Bonding, equilibria, maths and more

Octet rule

In the September issue David Read reviewed a recent research paper ‘Overcoming barriers in bonding’ that examined the order in which different types of bonding should be introduced to students. The authors make a compelling case for starting with covalent bonding, followed by polar covalent and then ionic. The article also cautioned against using the octet rule.

On our website, Walt Sautter from Nutley, New Jersey, US, said:

It would seem very easy to discuss the octet rule as a ‘rule’ which is often broken, instead of citing it as a law such as inertia which is never broken. That would make the order of discussion about bonding types irrelevant.

William Bare from Lynchburg, Virginia, US, added:

I once heard a colleague refer to this as ‘the octet suggestion’. I like that and use it in my classroom. There are only four elements on the [periodic] table (C, N, O, and F) for which the ‘rule’ even makes sense.

On LinkedIn, Deborah Boxall, a chemistry teacher in Raleigh, North Caroline, US, said:

I rephrase the octet ‘rule’ by saying, ‘With the exception of hydrogen and boron, atoms want to have at least eight electrons around them when in a compound. Some are perfectly happy with more than that.’ For those students that get hung up on the number of valence electrons associated with the atoms, I explain how to minimise the formal charge which usually satisfies them.

Joseph Merola, a professor of chemistry at Virginia Tech university in the US, isn’t convinced:

If there is ‘caution’ about the octet rule, where does one go from the suggested point? Do we drop all ‘approximate’ approaches such as VSEPR, hard and soft acid and bases, hybrid orbitals,etc? 

I find these to be useful constructs even though I will ultimately go into more detail about their foundations and molecular orbital theory for the latter. I think the octet rule still has a place and I don’t agree with the premise of the posted article.

However Valarie Broadhead, a high school teacher from San Juan Capistrano, California, US, said she plans to adopt this approach:

Always looking for ways to improve teaching/learning. These topics are coming up and I will be switching up the sequence in teaching bonding so that students are able to relate electronegativity with covalent bonds, then polar covalent, then ionic. It will be interesting to see if this results in increased understanding for students and improvement in summative assessment results.

Understanding equilibrium

Also in the September issue our CPD article showed how you can help your students understand equilibria and Le Chatelier’s principle. Steve Hacker described some ideas for teaching this topic, including the classic cobalt chloride experiment.

On Facebook, Elaine Hood, from Sandhurst, UK, commented:

I’ve been doing this demo for many years to illustrate equilibrium and Le Chatelier’s principle. It always amazes the pupils.

Alastair Gittner, a science teacher from the UK, added his own idea:

Dynamic equilibrium analogy: people in MacD’s. Roughly same no’s in queue, some in seats, some in between, constantly changing…

On LinkedIn,

Sheelagh Halstead, from the Pietermaritzburg area, South Africa, suggested this activity:

I have always loved teaching chemical equilibrium, and like other contributors believe that at school the key concepts are the reversibility and dynamic nature of chemical reactions. However, as teachers we need to carry through and ensure the analogy has been effective, and scaffold our students’ reasoning.

In Grade 11, when studying phase equilibrium, we played the paper ball throwing activity mentioned by Orvis and Orvis () and we also included variables of open and closed systems, and increased temperature. Students would then map aspects of the model to the relevant concepts and we’d discuss limitations of the model. Now thanks to further ideas in the article, in future I will also include the iodine system under solubility equilibria.

In Grade 12, when equilibrium was in the curriculum, the students could easily recall the paper ball game, and I included many practical exercises. In order to scaffold their thinking about ‘explain, in terms of Le Chatelier’s principle why...’ 

I required them to write down for each change in the system their action, the stress caused, the reaction favoured, the effect on the products concentration, and finally the observable effect.

Creative assessment

Last month David Read reported on a novel form of assessment, creative exercises (CEs), which promotes students’ linking of concepts within chemistry.

Allen Mcfarlane, a science teacher from Topeka, Kansas, US, said:

I am just about to write an assessment for 6th Grade chemistry and this article has changed my thinking about how I might do that. This sounds like a mind-mapping exercise and that would be interesting to give the students instead of the standard test I would usually give.

The article’s original author, Scott Lewis, left a message on our website:

We have developed a series of CEs for general chemistry (first and second term) and are happy to share what we’ve developed. If any instructors or researchers are interested please email me at slewis@usf.edu.

So far, the feedback from instructors who have incorporated them into their assessments have been positive and many have indicated that reading their students’ responses to CEs provided a unique insight into student thought processes regarding the content.

