# 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

# 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/

# The Future We Deserve – Bootleg Oil

The Future We Deserve a collaborative book project to create a vision of the future is finished and launched as of yesterday. I cannot describe how good the book is to read. Perhaps it has been best expressed by Vinay in the introduction.

It is all available to read online, You can download the PDF or buy the book. I contributed to the book in the 11th hour after a moment of inspiration about a future scenario. Vinay encouraged me to write it up for the book. It is freely available online so to help promote the launch I reblogging my contribution to the book.

# Bootleg Oil

After reading a blog post by Noah Raford I was awakened to the fact that visions of the future are typically commissioned by the wealthy and as such are horrendously narrow in their vision. How will the the glittery sustainable technology we all wish for change the world?

# Jay on Fascism in the UK

My friend Jay @thejaymo made a wonderful series of tweets a few days ago taking a list titled The 12 Warning signs of Fascism and attaching each to a picture, article or news story in the UK. Read the storify

The 12 warning signs of fascism seem to have evolved from an article written by Dr. Lawrence Britt (“Fascism Anyone?,” Free Inquiry, Spring 2003, page 20) inside it he outlined Fourteen Defining Characteristics Of Fascism.

The impermanence of twitter compels me to commit his efforts into a blog so that it may be more easily shared and retrieved.

# The Needs of Others

I gave a talk at the open source hardware user group recently titled “The Needs of Others”. It was half outlining what is known about the effective delivery of technology aimed alleviating technology and half talking about how faithful reproduction of physical objects at any reasonable scale is dependent good documentation and then exploring the challenges all int he context of Free and Open technology. Unfortunately I only had 20 minutes while it was at least an hours worth of talking.

I really enjoyed it and the other two talks we great.

It was the first time I had to talk about the topic so the practice was great and I now have a better feel for it. Might ask a few ewb branches if they need a speaker

# My time

It’s been a good long while since my last post. In truth I am not a blogger by habit. I do things, or I think about doing things. Writing about the things I am doing or thinking about is a forced action for me. Ironic in light of the documentation bent I am pursuing.

I recently applied for a job. Both shocking to those who know me that I could muster up the effort and attempt to pursue something resembling a typical life path, and shocking to those who don’t for that this should stand out as anything remarkable. Surely for all my whining about having no money or job I should pursue gainful employment with all the vigour afforded to me by my body in the waking hours.

Nevertheless I applied for a job and was forced to commit the past two to three month of my life onto paper. Continue reading

# We Are The Elite

To the “99%”,

Yesterday I tweeted this

“Top 1% of earners globally is anyone with an annual income of £22000 #perspective#occupyearth #occupyeverywhere http://t.co/YXh6sVMs”

“@jumplogic Good perspective. We are the 99.99%. Stop international profiteering and private pillage of public good worldwide. #OccupyEarth”

I agree with the second half, however I have a problem with the statement “we are the 99.99%”. Continue reading

# Quick Update

A quick update over what has been happening with the documentation project and why I’ve been quiet.

I’ve added some of my work to http://www.appropedia.org/Hexayurt_Plywood . Images to be added as I make ones I am happy with.

I’ve started migrating the work onto opensource platforms. I’m learning how to use Scribus and Inkscape. Not sure if I’ll also learn freeCAD, at this moment I think the accessibility of SketchUp and the 3Dwarehouse to be more useful. Continue reading

# Filler

I’ve got an exciting new project that I hope to launch within a week so stay tuned. Still need to name it. Self indulgent teaser here.

In other news: