquisitiveness of students hinder their mathematical progress simply because they desire to understand why techniques or methods work before they are adequately able to do so. Continue reading

# Rant on Victory for Activists

Things said on twitter pass too quickly so I preserve my rants here for future reference.

Razi@jumplogic Aug 27

Had a realisation I hate. The intellectual disintegration in all rights movement is a mathematical certainty and a direct effect of success. Continue reading

# Rant on Nuance

Things said on twitter fade far too quickly so I preserve rants for future reference

I understand nuance is lost when making digestible messages, but still surprised some people believe the simplified version uncritically.

# Massive Small Change

Forgive the obvious joke

The Engineers Without Borders UK Professional Network (EWB-UK PN) held their first conference on Saturday 22nd June. And what a conference it was. It was titled “Massive Small Change“, here is the hash tag for the live tweets #massivesmallchange. (Ignore Ianrosmarin’s individualised V3 promotions, it gets good afterwards.) If I had to summarise it I would say it was about non-linear effects of intervention and how with changes of approach we can enact real, self-sustaining progress.

The idea of moving beyond community involvement to community investment remained strong throughout the day. The victim image limits the options we are willing to entertain. Despite perceptions there is a lot of money available in these communities, often tied up in other necessities. If we can provide the opportunity to invest in catalytic improvements, the same revenue stream can be re-fed into other investments and free up ever greater shares of ever growing income.

The talks were brilliant, particularly the ones I attended in the main hall. The topics broad yet on the whole focused, building upon and complementing one another without ever repeating themselves. Continue reading

# 2013 Sustania 100 – Part 1 Building Sector

This post is intended to be read alongside this publication.

My impressions, thoughts and comments on the innovations in the 2013 Sustania 10o, an “annual guide to 100 innovative solutions from around the world that presents readily available projects, initiatives and technologies at the forefront of sustainable transformation.”

Read their page first then come to me. EDIT: Last year’s winners Azuri presented at the EWB Massive Small Change Conference I already wrote up  my impression on their 2012 winner in the last paragraph of a previous post.

# E.F. Schumacher on Natural Capital

To press non-economic values into the framework of the economic calculus, economists use the method of cost/benefit analysis. This is generally though to be an enlightened and progressive development, as it is at least an attempt to take account of benefits which might otherwise be disregarded altogether. In fact, however, it is a procedure by which the higher is reduced to the level of the lower and the priceless is given a price. It can therefore never serve to clarify the situation and lead to an enlightened decision. All it can do is lead to self-deception or the deception of others; for to undertake to measure the immeasurable is absurd and constitutes but an elaborate method of moving from preconceived notions to foregone conclusions…The logical absurdity, however, is not the greatest fault of the undertaking: what is worse, and destructive of civilisation, is the pretence that everything has a price or, in other words, that money is the highest of all values.

– Small Is Beautiful: A Study of Economics as if People Mattered (Page 31), E.F. Schumacher

# Devon Double Hexayurt

One problem with categorising dates by the weekends i.e  “First weekend in June” is you forget what other events approximate to it, such as a friend’s birthday. So where was I instead of reconnecting with old friends? In a field, in Devon, with a bunch of strangers. I will be vague with names since I cannot recall which individuals requested not to be photographed and uploaded.

Meet Nick. Nick has been living in a field for a few months. He decided he would like to live off-grid in a sustainable fashion and that his housing solution would be a Hexayurt. We were supposed to build it in December with the aid of wind, rain, and limited daylight but that had to be delayed. In the meanwhile Nick lived in a van, and we waited for the sun.

# Maths Triage

Should any experienced educator spot any mistakes in my methods please alert me to them.

A latent dream to become an educator has taken great leaps forwards. With great luck I might be accepted onto teacher training course, despite losing many of my application slots (a grand total of 3) to schools that have yet to remove vacancies from the system, and are even slower to reject me after informing me that there is no space. I am also waiting on my previous employer to respond to my reference request should he ever find a free moment in between providing water and medicines to Malians.

In the meanwhile I am tutoring and as yet remain far below any threshold for reporting my earnings. I do wish I could pay tax. I initially advertised to provide free maths and physics tuition up to GCSE. In the meantime I am revising my A-Level and university maths and will tutor these once I am confident enough to devise teaching strategies. I am now charging new tutees, we negotiate but it averages about £10 per hour and I eagerly wait for the time when honestly will allow me to charge £15.

# One a Day – 1

Articles I’ve read in the past week. One for every day.

### Four Futures

There are therefore four logical combinations of the two oppositions, resource abundance vs. scarcity and egalitarianism vs. hierarchy. To put things in somewhat vulgar-Marxist terms, the first axis dictates the economic base of the post-capitalist future, while the second pertains to the socio-political superstructure. Two possible futures are socialisms (only one of which I will actually call by that name) while the other two are contrasting flavors of barbarism.

http://jacobinmag.com/2011/12/four-futures/