Maths for chemistry

Michael Seery started a conversation on our blog on the topic of maths for tertiary education:

If you want to get a good conversation going in the chemistry staffroom, bring up the issue of maths. No one, it seems, is any good at maths any more. People will argue that it isn’t taught the way it used to be and students don’t know how to apply it to chemistry.

Different education systems have different requirements for maths at university level. [...] In the UK, some universities require maths at upper school level, others don’t. This means it is difficult to pinpoint where the problem – and there is a problem – lies.

Michael wonders who should be teaching maths to undergraduate chemists? Should it be chemists, in contexualised ‘maths for chemists’ sessions where students apply the skills directly to a chemical problem? Or should maths teachers develop students’ understanding before the chemistry is introduced?

On LinkedIn, Heidi Rosenberg, an adjunct professor at Mesa Community College in Phoenix, Arizona, US, said:

Yes it is very surprising how little math the students seem to know. I know I learned how to convert from unit to unit in high school math at about age 11 or 12 in England. I now live in the US and teach chemistry at college level and I have to teach how to rearrange equations, significant figures, unit conversions and scientific notation. Some students really struggle! I haven’t even arrived at the mole yet this semester.

Jeremy Mansell, a science teacher at Waitaki Boys’ High School, New Zealand, said:

I too struggle with the maths my students have coming into chemistry, particularly in the first year we split into the individual sciences (Year 12 in New Zealand). Most of them are quite adept at rearranging formulae but struggle using logs in pH calculations (and deriving formulae from this) and converting ml to l. I have been teaching logs as a first lesson before 

I begin any of the acid base stuff but have just started to liase with the head of mathematics about timelines to hopefully ensure they have covered the required techniques in maths shortly before we do it in chemistry. The main problem I see is too much faith is placed on the calculator and not enough on the theory, I have had kids quote some ridiculous pH figures because it was what was on the screen of their calculator.

Alexander Loudon from Ireland, said:

From my experience teaching, students place a significant amount of emphasis on learning off equations instead of understanding them. The mole being a prime example, where students desperately try to learn off specific equations. However if the emphasis was on understanding the underlying relationships between Avogadro’s number, molar masses etc, I believe that a lot of the formulas would become instinctive.

Michael Seery replied:

This is a particular pet topic of mine – I really dislike when we teach students dilution calculations for example by just applying a formula, rather than going through it using first principles. The latter approach means they are forced to work through what is going on in terms of moles, and also means they can apply it to more complex scenarios. Unfortunately not everyone agrees the V₁ M₁/n₁ formula should be banned!

On Twitter, David Smith, an academic at the University of York, said: 

We have tried various methods of maths teaching at York. My view is contextualised maths does work best.

Back on the blog, Kristy Turner, a chemistry teacher in the UK, described her own experiences:

There are some fundamental issues with mathematics in primary and even early secondary education. However given that many secondary schools can’t put a specialist maths teacher in front of all their maths classes, I can’t see the current situation improving anytime soon! Dare I say there is also a societal issue where it is ok to say you’re rubbish at maths (whereas few would admit to not being able to read). [...] The maths modules I had at undergraduate level were taught by mathematicians (I don’t have A-level maths) and were terrible. I wanted the context and I never got it.

Robert Jenkins commented:

I work in student support and specialise in helping students with mathematics. I am also a chemist myself and can appreciate the difficulties trying to enthuse students about maths. I am not sure whether ‘Maths for...(whatever)’ modules are suitable and neither are pure maths modules given by mathematicians. Chemistry departments should have a proportion of faculty members skilled in maths who should be able to draw the relevance out of the subject area. Your example of logarithms is good; an explanation of their motivation (as a way to solve and manipulate exponential equations) can lead naturally to the Arrhenius equation and what you can do with it. However the fundamental manipulation skills cannot be discounted. Good choices of examples can overcome this.

Patrick O’Malley replied:

At the University of Manchester we have considerably increased our maths for chemistry content in the last few years and assessed units are now taught in both semesters of the 1st and 2nd year. We have found that mathematicians just do not appreciate the maths content required by chemists so the modules are taught by chemistry staff including myself. Its not taught in a traditional lecture fashion and in the 2nd Year we use essentially a flipped approach using our own Khan-type tablet-generated screencasts for content delivery backed up by face to face clinics or workshop activities. The examples used are all chemistry oriented.

First impressions at least suggest that we are eliminating some of the fear factor for certain students and lecturers can now include mathematically oriented topics in all years with some confidence.

I agree of course that the school preparation and treatment of mathematics leaves a lot to be desired but I doubt if we can change this in the near future so we have to do the remedial work ourselves.

Finally, in the March issue Paul Yates argued that university chemistry teachers do a good job when faced with this challenging problem. Take a look at his Endpoint column ‘Supporting mathematics for chemists’.